STUDY OF .4T'RIOSPEIERIC PUShIA SPFUY PROCESS WITEi THE EMPEMSIS ON GAS SHROUDED NOZZLES

Miodrag hl. Jankovic

A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy

Graduate Depanment of Mechanical and Industrial Ecgineenng University of Toronto

Q Copyright by hiiodrag M. Jankovic 1997.

National Library I*I of Canada Bibliothéque nationale du Canada

Acquisitions and Acquisitions et Bibliographie Services services bibliographiques

395 Wellington Street 395. nie Wellington Ottawa ON K1A ON4 OttawaON K l A O N 4 Canada Canada

The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, loan, distribute or seil copies of this thesis in microform, paper or electronic formats.

The author retains ownenhip of the copyright in this thesis. Neither the thesis nor substantial extracts fiom it may be printed or othenivise reproduced without the author's permission.

L'auteur a accordé une licence non exclusive permettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la fome de microfiche/film, de reproduction sur papier ou sur format électronique.

L'auteur conserve la propriété du droit d'auteur qui protège cette thèse. Ni la thèse ni des extraits substantiels de celle-ci ne doivent être imprimés ou autrement reproduits sans son autorisation.

STUDY OF AThIOSPEIEFUC PLASMA SPRAY PROCESS WITH THE EMPEMSIS

ON GAS SHROUDED NOZZLES

Ph.D. Thesis, 1997.

Miodrag M. Jankovic

Department of Mechanical and Industrial Engineering

University of Toronto, Canada.

An atmospheric plasma spraying process is investigated in this work by using

experimentai approach and rnathematicd modelling. Emphasis was put on the gas shrouded

nodes, their design, and the protection against the mixing with the surrounding air, which they

give to the plasma jet.

First pan of the thesis is dedicated to the analysis of enthalpy probe rnethod, as a major

diagnostic tool in this work. Systematic enor in measuring the stagnation pressure, due to a big

temperature difference between the plasma and the water-cooled probe, is investigated here.

Parallel measurements with the enthalpy probe and an uncooled ceramic probe were performed.

Also, numerical experiments were conducted, using the k-E mode1 of turbulence. Based on the

obtained results, a compensating algorithm for the above error is sugçested.

Major objective of the thesis was to study the plasma spraying process, and potential

benefits fiom using the gas shrouded noules. Mathematical modelling was used to perform the

parametric study on the flow pattern inside these nodes. Two noules were used: a commercial

conical noule, and a custom-made curvilinear noule. The later is aimed towards elirnination of

the cold air entrainment. recorded for the conical nonle. Aso, pararnetnc study on the shrouding

gas and its interaction with the plasma jet was cûrried out. Two modes of the shouding gas

injection were tened: through sixteen injection ports, and through a continuous slot, surrounding

the plasma jet.

Both noules and borh injection modes were thoroughfy tested, experimentaily and

numerically. The curvilinear nozzle completely eliminates the cold air entrainment and yields

significantly higher plasma temperature. Also, injection through the continuous slot resulted in

a much better protection of the plasma jet. Both nonles were used to perform the spraying tests.

Obtained coatings were tested on porosity, adhesion strençth, and micro-stnicture. These tests

indicated better micro-stmcture of the coatings sprayed by the c u ~ l i n e a r nonle. Aiso, their

porosity was siçnificantly Iower, and the adhesion strength was higher for more than 25%. The

overall results suççest rhar the curvilinear nozzles represent a much better solution for the gas

shrouded plasma spraying.

1 am deeply indebted to Professor lavad Mostaghirni, my supervisor, for his guidance

throughout the course of this thesis. He is always patient, encouraginç and resourcehil. His

nurnerous susestions and result onented approach helped me to complete this demanding work.

I would ais0 like to thank Ontario Hydro Technologies for providing me with financial

support and granting me access to their experirnental facilities. 1 am especially thankful to John

Noça, whose personal involvernent in every stage of the project made it al1 possible.

Further on, I wish to thank the Depanment of Mechanical Engineering and Professor

Mostaçhimi for ganting me cornputer time and providin~ me with the software necessary for the

completion of modellinç work.

Thanks are then extendeci to my fellow smdent Maha Masri and to research fellow Valerij

Pershin for their friendship and cooperation in perfoming the experimental work.

Finally, 1 wish ro rhank my wife Marina. and my daughters Bojana and Anna, for their

patience and support throughout t he course of rhjs thesis.

TABLE OF CONTENTS

Chapter Page

1. INTRODUCTION 1

1.1. BACKGROUND 1

1.2. OUTLINE OF THE THESIS 6

2. MATHEMATICAL IMODELLING OF PLASMA FLOWS i l

2.1. THERMAL PLASMA BACKGROUND 11

2.2. TRANSPORT EQUATIONS 14

2.3. EQUATIONS FOR PARTICLE TRAECTORIES ZLND HEAT

TRANSFER 16

2.3.1. Trajectory calculations 17

2.3 2. Heat and mass transfer 20

3. EXPERIMENTAL FACILITY AND MEASURING

TECHNIQUES

3.1. DC SPRAYING GUN CI-LMACTERISTICS

3.2. MEASUFUNG DEVTCES .AND TECHNIQLrES

3.3 . DYNAMlC PITOT-PROBE

4. ENTHALPY PROBE SYSTEM

4.1. PEUNCIPLE OF MEASUREMENT

4.2. ERROR IN STAGNATION PRESSURE M E A S W M E N T S

4.2.1. Influence of viscosity on stagnation pressure measurements 40

42.2. Influence of inclination angle of the velocity vector to the probe

axis on stagnation pressure measurements 43

4.2.3. Influence of turbulence on measurements of stagnation pressure 44

4.3. INFLUENCE OF THE TEMPERATW BOUNDARY LAYER ON

ïHE STAGNATION PRESSURE MEASWREMENTS 47

4.3.1. Experirnental results on non-isothermal Pitot-probe measurements 49

4.3.2. Numencal simulation of the water-cooled probe irnmersed in a

plasma jet 5 1

4.3.3. Parallel measurements of the stagnation pressure by a

water-cooled and an uncooled probe 54

4.3.4. Theoretical aspects of the boundary layer around the tip

of the probe 56

4.4. ERROR IN ENTHALPY MEASUREMENTS 6 1

4.4.1. Error due to assurnption of identicai heat transfer in two regimes of

the probe operation 64

4.4.2. Error in indirectly measured quantity 69

4.5. DESIGN PARAhlETERS OF THE PROBE 70

4.5.1. Probe çeometry 7 1

4.5.2. Estirnated error of measurement 72

5. CAS SHROUD NOZZLES 74

5.1. FREE JET CALCULATIONS 75

5.1.1 . Flow çeometry and boundary condition 76

5.1.2. Inlet profiles of temperature and velocity 79

5.1.3. h improved power-law approach 82

5.1.4. Calculation of the free plasma jet 86

5.2. EVALUATION OF THE PERFORMANCE OF A CONICAL NOZZLE 94

5.2.1 Flow geometry 95

5.2.2. Influence of the noule angle 97

5.2.3. Influence of the arçon flow rate 1 O0

5.3. CURVILlNEAR DESIGN OF THE GAS SHROUDED NOZZLE 1 03

5.4. ENERGY BALANCE OF THE NOZZLE 105

5.5. FLOW PARAMETERS rN THE FREE JET REGION 107

6. SHROUDING GAS AND ITS IMPACT ON THE PLASMA

JET PARAMETERS 6.1. SHROUDING GAS NJECTED THROUGW SERiES OF SMALL PORTS

6.1.1. Interference between two adjacent shrouding gas jets

6.1.2. Plasma jet with the shrouding ças

6.2. SHROUDING GAS iNECTED THROUGH THE CONTMOUS SLOT

6.2.1. General parametric study

6.2.2. Influence of the annular dot diameter

6.2.3. Maximum flow rate of the shrouding gas

6 .3 . FLOW PARAMETERS OF T E PLASMA JET WITH THE

SHROUDING GAS

7. PARTICLE BEHAVIOUR AND SPRAYrNG TESTS 7.1. PARTICLE TRAJECTORIES VELOCITIES

7.2. PARTICLE TEMPERATURE HlSTORY - - - - - - - - - - 7 3 , . C O A T ~ G ~ U ~ ~ N - - - - - - - - - - - - - -

7.3.1. Metalloçraphy tests

7.3 -2. Porosity tests

7.3.3 Adhesion tests

8. CONCLUSIONS AND RECOMMENDATIONS REFERENCES

APPENDIX

vii

LIST OF FIGURES

Fig. 1.1. Schematic of the sprayinç çun.

Fig. 2.1. Typical heating stages of a particle.

Fig. 2.2. Microscopie photoçraphs of Zirconia powder.

Fig. 3.1. Experirnental facility.

Fig. 3 2. Volt-Amper characteristic of the gun.

Fig. 3 -3 . Experimental setup.

Fig. 4.1. Schematic of the enthalpy probe system.

Fig. 4.2. Measurement emor due to viscosity.

Fig. 4.3. Relative error due to inclination angle.

Fig. 4.4. Relative error due to turbulence.

Fig. 4.5. Schematic of the calculation domain.

Fig. 4.6. Predicted error in stagnation pressure measurements (P. = 10' Pa).

Fig. 4.7. Thickness of thermal boundary layer around the probe tip.

Fig. 4.5. Error of measurement - experimental data.

F ig 4.9. Velocity, temperature. and pressure distribution in the vicinity of the stagnation point.

Fig. 4.10. Factor 5 as a funcrion of dynamic-to-free Stream pressure ratio.

Fig. 4.1 1. Systematic error in stagnation pressure measurements.

Fig. 4.12. Relative emor in detemining the extemal heat transfer.

Fig. 4.13. Sensitivity of the probe.

Fiç. 4-14. Maximum relative error in enthalpy measurement at the jet a i s .

Fie. 4.1 5 . Relative error in enthalpy rneasurement.

Fig. 5.1. Schematic of the calculation domain.

Fig 5 2 . Velocity profiles for different values of power-law exponents.

Fig. 5 3. Temperature profile5 for different values of power-law exponents.

Fig. 5.4. Stagnation pressure profiles for different values of power-law exponents.

Fig. 5.5. Output voltage of the pressure transducer.

Fig. 5.6. Profiles of the stagnation pressure.

Fig. 5.7. Idet profile of velocity.

Fig. 5.8. Idet profile of temperature.

Fig. 5.9. Iso-contours of velocity.

Fig. 5.10. Iso-contours of temperature.

Fig. 5.1 1. Iso-contours of argon mass fraction.

Fig. 5.1 2. Axial distribution of velocity.

Fig. 5.13. &al distribution of ternperature.

Fig. 5.14. Axial distribution of argon mass fraction.

Fig. 5 - 15. Iso-contours of velocity. Experimental and theoreticai.

Fig. S. 16. Iso-contours of temperature. Experimental and theoretical.

Fig. 5.17. Iso-contours of argon mass fraction. Experimental and theoretical.

Fie. 5.18. Streamlines inside the calculation dornain.

Fig. 5.19. Strearnlines close to r he spraying gun exit.

Fig. 5.20. Schematic of the flow domain.

Fig. 5.2 1 . Overall corn putarional dornain.

Fiç. 5.22. Isometric view of the shrcuded noule.

Fiç. 5.23. Streamlines inside the nouie for different n o d e angles.

Fig. 5 .X Quantity of the entrained air for different angles.

Fig. 5.25. Strearnlines inside the noule for different flow rates.

Fig. 5.26 Quantity of the entrained air for different flow rates.

Fig. 5.27. Schematic of the c u ~ l i n e a r nozzie.

Fig. 5.28. S trearnlines inside the c u ~ l i n e a r nouie .

Fig. 5.29. Streamlines in close-to-r he-wall reçion of t he curvilinear noule.

Fig. 5.30. Wall heat flux for different noule.

Fig. 5.3 1. Wall heat loss for different n o d e angles.

Fiç. 5-32. Enthalpy ratio for conical noule with different angle.

Fig. 5.33. Wall heat losses for different values of the power input.

Fig. 5.34. Calculated radial profiles of temperature at the n o d e outlet.

Fig. 5.35. Calculated radial profiles of velocity at the nozzle outlet.

Fig. 5.36. Radial profiles of stagnation pressure at the n o d e outlet.

Fig. 5.37. AKial distribution of velocity.

Fig. 5.38. Axial distribution of temperature.

Fig. 5.39. Axial distribution of arson fraction.

Fig. 5 .do. Velocity iso-lines for curvilinear noule.

Fig. 5.4 1. Temperature iso-lines for curvilinear nozzle.

Fig. 5.42. Argon fraction iso-lines for curvilinear nozzle.

Fig. 5.43. Velocity iso-lines for conical nozzle.

Fig. 5.44. Temperature iso-lines for conical nozzle.

Fig. 5.45. Argon fraction iso-lines for conical nozzle.

Fig. 6.1. Schematic of the shrouding gas injection.

Fig. 6.2. Schematic of the calculation domain.

Fig. 6.3. Velocity profiles of the circular shroud jet.

Fig. 6.4. Argon fraction profiles of the circular shroud jet.

Fig. 6.5. Axial distribution of velocity.

Fig. 6.6. Axial distribution of argon fraction.

Fig. 6.7. Boundaries of the main plasma jet and the circular shroud gas jet.

Fig. 6.8. Schematic of the calculation domain.

Fig. 6.9. Axial distribution of plasma velocity.

Fig. 6.10. Axial distribution of plasma temperature.

Fig. 6.1 1. Axial distribution of argon fraction in plasma jet.

Fig. 6.12. Streamlines in the vicinity of the nozzle.

Fig. 6.13. Schematic of the noule with a slot shrouding gas injection.

Fig. 6.14. Axial distribution of the plasma jet temperature.

Fig. 6.15. Axial distribution of the plasma jet argon fraction.

Fig. 6.16. kvial distribution of the plasma jet temperature.

Fig. 6.17. Axial distribution of the plasma jet argon fraction.

Fig. 6.18. Axial distribution of the plasma jet temperature.

Fig. 6.19. Axial distribution of the plasma jet arson fraction.

Fig. 6.20. kwid distribution of the plasma jet velocity (Entire flow domain).

Fig. 6-21. Axial distribution of the plasma jet velocity (Part of the flow domain).

Fig. 6.22. Axial distribution of the plasma jet temperature.

Fig. 6.23. h i a l distribution of the plasma jet argon fraction.

Fig. 7.1. Schematic of the panicle injection.

Fig. 7.2. Envelope of the trajectories for curvilinear noule.

Fig. 7.3. Envelope of the trajectories for conical noule.

Fig. 7.4. Average velocities of the panicles for curvilinear noule.

Fig. 7.5. Average velocities of the particles for conical noule.

Fig. 7.6. Radial distribution of average panicle velocities.

Fig. 7.7. Particle twin images.

Fig. 7.8. Jet from the conical n o d e .

Fig. 7.9. let from the curvilinear noule.

Fip. 7.10. Temperature histories of the partictes - curvilinear n o d e .

Fig. 7.1 1. Temperature histories of the particles - conical n o d e .

Fig. 7 11. Cross-section of iron-aluminide coating sprayed with cunilinear nozzie.

Fig. 7.13. Cross-section of iron-aluminide coatinç sprayed with conical noule.

Fig. 7.14. Cross-section of chromium-oxide coating sprayed with c u ~ l i n e a r node .

Fig. 7.15. Cross-section of chromium-oxide coating sprayed with conicai noule.

Fig. 7.16. Specimens for adhesion tests.

Fig. 7.1 7. Cross-section of the specimen sprayed with the c u ~ l i n e a r noule.

Fig. 7.18. Cross-section of the specimen coating sprayed with the conicai noule.

Fig. D. 1. Input function and system response function.

Fig. D.Z. Schematic of the pneumatic part of the measunng system.

Fig. D.3. Schematic of the dynamic Pitot-probe heatins.

Fig. D.4. Heating cuwes of the probe tip.

Fig. D.5. Recorded voltaçe output of the pressure transducer.

Fig. D.6. Parallei dynamic and static Pitot-probe measurements.

Fig. E. 1. Veiocity distribution in the boundary layer.

Fig. G. 1. Calibration curve for micro-orifices.

LIST OF TABLES

TABLE 2.1. Equations and Variables.

TABLE 2.2. Mode! Constants.

TABLE 6.1. Shrouding Gas Parameters.

TABLE 7.1. Average Particle Velocities (Experimental Values).

TABLE 7.2. Percentage of the Completely Melted Particles.

TABLE 7.3. Results on Porosity Measurements.

TABLE 7.4. Results on Adhesion Tests - Specimens Sprayed with Conical Nozzie.

TABLE 7.5. Results on Adhesion Tests - Specimens Sprayed with Curvilinear Nozzie.

LIST OF .APPENDICES

APPENDIX A: TRANSPORT EQUATIONS FOR FLUID FLOW

APPENDIX B: COEFFICIENTS a,, a?, a, M EQUATION FOR DRAG FORCE

COEFFICIENT

APPENDIX C: DC SPRAYTNG GUN SYSTEM

APPENDIX D: DESIGN PARAhETERS OF DYNAbfIC PITOT-PROBE SYSTEM

APPENDIX E: DERIVATION FOR EXPRESSION FOR ERROR IN MEASUREMENT

OF DYNPLMIC PRESSURE BY A WATER-COOLED PROBE 185

APPENDU F: CALCULATION OF TEMPERATURE FROM THE MEASURED

EPl.mALPY 190

APPENDIX G: C.4LIBRATION CURVES FOR MICRO-ORIFICES 193

APPENDIX H: HEAT TRANSFER COEFFICIENT FROM PROBE WALL TO TKE

COOLlNG WATER 194

APPENDIX 1: LISTTNG OF THE PROGRAM FOR CALCULATION OF PLASMA

E T PARAMETERS 196

APPENDIX J: GAS PROPERTES 20 1

APPENDLY K: PROPERTES OF IRON-.ALUhIINTDE POfVDER 203

NOMENCLATURE

Uppercrse sym bois:

Surface area.

Biot Number.

Radiation field intensity.

Constant describing the error of the Pitot-probe measurements.

Drag force coefficient.

Specific heat capacity.

Turbulence mode1 constants.

Diameter.

Force, shape factor.

Fourier number.

Draç force.

Basset history term.

Thermop horesis force.

Rate of production of kinetic e n e r g of turbulence.

Electncal curent.

Flux of species 1.

Knudsen number.

Lençth.

Latent heat of hsion.

Latent heat of evaporation.

Characteristic length scale of turbulence.

Mach nurnber.

Nusselt number.

Electnc power of t he spraying Sun.

xiv

Prandti number.

Heat, energy transfer.

Heat losses of the entire spraying gun system.

Heat loss of the spraying gun only.

Heat loss in the electrode leads.

Radius.

Reynolds number.

Rate of production of species l due to chemicai reaction.

Sourcdsink tenn due to radiation.

Source/sink term for general variable.

Temperature.

Turbulence intensity.

Average velocity, voltage.

Volume.

Probe velocity.

Liquid fraction.

Partition fùnction.

Lowercase sym bols

a - Acceleration.

Empirical coefficients for drag force coefficient.

Speed of liçht.

Diameter.

Error coefficient, arbitrary function.

Deçeneracy of the atomic level.

Enthalpy, convective heat transfer coefficient, height, Planck constant.

Kinetic energy of turbulence. arbitrary constant, Boltzmann constant.

Length.

iMass, power-law exponent. arbitrary constant.

Mass fraction of species 1.

lMass flow rate.

Power-law exponent, nurnber density.

Pressure.

Heat flux.

Radial coordinate, radius.

AnnuIar dot width.

Time.

Components of instantaneous velocity.

Components of fluctuating velocities.

Axial direction.

Greek sym boIs:

Difference.

GeneraI difision coefficient.

Angle of the noule. thermal difisivity.

Sensitivity of enthalpy probe.

Boundary layer thicknesses for velocity and temperature.

Delta tensor.

Dissipation of kinetic energy of turbulence, emissivity, porosity,

error of rneasurernent .

Energy difference between the atornic levels.

General variable.

xvi

Indices:

P

c 1

cold

3

cff

H

hot

1

in

inj

Efficiency.

Heat conduct ivity .

Wavelength.

Viscosi ty .

Radiation frequency, kinenatic viscosity.

Ludoif s number.

Inclination angle.

Density .

PrandtVSchmidt numbers, S teffan-Boitzman constant.

Time.

Stress tensor.

Pressure ratio factor describig error of measurement of enthalpy probe.

Ratio of boundary layer thicknesses.

Partial.

Specific heat capacity ratio.

For panicle.

Centre line.

For cold sas.

For sas.

Effective propenies (turbulent + molecular)

Hydraulic.

For hot ças.

In axial direction.

lnternal.

For panicle injection.

isot -

J -

m - njsot -

out - sh - t - W - 1 - O -

For isotherrnal curve.

In radial direction.

Measured value.

For non-isothermal curve.

External.

For shroud gas.

Total or stagnation.

For coolant water.

For aspiration mode of the enthalpy probe operation.

For no aspiration mode of the enthalpy probe operation

Free Stream values.

xviii

1. INTRODUCTION

1.1 BACKGROUND

At room temperature rnost gases consin of electrically neutral panicles, molecules or fiee

atoms. Random movement of these panicles, and associated kinetic energy, can hardly create any

dismption to their electronic structure. With an increase in temperature, the random movement

of molecules and free atoms becomes more intense and as a result free elecrrons and ions may be

created. The degee of ionization at increased temperatures is quite dissimilar for different gases.

For example, ionization of a r ~ o n Stans at 6000 K, while cesium vapour reaches a comparable

deçree of ionization at only 1500 K "'

At 20000 K nearly all gases are highly ionized, with sigificant number of free electrons

and the ability to conduct electncity. They are called the plasma. If the ças temperature, ("heavy

particle" temperature) is approximately equal to the electron temperature, one may Say that such

a plasma approaches equilibriurn. This is known as "thermal plasma", with temperature of

typically 1OOOO K or more. At such a high temperature, the interaction between the gas and the

injected particulates of matter is highly intensified. Based on this fact, many thermal plasma

technologies have been developed in the last few decades. In plasma synthesis, for example. a

hi& temperature of the plasma Sas enables chemical reactions between the components that are

completely non-reactive at lower temperatures"' In plasma spraying, thermal plasma is used to

melt the particles ofpowder (particles in funher text) and acceierate them towards the substrate

to be coated. The most recent developments in thermal plasma processing include plasma

decomposition of toxic and waste matenals"'.

Plasma sprayinç was discovered in the early 60's and since then it has become one of the

most exploited methods for coating of various base materials'? Materids that are effectiveiy

sprayed today are metailic powders, cerarnics, even polyrners. Contrary to its very simple and

straiçhtfoward concept, the thermal sprayinç process is very complicated and hard to optirnize,

due to a geat nurnber ofprocess parameters that have to be balanced toçether to obtain a coatinç

of çood quaiity. There is also a wide diversiry in the ways of çeneratinç the thermal plasma as a

heating medium, and accordingly we have rnicrowave plasma, W (radio frequency ICP) plasma,

DC plasma, etc. The most popular way of generating thermal plasma for plasma sprayinç

purposes is the use of DC spraying çuns. In DC spraying çun, the electric arc is established

between the cathode and the anode. Gas is injected coaxially with the arc in order to stabilize it.

A typical DC spraying çun is presented in Figure 1 .1 .

The overall spraying process could be divided into several zones. as shown in Fiçure 1.1.

[n "cold gis tlow zone." a cold gas (typically arson) is injected, and heated by Joule effect in the

"arcing zone." With interna1 particle injection, the panicles are injected into the plasma jet

downstream of the anode section. The extensive momentum and energy transfer from the plasma

gas to die particles takes place in the "panicle fi-ee flight zone". In the "deposition zone," particles

strike the substrate. cool. soli di^. and form a layer of protective coating.

Significant progess in plasma spraying has been achieved since its early days.

Technologies of the substrate pre-treatment have been developed, which can significantly improve

the quality of the coating. . A h , deveiopments were made in the post-treatment of the coated

substrates. The developrnent in cornputer techniques and robotics brouçht about certain

hprovements in the domain of process control. New technologies for powder manufacturing and

its pre-treatment had their impact on the variety of the coatinçs produced, and on their quality.

The most recent development trends in plasma spraying concem sprayinç inside chambers with

a cont rol led atmosp here. ExcelIent results have been achieved with spraying in a vacuum ("?

Also, spraying in a chamber with an elevated pressure is currently being investigated?

Although the latest effons in spraying in a controlled atmosphere have started a new

chapter in plasma spraying, atmospheric pressure spraying (APS) remains strongly predominant

in industrial applications. This is because of the very hi& cost of building a controlled atmosphere

chamber, as weii as of maintaining constant pressure inside. This limits its use exclusively to the

coatinçs that are difficult to obtain under atrnospheric conditions, and to those where the highest

possible quality is necessary. Therefore, M S has its future in the coatinç industry and effons

are made to improve the overall process and the coating quality. This is a mukidisciplinary area

and it involves scientists of different backçround. Plasma flow parameters, temperature, velocity,

and ças composition, are the focal points of interest in applied fluid mechanics. They represent

the dnving forces for particle heatinç and acceleration towards the substrate, and particuiar

attention is paid to t hose parameters.

In the early stages of plasma sprayinç development, the experimental investigations of

plasma flow parameters were strongiy favoured compared to the theoretical ones. The reason was

a lack of reliable data on which basic theoretical postulates could be built. In recent years,

scientists have also focused on mathematical modelling of the phenomena occumng durinç the

plasma sprayinç process. Reasons for this are related to the difkulties and the limitations in

conduaing the detaiied expenmental studies in a hiçh-temperature environment. Today, we have

siçnificant progess in modelling of the free plasma flows ('*'), as well as in modelling of the

plasma flows with the injected panicle~'~-'~'. This is a good startinç point for further development

of APS, in terms of improvinç the plasma flow parameters.

One of the ways to improve these parameters is to introduce a gas shrouded nozzle, as

an extension to the sprayinç Sun. Gas shrouded nozzles are used to inject a secondary gas (e.g.,

cold kgon with arçon plasma jet), in an arrangement that surrounds the main plasma flow. The

purpose of this secondary ças is to delay or minimize the mixing of the argon with the

surrounding air. Molecules of nirroçen and oxygen from the air are subjected to thermal

dissociation when heated by plasma. This endothemic reaction removes energy frorn plasma and

results in a sharp drop of velocity and temperature. A more important objective of a gas shroud

is to minimize the difision of oxygen into the main plasma flow and tailflame, resulting in

reduced oxidation ofthe injeaed powden before their impact on the substrate. The first tirne gas

shrouded nozzles are mentioned in .4PS was in US patents(1'."? Since then, they have been used

with some success.

The theoreticai basis for sprayinç with a Sas shroud has it origins in compound jets. or jets

in CO-tlowing or counter-flowinç ~trearns(''~~? This problem has been investigated by a number

of authors in the past and is still of keen interest in a number of applied Buid mechanics

problemsmm The most important parameter of compound jets is the relative velocity between

the two streams, or the ratio between the initial velocity of the main jet and the velocity of the

surrounding n r e q Un, , where U, and U, are the velocities of the main jet and the shrouding

gas, respectively. Depending on this ratio. jets may be referred to either as "weak" (Un, = 1)

or "strong" (Un, >> l)? Generally speaking, "stronç" jets mix with the surroundinçs much

Faster than the "weak" ones. h the case of a "stronç" jet, high velocity gradients in the fringes of

the jet create more shear stress. and the sheîr layer propagates faster towards the avis of the jet.

h typical example of the "weak" jet is the one that emerges from the jet ençine of an airplane. In

this case U, is the velocity at which -gis emerses from the engine. and U, is the velocity at which

the airplane travels. They are of the s m e order of magnitude and the ratio UJU, is close to unity.

The trace of combustion products, toçether with the dispersed particles, can be seen long after

the airplane has disappeared. In thermal plasmas, however, it is difficult to create a "weak"

compound jet, because ofthe large difference between hot and cold ças velocities. T ypically, the

ratio U& is between 50 to 100. However, the presence of the shrouding gas delays the mixing

process h u l a r jet of the shrouding ças presents some form of a rnixing barrier to the

surrounding atmosphere, usually air. The air mixes with the shrouding ças first, and then it starts

gradually to mix with the plasma jet. The end result is lower fraction of air throughout the

"particle free flight zone" in case of the ças shrouded plasma jet.

In order to make a ças shrouded noule work effectively, it had to be properly designed

and well optimized. Its presence not only prosides the spraying gun with the secondary gas, but

also significantly affkcts the main plasma flow by creating additional plasma-to-wall losses. In that

sense, it has to be shaped in such a way to minimize those losses and to create the least possible

disturbance to the main plasma fiow. Nso, as a part of the spraying gun, it has to be properly

cooled to withstand high plasma temperatures. Being exposed to the extreme heat fluxes from

the plasma, thermal stresses play siçnificant role in designing such a noule. Finally, the

arrangement of the seconda- Sas flow will determine its potential to protect the main plasma

flow against mixinç with sur round in^ air. Al these factors are very important in designing a

shrouded noule and they have to be carefuUy baianced toçether in order to make an effective tool

that can improve the MS process.

1.2 OUTLNE OF THE THESIS

The work presented in this thesis is aimed at increasing our knowledge about thermal

plasma jet ernerging from a DC spraying gun. Ernphasis will be put on gas shrouded noules and

their influence on the main plasma flow and the behaviour of injected particles. The approaches

to be used are both theoretical and experirnental. The major thesis objectives could be listed as

follows:

1) Detailed analysis of the enthalpy probe method for stagnation pressure and enthalpy

meanirements in plasma flows. Investisate the error in stagnation pressure measurernents

caused by large temperature difference between a water-cooled probe and plasma.

2) Use the e'cistins mathematicai models for plasma flow calculations to perform a

parametric study of the sprayinç process wïth gas shrouded nodes.

7

3) Based on the above parametnc study, develop and test a new noule design which results

in significant improvement in coating quality.

4) Use the established mathematical model, with flow geometries simulating the real

shrouded noules, in order to predict the plasma flow parameters and particle parameters.

Collect the experimental data on the sarne parameters and ver@ the models used.

5) Perform spraying tests and analyze the coatings obtained. Correlate the results on the

coating quality to the measured and predicted parameten of the plasma and of the injected

particles.

Matenal to be presented in this work is orçanized in eiçht chapters. Chapter 1 contains

introductory notes, the background on thermal plasma in generai, and on thermal plasma spraying.

This thesis outline is also a pan of the same chapter.

Mathematical model to be used is based on the k-E mode1 of turbulence with ail the

constants adjusted according to the present knowledçe of the plasma flow nodelling. It is

described in detail in Chapter 2 . A complete set of the conservation equations for plasma flow

calculations is siven. .Uso. it contains the equations that descnbe the panicle movement and the

heat transfer between the panides and the plasma flow. Couplinç between these two independent

models. and its relative importance is also discussed here.

In order to verify the models and calculations, a detailed experimental investigation will

be cmied out. Details about the expenmental facility, the experirnentd methods and diagnostic

tools to be used are given in Chapter 3 . An enthalpy probe will be used to measure the free jet

parameters, stagnation pressure. plasma enthalpy, and its composition. From the measured

parameters, plasma velocity and plasma temperature will be calculated. For the parts of the Oow

unaccessible by the enthalpy probe. a dynamic Pitot-probe will be used to measure the stagnation

pressure.

Since the enthalpy probe method will be used to collect most of the experimentai data in

this work it is descnbed in more detail than other experimental techniques. This analysis is given

in Chapter 4. Systematic errors in the stagnation pressure rneasurements will be described here.

Emphasis will be put on the error in staçnation pressure measurement due to the thermal

boundary layer. A set of parallel measurements by the water-cooled enthalpy probe and an

uncooled ceramic probe will be camed out in order to examine this error. Also, the systematic

emor in enthalpy measurement will be examined. This error is due to an assumption of the

identical extemal heat transfer during the two stages of the probe operation. Influence of the mass

flow rate through the probe channel, as well as of the flow regime around the probe, will be

examined here. Finally, the overall systematic errors in the staçnation pressure and the enthalpy

measurements for the probe will be estimated.

The suggested mathematical mode1 will be used to perform detailed parametric study of

the g i s shrouded nonles. presented in Chapter 5. First pan of the chapter deals with free plasma

jets. At this stage, panicular attention will be paid to the inlet flow parameters. An improved

version of the power-law scheme(>, based on the calculations and measurements, will be

suggested here. The most important task of this investigation is to identiQ the parameters that

have the biggest influence on three imponant aspects of the shrouded noule:

- interna1 flow of the main plasma gas.

- wall heat fosses,

- particle injection.

Based on this analysis a new desiçn of the shrouded noule will be proposed. The new

design is expected to result in a better arrangement of the main plasma fl ow and in the improved

flow parameten, velocity and temperature. Improved profiles of velocity and temperature will

result in improved particle heating, which is panicularly imponant for the ceramic powders with

a hi$ melting point. New design of the shrouded n o d e wil1 be thoroughly tested and examined

in tems of capability to withstand the hiçh plasma temperatures and to successfully inject the

particles.

A parametric study on the shrouding gas arrangement, and its influence on the main

plasma flow will be presented in Chapter 6. Parmeters such as mass flow rate, velocity of the

shrouding gas, and the arrangement of the shrouding gas injection will be examined. Also, a

detailed numericd study will be performed in order to examine the ability of the existing shrouded

nozzles to protect the main plasma flow açainst rnixing with the surrounding air. The results of

the calculation wiI1 be compared to the expenmental results obtained for the jet emerçing frorn

the spraying y n , with the shrouded noule, and the shrouding gas injected.

The results of the calculation on panicle trajectories and temperature histones, for

different spraying gun configurations, will be presented in Chapter 7. Results will be correlated

to the flow patterns yielded by two different noules, and possible improvernentç will be

recognized. Several spraying tests will be performed in order to correlate the coating quality to

the plasma flow pararneters, and to the pmicle pararneters. Coating quality tests to be performed

are: 1) metalloçraphy tests to examine the microstructure, 2 ) adhesion tests to examine the

bonding strength between the coating and the substrate, and 3) porosity tests.

Finally, in Chapter S conclusions will be drawn and recommendations for practicai M S

process will be made. .USO, recommendations for future work on the design of the gas shrouded

nozzies will be listed. and the most promising improvement directions will be pointed out.

Major contributions of this work (in order of appearance) could be listed as follows:

1) Analysis of the systematic error in staçnation pressure measurements by an enthalpy

probe, due to the thermal boundary layer.

2) Analysis of the systematic error in enthalpy measurements by an enthalpy probe, due to

the assumption of identical extemal heat transfer during the two stages of the probe

operat ion.

3 ) An improved method for assigning the inlet profile of temperature and velocity, based

on the power-law scheme and the stagnation pressure measurement.

4) Complete parametric study of the gas shrouded nodes used in plasma spraying and

identification of the moa important parameters that influence the intemal plasma tlow.

5) X new design of the Sas shrouded nonie, with cu~ l inea r walls, based on the analysis of

the streamlines inside the commercial conical nozzle.

6 ) Complete parametric study on the shrouding gas flow and its influence on the main

plasma Bow.

2. MATHEMATICAL MODELLING OF PLASMA FLOWS

2.1. THERiiIAL PLAS hI.4 BACKGROUND

DC plasma guns produce high temperature, and high velocity turbulent plasma jets.

ma the ma tic al modehg of thermal plasma jets is based on a standard approach in rnodelling the

turbulent free jets. Several assumptions have to be introduced in order to form a complete, closed

set of partial differential equations of motion. These assumptions are:

- Plasma is in the state of Local Thermodynarnic Equilibrium (LTE).

- Plasma is optically thin (transparent to the radiative energy fluxes).

- Flow is steady.

- Gravity effect is ne-Iiçible.

- Viscous dissipation is neçligible.

When the Sas is in a nate of complete rhermodynamic equilibrium, it is possible to express

the particle densities of al1 the species as a Function of thermodynamic parameters (pressure,

temperature). Partially ionized gases are said to be in a complete thermodynamic equilibrium

when four equilibrium conditions are fulfilled('),

12

a) Excitation equilibrium - the population density of the excited States follows Boltzmann

relation.

b) Ionization equilibrium - the population density of charged species is descnbed by the

Saha equation.

c) Kinetic equilibrium - the velocity distnbution for species is descnbed by Maxwellian

distribution hnction.

d) Radiation field intensity is çiven by Planck distribution.

In the above equations i i denotes the number density of the particles on the upper energ

level I, lower energy level k, of the eiectrons r , and of the ions. The corresponding deçeneracies

are denoted with g, E, is the energy difference between the levels, k = 1.38 1 x IO*" JK is the

Boltzmann constant and T is the particle temperature. Mass of the individuai particle is m, its

velocity is W, h = 6.626 x 1 o ' ~ J sec is the Planck constant, v is the frequency of the photons, and

c is the speed of light.

Most thermal plasmas approximately satisfy the first three conditions. A partiaily ionized

gas is transparent to radiation in many frequencies, and therefore emitted radiation escapes the

plasma, thus violating the equilibrium condition However, these plasmas may fiequently be in the

state of L E , where t h e first three equilibrium conditions are fuifilled. For LTE to exist, it is

necessary that the collisional rates ofenerg transfer between the particles are dominant over the

corresponding radiative rates. This condition is very ofien fulfilled in thermal plasmas at

atmospheric pressure and we may Say that the assumption of LTE is generally valid. The most

convenient consequence of L E is that the plasma can be treated as a single fluid, where any

thermophysical property can be expressed as a fùnction of one temperature and pressure. They

are tabulated for different çases and it is very easy to incorporate them into the calculation.

The assurnption of optically thin plasma is reasonable for monatomic and diatomic gases

(arçon, helium, n i t rop . oxvçen, etc. ), which are ~eneraily used in thermal plasma processes. The

above assumption ailows us to include the net radiation losses in the enerly equation. Volumetric

radiation source term in the energ equation is a function of temperature. pressure, and chernical

species. It c m be tabulated for different gases and easily incorporated into the calculation.

The last three of the assumptions represent standard approach in the modelling of

turbulent gas flows. Being turbulent, the ff ow is unsteady with respect to the instantaneous flow

parameters. Wkh respect to the time-averaged parameters it is aeady, provided that the operating

conditions of the plasma gun remain constant. Gravity forces are not important in gas flows due

to hi& inertia of the ças. Viscous dissipation is also of no importance. It is wonh rnentioning that

in thermal plasmas, at a temperature of about 15,000 K, viscosity of the gas is about ten times

higher than at room temperature. However, viscous dissipation is still negligible compared to

other energy transfer modes (convection, difision, radiation)'?

2.2. TRANSPORT EQUATIONS

The mathematical mode1 is based on the full elliptic Navier-Stokes system of differential

equations, with the Reynolds method of averaging the time-dependent equation~'~', together with

the standard k-e mode1 of turbulence(30' The plasma jet was treated as a steady state,

axisymmetric, turbulent tlow The time-averaçed goveming equations al1 have similar stmcture.

Therefore, it is possible to te the conservation equation for generai variable 4, with the gexral

dfision coefficient T4 and çenerai source t e m S,. General difision coefficient, in the example

of viscosity, represents the sum of rnolecular and turbulent viscosity.

Conservation equation for general variable is çiven by

where the lin of equations, with corresponding variables, coefficients, and source ternis, is given

in Table 2. I .

16

In case of axisymrnetnc free jets, the constants of turbulence model, C, and C-, are the

functions of velocity distribution throuçhout the jet?

au 6 , C I au cl .

where 6 is the boundary layer thickness at a çiven axial distance x in the jet, AU is the difference

between the centre line velocity Uc, and the velocity of the surrounding atmosphere (which is

usually not movinç). hnalysis of the velocity distribution within a typical plasma jet, showed that

the factor f is zero in the short potential core of the jet. In other regions its value is within the

range off = 0.96 - 1 . O 4 This means that the mode1 constants do not change significantly for most

of the jet. For this reason, constant values were adopted for C, and C,, and they are listed in

Table 2.2 together with the other model constants.

TABLE 2.2. Model Constants

2.3. EQUATIONS FOR PARTICLE TRlJECTOlUES AND HEAT TTMNSFER

Majority of thermal plasma technoIo-ies involve a second phase, dispersed in the main

plasma flow. In plasma sprayinç the second phase is represented by the injected particles, to be

deposited onto the substrate. Injected particles are exposed to a very high temperature and

velocity of the plasma fiow. They experience the influence of numerous forces that cause them

to accelerate towards the substrate. These rnechanisms will be explained in more detaii in the

following text.

2-3.1. Trajectory calculations

The trajectories of the particles injected into the thermal piasma can be calculated by

establishing the balance of al1 the forces that thermal plasma flow exens on the individual particle.

There is a large number of forces that a a upon a single pmicle dispersed into the fluid fl~w"'.~~'.

Their relative importance depends on the panicle size distribution, and also on the main flow

parameters. Forces affecting the panicle acceleration in thermal plasmas are

3 * -.*

where F represents the inertid force, m is the mass of the particle, a is the acceleration, FD is the --? --P -+

viscous drag force, F, is the Basset history tem, F;, is the thermophoresis force, and F, is the

gravity force. In their analysis of themal plasma reactors, Lee and Pfender'33' have examined the

circumances under which some of these forces rnay be neçlected. Viscous drag force is the rnost

dominant in the two-phase dispersed flows and cannot be neglected under any circurnstance. The

Basset history rem is imponant for panicies that are rnoving with small relative velocity to the

main flow. This is the case in the regions close to the nibstrate, where the pmicle velocity

approaches the plasma velocity. However, this efféct is comparable to the viscous drag force only

for large particles. more than 100 kirn in diameter. Siace in plasma spraying size of the parîicles

is typicaily in the 40-80 prn range, this term could be neçiected. Thermophoresis effect is

important for smail relative velocities between the particle and the plasma flow, and for high

temperature gradients (-1 0' Wm). Injection of the pmicles could be divided into two stages:

1) penetration stage,

2) relaxation stage.

In penetration stage, the relative velocity between the particles and the main flow is very

high. Dunng the relaxation stage this relative velocity decreases, but the particle reaches the

region where temperature çradients are much lower than dunng the penetration stage.

Combination of these two imponant parameters is such that therrnophoresis effect for particle

sizes used in plasma spraying, is always negligible compared to the viscous drag force.

We conclude that the only important force that plasma exens on the particles is the

viscous drag force. It is worth mentioning thar the gravity force is also of very little importance

since the particles are very smd (10-80 pm). According to Lee and PfendeP3), for typical plasma

ffow parameters, the ratio between the viscous drag force to the gravity force is FD/G=600 for

Dp=50 p. The acceleration of an individual particle a,, due to a drag force, could be calculated

as follows:

where ir,, is the particle velocity in i~ direction. Trajectory of the panicle can be obtajned by

integrating the above equation twice. Term FD is given bSY'

where p is the molecular Mscosity of the fluid. Re is the relative Reynolds number, defined by the

relative speed between the gas and the particle. Drag coefficient CD is assumed to obey the

folIowing serni-empirical correlation.

where al's are constants and are given by Morsi and Ale~ander<~'(Appendix B).

The nature of turbulent tlows is stochanic, and in reality particles of the same size and the

same injection parameters uill not follow the sarne path. This phenornenon is taken into account

by introducing the instantaneous plasma velocities in particle trajectory caiculations. Plasma

velocity consists of time-averaged component U,, and fluctuating component u,'. The values of

u:, which prevail during the lifetime of a fluid eddy that the particle is traversing, are assumed to

obey a Gaussian probability distribution

where - 1 < 5 < 1 is a normally distnbuted :andom number. Assurning isotropy of the turbulence,

fluctuating components could be obtained from k-E mode1 of turbulence

The value of 5 is randomly chosen and is valid for the charactenstic life time of an eddf3".

defined as

The values of the flumating components are updated whenever the particle leaves a computation

ceil. Taine interval in which an integation of the equations is performed, is obtained by balancing

the two tirne scales, the lifetime of an eddy, and the time partide needs to cross the computation

celi. Perfoming the trajectory calculations multiple times, it is possible to obtain the dispersion

of panicle trajectories.

2.3.2. Heat and mass transfer

Upon injection. a particle is subjected to intensive convective heating from the plasma-

As the ternperature of the panicle increases, the radiation from the particle becomes more

imponant and the net heat uansfer from plasma ro the particles is the balance between these two

mechanisms. Calculath- the ternperature field of the paxticle is a very dificult task, considering

different shapes of the individual particles, with the resulting irreylar temperature distributions

inside the panicles, as well as the time dependence of the overall process. Some simplifications

and assurnptions are needed in order to fom a closed set of differential equations that represent

the heat and mass rransfer to a sin-le particle.

Heatinç of a single panicle can be divided into several stages (see Figure 2.1):

- Heating of the solid particle (temperature increases from room temperature to the

me1 ting point),

- Melting (temperature remains constant),

- Heating of the molten panicle (temperature increases from the melting point to the

boiling point).

- Evaporaticn (temperature remains constant till the particle disappears completely).

From the plasma spraying point of view it is desirable to adjust the injection parameters

and the plasma parameters so that a11 the pmicles are cornpletely morten but have not reached

the boiling point before impact. This is not easy to achieve, since the different size particles

behave differently upon injection. Heating of the single particle strongly depends on the drag

force, since it defines the panicle residence tirne in plasma. The particle inertia to heating is also

different depending on the size. The following assumptions are made in order to simpliS the

problem:

i i

solid Mclting of Heating of the - panicle : the panicle , molten pnnicle Evapontion ,

1

Residence time

Fig. 2.1. Typicnl herting stages of n particle.

a) Solid and molten particles are both spherical in shape.

b) Internai conduction of the particle is neçiiçible.

c) Vaporization from the free surface of the moiten particle, charçinç effect, non-

continuum effect, and the effect of stronçly varying plasma propenies are neglected.

Spraying powders corne in different shapes. For example, zirconia powder rnay be

purchased as spherical or as "flaky" Figure 2.2 shows the photographs of zirconia powder

obtained by microscope, at 200 times magnification. We can see that the sphencai panicles are

almosr perfect spheres. while the "flaky" particies have much more irregular shape in order to

increase the surtàce area and intensiQ the heat transfer. However, they may be approximated by

the spheres with very irre~ular surtàce. For cdculation of the drag force, they are treated as

spheres, while for the heat transfer caiculation a shape factor F is introduced. It represents the

surface area ratio benveen the real surface and an ideal sphere of the same diameter. Once the

particles start to meit, they become spherical in shape due to the surface tension forces.

The Biot number is a criterion that determines whether the intemal conductior, is

important or not:

where h is the convective heat transfer coefficient, D, is the particle diameter, and Kp is the

thermal conductivity of the particle. If the Biot number is siçnificantly smaller than unity, the

interna1 heat conducrion can be neglected. This cnterion is very often satisfied since the particle

size is very srnail. The situation where tb.is criterion is most likely to be violated is in the injection

sage for the ceramic panicles with low thermal conductivity. The ratio h / ~ , for zirconia pmicles

couid be as hi& as 200-300 m-'. However, for the panicles 0,=50 Pm the Biot number does not

exceed Bi=0.0 1 5 , which sussests t hat the internai conduction could be neglected.

a) Sp hericnl zirconia powder.

b) "Flüky" zirconia powder.

Fig. 2.2. Microscopie photographs of zirconia powder.

Vaporization from the free surface starts to occur once the particle has reached the

melting point. The side effect of this mass transfer mechanism is a reduced heat transfer korn

plasma to the particle. This effect, to~ether with the effects of panicle charging, strongly varying

plasma properties, and non-continuum effects, were studied in detail by Lee? For fine malysis

of the heat and mass transfer between plasma and the pmicles, they dl have to be considered.

However, the aim of this work is to perform a global parametric study of the particle behaviour

for different plasma parameters. Numencal tests performed by introducing ail of the above effects

have shown that the mon imponant factors in predicting the pmicle behaviour are the drag force

and the plasma temperature. The first one determines the particle residence time in plasma, and

the second one is the driving force for panicle heating. The combination of these two has a much

big~er influence on the particle behaviour than al1 of the above effects. For this reason they were

neglected in this work.

Heat and mass transfer benveen the panicle and the plasma, occurs within several stages:

- Heating of the solid particle

d T ~ - hFA(T - T p ) - E ~ O A T ~ ' ' = Q m,C,- - d.r;

net

where rn, is the mass of the particle. T', is the panicle temperature, T is the plasma temperature,

h is the convective heat transfer coefficient. F is the shape factor, A is the surface area of the

approximated sphere, E, is the emissivity of the panicle, (J = 5 . 6 7 ~ 10" W/m2T" is the Stephan-

Boltmiann radiation constant. and Q, is the net hear transfer from the plasma to the particle. The

initial condition for the above equation is T,, = T,,,,,.

Convective heat transfer coefficient. h. may be calculated by using the correlation of Ranz

where K is the thermal conductivity of the plasma gas, Re is the Reynolds number based on the

relative speed. and Pr is the Prandtl number.

- Meltins of the solid panicle

During this stage, the panicle temperature remains constant. Tp = T,,,,,. The liquid

fraction X could be calculated as

where L,is the latent heat of fusion. The net heat transfer Q,, can be calculated frorn Equation

2.17. for F=I, and T, = Tm, ,,,.

- Heating of the molten particle

Once the panicle completely melts (X=I ), its temperature Stans to increase açain. Energy

balance is given by

d?P 4 - hA(T - Tp) - e,aAT,

= Q,,, M~C,- -

dz

26

where the only difference frorn the Equation 2.17 is that the shape factor is missing, since the

particle is spherical now.

- Evaooration of the particle

This stage should be avoided by properiy choosing the injection parameten. However,

if sorne of the smallest particles reach this stage, their diameter will change in time as follows:

where p, is the particle density, L, is the latent heat of evaporation. The net heat transfer Q,, c m

be calculated from the Equation 2.20, for T, = T'pw4,,on.

The presence of the panicles in plasma gas creates momentum and energy sinks.

Importance of these momentum and energy sinks depends on the panicle feedrate. For hiçh

feedrates these sink t e m have to be included in the transport equations for fluid flow. First step

is to calculate these sink term~('~'. Calculated sink tems are then used to reiterate the flow

parameters, by introducinç them into the transpon equations for fluid flow. New fluid flow

parameters result in new value of the rnomentum and energy sink tems due to the presence of

panicles. The complete procedure has to be repeated 2-3 times until the convergent solution is

achieved. For low feedrates, the influence of the particles on the plasma flow parameters is

limited, and the couplinç between the phases is not irnponant. Most of the experimental and

modelling work in this thesis is done for relatively low feedrates, and the coupling between the

phases was not taken into account.

3. EXPERIMENTAL FACILITY AND MEASURING

TECHNIQUES

Experimenral spraying facility is schematicaiiy presented in Figure 3.1. Major components

of the Fxility are the following:

L - Gas botries,

2 - Powder feeder,

3 - Control console,

4 - Spraying gun,

5 - Power supply,

6 - Hiçh-frequency arc starter,

7 - Differential temperature transducer,

8 - Water purnp,

9 - Flowmeter on the city water line.

The entire system consists of four sub-systems (circuits), which are independently

controlled, and are necessary for spraying gun operation:

- electrical system

- cooling water system

- gas systern

- powder feeding system.

They are a11 connected to the control panel, which enables remote start and operation of the

Spraying Gun. Toçether they form the Sprayinç Gun system, and are described in more detail in

the Appendix C.

3.1 DC SPRAYING GUN CHARACTERISTICS

One of the most important characteristics of the DC plasma generators is their Volt-

Ampere characteristic, which defines the actual electrical power that the Gun draws from the

power supply. It depends on the power supply parameters, the length and the resistance of the

electrode leads, the cathode-anode configuration of the Gun, and on the plasma gas used. It is

necessas, to examine this characteristic for the actual configuration of the above components.

Any changes to the configuration will affect the volt-ampere characteristic, and it has to be re-

examined. Figure 3.2 shows the Volt-hmpere characteristic of the Miller SG-100 gun, for the

Curent [A]

Fig. 3.2. Volt-Ampere characteristic of the Gun

existing power nipply, electrode leads, for subsonic configuration of the cathode and the anode,

and for the argon as a plasma gas. It is evident that the voltage is almost independent on the

operating current.

Actuai energy transfer to the plasma gas &,, is ghen by the total electnc power,

reduced by the heat losses QI.

The heat losses occur in the Spraying Gun and in the electrode leads. Total heat loss can be

calculated as follows

where m,is the flowrate of water cooling the spraying gun, C, is the water heat capacity, m,

is the fi owrate of water cooling the electrode leads, and A 7, and A T, are the corresponding

increases in cooling water temperature for the çun and for the electrode leads, respectively.

Efficiency of the torch q can now be caicuiated as

Calorimetnc measurements showed that the efficiency of the gun, and the actual electrical

power depend stronçly on the type of gas, and very Iittle on the gas flow rate.

Average enthalpy per unit mass of the arc heated ças h,,, cm be calculated as

where mg is the plasma gas O ow rate. Average enthaipy of the plasma gas is, obviousiy, a function

of the gas flow rate. The last two parameters, together with the electnc power of the gua

determine the temperature and the velocity of the plasma gas, which are very important

parameters in plasma sprayinç.

Equations 3.1-3.4 represent calorirnetric balance of the spraying gun, and they are the

aarting points in defining the plasma gas veloàry and the temperature. More about this procedure

wiIi be said later in the text.

3.2. MEASURTNG DEVICES AND TECHNIQUES

In order to collect the experirnemai data relevant for thermal plasma spraying process, two

independent rneasuring techniques will be used in this work,

- enthdpy probe,

- dynamic Pitot-probe.

A schematic of the experirnental setup (sprayinç çun and rneasuring devices) is shown in

figure 3 3. The setup consists of the following major cornponents:

1 - Probe (enthalpy or dynamic Pitot-probe),

2 - Enthalpy probe system,

3 - Lasers,

4 - Camera with the filter,

5 - Fibre optics,

6 - Cornputer,

7 - Video-recorder,

8 - Spraying y n ,

9 - X-Y tabIe,

10 - Optical pyrometer with electronics box and readout.

The enthalpy probe. as a main diagnostics tool in this work, will be discussed in detail in

Chapter 4.

3.3. DYNAMIC PITOT-PROBE

Dynarnic Pitot-probe measurements were first done by Barkan and Whitman(3g' in 1966.

They rneauired the stagnation pressure in thermal plasma jets. They also established the criteria

for choosinp the probe dimensions and the pressure transducer. In 1969 Voropaev et al'") used

the same method in thermal plasma measurements, with the probes of various shapes and size.

In more recent years, P.Stefan~vic''~' re-analyzed the method and developed the algorithm for

stagnation pressure rneasurements. He also established the cnteria for evaIuation of the dynamic

characteristic of the system probe-transducer, with the data processing routines and

recommendations for the probe design. This alçorithm was successfblly used for stagnation

pressure measurements in air plasma by P.Pavlovic et al'"'.

The idea on which the dynamic Pitot-probe measurements are based, is very simple. The

probe travels across the diarneter of the plasma jet (or any other high-temperature Bow) with

constant velocity FV, This velociy has to be above certain minimum value at which the probe tip

reaches the melting point, and possible senous disfigurement. The darnaged tip of the probe may

significantly change the Bow pattern around the probe and affect the stagnation pressure

measurements. On the other hand, this velocity has to be smaller than a certain critical speed,

below which serious distonion of the recorded signal occurs. This critical value is determined by

the dynamic characteristic of the measuring systern. In order to design a dynamic probe system

for successfùl measurements in themal plasma, it is necessary to carefdly choose al1 the

components of the system: the probe, the pressure transducer, and the data acquisition board.

Details about the dynamic Pitot-probe sysrem design are given in the Appendix D.

4. ENTHALPY PROBE SYSTEh.1

Enthaipy probe was introduced in early 60" as a diagnostic tool for high-temperature fluid

flow~'~.'". Since then it has been widely used'*") for simultaneous measurements of. primarily,

enthalpy and stagnation pressure. and also of the composition of a high temperature gas. It is

considered to be a reliable diagnostic tool in the temperature range of 2000- 14000 K.

4.1. PRINCIPLE OF hIEASUREhlENT

Enthalpy probe is a water-cooied Pitot tube diar is used to scan the plasma flow tield, one

point at a time, in order to give information about stagnation pressure and enthal py of t he plasma

jet at the observed point. Velocity measurements are based on the Bernoulli equation, similar to

the classic Pitot-probe measurements. Assuming that the gavity forces and the viscous effects

are negligible, the pressure and the velocity are related as follows

where p, is the total or stagnation pressure at the stagnation point (measuring point in this case),

3s

p, is the static or flow pressure. Term pUV2 is calleci the dynamic pressure, where velocity U and

the density p, are the parameters of the undisturbed flow field (prior to the probe insertion), at

the measuring point. For the known gas density, it is easy to calculate velocity LI as

Enthalpy measurement is based on the energy balance of the probe. Two measurements

are necessary for each measuring point in order to obtain the value of the enthalpy. Increase in

the temperature of cooling water is monitored for two diEerent modes of the probe operation:

a) with aspiration of the ças throuçh the probe channel, b) without aspiration.

As indicated in Figure 4.1, dunng the "rvith aspiration" stage, heat transfer from the

plasma to the cooling water of the probe occurs on both, extemal and internai surfaces of the

probe (qm and q,, respectively). During the "without aspiration" stage, only the eaernal surface

of the probe is exposed. The main asnirnption, on which the method is based, is that the extemai

heat transfer is identical during the rwo stages of probe operation. Therefore, the difference

between the total heat transfer between the above two stages is equal to the heat transfer from

the plasma to the internai surface of the probe, only. At the sarne time, this difference is equal to

the enthaipy change that plasma gas undergoes dong its way throuçh the chamel of the probe.

The overall energy balance is given by the following set of equations

41 = qout + 4 i n = m C w PW AT,

where indices I and O refer respectively to the probe operating with and without aspiration of the

gas through the central channel. Total heat nansfer from the piasma to the cooling water is given

by q, the flow rate of the cooling water is denoted by m, C, is the specific heat capacity of the

cooling water, AT is an increase in the water temperature, mg is the gas flow rate through the

central chamel, h, is the enthalpy of the plasma gas at the tip of the probe (measuring point),

and h,, is the enthalpy of the plasma ças that is leaving the probe. The enthalpy of the plasma

gas at the measuring point can be calculated as

A T . - A TA

The riçht hand side of the equation (4.4) consists of quantities that are, either easy to rneasure

(m, rn, PT,, AT,), or could be obtained from thennodynamic tables (C, hCdJ

Enthalpy probe system is schematically presented in Figure 4.1. The probe consists of

three pieces of tubing assembied toçether in a way that enables the coolant water to circulate and

remove the heat from the system. A custom machined cap is welded to the tubing pack to seal

the tip. The tubinç pack is welded to the housing of the probe, equipped with the inlet and the

outlet water terminals. together with the terminal for sas temperature measurement. A micro-

orifice with the pressure taps is provided for the sas flow measurements. Additionai enthalpy

probe system components are as listed:

1 - Piston water pump, Dayton 5K4455C. 0.5 HPI

2 - Cooling water flowmeter, Omeça ET-1 05, 0- 1900 milmin,

3 - ON-OFF valve on the gas line ro enable smooth transition between probe operation

modes (with and wit hout aspiration),

4 - Vacuum purnp, Magnetek Ji3 IP075N model 0.4 HP,

5 - Oxygen analyzer, Illinois Instruments Inc. model 3000, with high-purity, high-

density stabilized zirconia,

6 - Etype thennocouples (Iron-Const.) for rneasuremenrs of the coolant water

temperature, and the Sas temperature,

7 - Calibrateci micro-orifice for ças flowrate measurements. A set of orifices is provided

with the hole diameter 0.6-1.2 mm for different ranses of gas flowrate (calibration

curves are given in the Appendix F),

8 - Differential pressure transducers, Omega 16 1 PC and 1 QPC, with the range

0- 1 psid and 0-5 psid. respectively.

9 - Pressure transducer power supply and readout,

10 - Data acquisition board National Instruments MIO-16.

4.2 ERROR IN STAGNATION PRESSURE MEASURERIENTS

Measurements of velocity are based on Bernoulli equation (1. I ) , which correlates

measured value of the stagnation pressure to the static pressure and the gas velocity. It is valid

under the assumptions of stationary fl ow of inviscid, perfect fluid. and for the streamline that çoes

through the stagnation point. Since an enthalpy probe bas finite dimensions, and it is used for

measurements in real fluids these assurnptions are not completely fulfilled. This results in certain

systematic error, and it could be summanzed in the following equation

wherep, is the measured, whilep, is the theoretical value of the stagnation pressure, which could

hypothetically be recorded by an ideal probe that does not disturb the flow tield. According to

~resvin"", C is a hnction of the following dimensionless parameters,

where Re is the Reynolds number, defined for the probe diameter and the velocity of the

undisturbed fluid. M is the Mach number, ic is the specific heats ratio, Tu is the intensity of

turbulence, 0 is the inclination angle of the velocity vector to the âuis of the probe, d'D is an

inside to outside probe diameter rario. and KPI is the Knudsen number. The last tenn represents

the ratio between gas relaxation time 7, and charactenstic time of motion of the Sas molecules,

in the vicinity of the probe tip.

For measurements in free thermal plasma jet, the slip effect (Knudsen nurnber), and the

gas relaxation t h e are not important. These effects are imponant only for low pressure plasmas

@ < 100 Pa). .Uso. for subsonic plasma jets, Mach number and specific heat ratio are not

important in determining the measurement error. This leaves us with four important parameters

detemining the systematic error in stagnation pressure measurements, rnolecular viscosity

(throuçh the Reynolds number), probe diameter ratio. velocity vector inclination ançle, and

turbulence intensity. These paramerers are important in any Pitot-probe measurements, and they

have to be taken into account in determining the dimensions of the water-cooled Pitot-probe.

They will be discussed in detail in the followin~ tes .

4.2.1. Influence of viscosity on stagnation pressure mensurements

Bernoulli equation is derived under the assumption of perfect fluid, where viscosity is

negligibly small. For the flow around the probe, the above assumption is vdid for Reynolds

numbers Re>200, which is confirmed with a senes of experiments(5"s? For low velocity flows

at hi& temperatures, where viscous forces reach the sarne order of magnitude as inenid forces,

viscous effects have to be taken into account. Depending on the magnitude of Reynolds number

and on the geomerry of the probe tip, the rneasured stagnation pressure becomes larger than the

value obtained by Bernoulli equation. The first anempts to compensate for this error were made

by M. Barker"? Based on her experiments with the probe submerged into the water, she

suggested a correction formula rvhich is valid for Re < 60.

The above formula is graphically presented in Figure 4.2 as curve 1.

~omman'") has performed an integration of Navier-Stokes equations for stationary

viscous flow around the sphere. Taking into account the thickness of boundary layer he obtained

the followinç correction formula

which is çraphically represented in Figure 4 7 as curve 2. The same expression for the flow

around a cylinder in cross tlow is the following

represented by curve 3 in Figure 4.2. Experirnental data obtained by Hurd et al"") and Shoulter

1 - Eqn. 4.7 2 - Eqn. 4.8 3 - Eqn. 4.9

Exper. '%

4 - -1.255 5 - 0=0.337 6 - UD4.530

Plasma .3 4 m 1 . 3

Reynolds number

Fig. 4.2. Measurement error due to viscosity effects.

and Bleyker"" for different if D ratios. do not agree with Homman's experiments at low Reynolds

numbers. and discrepancies tiom theoretical surves are significant. The main reason is that

equations (4.7) and (4.9) do not take into account the eEect of dD ratio on rneasurements.

Dresvin et al"" have performed experiments in plasma and their results are also inciuded

in Figure 4.2. Experimental results in plasma are in good agreement with correction formulas

(4.7) and (4.9). From the above diagram it is obvious that the error of rneasurement increases

with a decrease in d D rario. Xlso, this error is higher for low Reynolds numbers. Enthalpy probes

that are used in themal plasma rneasurements have diameter ratios of typically d/D < 0.4. and are

frequently used in the finges of the jet, with lower values of Reynolds number. For this reason

it is recommended to compensate for the error of measuremeni due <O viscous effects. Equations

(4.7) and (4.9) offer an easy to use algorithm.

4.2.2. Influence of inclination angle of the velocity vector to the probe axis on

the stagnation pressure measurernen ts

The use of Bernoulli equation to correlate the velocity with the stagnation pressure

assumes collinearity between the probe a i s and the velocity vector. In case where certain

inclination angie exists between the two. (@>O0) , the measured stagnation pressure is lower than

the theoretical value, measured when 8=0°. The corresponding emor is given by the following

expression'5g'

Magnitude of this error, detemined by constants k and m. depends on the shape of the

probe tip, diarneter ratio d D, and on the Mach number. For inviscid. incompressible, stationary

flows (Re > 300). and for a tlat cylindrical tip, constants k and m are piven by the followinç

empirical fomiu~ae(~~'

From equation (4.10) a criticai inclination anrle, 8, could be defined as an angle at which the

error in measured stagnation pressure does not exceed 1%. Relative error estimated for different

values of probe diameter ratio d D is piven in Figure 4.3. We can see that this error decreases

with an increase in d D ratio. For example, probe with rLD=O.î has a cntical angle of 0,=7",

while the probe with d D=O. S has a criticai angle of O,= 1 7".

Inclination angle [Deg.]

Fig. 4.3. Relative error due to inclination angle.

42.3. Influence of turbulence on measurement of stagnation pressure

Bernoulli equation is valid for laminar flow of perfect fluid. M e n using the Pitot-probe

and Equation 4.1 - for diasnostics of turbulent jets, an additional error is introduced. Turbulent

jet could be looked upon as a sequence of vortices of different size. The large Buctuating

cornponents with low frequencies correspond to the large vortices, while the small fluctuations

with very high 6-equenties correspond to the small vonices. Frequency spectra is continuous and

very wide 0-5 Wis3' However, standard Pitot-tubes are measurement instmments with high

inertia, because of the large pneumatic pan between the probe tip and the membrane of the

pressure transducer They are not capable of recording these fluctuations, and they record a tirne-

integrated signal.

Turbulent jets are types of flow with a dominant flow direction. They have practically

only one significant component of average velocity, and that is velocity U in the axial or in the

flow direnion According to the Reynolds averaging, the instantaneous values of pressure p.and

velocity u consist of tirne-averaged values @. and LI) and fluctuating components @', zr', v', w').

If the only fluctuating component of veiocity was in the axial direction, u', the inertia of the

pressure transducer would allow the probe to rneasure the average veiocity LI without error.

However, fluctuating components v' and w', perpendicular to the average velocity LI, result in -?

innantaneous velocity vector ri, having an inclination angle to the axis of the probe. This causes

the probe to rneasure the average veiocity U wit h certain error. M e r substituting the components

LI, v' and w', into the vector fom of Bemouili e q u a t i ~ n ( ~ ~ ' and after simpiiyng the scalar product - .- (U - t i ) , the instantaneous value of staenation pressure becomes

Measured value of the stagnation pressure is

where the assumption ir" = 8 + w" about isotropy of turbulence in êujsymmetric jets"') is utilized.

Relative error in measurin~ the stagnation pressure. due to the presence of turbulence is

where Tu is the intensity of turbulence. Equation (4.14) is graphically presented in Figure 4.4. We

can see that for turbulent flows with intensity of turbulence Tu<t5%, systematic error is smail

( ~ 2 % ) and could be relatively accurately determined from equation (4.14). At higher turbulence

intensities equation (4.14) yields unrealistically high values for this error, because it takes into

account only the intensity of the velocity vector, but not its direction. If the probe is perfectly

coaxial with the time-averaçed velocity vector, the presence of the fluctuating components

perpendicular to the axis (v' and lu'), results in instantaneous velocity vector u, having an

inclination angle to the axis of the probe. With the increase in turbulence intensity over 15%, the

inclination angle becomes siçnificant, as well as the error involved (defined by equation (4.10)).

In that case, a neçative systematic error due to inclination angle, compensates panially for the

positive systematic error due to turbulence. This compensation is bigger for the probes with

smaller dD ratio, since they are more sensitive to the inclination angle.

! . . . . . - . . . 1 - Eqiiation (4.14)

Turbulence intensity [%]

Fig. 4.4. Relative error due to turbulence.

4.3. INFLUENCE OF THE TEMPERITURE BOUNDARY IAYER ON TEE

STAGNATION PRESSURE MEASUREMENTS

Previously dismssed errors in stagnation pressure measurements are generally applicable

for any Pitot-probe measurements, under isot hermal conditions. When using the water-cooled

probes, there is one more effect that has to be taken into account, and that is the effect of thermal

b o u n d q layer. The pressure changes in thermal boundary layer around the tip of the probe, and

is different than the value that would be rneasured with the probe that is at the same temperature

as the Free Stream.

First to compensate for this error were Smith and ~hurchill'~! They introduced the

following correction tem. obtained from the m a s and energy balance,

where T. is the fiee strearn temperature and 7; is the probe surface temperature. Mauimurn error.

thus. could reach 50% when T. > > T7

In the theorerical work of Mostaçhimi and ~fender '~ ' ) boundary layer theory is used to

account for the above error Velocity, temperature, and pressure distributions in boundary layer

are given by

48

where index = refers <O the free Stream values of temperature, pressure and velocity, m and n are

exponents that depend on the type of flow, and 6 and 5, are velocity and temperature boundary

layer thicknesses, respectively. Boundary Iayer thicknesses are related to each other through the

factor C which is a function of Prandtl number, 648 = =(Pr). From Bernoulli equation, the

velocity is reIated to the measured value of stagnation pressure as follows

where factor f is derived as

Equation (4 18) reduces to equation (4.151 obtained by Smith and Churchill, for m=2n, <=1/Pr,

and P d . For the more probable case. r n = ~ 2 , and for Pr=0.7. factor f becomes

with the maximum error of K!?/0.

33.1. Experimentrl results on non-isothermal Pitot-probe mevurements

Fist to experimentally prove that there is an error in stagnation pressure measurements,

related to the thermal boundary layer. was Aian a are'? He designed an expenment with a coid

nitrogen jet, and with a probe that was heated by a h i ~ h fiequency induction heater. The probe

temperature was gradually increased and the stagnation pressure was measured. The obtained

results were then cornpared to the stagnation pressure measurements under the isothennal

conditions. He found that with an increase in temperature difference between the probe and the

coid nitroçen Stream. the discrepancy between the measured stagnation pressure and its

isot hermal value, almost exponentially increases.

These experiments isolated the influence of the temperature drop in the boundary layer

on the stagnation pressure measurements. They also proved that the value of stagnation pressure

has an influence on the relative error of measurement. For a maximum temperature difference

obtained between the probe tip and the cold stream, the relative error of measurement can Vary

from 10% to 50?G. depending on the value of the rneasured stagnation pressure. This significant

drop in relative error of measurement could be due to changes in the thickness of thermal

boundary layer around the probe tip. Higher value of the stagnation pressure corresponds to the

higher value of free strearn velocity. High velocity tends to suppress the boundary layer around

the tip of the probe. which tends to decrease the relative emor in stapation pressure

measurements.

Measwements in a cold ças Stream by a heared probe do not have practicai application.

On the other hand, measurements with a water-cooled probe in a hot ças stream have significant

application in diagnostics of hi& temperature flow fields. The same error of measurement occurs

in this case, but with a neçative sign (probe rneasures the lower stagnation pressure). In reality,

a hiçh temperature rneasurement. differs signiticantly from the one simulated in Alan Hue's

experiment. where the probe was stagnant and the Sas stream parameters did not change. The

enthalpy probe scans the high temperature jet in a point-by-point fashion, experiencing different

flow conditions around the tip.

h intereainç experiment was perfonned by Fincke, Snyder, and Swank(%', where laser

light scattering was used parallel to an enthalpy probe to measure the temperature and velocity

of argon plasma. Measurements were taken on the a i s of an argon plasma jet, at an axial location

of 2 mm downstream of the gun exir, for different operating powers of the gun, resulting in

plasma temperatures in the range of 1 1,000 - 13,000 K. Agreement of the measured parameters

was found to be satisfactory, within the uncertainties of the expenmental methods. Results on the

plasma vefocity indicated that the values obtained by an enthalpy probe are systematically lower.

However, the discrepancies in the measured parameters were not nearly as high as the

extrapolation of Aian Hare's results would suggest. The temperature difference between the

plasma and the water-cooled probe was more than 10,000 K in al1 of the tests performed by

Fincke et al, compared to only about 2,000 K in Xlan Hare's experiment. Different findings in the

above two expenments. suggest that an analog between a heated probe in a cold gas stream, and

a water-cooled probe in a hot gas stream, can hardly be made. The differences in stagnation

pressure and vefocity for the rwo cases, result in a different rhickness of thermal boundary layer

around the probe tip and a different measurement error

For adequate analysis of the descnbed error in stagnation pressure measurements, more

experirnental results are needed A simple expenment, like the one with the heated probe, is not

possible in thermal plasma because the probe tip temperature cannot be controlled with a high

accuracy. Aiso, an ideal isothermal probe rneasurement of the stagnation pressure in thermal

plasma flows, with temperatures of up to 10,000 EC, is not possible. However, parailel

measurernents by a water-cooled probe and an uncooled (Le. a ceramic) probe can give some

information about the described enor The probes could be desiçned to have exactly the same

dimensions, and hence eliminate some of the errors described in the previous text. Mso, numencal

simulation can provide some information on chançes that flow parameters undergo within the

themai boundary layer around the probe tip.

1.3.2. Numerical simulation of the water-cooled probe imrnened in a plasma jet

Bernoulli equation (4.1) is valid dong one streamline, and it States that the sum of kinetic

energy and pressure is constant. The strearnline, that coincides with the axis of the probe, ends

at the stagnation point. Aiong the way, the kinetic energy transfomis into pressure. At the

stagnation point, the velocity becomes zero and the entire flow energy is transformed into the

stagnation or total pressure. In order to examine this rnechanism more closely, and its dependence

on the difference between the free strearn temperature and the temperature at the stagnation

point, a series of numerical experiments were performed. A free jet was simulated, together with

a jet and a probe imrnersed in it. Various tlow conditions around the probe tip were simuiated by

chanting Y the values of dynamic-to-fiee aream pressure ratio, and the difference between the fiee

Stream temperature and the probe rip temperature.

The numerical procedure used was based on the k-E mode1 of turbulence and on the full

elliptic set of the çoverning eq~ations"~ Geometricai parameters and the gnd size were specified,

and the cdculations were perfomed by FLUENTa' software package for fluid flow cdculations.

Calculation dornain is schematically presented in Figure 1.5, where the probe is located at the avis

of the jet. Calculations were performed in two steps. First. the entire calcuiation domain, around

the probe with extemai diameter of &. 8 mm, was taken into account to obtain the global fl ow

picnire. Numencal grid used was 52x52. .Mer that, calculation was performed only in the narrow

region in Front of the probe tip, represented by a thick line in Figure 4.5. Actual dimensions of

the domain were 4 mm x 2 mm, with numerical grid used 32x32. Input values for this calculation

were taken From the previous step.

Simulation was performed for several values of the dynamic pressure in free jet,

4365 Pa, 1919 Pa. and 435 Pa. The temperature of the probe tip was changed from

isothermal case, T,=S000 K. (plasma is assumed to be at T.4000 K) to the value that

approximately corresponds to the case of water-cooled probe, T'=500 K. Results are presented

Open boundary

Symmetry axis subdomain

Fig. 1.5. Schemrtic of the caiculation domain.

probe /

Temp. difference [KI

Fig. 4.6. Predicted error in stagnation pressure measurement (P,=l~"a).

in Figure 4.6. The error of measurement is given as E=APJU,-, where Al',-, represents the

value of dynamic pressure obtained in the isothermai case. T,=5000 K. We cm see that the error

of measurement depends on the dynamic-to-tee Stream pressure ratio, AP,/P,, similarly to the

case of the heated probe in the cold jet. With an increase in the pressure ratio, the error decreases.

The above analysis is equivalent to the expenments conduaed by Aian Hare. The flow parameters

were kept constant and the probe tip temperature varied. ln this case, the systematic error has a

negative si= Le., the probe measures a lower stagnation pressure than the theoretical, isothemal

value. Magnitude of the error in the case of water-cooled probe is lower than in the case of heated

probe due to hiçher values of dynamic-to-free Stream pressure ratio.

Another conclusion that couid be drawn from the numencai simulation was about the

thickness of thennal boundary layer surroundinç the tip of the probe. It is assumed that the edge

of the thermal boundary layer is at the point where the plasma temperature drops below 99% of

the value in the isothermal case. The thickness of the thennal boundary layer obtained for

different values of dynamic-to-free Stream pressure ratio is shown in Figure 4.7. The thickness

o. 1 1 i 04 I o - ~ 1 O-* 1 0-1

Press. ratio - AP(P_ Fig. 17. Thickness of thermal boundny layer around the probe tip.

54

of thermal boundary layer rapidly decreases with an increase in the dynamic-to-free strearn

pressure ratio. This is in ageement with the results presented in Figure 4.6.. where lower values

of error for higher values of dynamic-to-free strearn pressure ratio are the consequence of

reduced thickness of boundary layer around the probe tip.

43.3. ParaIIel rneasurements of the stagnation pressure by a water-cooled and an uncooled

probe

In order to examine the error in stagnation pressure measurements by a water-cooled

probe in a hi& temperature jet, an experiment was carried out by using two different probes. h

custom-made enthalpy probe, with internai to extemal diameter ratio dlD= 1 .Dl. 8 mm, was built

together with an uncooled (ceramic) Pitot-probe. The ceramic Pitot-probe was made by casting,

using Thoria (Tho,) powder because of its çood mechanicd propenies, and hi& melting point

(3200 K). The dimensions of the ceramic probe were chosen to match those of the water-cooied

probe, in order to eliminate other sources of error Prelirninary measurernents in a cold arçon jet

were performed and the probes were measunng the same stagnation pressure.

An optical pyrorneter. Raytek Thermalen, was used to rnonitor the probe surface

temperature close to the tip of the probe. Miller T h e d sprayinç gun SG- 100 was used to create

an argon plasma jet with a mass flow rate of m = 1 g/s. An attempt to move the probes into

different resjons of the jet was not successfÜl, because of the insufficient accuracy of the

positioninç system. The results obtained were not comparable. For this reason another approach

was adopted. The probes were fixed at the avis of the jet, 35 mm away fiom the gun. In order

to simulate different flow conditions around the tip, the spraying gun was operated at different

power levels. The Sun power was changed from 8 to 2 1 kW, which yielded the fiee stream

temperature around the tip in a range of 1500-5500 K (calculated frorn the enthalpy

measurement s).

Temp. difference [KI

Fig. 1.8. Error of mensurement - experimental data.

Results obtained are summarized in Figure 4.5, where the ratio of the dynamic pressure

rneasured by a water-cooled probe and by an uncooled probe, respectively is given as a hnction

of the corresponding difference in the probe tip temperature. It is important to note that this

dinerence is not equal to the difference benveen the free stream temperature and the temperature

of the water-cooled probe. The ceramic probe temperature is lower than the free stream

temperature due to radiation and heat conduction through the probe. However, the trends of the

measurernent error could be examined fiom the above experiment. The experimental values fiom

Figure 4.8. suggest different trends in error from the curves recorded by Alan Hare(62' in his

heated probe measurements, and the curves from numencal simulation. The main reason for this

discrepancy is that every point s h o w in Fiçure 4.8. corresponds to a different value of the

dynamic pressure. This is a typical situation in enthalpy probe measurements, where practicaily

at every meamring point we have a different value of dynamic pressure. Therefore. the effects of

the temperature difference between the probe tip and the free Stream, and of the level of the

measured stagnation pressure, cannot be looked upon independently. The correction formulas

suggested by Smith and Churchill (equation 4.15) and by Mostaghirni and Pfender (equation

4-19), do not take into account the level of the stagnation pressure measured. This is the reason

why these equations overestimate the measurement error (up to 50% according to the equation

4.15, and up to 32% according to the equation 4.19).

Compared to the results obtained from the numerical simulation, experimental results

suggest a higher systernatic error in stagnation pressure measurement. Accuracy of the numerical

simulation is iimited in the vicinity of the stagnation point. To perform meaningfbi calculation, it

was necessary to take into consideration a relatively large domain in front of the probe. In order

to improve the accuracy of the calculation, a second step was introduced where a much smaller

region in the vicinity of the staçnation point is considered. A Iink between the two steps is

provided by assigning the appropnate boundary values, obtained in the first step. A much finer

grid allowed much finer calculation in the vicinity of the stagnation point. However, sorne

accuracy is lost in the process of passinç the information from step one to step two.

The temperature difference between the plasma temperature and the probe tip temperature

does not provide al1 the information on measurement error. The followinç analysis is based on the

integration of the Bernoulli equation within the boundary layer, by utilizing some of the findinçs

from the numerical simulation.

4.3.4. Theoretical aspects of the boundary layer around the tip of the probe

Schernatic presentation of the changes that temperature, velocity and pressure undergo

in the vicinity of the probe tip is given in figure 1.9. Two cases are presented, non-isothennal

(dotted line) which refers to the water-cooled probe, and isothermal (solid line) which refers to

- - - - - - - - - - - - - - - - - - -

Fig. 1.9. Velocity, temperature, and pressure distribitioninthe v<ciniQ of the

stagnation point.

an uncooled probe thaî has the sarne temperature as the free Stream. A very important concIusion

fîom the numerical expenments is that the thickness of the temperature boundary layer depends

on the dynamic-to-free stream pressure ratio. Asa, a decrease in velocity, accompanied by an

increase in pressure stms to occur out of the boundq layer, within the stagnation zone in front

of the probe tip. ïhe values that velocity and pressure have upon reaching the boundary layer are

denoted as u, and p, . Within the boundary layer, temperature sharply drops from the free stream

value T- to the probe temperature TF The curves that descnbe the recovery of pressure h m the

kinetic energ are different for isothernal and non-isothermal case (solid versus dotted line).

Resulting pressures at the stagnation point are P,-, and P,,, respectively.

In order to estirnate the error of the stagnation pressure measurement, it is necessary to

perform the integration along the isothemai and non-isothemal cuve, within the domain of

interest @=O4 orp=pS-pl-- andp=ps-pf-nua). The integration is performed assurning that the gas

is ideal and incompressible, (p=p(ï)). Detai!cd derivation is given in Appendix E. For the error

of rneasurement we can write

M e r performinç the integration (described in Appendix E), the error of measurement becomes

where Apt., is the dynamic pressure measured in the isothermal case. Factor represents the

portion of the overall pressure change that takes place inside the thermal boundary layer around

the probe tip.

Pr- isoi - Pa

It is a function of the dynamic-to-free Stream pressure ratio ar the point where the measurement

is taken. Based on the numerical tests performed, it is found by cume fitting that the above

dependence has the following form

Dependence of the factor j on the dynamic-to-free stream pressure ratio is given in Figure 4.10,

within the domain of values typical for free plasma jets.

Equation (-1.21) ives relative error of measurement, and may be used oniy as a first

approxirnarion. For more reliable estimate of the relative error of measurement, equations E. 1 1

(Appendix E) and (1 23) have to be used in an iterative procedure, described in Appendix E.

Generdly, 2 or 3 steps are sufficient to reach the convergent solution.

Systematic error in dynamic pressure measurements of the argon plasma jet, estimated

using the equations (4.2 1 ) and ($23). is given in Figure 4.1 1, together with the experimental

results obtained by usinç the water-cooled and the uncooled probe. Aso, systematic error

estimated by equation ( 4 15) (Smith and Churchill) and equation (4.19) (Mosta~himi and Pfender)

is presented. The equations (4 21) and (1.23) predict rnuch Iower error than equations (4.15) and

(1.19), and they are much closer to the expenmentd curve. The difference is clearly a

consequence of introducinp a factor <, or the influence of dynamic-to-free stream pressure ratio

on the systematic error of measurement .Aiso. the shape of the curve is sirnilar to the experimental

curve. It predicts the maximum error at a temperature difference of about 500 K and gradua1

decrease in systematic error as the temperature difference increases. Maximum value of the

relative systematic error is found to be around 10%.

Experimental results sugçest lower error, but it should be kept in mind that an ideal

isothermal meaairement could not have been perfonned by the ceramic probe. The ceramic probe

measurements were also in error. due ro temperature difference between the free stream and

ceramic probe tip. The true value of the systematic error made by the water-cooled probe, is

Fig. 4.10. Factor E, as a function of dynnmic-to-free stream pressure ratio.

- - - - expcrirncnt - - Eqn. 4.19

-

O 1000 2000 3000 4000 5000 6000

Temp. difference [KI

Fig. 4.1 1. Systemrtic error in stagnation pressure messurement.

higher than the above expenment suggested. The value of the expenment performed is that

it indicated the trend of the systematic error of measurement. Aiso, it has shown that this

error is limited, rather than monotonically increasing with an increase in the temperature

dserence between the free aream and the probe tip. This is a consequence of two parameters

thaî have opposite influences on the error. Generally, in high temperature jets, regions with

high temperature have a high velocity. An increase in velocity tends to suppress the boundary

layer and to minimize the above error. At the same tirne an increase in temperature is followed

by an increase in temperature gradient within the boundary layer around the probe tip, and

an increase in the measurement error.

Both these parameters have to be taken into account in an attempt to estimate the

systematic e m r in staçnarion pressure measurements. Equations (4.21), (4.23), and (E. 1 1)

offer an easy to use algorithm for calculation of the above error. Velocities are proportional

to the square root of the memred dynamic pressure, so the calculated values of velocity have

lower relative error (maximum up to 3 4 % ) . However, it is recommended to introduce the

suggested compensations in velocity calculations.

4.4. ERROR N ENTHALPY MEASUREMENTS

Enthalpy measurement by a water-cooled Pitot probe is a typical calonmetic

measurement. The measured quantities of hear transfer from the plasma to the coolant water

are used to estimate the enthalpy of the gas at the measuring point. The method was described

in detail in Chapter 4.1. The mon important issues in determinhg the accuracy of the enthalpy

measurement by an enthalpy probe are:

- probe sensitivity,

- condition of iso-kinetic aspiration at the measuring p ~ i n t ' ~ . ~ " ,

62

- vaiidity of the assumption of identical heat transfer firom the plasma to the external

probe surface, during the two stages of probe operation.

The accuracy in determining the gas enthalpy (Equation 4.3), strongly depends on the

difference in heat transfer dunnç the two stages of the probe operation (q, and q 0 ) More

reliable readings ofthe enthalpy are obtained with an increase in this diEerence. Henceforth,

the sensitivity of the probe P is defined as follows

41 - 40 A Tl - AT, 13 = - -

It is particularly irnponant to have çood sensitivity in the finges of the jet, where the levels

of the basic siçnals, AT, are small. However, it is not easy to design a prabe with good

sensitivity. The ratio d/D is typically 0.2-0.4, which results in a much bigger surface area for

heat transfer from the outside than from the inside of the probe. Also, the diameter of the

innermost tubing is typically around I mm, which makes it very hard for plasma gas to flow

through. Generally, vacuum pumps are used to force the flow. There are a few things that

could be done to improve the sensitivity of the probe:

1) Design a probe with a long "neck" and a short "tip".

2) Maximize the ci D ratio to obtain more favorable balance of the heat transfer.

3) Increase the mass flow rate throuçh the central channel of the probe.

The first objective cm be achieved without risking a lack of performance of the probe

as a diagnostic tool for stagnation pressure. A long "neck" of the probe will enable the hot

gas, flowing throuçh the channel of the probe, to cool almost to the room temperature. On

the other hand, shon "tip", or part of the probe exposed to the plasma, will significantly

reduce the extemal heat transfer. The increase of dû ratio is limited by two things: a)

dimensions of the tubing available on the market. b) spatial resolution in stagnation pressure

rneasurements decreases, and the error of measurement increases with the increase in dD

ratio. Finaily, increase in the mass flowrate through the channel of the probe will certainly

increase the internai heat transfer. It will not affect the stagnation pressure rneasurements

since they are taken during the stage without aspiration. However, an increase in the internal

flow may affect the extemal flow picture, and other errors may be introduced.

During the aspiration stage of an enthaipy measurement, it is very important that the

aspiration of gas is iso-kinetic. It means that the flow rate of sample gas, sucked by the

vacuum pump, is equai or less than the plasma flowrate through the surface area identical to

the internal cross-section of the probe. If this condition is not fulfilled, plasma gas is

accelerated at the "mouth" of the probe, creating a 80w pattern with streamlines converging

to the probe tip. Therefore, spatial resolution of plasma measurement is considerably violated.

The results ofmeasurement do not represent the average plasma parameters over the surface

area identicai to the intemal cross-section of the probe, but over an area much bigger.

It is earemdy difiicult to account for a measurement error introduced by violating the

condition of iso-kinetic aspiration. In practice, however. it is frequently violated due to a need

for good probe sensiticity For example, if the probe has an internal diameter of d = 1 .Z mm,

and the flow rate through the probe exceeds the iso-kinetic tlow rate by 100%, the

corresponding area in plasma jet has a diameter of d = 1.7 mm. The error of measurement

introduced by the above aspiration conditions, may be acceptable for the regions with srnall

gradients of plasma parameters in radial direction, but in the fnnges of the jet this error

becornes significanr .

4.1.1. Error due to assumption of identical heat transfer in two regimes of the probe

opera tion

Enthalpy rneasurements are based on the assumption of an identical exiemal heat

transfer dunng the two stages of the probe operation. The accuracy of the measurements is

directly related to the validity of this assurnption. It is reasonable to expect that for high-

power, high flow rate sources (20-30 gs), and for the enthalpy probe with an outside

diameter of up to 5 mm, the above assurnption is fulfilled with negligible error. For the

spraying çuns that are generaily used in APS, power of up to 40 kW, and gas fl ow rate of

typically 1 gis. the error in the above assumption may be significant.

In order to examine the heat transfer from the plasma to the outside and the inside of

the probe, a senes of numencal expenrnents were performed usinç the mode! proposed in

Chapter 2. A free arçon plasma jet is considered here, with the flow rate of 1 g/s. emerging

60m the plasma gun operating at 19.6 kW. .A water-cooled probe is simulated by introducing

a solid wall into the calculation domain, at x = 30 mm away from the y n . A sketch of the

calculation domain, with al1 the boundanes, is presented in Figure 4.7. Thermal boundary

condition of the solid wall. representins the water-cooled probe, was defined in terms of the

convective heat transfer coefficient. h=3S k W r n ' ~ . of the cooling water and the water

temperature, Tw=190 K. Details about estimating the above parameters are given in Appendix

H. Hencefonh, it was possible ro calculate the heat transfer from the plasma to the walls of

the probe. Al1 the flow parameten and the boundary values were kept constant, and only the

gas flow rate throuçh the channel of the probe varied. The results are presented in Figure

4.12. The difference in heat transfer from the plasma ro the extemal surface of the probe,

Aq,, for the two stages of the probe operation, is given by

where indices (wo) and (wtth), refer to the probe operating without and with gas aspiration,

respectïvely. The error in determining the external heat transfer, by assuming it identicai for

the two stages of the probe operation is given by

where m is the gas flow rate through the channel of the probe, and rn, is the spraying gun

flow rate. It is evident that with the increase in the gas flow rate through the channel of the

probe, the error in determinin- the external heat transfer is increasing. It can reach 7% for

unrealinicaily hi& flow rate ratio (mlm, = 0.5). For typical flow rate ratio of mlm, = 0.1, this

error is acceptable at 3%. At the same tirne the sensitivity of the probe increases with an

increase in mlm, ratio, as shown in figure 4.13.

In reaiity, the flow rate through the channel of the pobe is Iimited by the pressure drop

dong the aspiration tract of the systern. For the enthalpy probe system used in this work, the

maximum flow rate through the probe channel was m = 0.12 g/s, for typical spraying

conditions, with m , = 1 g s . Sensitivity of the probe, determined expenrnentally by using

eqauation (1.24), and the recorded increase in coolant water temperature ATl and AT,, is

also giveven in Fi y r e 4.13. The dots represent average value of sensitivity for a given gas Bow

rate through the probe channel. Enor bars represent the standard deviation.

By assurning an identical extemal heat t m f e r for two modes of the probe operation,

an error is introduced in calcuiation of interna1 heat transfer. This error has an absolute value

of Aq,,,, which is equal to the error Aqmt- The relative error in determining the internai heat

transfer can be estimated according to the following formula

Fig. 4.12. Relative error in determining the external heat transfer.

Fig. 4.13. Sensitivity

0.4 0.5 0.6

of the probe.

It has a neçative sign, which means that the measured enthalpy (interna1 heat transfer)

is lower than the reai value. The maximum relative error is recorded at the point closest to

the gun exit (x = 30 mm), on the mis of the jet (Fig 4.14). We can see that for typical mass

flow ratio of mlm, = 0.1, the relative error has a value of 7.5%. It is important to notice that

with the increase in mlm, ratio, the relative error decreases untill it reaches minimum value

for m/m, = 0.25. This is very interesting, because despite the increase in the absolute error

of meanirement, the relative error nill decreases. At the same time for higher values of mlm,

ratio, the sensitivity of the probe is hiçher, which enables better results in the fringes of the

jet. On the other hand, the value of mlm, ratio is limited by the condition of iso-kinetic

aspiration. For the argon plasma jet under consideration, average iso-kinetic flow rate was

around 0.05 gk, suçgestinç an mlm, ratio of about 0.05. By simply adopting the value of

m/m, = 0.25, su~~es ted by the above analysis, one would violate the condition of iso-kinetic

aspiration by 400% and larçeiy increase the uncertainty of measurements. It can be concluded

that the value of fI ow rate ratio, mlm, has to be carefully balanced between two opposite

requirements: a) minimize the relative error under consideration and increase the probe

sensitivity by increasinç mlm, ratio; and b) maintain good spatial resolution of the

measurements by decreasing mlm, ratio, and keepinç it close to the iso-kinetic condition.

In order to examine the intluence of the probe position on the error of measurement,

additional numerical experirnents were performed. The probe was simulated at different axial

locations, x = >O - 60 mm away from the gun, for few discrete values of mh, ratio. The

results are summarized in Figure 4.15, where relative error of measurement is given as a

function of dimensioniess enthalpy hlh,,. The reference value of enthalpy, hm, represents

the maximum value of enthalpy recorded by the probe, at the point closest to the spraying

gun, x = 30 mm. The aigorithm used in this work to compensate for this error was simple and

straightj?iorward. Corrections are first made for the measuring point at x = 30 mm, at the avis

of the jet, by using the d i a g m on Figure 4.14. Upon determining the maximum value of the

measured enthalpy, hm, the diaçram on Figure 4.1 5 can be used for other measuring points

in the jet.

Fig. 4.14. hIaximum relative error in enthnlpy messurement nt the jet axis.

Fig. 4.15. Relative error in enthalpy measurernent.

4.42. Error in indirectly measured quantity

The total enthalpy of plasma ças is an indirecriy measured quantiry, and the relative

error of measurement is dependent on the relative errors of the measuring devices used'"'.

The following formula describes relative error in enthalpy measurements

6 h 6172 6 ( A T , - A T ) - =

6K r(-w)2 + ( O )2 + (-l2 + h m w A T , - AT, K

where the tems on the right hand side of the Equation (4.25) represent relative errors in

rneasuring the relevant quantities. Relative accuracy in measurement of water fl ow rate by the

rotameter, 6m j'ni, is esrirnated at I ? / o Relative accuracy in measurement of the temperature

difference of cooling water depends on the level of basic signal, but for the most of the jet it

is 6 ( A T , - h T J ( A T, - A T,,) = 340. K is the calibration constant obtained during the

calibration of micro-orifices (tlow rate vs. pressure drop). Corresponding relative accuracy

is estimared to be 6KIK = 2%. The density p in front of the orifice is calculated kom the

measured gas temperature, and its relative accuracy is within 2%. The pressure drop at the

Mao-orifice, Ap, is measured directly by differential pressure transducer with an accuracy

of 1%. By substitutinp al1 the above values into Equation (4.28), the total error in enthalpy

measurernent does not exceed 5% for most of the jet. It is expected to be slightly higher in

the fringes of the jet, because of the lower basic sigals in the water temperature

measurements. but not to exceed 10%.

4.5. DESIGN PARAhIETERS OF THE PROBE

After the analysis in the preceeding te-, major manufacturing requirernents f'r an

enthalpy probe rnay be surnmarized as follows:

1) Good strength and suficient cooiing of the probe:

The probe is exposed to very high temperatures (up to 10,000 K), and has to be

cooled extensively, which creates significant thermal stresses. The cooling channels

of the probe have to be large enough to enable sufficient flow of the coolant water.

Generally, a hi& pressure pump is used to force the flow of the coolant. The chosen

tubing diameters and wall thicknesses have to be capable of withstanding the

pressure and the t hemal stresses.

2) Good spatial resolution and accuracy in stagnation pressure measurements:

Since the plasma jets are, typically, 10 mm in diameter, significant pressure gadients

are expected at cenain reçions of the jet. In that sense, the internai diameter of the

probe. d. has to be small enough in order to yield accurate pressure readings. Due to

the high level of turbulence in some portions of the jet, the probe must not be very

sensitive to the ande - of t he velocity vector (see Figure 4.4). This requires smaller ri D

ratios.

3 ) Good sensitivity and accuracy in enthalpy measurernents:

Accuracy and sensitivity in enthalpy measurernents are discussed in Chapter 4.4.1.

Major manufacturing requirements in that regard are to build the probe with long

"neck" and "short" tip, and to increase d D ratio.

It is obvious that some of the above requirements contradicr each other. This means

thai one cm never manufacture a probe that is, at the same time small enough to achieve the

highest possible accuracy in stagnation pressure measurements, and to be extremely sensitive

for enthalpy measurements. A compromise has to be made between the two opposite

requirements in order to Set an optimal tool for both of the measurements.

4.5.1. Probe geornetry

The probe i s assembIed out of three pieces of SS 304 tubine, with the following

diameters:

- 4.76 mm OD / 3.74 mm ID

- 3.05 mm OD / 2.39 mm iD

- 1 . 6 5 m m O D / 1 . 1 9 m m I D

The inside to outside diameter ratio of the probe is dD = 1.19/4.76 = 0.25. The pack

oftubinç is radially bent together at 90" with the curvature radius of r = 30 mm. The "tip" of

the probe is 1 = 25 mm long, whiie the "neck" is L = 150 mm (see Figure 1 . 1 ). This gave the

"tip" to "neck" ratio of 1 6 The tip of the probe is manufactured of the solid SS 304 piece,

to match the tubins diameters. It is welded to the tubine pack by using electron beam

welding.

The housine of the probe is made out of 1" OD SS 3 16 tube. Corresponding

diaphragms are attached to separate the cooling and the gas chambers of the probe. The

housinç is assernbled by usinç a laser spot welding technique. Standard flançe is provided to

support the micro-orifice. Tubes of 1/4 " OD are welded to the housing to provide cooling

water ports, gas exhaust, pressure taps for micro-orifice, and the gas temperature

measurement port.

4.5.2. Estimated error of measurement

The desiçned probe has an outside to inside diameter ratio d D = 0.25. As a fint

approximation, it is assumed that the probe has a flat tip. With the use of correction factor

(Equation (4.9). cume 3 in Figure 4 2). the estimated systematic error does not exceed 1.5%

for al1 reasonable values of Re number. From Figure 4.3, it is evident that the critical

inclination q l e 8, = 7". while the accuracy of the positioning system is estimated to be 13".

Thus, systematic error involved does not exceed - 1 %. From Figure 4.4, we can see rhat for

turbulence intensities of up to 30%. the probe is making an error which does not exceed 5%.

The sum of the above errors does not exceed 5.5%. The error due to thermal

boundary layer. with the adopted correction factor (Equation (4.21), is estimated to be

between 0% and -1 O?& The total error is expected to fa11 in the range of -5% to 5%. Some

discrepancies from the expected behavior may be expected in the fringes of the jet due to

higher level of turbulence. lower values of the measured pressure, and low Re numbers.

The stagnarion pressure is rneasured directly. by using differential pressure rransducer.

Relative accuracy of the measurernent depends solely on the accuracy of the transducer, and

it is within 1%. The total accuraq of the stagnation pressure measurement is estimated to be

26% for most of the jet. Corresponding error in calculated velocity is lower than i3%.

Error in enthalpy measurements consists of two parts: a) error in detemining the

internai heat transfer h m the plasma to the probe. estimated to be 12% (afler compensating

for it); and b) error in indiredy rneasured quantity, estimated to be 15%. The total accuracy

of the enthalpy measurement is estimated to be 17%.

M e r the process of collectinç the experimentai data by the probe is finished, equation

(4.3) can be used to calculate the distribution of plasma enthalpy. Stagnation pressure is

recorded directly and can be used without changing in fbrther processing of the experirnental

data. Caldation of temperature from the measured enthalpy is descnbed in Appendix F. The

accuracy of calculated temperature depends on the accuracy of gas composition

measurements. In this work, it is assumed that the oxygen and the nitrogen from air have

equal diaision rates into the argon plasma, and that the air content in the jet can be easily

calculated from the oxygen content. The later was measured directly by using the oxygen

analyzer, with very hiçh accuracy of 10.2%. However, the above assumption introduces

certain error in caiculation of the temperature (descnbed in the Appendix F). With adequate

tabulating, temperature vs. enthalpy, the calculation error can be minimized, and it is

estimated to be within 2 10%. Listing of the FORTRAN program for data processing is

presented in Appendix 1.

5. GAS SHROUDED NOZZLES

Gas shrouded noules are generally used as an extension to the spraying gun. Their

funcrion is to introduce a secondary ças in a flow arrangement that surrounds the main plasma

flow, thus creatinç a shroud of cold ças. In order to evaluate the performance of a gas shrouded

nozzie, it is necessary to examine in detail the flow pattern inside the noule. Since gas shrouded

noules have to be warer-cooled, it is necessary to account for wall losses. A very challenging part

of the n o d e design is to shape the walls properly, in order to rninimize these losses, and to create

minimum possible disturbance to the main plasma Bow.

Some additional constraints exist in designing a ças shrouded nozzle. Thermal spray

powders are normally injected at the outlet OF the spraying gun, and they have to travei through

the entire lençth of the noule on their way towards the substrate. Since injected panicles tend

to disperse radiaiiy as they travel dong the ais , divergent noules are required. The length of the

n o d e is also important, and should be selected in such a way that would reduce the energy losses

to the cold walls. However, the requirements for proper cooling of the noule, as well as for the

proper injection of the secondary ças, impose some limitations in choosing the nozzie length.

Finally, the noule should be relatively easy to manufacture, install and replace.

In an attempt to evaluate a ças shrouded nozzle, first step is to examine the free jet

emerçing from a DC sprayinç gun. After that, the plasma flow emeqing from a gas shrouded

n o d e cm be examined, cornparison with the free plasma jets made, and possible improvements

75

recognized. For this reason, the followin~ text deals with the free plasma jet calculations.

Boundary condition and the inlet profiles of temperature and velocity will be discussed here.

5.1. FREE JET CALCULATTONS

Since the early days of theoreticai fluid mechanics, free jets have been of interest to many

scientists. Their reçuiar structure and accessability for expenmental investigations, enabled the

scîentists to establish a number of integal methods for calculating the parameters of free turbulent

jets. A review of the early works in this field is presented by ~ajaratnam"? The development of

themai plasma technolotjes in 1960's brouçht into focus a new family of turbulent jets - plasma

jets. Being extremely non-isothermal types of flow, they required new approaches and methods

for calculating the jet parameters. Early attempts in calculating the plasma jet parameters were

based on the integrai methods, by utilizing the expenmental results for establishing the necessary

constants. The review of these works is presented in the book by ~ . ~ . ~ b r a m o v i c h ( ~ ?

Rapid development of cornputers technique in the 1980's revolutionized the theoretical

work in plasma jet calculations. Numerical methods offered some possibilities in the areas where

the integral methods exhibited their weaknesses and limitations. It becarne possible to get

solutions for very complex flow problems (CO-flowing jets, mixing jets, jets with the dispersed

second phase) by using the numerical approach. There are numerous examples of successfblly

used numencd approach in solvinç cornplex problems in thermal plasma field (7.66.67.68.69)

In this work the numerical approach wi1l be used to calnilate the parameters of the plasma

flow emerging from a DC Spraying Gun. The term free jet is used here to refer to the flow

emerging directly fiom a DC gun, without any shrouding nozzies or attachments. General

conservation equations are presented in Appendix A. In the following text, general calculation

procedures, boundary condition, and the results will be presented.

5.1.1. Flow geometry and boundary condition

The first step in an attempt to nurnencally solve the Buid flow problem is to establish a

domain of interest and setup the boundaries. Typical domain of calculation for the free jet is

presented in Figure 5 . 1 . Boundaries that surround the domain are Iisted as the inlet, the side

boundary, the outlet, and the symrnetry auis. The jet is asnimed to be two-dirnensional(2-D), a..-

symrnetric. For argon plasma jet, it is necessary to calculate the axial and the radial component

of velocity, U and V, temperature T. kinetic energy of turbuience k and its dissipation E, and mass

fraction of argon p,,. It is necessary to provide the boundary values for al1 these parameters.

Side boundary

Fig. 5.1. Schematic of the calculation domain

1) InIet boundary

As we can notice from Figure 5.1, the inlet boundary consists of DC gun exit, or the

nozzie, the solid wall (part of the water-cooled DC gun), and the open boundary. In the following

text they will be referred to sirnply as inflow, solid wall, and open boundary, respectively.

a) Inflow:

3 2 2 k = - T u U k 2

and r = C -

where r is the radial coordinate, R, is the radius of the Sun exit, U, and TCl are the central line

values of axial velocity and temperature, rn and i t the power-law exponents, Tu the turbulence

intensity, C, is the constant of turbulence model, and L, is the characteristic length for calculation

of dissipation of kinetic energy of turbulence.

U = V = O and T = T W

where the wail temperature, T, is assumed to have the following distrib~tion'~~)

The wall temperature inside the gun channel is not known. It is assumed that at the exit it has a

value of T, = 700 K. At radius R, the above logarithmic distribution yields the room temperature

T' = 300 K.

The wall shear stress, as well as the near-wall turbulence quantities, are calculated

according to the log-law meth~d"~'.

2 ) Side boundary and outlet boundary

Side boundary, outlet boundary, and the part of the inlet boundary are treated as open

boundaries, or fixed pressure boundaries. The pressure at these boundaries is assigned a value of

atmosphenc pressure. Depending on the flow conditions inside the domain, the fluid may either

enter or exit throuçh these boundaries. In a case when the fl uid enters through the boundav,

values of m,, T, Tir, L, have to be specified. Veiocities U and V are calculated by solving

momentum equations, assuminç no momentum losses. In a case when the fluid exits the

boundary, the same procedure is used by using the upstream values of the above parameters.

3) Symmetry axis

On the symmetry axis al1 radial gradients are equal to zero, as well as the radial velocity

. * and V = O - = O w h e r e @ = U,T,k,e,rnAr, ar

5.1.2. Inlet profiles of temperature and vetocity

The inlet profiles of velocity and temperature are assumed to be governed by power-law,

Equations (5.1) and (5.2). This method was suç~ested by ana"') and improved by iee'? Since

then, it has been used in a number of nurnencal works in the thermal plasma field. In standard

power-law approach, two measured parameters are used to calculate the radial distributions of

velocity and temperature at the ourlet cross-section of the DC spraying s i n . These parameters

are the mass flow rate of the plasma ças, measured directly, and the ent haipy of the plasma gas,

measured indirectly throuçh calorimetnc losses of the y n . The method could be summarized in

the followinç few steps:

I ) Assume the values of the power-law exponents m and 11.

2) Assume the values of centre line temperature and velocity, T, and Ud.

3) Calculate the radial distributions of U(r) and T(r) by using Equations (S. 1) and (S.?).

4) Check if the following conditions are satisfied

m h g plasma - - 2n l r h(T)p(T)U(r)rdr O

where the lefi-hand-side term of the equation (5.6) represents energy transfer from

the gun to the plasma.

5) If the conditions (5.5) and (5.6) are not satisfied, adjust 7; and Uc,.

The above method has cenain shoncomings. Values of T, and U, are generally not

known, and they are lefi to be calculated based on the assumed values of power-iaw exponents

m and n. The last two rnay be determined through charactenzation of a particular plasma gun.

It is very difficult to rnake any generalization, because different gun geometries will result in

different values of power-law exponents. Aiso. for a pmicular gun, these values may vary for

different operating parameters. the mass flow rate and the electric power. The above algonthm

is extrernely sensitive to the values of power-law exponents. The profiles obtained for one pair

of exponents differ signif'cantly from the profiles obtained for the other pair of exponents. This

is iliustrated in Figures 5 . 2 and 5 3 where the profiles of velocity and temperature at the outlet

of the spraying gun are çiven for different combinations of m and n, and for the fixed values of

the mass flow rate and the gun power. In addition to this, corresponding profiles of velocity and

temperature will determine the stagnation pressure profile. The profiles of stagnation pressure,

for different combinations of power-law exponents are given in figure 5.4.

We can see that the sta-nation pressure profiles may have quite different shapes for

different combinations of porver-law exponents. M e n integated over the surface area of the gun

outlet cross-section, they yield different values of the force. This is a force that when the fluid is

brouçht to a complete stop, would act on the object of the exact same surface area. The

difference in this force between the two extreme cases presented in Figure 5.4, is as large as 57%.

Frorn a purely mathematical point of view, there is a unique solution to the above problem. In

other words, there is a unique set of parameters mch as U, Td, mm. and rz, for which the conditions

(5.5) and (5.6) are fulfilled, and the profile of stagnation pressure yields the correct value of the

above-mentioned force.

1 2 3 4

Radial coordinate [mm]

Fig. 5.2. Velocity profiles for different values of power-iaw exponents.

1 2 3 4

Radial coordinate [mm]

Fig. 5.3. Tempera t ure profiles for different values of power-lnw exponen ts.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Radial coordinate [mm]

Fig. 5.4. Stagnation pressure profiles for different values of power-law exponents.

5.1.3. An irnproved power-lnw appronch

The followinç method is based on the standard power-law approach, with one

modification: a measurement of stagnation pressure profile at the exit of the plasma gun is

included. This measurement elirninates the uncertainty introduced by estimating or assuming the

values of UcL c,, m. and I I . Expenmental tool for stagnation pressure scanning is the dynarnic

Pitot-probe, descnbed in Chapter 3 . it is easy to use and it gives reliable results. Now, it is

possible to define the profiles of velocity and temperature without previous knowledge of their

centre line values or the values of power-law exponents. The algorithm is based on the following

few steps:

1) Assume the vaiues of the power-law exponents m and 11.

2) Assume the values of centre line temperature and velocity, Tcf and II,.

5 ) Calcuiate the radial distributions of U(r) and T(r) by using Equations (S. 1) and (5.2).

4) Check if the conditions (5.5) and (5.6) are satisfied. If they are not, adjust the values

of Tc, and QI and repeat the steps 2 4 .

5) Check if the following condition is satisfied

where F is the force that the fluid brou~ht to a complete stop would exert on the object

of the surface area equal io the plasma y n exit.

6) If condition 5 is not satisfied, edjust the values of m and r ~ , and repeat the steps 1-5.

400 450 500 550 600

Elapsed time [msec]

Fig. 5.5. Output voltage of the pressure transducer.

Diameter [mm]

Fig. 5.6. Profiles of the stagnation pressure.

O 1 2 3 4 5

Radial coordinate [mm]

Fig. 5.7. Inlet profile of velocity.

Radial coordinate [mm]

Fig. 5.8. Inlet profile o f temperature.

Typical signal recorded by the dynarnic Pitot-probe method, used at the exit cross-section

of the sprayinç çun, is presented in Figure 5.5. Figure 5.6. presents the profiles of stagnation

pressure: the experirnent al curve obt ained by superposition of 5 successively recorded profiles,

and the curve obtained from the calcu lated velocity and temperature profiles. Figures 5.7. and

5.8. represent the calculated profiles of temperature and velocity by using the improved power-

law method. The above algorithm is used to determine the input velocity and temperature profiles

for SG- 100 spraying yn, operatinç at P,=19.6 kW ((1=28 V, 1=700 A), and with argon flow rate

of m= 1 g/s. This panicular regime is used for most of the analysis in this work. The obtained

values of centre line velocity and temperature are: LI,= 1090 m/s and Tc,= 13490 K. Power-law

exponents were: m=2.6 and 11=7.8. At the same tirne recorded profile of the stagnation pressure

is very close to the one calculated fi-om the obtained velocity and temperature profiles. The above

values were used to perform the calculations on the free plasma jet parameters.

5.1.1. Calculrtion of the free plasma jet

Calculation of the free argon plasma jet is performed by using two modifications of the

descnbed mathematical model, parabolic and elliptic. The parabolic model is fkequently used in

modeliing of plasma jets due to the relatively short CPU time it requires. The code used here was

developed by Lee(n, with the calculation boundary coinciding with the actual jet boundary.

Momentum equation is transformed into conservation equation for the dimensiodess Stream

function(? The boundary condition at the jet boundary considers the entrainment rate of the jet.

It should be estimated in such a way to produce the profiles that do not have sharp tmncation or

a long tail at the jet boundary. The çrid used was 250 nodes in axial direction, and 60 nodes in

radiai direction. Caiculation time on the SunSparc station was approximately 3 minutes.

The elliptic model was based on the ff exible code provided within the FLUENT software

packaçe. Boundary conditions were specified as idow, solid wail as a part of the inlet boundary,

and the open (fixed pressure) boundanes. Grid used was 52 x 52, and to achieve convergence

it required approxirnately 2.5 hours on the SunSparc station. Both models were using temperature

and species dependent properties (tabulated and presented in the Appendix J).

Experimental results were coilected by using the water-cooled enthalpy probe, described

in Chapter 4. The probe moved in axial and radial direction to map the free jet in a point-by-point

fashion. The range within the probe moved was 30-70 mm fiom the çun exit, and 0 - 6 m from

the jet axis.

The results are presented in the f o m of iso-contours of velocity, temperature and mass

fraction of argon, as well as the axial distribution of the same parameters. Figures 5.9-5.11

present the iso-contours of velocity, temperature and argon mass fraction, obtained by parabolic

and elliptic rnodels.

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.9. Iso-contours of velociiy.

Axial cordinate [mm] Fig, 5.10. Iso-contours of temperature.

L 10 i Parabolic

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.1 1. ho-contours of argon mass fraction.

It is evident that the paraboiic model predicts longer isothems and veiocity iso-contours,

or in other words elliptic model predicts sharper jet decay in axial direction. The difference is

significant despite the fact that al1 the input parameters were the same. Figures 5.13-5.14 show

the axial distribution of the velocity, temperature and argon mass Fraction, predicted by both

models, in cornparison with the expenmental results. We c m see that the expenmental results fdl

much cioser to the elliptic modei curves. For most of the caiculation domain theoretical values

fiom the eiliptic modei are within the error rnargin of the expenmental method.

In addition, iso-contours of temperature, velocity and argon fraction, obtained by the

eiliptic model, were compared to the ones obtained by expenmentai rnapping of the jet, Figures

5.15-5.17. Much better agreement in the Iength of the iso-lines was noticed, which is in

accordance with the recorded axial profiles. The expenmental isolines are slightly shifted towards

0.02 0.04 0 -06 0.08

Axial coordinate [ml

Fig. 5.12. Axial distribution of velocity.

1

- parabolic - r -- - elliptic I

- exper. I

i -

0.02 0.04 0 .O6 0.08

Axial coordinate [ml

Fig. 5.13. Axial distribution of temperature.

0.00 0.02 0.04 0.06 0 .O8 0.1 0

Axial coordinate [ml

Fig. 5.11. Axial distribution of argon mass fraction.

the &Us. This is the consequence of lower sensitivity of the enrhalpy probe in the fnnges of the

jet, due to the lower level of the siçnals.

The strong discrepancies between the parabolic and elliptic rnodel have to be addressed

to the ability of elliptic model to take into account the movement of tluid surrounding the jet. The

streamiines predicted by the elliptic model. Figure 5.18, indicate that beside the main jet a strong

movernent of the surrounding air exists. Cold air is entrained by the plasma jet. and it enters the

open boundanes (throuçh the side boundary and the pan of the inlet boundary). Cold air

approaches the main plasma jet in a cross-stream pattern. The rnixing in the shear layer is not only

due to difision (rnolecular and turbulent), but aiso due to the convective fluxes of cold

air. Recent works in the field of entrainment of cold gas by themai plasma provided

substantid evidence that this process is more of an engulfment, rather than simple difision. This

engulhent is a very unsteady process, and is manifested by the plasma jet entrapping large

l- t Experiment

O I O 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.15. Iso-con tours of velocity. Experimental and theoretical.

Axial coordinate [mm]

Fig. 5.16. Iso-contours of temperature. Experimentrl and theoretical.

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.17. Iso-contours of argon mnss fraction. Experimental and theoretical.

masses of air. However, numerical simulation deds with average flow parameters, and this

entrainment is on average equivalent to the cross-stream mixinç between the plasma jet and the

surrounding air. Parabolic model predicts the entrainment of sur round in^ air, but driven solely

by ditfusion fluxes. It yields longer potential core of the jet, and the higher values of the plasma

jet parameters.

Figure 5.19 presents a detail of the streamlines in the vicinity of the spraying gun exit,

predicted by the elliptic model. Streamlines that represent the flow of the emerging plasma, are

slightly flexed towards the avis of the jet. Parabolic models predict divergent streamlines in this

region'?. Configuration of the streamlines, predicted by the elliptic model suggests that the cold

air cross-strearn penetrates the plasma jet in this region, thickening the shear layer. A direct

consequence is faner mixing of the jet with the surrounding air. a shorter potential core, and an

upstream shifl of the sharp decay in plasma jet parameters.

Open boundary

Fig. 5.18. Sireamlines inside the calculation domain.

Solid wall

L lnflow ;

I

Fig. 5.19. Strenmlines close to the spraying gun exit.

Experimental results confirmed the validity of the elliptic model predictions, and its

supenority to the paraboiic model. It gives very good qualitative representation of the large scale

mixing at the initial portion of the plasma jet. This mixing can significantly affect velocity and

temperature of the plasma jet, thus afTecting the heat and momentum transfer to the particles.

Also, the presence of oxyçen fiom air cm result in formation of oxides on the surface of the

particles, degrading the quality of the sprayed coatinçs. An improvement to the APS process is

offered by using gas shrouded nozzles. Shrouding gas, surrounding the plasma jet, can delay the

large sale mixing to the downstrearn portions of the jet. This can create a better environment for

particle heat and momentum transfer. Aiso. ças shrouded nonles enable the intemal injection of

the particles. Inside the nozzle, particles are not exposed to the oxygen from the air and are in

much better environment for heatin~ and acceleration. The gas shrouded nozzles and the

shrouding gas will be discussed in detail in the following te=.

5.2. EVALUATION OF THE PEIRFORMANCE OF A CONICAL NOZZLE

Commercially available noules are in the form of a simple, diverging conical diffuser. It

is believed that such a design satisfies the constraints in the shrouded nozzie design. Funher

analysis will, however, show that this is not the case. Detailed anaiysis should be carried out to

determine the optimal shape of the noule. The influence of the diffuser angle, gas flow rate,

energy losses, and the shape of the nozzie have to be examined carefùlly. These parameters will

determine the flow pattern inside the nouie and possible occurrence of cold air entrainment,

which causes a sharp velocity and temperature drop in downstrearns portions of the jet.

In order to evduate the performance of the shrouded noule, a series of numencal

experiments have been carried out. An argon plasma jet, emerging h m a spraying gun (Miller

SG-100) was sirnuiated. The gun was equipped with a gas shrouded n o d e in the shape of a

divergent, conical diffuser.

5.2.1 Flow geornetry

A schematic of the flow geornetry for the spraying gun with the gas shrouded nozzie is

shown in Figure 5.20. The flow domain c m be divided into three regions: 1 - the gun region, 2 - the shrouded noule region, and 3 - the free jet region. Modelling of such a system has usually

been confined to the free jet region, Le., region 3. This requires a knowledge of the plasma

temperature and velocity profiles at the outlet of the node , Le., region 2. These profiles could

be estimated £Yom a knowledge of the plasma enthalpy at the noule outlet, and the plasma gas

mass flow rate. Plasma enthalpy can be estirnated From the measured torch power and

calorirnetric meanirernents of the nozzie wall losses. The power-law scheme, described in Chapter

5.1 ., can be used to estimate the in!et profiles.

This approach is valid with no air entrainment, or recirculation within the noule. When

this is not the case, the above method is not valid. The approach adopted in this work is more

general. It includes both regions 2 and 3 in the computational domain. That way, possible air

entrainment and recirculation of the gas inside the noule can be appropriately accounted for. It

has been assurneci that the inlet conditions for reçion 2 can be estimated by the power-law

scherne, in the same way it was done for the free jet inlet conditions. The overail computational

dornain is shown in Figure 5.1 1. Isometnc view of the sas shrouded noule is given in Figure

5.22, which shows the centrai charme1 throuçh which the plasma ernerges, and the 16 small holes

for shrouding gas injection.

In an attempt to nurnerically smdy the shrouded nozzle, the mathematical mode1 described

in Chapter 2 was used here. Wall heat fluxes, and wall temperatures were detemiined by using

a boundary condition with the specified extemal heat transfer (convective heat transfer coefficient

of the coolant water and its temperature, by following the procedure descnbed in the Appendix

H). Free boundanes were treated as fixed pressure boundaries with an assigned value of static

pressure of one atmosphere at room temperature. The goveniing equations were solved using

reg ion

G u n Nozzle

Fig. 5.20. Schematic of the flow domain (dimensions in mm).

Fig. 5.21. Overall computational domain.

the FLUENT 4.2 package. In order to accurately predict the wall shear stress and heat loss in a

conical nozzie, a boundary titted coordinate system (BFC) was used('? This allowed the non-

standard geometry of the noule to be mapped into a cylindricd geometry. This feature becomes

even more important for curvilinear walls, which wil1 be discussed later. The numerical grid

consisted of 30x30 cells inside the nozzie and 50x50 cells in the fke jet region.

5.2.2. Influence of the nozzle angle

Fim experimental results obtained in the free jet region, with plasma emerging from the

conicai nozzie, indicated unexpectedly high content of oxygen at the jet mis. This pointed out that

some cold air entrainment is taking place close to the walls of the conicd noule. Entrainment of

Fig. 5.22. Isornetric view o f the shrouded nonie.

cold air occurs when the boundary layer separates fiom the cold nozzle wall, creating a strong

recirculating zone. Therefore, cold air entrained into the nozzle will cool the main plasma flow.

The parameter that is most responsible for the above boundary layer separation, is the angle of

the nozzie.

In order to funher investiçate the above, a detailed numencal investigation was performed

on the flow pattern inside a simple conical gas shrouded noule. Nonles with different difiser

angles were simulated using the Boundary Fitted Coorciinate (BFC) feature of the numencal

modefling software package. The initiai test case considered, a straight tube, 32 mm in length and

7.8 mm in diameter (the exit diameter of the plasma torch), and 30x30 grid.

DifEerent angles of the nonle were created by changing the outlet noule diameter. Note

that in the calculations to follow, only the flow patterns inside the nozzle were investigated, and

that the free jet region will be considered later in the text. Calculated resuits corresponded to an

argon flow rate of 1 iJs, and torch power input of 19.6 kW ( U 4 8 V, I=700 A).

Figure 5.23 shows the calculated flow strearnlines inside the nodes. For the straight

nozzle, (Fig 5.23-a) there was no air entrainment. Startinç from a diffuser angle of a=7. 1°, cold

gas was entrained inside the noule. For angles of a= 1 7.3'' and larger, the entrainment becarne

very significant and such a noule was almost useless for spraying purposes. The arnount of

entrained air as a function of the diffuser angle is shown in Figure 5.24. For angles greater than

a=7. 1°, entrainment of the cold air increased considerably. The quantity dmlm is the ratio of the

flow rate of entraineci air to the arson flow rate. For diffuser angles of a=20.6' the 80w rate of

entrained air becarne higher than the primary arçon Bow rate. This means that the average gas

enthalpy per unit mass at the outlet of the nozzle, compared to that at the inlet of the noule, is

reduced by more than 50% simply by rnixing with the entrained cold air. Consequently, nozzles

with such hiçh entrainment rates are not usefil1 for spraying purposes.

O 5 10 15 20 25

Diffuser angle [Degrees]

Fig. 5.24. Quantity of the entrained air for different angles.

5.2.3. Influence of the argon fiow rate

The flow rate of the argon plasma through the shrouded nozzie also iduenced the

envainment of cold air. Several test cases were investiçated to study thk influence. The diffuser

angle chosen was a= 10.7' (the angle of the existing commercial nozzle), and the flow rates of

the argon plasma were vaned from 1 to 3 S/s, within the range of feasible flow rates for the

spraying gun used. Results are presented in Figure 5.25.

When the argon flow rate was increased. the recirculation zone became larger, resulting

in an increased entrainment rate of cold air. Fiçure 5.26 quantifies this, by plotting the ratio of

entrained air and the argon flow rate, Jmlm. as a fünction of argon flow rate.

Fig. 5.25. Strenmlines inside the nomle for different fïow rates.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Gas mass fiow rate [gls]

Fig. 5.26. Quantity of the entrained air for different flow rates.

When the argon flow rate was increased from i g/s to 3 gk, Jmlm varied fiom 8% to 25%.

Compared to the effect of the diffuser angle, the extent of entrainment was Iess sensitive to an

increase in the plasma flow rate.

These results clearly indicated that the conical shape of the noule was not ideally suited

for its intended application. Noules with small angles suffered fiom a Iack of space for proper

interna1 particle injection. On the other hand, n o d e s with larger cone angles resulted in

significant entrainrnent of cold air within the noule.

To overcome such shoncomings of the standard design, a cu~ l inear noule profile was

proposeci. It is expected that such a design, based on the streamline analysis, could filfil both of

the design requirements: 1) proper intemal particle injection; and 2) no air entrainrnent.

5.3. CURVILINEAR DESIGN OF THE GAS SHROUDED NOZZLE

The suggested cu~ l inea r design of the noule is based on the anaiysis of the streamlines

inside the conical nozle. The idea was to shape the nozzle in such a way that its wall profile

coincided with the particular flow streamline which represented the total argon flow. This process

was iterative and needed several steps before an optimal profile was obtained. The angle of the

conical pan at the inlet remained constant at a=10.7", and also the length of the node . A

schernatic of the curvilinear noule is shown in Figure 5.27.

Curvilinear noule was manufactured by brazing an inserî inside the existing conicai

noule. The insert was machined out of copper, in an attempt to fit perfectly its extemal surface

into the conical diffuser. Its interna1 surface was then machined to curvilinear shape, determined

by the above analysis. The noule and the insert were brazed together by using a copper alloy in

order to maintain a good heat conductivity. After assembling the parts together, additional

machining was performed to obtain a smooth intemal surface of the curvilinear noule.

Conical nozzie

Fig. 5.27. Schematic of the curvilinear noale.

104

Extensive numerical tests were performed for the suggested nozzie design. Plasma gas

flow rate was varied between 1-3 S/s, and no entrainment of cold air was predicted. Flow

nreamlines for a flow rate ofm=2. g/s are shown in Figure 5.28. They appear to be srnooth, with

no cold air entrainment. The region with the maximum intemal diameter is exarnined more

closely, and the results are aven in Figure 5.29. Streamiines close to the wdl appear to be smooth

withour any vortices or recirculation zones.

Fig. 5.28. Streamlines inside the curvilinenr noale.

Fig. 5.29. Streamlines in close-to-the-wall region of the curvilinear noale.

5.4. ENERGY B A U N C E OF THE NOZZLE

Performance of the gas shrouded nonle is strongly dependent on the energy transfer that

takes place between the hot plasma ças, cold entrained air, and the water-cooled wdl of the

node . The energy balance of the shrouded nozzie may be written as follows

mh. in + dmh air = (m + dm)hou, + Q,,

where m is the plasma gas flow rate. dm is the flow rate of entrained air, Q,, is the overall heat

loss to the cooled nouie walls, h,, and hm, are average enthalpies of the plasma gas at the inlet

and the outlet of the nozzle, respectively, and h, , is the enthalpy of the cold air. The average

outiet plasma enthalpy hm, can decrease significantly with significant cold air entrainment. Aiso,

the wail heat loss, QaS, plays an important role in determining the outlet plasma enthalpy.

Wall heat losses were calculated for three different cases: a) straight tube, b) conical

nozzle with an angle of u = I r , and c) curvilinear noule. Wall heat flux dong the noule for

these three cases is given in Figure 5.30. The losses appear to be the smallest for the conical

nonle. There is almost no heat tlux from the plasma to the cooled wall in the region close to the

n o d e outlet. This is a consequence of the cold air entrainment. Cold air flows inside the nozzie

and prevents extensive heat transfer between the hot gas and the cold wall. The straight tube has

much higher wall heat fluxes than both of the noules. Total wall heat loss is obtained by the

integration of the heat flux over the entire area exposed to the heat transfer. Diagrarn in Figure

5.3 1 presents the overall wall heat loss, relative to the electrical power of the gun, for conical

noules with different angles.

Diagram in Figure 5.32 shows the ratio of ourler to inlet enthalpy for different angles of

the conical nozzle. We can see that it rapidly decreases for the angles where signifiant

entrainment of the cold air stms to occur. According to the diagram, the existing conical node ,

1

4

- -

A-' -i

11 / \

\- Y -t

- cunilifiear nozzle \. - - conical nozzie L. l

O Ï -+-.-.---.-*-.--

l

-1 ' 0.000 0.004 0.008 0.012 0.016 0.020 0.024 0.028 0.032

Axial coordinate [ml

Fig. 5.30. Wall heat flux for different nozzies.

30 .

7 - - conical nozzie - - - cun-ilincar nozzic '-1 -\

Diffuser angle [Deg]

Fig. 5.31. Wall heat loss for different noale angles.

with an angle of a = 10.7O. still has relatively good enthalpy ratio, despite the fact that it entrains

cold air. However, it should be kept in mind that for the same value of enthalpy, an air-argon

plasma has much lower temperature than the pure argon plasma, due ro dissociation of oxygen

and nitrogen molecules. Very small amounts of air will cause a steep drop in the plasma

temperature.

Wall heat losses also depend on the electricd power used to produce the plasma. Total

wall heat losses for the shrouded n o d e can be measured by calorimetry, descnbed in Chapter

3. Since this method yields total heat losses for the entire spraying gun system, including

the heat losses for the shrouded noule, it was necessary to perform two tests for each power

setting of the gun. Heat losses were measured separately for the gun operation with the nozzie,

and without it. The difference in the heat losses for two cases is assumed to represent the losses

for n o d e only. A cornparison between the experimental and numencal results is presented in

Fiyre 5.33. Both methods suççest sirnilar trend in wall heat Iosses; increase with an increase in

the spraying çun power. It appears that the calculation overestimates the wall heat losses, which

is later confirmed by the analysis of the flow parameter in the free jet region. This is due to

inadequacy of the k-E mode! in the close-to-the-wall reçions.

5.5. FLOW PARARIETERS €Di THE FREE JET REGION

The predicted temperature and velocity profiles at the outlet cross-section of the

c u ~ l i n e a r gas shrouded nozzle were considerably hiçher than those obtained for the standard

conical n o d e with a= 10.7". Results are presented in Figures 5.34 and 5.35, where the radial

profiles of temperature and velocity are presented at the nozzie exit. Also, the radial profiles of

stagnation pressure for two noules are compared. Predicted values are given in Figure 5.36,

parallel to the values recorded experimentally at the noule outlet cross-section by using dynarnic

Pitot-probe method. The difference between the two noules is evident. Also, agreement between

Diffuser angle [Deg]

Fig. 5.32. Enthalpy ratio for conical nozzles with different angle.

7 - - - conicd (exp.) - - i - curvil. (exp.) conicd (cdc.) - - - curvil. (cdc.)

Gun cuvent [A]

Fig. 5.33. Wall heat losses for diîferent values o f the power input.

109

the experimental results and the predicted values is relatively good. The biggest source of

uncenainty in the calculation are the wall heat losses. Discrepancies between the predicted and

the experimental values are primarily due to the wal1 heat losses being overpredicted.

The cuM1inear design presents a much better environment for pmicle heating and

acceleration within the node , since there are no recirculation zones where particles can get

trapped and cooled. More importantly, the higher values of temperature and velocity at the exit

of the nozzie were a much bener starting point for the additional pmicle heating that takes place

in the free jet reçion.

This is confirmed by the anaiysis of the flow parameters in the free Stream region of the

flow domain. For this purpose, calculations have been performed for the entire flow domain,

represented by the Figure 5 2 1. Velocity and temperature profiles assigned at the inlet of the flow

domain were exacriy the same as those used for the free jet calculations in Chapter 5.1. Results

- free jet \ - - LI0000 1 - conicd nozzle -

3 \ I \

-.- .CI - curvil. nozzle E 8000 - \ \ m = 1 gis - Q) e i '1

E 6000 \ \ - s l

4000 r - 1 l

2000 7 - l

O 0.000 0.002 0.004 0.006 0.008 0.010 0.012

Radial coordinate [ml

Fig. 5-34. Calculnted radial profiler of temperature at the nozzle outlet

free jet conicd nozzIe curvil. nozzle !Ys

Radial coordinate [ml

Fig. 5.35. Calculated radial profiles of velociîy at the n o a l e outlet.

- conical (calc.) - - - curvi1. ( c d ~ . ) --- - conical (exp.) -.-- - curvil. (exp.)

2 4 6 8

Radial coordinate [mm]

Fig. 5.36. Radial profiles of stagnation pressure at the nozzle outlet.

are presented in terms of â-ial distribution of velocity, temperature, and argon mass fraction,

Figures 5.37-5.39, for three different cases: a) free jet (without shroud nozzie), b) curvilinear

noule, and c) conical noule. Aso. experimental results, obtained by the enthalpy probe, are

given for curvilinear and conical nozzle.

The agreement between calculated parameters and experirnental measurements is

relatively good. The curvilinear noule yieids much higher temperatures for most of the flow

domain. Aiso, the argon fraction remains higher throughout the region. This is earemely

important, as far as metallic powders are concemed. Both nozzles give some improvement in

comparison to the fiee jet, because the rnixing with the surrounding air is fully eliminated in case

of the cuwilinear noule, and resti-icted in case of the conical noule. Isolines of velocity,

temperature and argon fraction are presented in Fiçures 5.40-5.42 for curvilinear noule. Top

portion of the diaçram çives the calculated values, while the bottom portion gives the

experimental ones. The same parameters for conical nozzle are presented in Figures 5.43-5.45.

For both nonles isolines obtained experimentally appear to be narrower in cornparison to the

- free jet 1

4

- - - conical nozzle --- - cuwil. nozzie - '3 - cunril. (exp.) ! n u - conic. (exp.) I

7

-1 l l

Axial coordinate [ml

Fig. 5.37. Axial distribution of velocity.

- free jet - - - - conical nozzle , 1 - --- - curvil, nozzle + - i

' - curvil (exp.) - - conic. (exp.) - i

Axial coordinate [ml

Fig. 5.38. Axial distribution of temperature.

- free jet - - - conicd nozzle - -.- - curvii. nozzle

- J - curvil. (exp.) - - conic, (exp.)

1 L

l r

i I

Axial coordinate [ml

Fig. 5.39. Axial distribution of argon fraction.

1 IS

theoretical ones. This could be due to the uncenainty of expenmentd results in the fringes of the

jet. Comparing the isotherms for the two nozzles, it is evident that the curvilinear n o d e yieids

much longer isotherms. This is confirmed by the irnaging system, where the length of the visible

argon flame (edge of the visible arçon plasma flame is rouçhiy 9000 K) is much higher in the case

of curvilinear nozzfe. It is also much more stable with Iess fluctuations.

Major conclusions that can be extracted from the above anaiysis of the flow parameters

for two different noules are the following:

- Conical nonles suffer from the cold air entrainment within the nouie, followed by

steep drop in plasma temperature, and an increase in the oxysen fraction. Only the

nonles with very small cone angles are free from the air entrainment.

- CuMlinear nonle compietely eliminares the cold air entrainment. resulting in a much

higher ff ow temperature throughout the region, and also lower oxygen concentration.

Mo dei -

I 1

!- Experimen t 7

I I I 1

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.40. Velocity iso-lines for curvilinear nozzfe.

t Experimen t I

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.41. Temperature iso-lines for curvilinerr nonie.

Erperiment

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.42. Argon fraction iso-lines for curvilinear nozzle.

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.43. Velocity iso-lines for conical nozzle.

t Experiment

O I O 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.44. Temperature iso-lines for conicrl noale.

Experimen t

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 5.45. Argon fraction iso-lines for conical nonle.

- Both nozzles give better flow pararneters than the Free jet, because of completely

eliminated or reduced mixing wirh the coid air dong the length of the nozzie.

Performance of the shroud noules with the shrouding gas injected, will be examined in

Chapter 6. The influence of the ilow parameters on the panicle injection, their melting, and

acceleration towards the substrate, will be examined in detail in Chapter 7.

6. SHROUDING GAS AND ITS IMPACT ON THE PLASMA

JET PAIWiMETERS

Gas shrouds were first mentioned in US patents(''-"'. The idea was to inject a secondary

gas (usually the same as the plasma sas) around the plasma jet, and delay the mixing with

surrounding air. Enuained air causes sharp drop in plasma temperature because of the dissociation

of oxygen and nitroçen molecules. .Aiso. the atornic oxygen is much more reactive then the

molecular, and the sprayed powders can be significantly oxidized. The above mentioned delay in

plasma rnixing with the surrounding air, can significantly improve the APS process in terms of

better pmicle heating and less oxidation.

Sorne of the commercially available a s shrouded nozzles are desiçned to introduce the

shrouding gas through a cemin nurnber of srnail ports surrounding the main plasma jet. This type

of the shrouding gas injection is based on the idea of the interference between the small jets as

they spread downstream. M e r a certain distance from the injection point, they fom a continuous

gas shroud around the plasma jet. The other type of injection is through an annular dot, creating

an annular jet of shrouding g i s . Both types of injection are schernaticaily presented in Figure 6.1.

With injection throuçh a finite nurnber of injection ports, a much higher initial velocity of the

shrouding sas, Us, is obtained for the sarne flow rate of the shrouding gas. In this case, the

velocity LI,, decays much faster than in the case of the injection through a slot. However, it is

expected that at the point where interference between the ças shroud and the plasma jet starts to

occur, it will still be much higher.

a) injection through a finite nurnber of ports.

b) injection through a dot.

Fig. 6.1. Schernatic of the shrouding gas injection.

This results in a higher shrouding-to-plasma velocity ratio, UJLI,. It is known fiom

compound jets theory that the jets with velocity ratio closer to unity, mix slower. On the other

hand, injection through a finite number of pons allows the surrounding air to flow through the

gaps between two adjacent jets, and fil1 in the region close to the plasma jet. In the case of

injection throuçh a slot, the air is evacuated from this region, leaving a dead tlow zone, where

only the main plasma ças and the shrouding gas recirculate.

In this chapter, both these injection methods will be evaluated, and their influence on the

p!asma parameters will be investigated numerically and experimentally. Only the curvilinear nozzle

will be used for this investigation, since it is proven to yield better plasma flow parameters''?

6.1. SHROUDING C A S INJECTED THOUGH SERIES OF SMALL PORTS

Shrouded noule with sixteen injection pons is schematically presented in Figure 5.22.

The pons are positioned equidistantly, on the circle of D = 40 mm, which is concentnc with the

cu~linear noule outlet, (1 = 12 mm. Resulting distance behveen two adjacent holes is x =7.8 mm.

The interference between two adjacent jets will be exarnined, and the resulting flow picture

detemined. Then, the influence of the shrouding ças on the plasma jet will be investiçated, both,

numencally and expenmentally.

6.1.1. Interference behveen two adjacent shrouding gas jets

Two circular jets, interfering wit h each other, present three-dimensional flow problem.

In order to obtain a numerical solution for this problem, the flow çeometry is set to present a part

of the free jet region, next to the shrouded noule. It is schematically presented in Figure 6.2.

Calculation domain

Fig. 6.2. Schematic of the cdculntion domain.

Radial and anplar coordinate axes are given in Fiçure 6 . 2 , while the s avis (axial) is

perpendicular to the plane defined by the two. Calcuiation domain consisted of 10x 10x 10 cells.

Calculation was performed for the shrouding ças flow rate of rn = 3.4 g s , injected

through 16 ports of d = l mm, with injection velocity of Us, = 165 m / s . Resuits are presented in

terms of velocity and arçon fiaction profiles at several planes perpendicular to the z a x i s , Figures

6.3 and 6.4. We can see that at the plane, z =10 mm, shear layers of the two adjacent jets have

reached each other, creating a continuous gas shroud from that point downstream. Farther away

fiom the node, velocity and arçon fraction profiles become more uniform. At z 4 0 mm we c a .

assume that the flow picture has become two-dimensional (no dependence on the angular

coordinate).

Axial distribution ofvelocity and arçon fiaction is given in Figures 6.5 and 6.6. In addition

to the case of circular shroud jet, a case with the shrouding gas injected through a continuous

Angular coordinate [mm]

Fig. 6.3. Velocity profites of the circular shroud jet.

Angular coordinate [mm]

Fig. 6.4. Argon fraction profiles of the circulrr shroud jet.

I t - -- annular circuiar j e t t i jet

1 I

I i - 4

0.00 0.01 0.02 0.03 O. 04 0.05 0.06

Axial coordinate [ml

Fig. 6.5. Axial distribution of velocity.

t - 1 circular jet l - - r annular jet

i

0.00 0.01 0.02 0 .O3 0.04 0.05 0.06

Axial coordinate [ml

Fig. 6.6. Axial distribution of argon fraction.

sior, 1 mm wide, was investigated. Wlth the same shrouding ças flow rate of m = 3 . 4 g/s, velocity

in this case was Ur,, = 16.5 m/s. The velocity decays slower in the case of amular jet created by

a continuous slot. Nso, the fraction of argon decays slower.

The small circuiar jet of argon shrouding ças becomes wider as it moves downstrearn,

sirnilarly to the arçon plasma jet. If we study them independently we cm plot their boundanes

in the z-r coordinate system. The jet boundary is assumed to be at the point where axial velocity

drops below 1% of the centre line value. ïhese boundaries are presented in Figure 6.7. If the jets

emerçe from the shrouded noale throuçh the outlets that are 13.5 mm apan. they start to

interfere at about z = 10 mm. At this particular distance, the velocity at the axis of circular

arçon jet is (1, = 105 m/s, while for the annular jet it is Us, = 12 mis. Argon fraction for the

circular jet is 4, = 0.6, while for the annular jet it is m,, = 0.8. This is an obvious difference in

important shrouding gas parameters. The implication of the above difference on the protection

that rhe shrouding Sas çives to the plasma jet will Se examined in the follo~ving text.

4 - - Shrouding jet -

- 4

1 !

l

L 1 l 1

1 Plasma jet I r - t i

Axial coordinate [mm]

Fig. 6.7. Boundaries of the main plasma jet and of the circular shroud gas jet.

6.1.2. Plasma jet with the shrouding gas

In case when the shrouding ças is injected through 16 ports, the overall flow picture is

three-dimensional (3-D). 3-D problems require a lot of processing tirne and the convergence

process is very sensitive. It becomes even more peculiar in the case of thermal plasma mixing with

the cold stread7'? where thennophysical propemes of the gases have to be defined over a wide

temperature range. Al1 these difficulties put some limitations on the numerical simulations

performed in this work. The computational domain, as a part of the free jet region, is

schernaticaily presented in Figure 6.8. The assiçned inlet flow parameters were those obtained at

the outlet of the curvilinear nozzle. Canesian coordinates were used, considering one quarter of

the entire free jet reçion. The numerical grid used was 30x30~30.

Fig. 6.8. Schemntic of the calculation domain.

12s

Two sets of calculation were performed independently, with and without the shrouding

gas. Results are presented in Figures 6.9-6.11 in tems of axid distribution of velocity,

temperature and argon fraction. Experimental results, obtained by the enthalpy probe, are

presented parallel to the predicted values. The theoretical and expenmental results are consistent

in terms of evaluating the protection thar the shrouding gas provides to the plasma jet. It is

evident that in the portion of the jet close to the nozzie, there is almost no difference in flow

parameters for two cases. The difference starts to occur at about z = 55 mm away from the

nozzie, which is only about 23 mm in front of the designated substrate location. At that distance,

the plasma temperature already dropped to about T = 5000 K, and most of the particle heating

and meltinç have already taken place. A t the same time, the mixing between argon plasma and

the airrounding air started much fmher upsrrearn, since the argon fraction dropped to m,, = 0.6.

The particles were exposed to the oxygen €rom the air for most of rheir travel through the jet.

From that point of view, the shrouding ças did not provide much protection against the oxidation

of the injeaed particles. It also failed to bring sigiificant improvement in plasma temperature and

velocity.

- 4

W/O shroud - - with shroud 3 wio shroud (exp)

9

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig 6.9. Axial distribution of plasma velocity.

1 I 1 i 1 I I 1

WIO shroud - - with shroud 1

3 WIO shroud (exp) 1

1 @ with shroud (exp)

1 l - l

I 4

-4

O 10 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig 6.10. Axial distribution of plasma temperrture.

- I w/o shroud - - with shroud -

7 W/O shroud (exp) - 2 with shroud (exp) ,

4

--- -- -

Axial coordinate [mm]

Fig 6.1 1. Axial distribution of argon fraction in plasma jet.

This could be linked to the presence of air in the region close to the plasma jet, near the

nonle oudet. In the plasma jet shear layer, miving between the argon plasma and the air is raking

place. causing significant drop in plasma temperature. Streamlines in that regïoh presented in

Figure 6.12, suggest that the cold air approaches the plasma jet in a cross-strearn pattern, similarly

to the case of fke jet. This is the main reason why there is almost no difference between the free

jet and the shrouded jet in the initial portion of the jet. Fanher downstream where the shrouding

gas stms to interfere wirh the plasma jet, there is an increase in argon fraction, temperature and

velocity compared to the free jet. However, this improvement is not significant and it cannot

improve the quality of the coatinç.

It is expected that the injection of the shrouding gas through a continuous slot will provide

better results. Preventinç air from coming into the contact with plasma in close-to-the-node

region is expected to result in improved plasma parameters (temperature and velocity). Also, the

argon fraction is expected to remain at higher levei throughout the free jet region.

Plasma i !

Fig. 6.12. Streamlines in the vicinity of the noale.

6.2. SHROUDING GAS TiYJECTED TEIROUGB TEE CONTNUOUS SLOT

A detailed parametnc study of the slot injection of the shrouding gas was canied out in

order to isolate dominant parameters and their influence on the protection of the plasma gas. The

parameters that were expected to have the biggest impact on the jet flow parameters were: a)

mass flow rate of the shrouding gas (determining the velocity for a given slot geometry), and b)

the dot dimensions (width s and diarneter D). Injection dot is schematically presented in Figure

6.13. It surrounds the n o d e outlet from which the plasma jet is ernerging.

Fig. 6.13. Schematic of the nozzle with a slot shrouding gas injection.

6.2.1. Generaï pararnetric study

In order to examine the influence of the shrouding gas flow rate and the slot dimensions

on the plasma jet parameters, a series of numerical tests were conducted. Test cases were

designeci to simulate different values of the shrouding gas 80w rate and its velocity, for different

width of the injection dot. The plasma jet was assumed to emerge from the curvilinear nozzle,

0.12 mm, at velocity and temperature assigied according to the values obtained from the noule

calculation. The shrouding Sas was emerçing frorn an annular slot, D = 40 mm. Its parameters

were chosen in nich a way to represent five different flow situations. with varying gas flow rates.

Muence of the gas flow rate is examined by assigning the constant shrouding gas velocity and

dserent gas 0ow rates. It is accomplished by changing the dot width, S. Similady, the influence

of the injection dot width can be examined by keeping a constant gas 80a

slot width, resulting in different shrouding Sas veiocities. Al the test cases

flow situations, are listed in Table 6 1 ., with accompanying values of

shrouding gas velocity. LI,., and the dot width. S.

TABLE 6.1. Shrouding Gas Parameters.

11 Test case 4 11 2.08 II 5.

1 Test case 5 1 2-08 2 O.

rate and changing the

representing different

he gas flow rate, m,,

130

Results are presented in Figures 6.14. and 6.15 ., where the axial distribution of argon

6aaion and plasma jet temperature are presented for difEerent test cases. In test cases 1, 4, and

5, where the gas flow rate was kept constant and the slot width was changing, it is observed that

the protection of the shroudinç gas improves with an increase in the slot width, S. despite the fan

that the lower values of the slot width were characterized with higher injection velocities. In test

cases 1, 2, and 3, the injection velocity was kept constant and the mass flow rate and the dot

width were increasing. It resulted in funher improvernents with an increase in these parameten.

From the obtained results it is evident that both, shrouding gas mass flow rate and width

ofthe injection dot, have significant influence on the protection that the shrouding gas provides

to the plasma jet. An increase in the dot width increases the length of the potential core of the

anmlar je< of shrouding sas. This has a positive influence on the protection that the shrouding gas

provides to the plasma jet, since it delays rhe miùng of the shrouding gas with the surrounding

air. Henceforth, the mixinç of the plasma jet with air is also delayed.

0.00 0.02 0.04 O .O6 0.08 0.1 O

Axial coordinate [ml

Fig. 6.14. Axial distribution of the plasma jet temperature.

Axial coordinate [ml

Fig. 6.15. Axial distribution of the plasma jet argon fraction.

6.2.2. Influence of the annular dot diameter

The diarneter of the annular slot for shrouding gas injection. D, also has influence on the

overail flow pattern and the protection of the shrouding gas. By changing the slot diameter, D,

for a given, constant, noule outlet diarneter, d, the distance between the plasma jet and the

annular jet of the shrouding gas also changes. That way, the dead flow zone (see Figure 6.1)

where the cold argon recirculates. becomes bigger. In order to test the influence of the slot

diameter. and the size of the dead flow zone. several test cases were designed. Argon plasma jet

parameters were kept constant, as well as the noule outlet diameter, d = 12 mm. Also, the

shrouding gas flow rate was kept constant, m, = 2.08 g/s, toçether with the width of the injection

dot, s = 1 mm. The only parameter that was changed in this case was the slot diarneter, D. The

values used were 20,40, and 56 mm. Corresponding values of the shroud gas velocity Il, were

20, 10, and 7.1 mis.

The results are presented in Figures 6.16 and 6.17. in tems of axial distribution of

temperature and argon fiaction of the argon plasma jet. From these diagrams it is not evident that

an increase in the annular slot diarneter improves the protection offered by the shrouding gas.

Values of the plasma temperature and the argon fraction remain within relatively narrow range

for ail three cases. Similarly to the dot width, the slot diameter is limited by the gas shroud n o d e

dimensions, and by the requirement s for proper shrouding gas injection. This leaves the shrouding

gas flow rate as the oniy parameter that brings improvements to the overall protection, and at the

same time is not limited by the geometry requirernents. The next set of tests is designed to

determine the maximum value of the shrouding gas flow rate.

0.00 0.02 0.04 0 .O6 O .O8 0.1 0

Axial coordinate [ml

Fig. 6.16. Axial distribution of the plasma jet temperature.

- no shroud - - - D 4 O mm -- - D=2O mm --- - D=56 mm

0.00 O .O2 0.04 0 .O6 0.08 0.7 O

Axial coordinate [ml

Fig. 6.17. Aria1 distribution of the plasma jet argon fraction.

6.2.3. Maximum flow rate of the shrouding gas

From the results presented in Figures 6.11 and 6.15. for the set of conditions specified in

the Table 6.1, it is evident that the protective potentid of the shroud gas increases with an

increase in the shrouding gas tlow rate. In order to establish sorne limit in the possible flow rate

increase, the following set of test cases was considered. Slot width and its diameter were kept

constant at s = 1 mm and D = 40 mm, the values that correspond to the actual shroud noule

available. Flow rate of the shrouding ças was assigned three different values, m,, = 1.08, 4.16.

and 6.24 gk. Shrouding Sas velocities were respectively, Us, = 10, 20. and 30 m/s. At the same

time, Bow rate of the arçon plasma was kept constant at m = I g/s. Results are presented in

Figures 6.18 and 6 19.

An increase in shrouding gas flow rate from m, = 2.08 g/s to rn, = 4.16 g/s has very little

influence on the temperature of the plasma jet, while it results in an increased argon fraction in

the downstream portion of the flow domain. Further increase from m,, = 1.16 gis to rn,, = 6.24

g/s, does not bring significant irnprovement in the plasma jet parameters. From the above it is

evident that the flow rate of the shrouding gas cannot be increased without limit. Very high

shrouding gas flow rate can significantly increase the cost of the gas consumption in an APS

process. Consequenrly some optimum has to be found, with improved parameters of the plasma

jet, and with the cost of spraying within acceptable limits. For the above test. it appears that the

limit value of the shrouding gas flow rate, uniil we have some meaningful improvements in the

plasma jet protection is around m,, = 4 g/s, yielding the shroud-to-plasma gas flow rate ratio

of about mSjm = 4. Similar value of the maximum shroud-to-plasma gas ratio is suggested in the

works of lee'') and Fleck Lee and ~fender"?

no shroud - - - m=2,08 g/s

Axial coordinate [ml

Fig. 6.18. Axial distribution of the plasma j e t temperature.

0.00 0.02 0.04 0.06 0.08 0.1 0

Axial coordinate [ml

Fig. 6.19. Axial distribution of the plasma jet argon fraction.

From the analysis presented in this chapter several conclusions can be extracted about the

protection that the shroudin~ gas gives to the plasma jet:

- increase in shrouding jas flow rate can siçnificantly improve the overall protection.

- increase in the injection slot width has also a positive influence on the protection of

the shroudinç sas.

- Diarneter of the circular dot, for a given shrouding gas flow rate, has no practical

influence on the overall protection.

- According to the numencal tests performed, the maximum shroud-to-plasma flow rate

ratio is approximated to be m,,,/nz = 1. Further increase does not bring significant

improvement in the plasma jet parameters.

136

6.3. FLOW PARAMETERS OF THE PLASMA JET WITH THE SHROUDING CAS

Actual noule used for these sets of experirnents and cdculations was the curvilinear

noule, with an annular slot for shrouding gas injection, s = 1 mm and D = 40 mm. Argon plasma

fl ow rate was m = 1 @S. with the spraying gun power of P,, = 19.6 kW ((1=28 V and 1=700 A).

Shrouding gas was arçon with m,, = 4.16 g/s, yiefding m,Jm = 4.16. Results are presented in

Figures 6.20, 6.22, and 6.23. in terms of axial distribution of veiocity, temperature and argon

fraction. Fi y r e 6.2 1 gives the velocity distribution within smaller portion of the flow domain,

where the measurements were taken.

It is evident from al1 four diagrams that the calculation suggested much better protection

by the shrouding ças. than it was recorded by the experirnent. Reason for this lies in relatively

poor design of the injection tract. The annular injection slot for shrouding gas was made by

modifying the injection throuçh sixteen injection ports. It was created by cutting between the

holes. At the same tirne. the intenor of the injection tract did not change. What represented a

çood injection chamber, with uniform velocity distribution in the case of the injection through

sixteen ports, was not a good solution for the injection throuçh an amular slot. Non-uniform

velocity distribution of the shrouding ças was observed, with significant radial component of the

shrouding gas velocity at some regions. Calculation assumed ideal, uniform velocity distribution,

with zero radial velocity of the shrouding Sas, and continuous, non-intempted shield of the argon

surrounding the arçon plasma jet.

Nevertheless, the experimental results showed some improvernent compared to the

injection through sixteen ports, where almost no protection by the shrouding gas was recorded.

It is believed that the properly desiçned conrinuous injection slot, with appropriate chamber for

velocity distributio~ would result in much better protection by the shrouding gas. The differences

in the calculated plasma jet parameters for two cases, injection throuçh the sixteen ports. and

injection through the continuous slot, are stronçly in favour of the slot injection.

- W I O shroud -- with shroud

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Axial coordinate [ml

Fig.

300

250 - CA

Bo0 % CI .- g150 - 3,

50

O

6.20. Axial distribution of plasma jet velocity. (Entire flow domain).

W/O shroud with shroud -

wlo shroud (exp) with shroud (exp) -

O .O6 0.08 0.1 0 0.1 2 0.1 4

Axial coordinate [ml

Fig. 6.21. Axial distribution of the plasma jet velocity. (Part of the flow domrin).

W/O shroud - -

r with shroud '3 w/o shroud (exp) C with shroud (exp)

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Axial coordinate [ml

Fig. 6.22. Axial distribution of the plasma jet temperature.

4 3 1

wlo shroud with shroud w/o shroud (exp) with shroud (exp)

0.0 ' 1 1

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Axial coordinate [ml

Fig. 6.23. Axial distribution of the plasma jet argon fraction.

7. PARTICLE BEHAVIOUR AND SPEWYING TESTS

Injection of the panicles is very sensitive part of the spraying process. The location and

the nurnber of injection pons. the type and the flow rate of the carrier gas, the particle feedrate,

and the angle of injection have to be chosen very carefuily in order to ensure proper injection.

Generaily, there are two types of injection, intemal and extemal. The extemal injection assumes

injection ports jun outside of the spraying gun. Upon injection, plasma cames the particies away

from the gun and there is no chance of melted particles stnking the cold nozzie walls and

solidiQing. On the other hand. they have less space and time to be properly melted and

accelerated. When spraying with Sas shrouded nozzles, the interna1 injection is generally used,

with the panicle injection point locar ed somew here near the gun-noule interface. Therefore, the

particles have the entire length of the nouie available for heating and acceleration towards the

nibstrate. The major problem with intemal injection is accumulation of the particles on the cold

nozzle wall surfaces. To avoid this, the injection parameters have to be carefully adjusted.

Schematic of the panicle injection, used in the spraying tests performed, is

presented in Figure 7 1. We can see that the injection ports are located within the spraying gun.

There are two of hem, symmetricaily positioned at 1 80". The angle of injection in this case is 90°,

but the injection pons of 100" and 80" were available, providing slightly upstream and

downstream injection. Hypothetical path of an individual particle is presented by a curved line.

It is desirable that the injection velocity is hiçh enough to ensure sufficient penetration of the

pmicle into the plasma. By reaching the regions with high temperatures and velocities, heating

Spraying gun ,

Shroud gas

Shroud

Fig. 7.1. Schematic of the particle injection.

and acceleration of the panicle is vastly improved. On the O t her hand, veq high injection velocity

will result in particles travelling al1 the way through the plasma and striking the opposite wall.

Since the particles corne with cenain size distribution (typicaiiy 40-80 pm), their mass distribution

could be nich that the biggest particles are 8 times heavier than the smallest ones. This means

that cenain optimum injection velocity has to be found. The envelope of possible trajectones

should be centred around the flow axis, thus enabling the smaller particles to penetrate

sufficiently, and preventing the biser ones fiom striking the opposite wall. The injection velocity,

which is assumed to be equal to the velocity of the carrier gas, is also limited by the requirement

for successfiii pneumatic transport from the powder feeder to the injection port. In practice. this

minimum flow rate of the carrier gas usually provides sufficient injection velocity for the

panicular powder. However, for each powder it has to be determined separately due to the

differences in particle density and size distribution.

in the sprayinç tests perfomed, the powder used was iron-aluminide (Fe+Ai) consisting

of 90% ion and 10% aluminum, with the size distribution of 53-75 Mm. These powders usually

corne in the form of two-layer particles, with an iron core and an aluminum coating. Upon

melting, mixeci crystalline stnicnire is created by dfision. Thenno-physical properties of the iron

and af~rninurn '~~~' are given in the Appendbc K For calcuiation purposes, the effective properties

of the powder were calculated by applying the rule of mixing. Injection velocity was determined

based on the minimum carrier ças flow rate necessary for successfùl pneumatic transport from

the powder feeder to the injection port. U,, = 7.2 m/s. Feedrate used was m, = 20 glrnin. The

sprayine gun parameters were identical to those used for enrhalpy probe measurements

(U=B V, 1=700 4 m=l ds) with argon as plasma gas.

Spraying tests were perfomed for both nozzles, curvilinear and conical, with and without

the shrouding gas introduced, and also without the noule. Substrate was located at x = 100 mm

away from the sprayinç çun. Correspondinç calculations were carried out, usinç the method

described in Chapter 2. Sprayinç tests were monitored by laser imaging ~ystern'~~), and the pmicle

velocities were calculated. Results are presented in the foilowing text.

7.1. PARTICLE TR4JECTORiES AND VELOCITES

Envelopes of the trajectories were obtained by using the average trajectories for the

particles from upper and lower limit of the size distribution. They are presented in Figure 7.2 for

the curvilinear noufe and in Figure 7.3 for the conical n o d e . We can see that the envelope is

narrower in the case of sprayinç with curvilinear nozzie for about 20%. This is confirmed with

the Bow visualization during the spraying tests, where the trajectories of individual particles were

also less dispersed. The result is a better sprayinç efficiency since less pmicles are missing the

target. We can al= see that for both noules, for a given injection velocity, the envelopes of the

trajectories are clear from touchinç the wall. In case of the curvilinear noule, the edge of

Axial coordinate [mm]

Fig. 7.2. Envelope of the trajectories for curvilinear nozzlr.

Axial coordinate [mm]

Fig. 7.3. Envelope of the trajectories for conical noale.

the enveiope is much closer to the nozzle wall, making it more sensitive to the changes in

injection parameters. This is confirmed by expenments, where some panicle deposition was

observed for the increased feedrates and injection velocities.

On their way through the plasma, particles interact with nirbulent eddies. They cm direct

a particle to different reçions of the jet, with higher or lower values of plasma temperature and

velocity. Resultinç particle rrajectory is a stochastic funcrion of interacting with these eddies.

Modelling of this phenomenon is descnbed in Chapter 2. In order to compare two different

plasma flows, and evaluate their potentiai for panicle heatinç and acceleration, it is necessary to

rernove this stochastic component t o m the calculation. This method is frequently used in

practice (81,8283.84) and is based on the analysis of an individual particle for the average plasma

parameters. Results on particle velocity calculations are presented in Figures 7.4. and 7.5. for

c u ~ l i n e a r and conical noule, respectively Panicle velocities are presented for three discrete

particle sizes. The srnailer particles travel faster, which is in agreement with the force balance

presented in the Chapter 2 . Aiso. it is evident that the cunilinear n o d e yields around 10 %

higher particle velocities. This is in agreement with the plasma velocity distributions for the two

nozzies.

Companson could be made between the calculated panicle velocities and expenmental

values, obtained by Maha Ma~ri"~), by using the laser imaging system. The above calculation is

perfomed by usinç Lagrangian approach, following the particle dong its path through the

plasma, and calculating the forces based on the average plasma parameters. Laser imaging system

is focussed on one particular control volume, through which the particles of different sizes and

velocities are passing, greatly influenced by the turbulence of the jet. The only information the

system gives is a distance that the particle moved during two narrowly spaced exposures (20 psec

apart). We can assume that the measured velocities are the instantaneous velocities, but they

cannot be associated with the panicle size. In order to make a meaninçful cornparison with the

experimental data, a simulation was camed out where a large number of particle trajectories and

velocities were examined at the location correspondinç to the measunng control volume. Full

O IO 20 30 40 50 60 70 80 90 100

Axial coordinate [mm]

Fig. 7.4. Average velocities of the particles Tor curvilinear nozzle.

150 1

I

Axial coordinate [mm]

Fig. 7.5. Average velocities of the particles for conical nozzle.

stochastic approach (descnbed in Chapter 2) was used here, and an average radial velocity

distnbution is calculated for an axial distance x = 100 mm away from the spraying gun (standoff

distance for the spraying tests).

Results of the calculation are presented in Figure 7.6. in terms of radial distribution of

average particle velociry at the above cross-section. We can see that the particle velocity

distributions have similar shape to the plasma velocity distribution at the outlet cross-section of

the shroud nozzie (see Figure 5.35). Spraying with no n o d e , resulted in the highest centreline

particle velocity. On the other hand. both cases of noule spraying resulted in more unifonn

velocity distribution. Aiso. the curvilinear noule yields about 10% hiçher velocities than the

conical one throughout the dornain of interest. This is consistent with the analysis of the individual

particles.

Experimental results"" are gven in the Table 7.1. The observed controi volume had a size

of approximately 25x25 mm, with a jet symmetry âuis coinciding with the symmetry line of the

- -.- curvilinear n o d e

- - - conical nozzle - no nozzle

Radial coordinate [mm]

Fig. 7.6. Radial distribution of average particle velocities.

control volume. Panicles ro be processed were chosen to be as close as possible to the x = 100

mm line. No systematic distribution along the radius was observed, so the results are given in

t e m s of average velociries for different noule configurations. Typical twin images of the

parricles are shown in the Figure 7.7 . wirh caiculated distances between them and corresponding

particle velocities.

Table 7.1. Average Particle Velocit ies (Experimentnl Values(u)).

NO nouie 1 ~urvii inenr nozzle 1 Conicai nozzie I

d l = 137 mm VI = 98.74 min d 2 3 1.53 mm v2 = 76.40 m i e 63- 1-83 mm v3 = 31.53 mis J4= 1.U mm VJ = !E-15 nus d 5 - 1.65 mm v5 = 8 W f mis Jti- 1.84 mm v6 = 31.99 mie d7= X f mm

Fig. 7.7. Particle twin images'"!

The experimental values are systematically lower than the theoretical ones. No nozzie

situation yielded higher particle velocities throuçhout the entire control volume. The difference

berneen the two nozzles is not as big as suggested by the caiculation. This could be explained by

the agglomeration of the pmicles, very cornrnon during the spraying process. Upon injection, two

or more particles can çet fused together, dramatically increasing the mass of the panicle.

Therefore, the velocity of such a particle can be significantly lower than the one of a single

panicle. Some of these agglomerated panicles were included in the averaçing process, because

the laser imaçing system is insensitive to the particle size distribution. Visual observation of the

plasma jet, seeded with panicles, can give a certain idea about the extent of the agglomeration.

The agglomerated parricles appear much brighter and bigger, and their trajectories are downward

parabolas. Observation of the above spraying tests confinned that more agglomeration was taking

place when spraying with shrouded noules. Due to less roorn for pmicie dispersion in the case

of curvilinear noule, it is likely that it causes more agglomeration than the conical nozzie.

7.2. PARTICLE TEMPEMTURE HISTORY

Panicle temperatures are dictated by the temperature of the plasma flow The curvilinear

nozzle yields much higher plasma temperature than the conical one, which is proved by

monitorinç of the area just outside the noule, Fiçures 7.8 and 7.9. It is evident that the plasma

temperature is hiçher since the briçht core of the plasma flame is much longer. The temperature

of the injected particles in the case of cunilinear nozzie is also higher since the vaporization from

the surtàce is evident. Vaporization sans when the particle has reached the melting point. In case

of the conicd n o d e there is no mrfàce vaporization, meaning that the particles have not reached

the melting point.

Sirnilady to the panicle velocity analysis, it is important to analyze the temperature history

of an individual particle. When calculated for average plasma flow parameters, they can be used

Fig. 7.8. Jet from the conical nozzle? Fig. 7.9. Jet from the curvilinear node(?

to evaiuate the potential for heatinç and melting of the panicles. Temperature histories for three

different particle sizes are presented in Figures 7.10. and 7.1 1. for curvilinear and conical noule,

respectively. We can see that upon injection, the particles heat rapidly until they reach the melting

point. The particles with smaller diameters melt faster. Aiso, compared to the conical nozzie

situation, correspondinç panicles sprayed by the curvilinear noule melt faster and have higher

temperature upon reachinç the subst rate (x = 1 00 mm). In addition, the particles with diameter

d = 75 pm are not completely melted in case of the conical nozzie. The above results suggest

significant irnprovement in particle heating and melting, when spraying with the cuwilinear

nozzles. This is in agreement with significantly hiçher plasma temperatures, yielded by the

curvilinear nozzie. It is also imponant to notice that none of the particles have reached the boiling

point.

In order to examine the behaviour of a large number of the particles, a full stochasric

mode1 has to be used. Results are presented in the Table 7.2. in terms of the percentage of

completely melted panicles for different noule configurations.

Axial coordinate [mm]

Fig. 7.10. Temperature histories o f the particles - curvilinenr nonie.

Axial coordinate [mm]

Fig. 7.1 1. Tempernture histories of the particles - conical nonle.

Table 7.2. Percentage of the Completely Melted Particles.

1 conical nozzle 1 88.7 1

Flow configuration

curvilinear nozzle

1 no nozzle 1 78.3 1

Percentage of the powder

melted [%]

98.3

It is evident that in the case of cuniiinear noule very few particles rernain unmelted, less

than 2%. In case of sprayinç with the conical node, or mithout a nonle, a fairly large percentage

of the particles rernain unmelted, 1 1.3% and 2 1.7% respectively. That can significantly decrease

the quality of the coatinçs, in tems of higher porosity, lower adhesion strength, and an irregular

microstnicture. Al1 these parameters will be examined in the following tea.

7.3. COATING EVALUATION

In order to evaluate the coatinçs obtained by the spraying tests described in the above

text, several independent tests were camed out. Microstnictural evaluation of the coatings was

performed by met allograp hy tests on the cross-sections of iron-alurninide and chromium-oxide

coatinçs. Also, porosiry test was performed on the pieces of iron aluminide coatings, separated

tom the substrate. Finally, adhesion tests were performed on the iron-durninide coatings, sprayed

on the standard test specirnens.

7.3.1. Metallograp hy tests

Microstmctural evaluation of the coatinçs sprayed was carried out using the optical

microscope with a rnagnïfication of 100 times to 400 times. Sarnples for metallographic tests were

prepared by cutting the obtained coated substrates with a diarnond saw. The exposed cross-

sections were then polished on the polishing wheel, with the final step done by a 3 Fm polishing

paste. Examples of the microstructure of some of the coatings are presented in Figures 7.12.-

7.15. Figures 7.12. and 7 13. present cross-sections of the iron-aluminide coatings sprayed by the

curvilinear and the conical noule, respectively. It is evident that the coating sprayed with the

curvilinear noule has siçnificantly better microstructure. Splats are of regular shape, thin and

elonçated. The coatin~ sprayed with the conicai noule has much more irregulanties, cavities and

embedded sphencai particles. This is a sign of insufficient melting. It is worth rnentioning that the

spraying parameters ( I I = 28 V, I = 700 A, Pt,= 19.6 kW, and rn = I g/s of pure argon), were

stiçhtly lower than recomrnended for this type of ~ o w d e P ) (LI= 27 V, I = 900 4 P,,= 24.3 kW

and rn = 1 ds). In spite of that, spraying ~ 4 t h the cu~ l i nea r noule resulted in a very good quality

coating, much better than the one sprayed with the conical nozzle. This leads us to a conclusion

that it is possible to obtain coatinçs with good quality, with substantial energy savinçs by spraying

with curvilinear noule.

An attempt to spray cerarnic powder, chromium-oxide (Cr,O&, with the above parameters

was unsuccessfÙ1 with both nodes. Cerarnic powders with hiçher melting points require addition

of hydroçen or some oiher ças to the arçon. In order to spray ceramic powder, it was necessary

to use argon-hydroçen mixture ( 1 0 % hydroçen). Good heat conductivity of the hydrogen

improved the convective heat transfer from the plasma to the particles. It resulted in extended

electric arc and in higher voltage of the spraying çun (U = 36 V, I = 700 A, Pd= 25.2 kW, and

m = 1 d s of argon-hydrogen mixture).

Cross-sections of the chromium-oxide coatings are presented in Figures 7.14. and 7.15.

Fig. 7.14. Cross-section o f chromium-oxide coating spnyed by curvilinear noale.

Fig. 7.15. Cross-section of chromium-oxide corting sprayed by conical nonle.

for c u ~ l i n e a r noule and conical noule, respectively. We can see that both coatings have very

good granular structure. rvithout rnany irreylarities, cavities, and unrnelted particles. This is a

consequaice ofrelatively hiçh electrical power, and spraying with the mixture rich with hydrogen.

Resulting spraying conditions are well above the bare minimum for successful coating. Therefore,

shortcomings of the conicai n o d e were not exhibited in this case. Attempts to spray with lower

powen were not ~ccessfbl due to electric arc instabilities. Additional tests are needed to examine

the spraying conditions under which the differences between the two nozzles will start to occur.

One way would be to attempt spraying with argon-hydrogen mixtures with lower hydrogen

percentaçe (5% for example).

7.3.2. Porosity tests

In the p orosity tests performed, open porosity (surface connected pores) was measured

by using the Archimedes weighinç rneth~d(~? This standard method is based on three weight

measurements of the coating under the examination. First, the weight of the dry coating is

measured, m,, Afier that, air is rernoved Born the pores inside the vacuum chamber. The coating

is then filly submerged. ailowinç uater to fil1 the pores. The second measurement is taken with

the coating fully subrner~ed into the water, m,, ,, Finally, the w e i ~ h t of the wet coating is

measured, m,,. Open porosity, E , can be now calculated as follows

Iron-aluminide powder was sprayed ont0 a copper substrate, to ensure easy removal of

the coating. Weiçhing scale with high precision is needed for these measurements, and in this

case the accuracy was O. 1 mg. Results are presented in Table 7.3 .

Table 7.3. Results on Porosity kIeasurements.

Two coating samples were sprayed with the conical noule, and one each, with the

cu~linear n o d e and without the noule. The coating obtained by the curvilinear nozzie has the

lowest porosity, 7.8%. Results obtained for the samples sprayed by conical nozzle are very

consistent. The sample sprayed without a noule has the highest porosity. These results are

consistent with the rnetalloçraphic tests presented. Lower porosity in case of the spraying with

curvilinear noule is a consequence of better melting and slightly higher impact velocities.

Porosity

I%I curvilinear

conical 1

7.3.3, Adhesion tests

Wet coating

kI

Nozzle

config.

Adhesion tests were done accordinç to the standard method for testing the flame sprayed

coat ing~(~? Standard cylindiical specirnens made of steel were used for this purpose. The

specirnen dimensions were 23-25 mm O.D., with a heiçht of 25.4 mm, and the surface to be

coated was sandblasted. Two noules, curvilinear and conical, were used to spray the coating

ont0 the standard specimen. M e r coolinç, an adhesive was used to bond two specimens toçether,

one coated and one uncoated (Figure 7.16). The adhesive used was G2 Epoxy, manufactured by

Industrial Formulators of Canada, with the adhesion strength of 27.5-4 1.4 ~lrnrn ' .

0.223 17

0.74847

M e r the period necessary for adhesive hardening, the specirnens were submitted to the

Dry coating

kf

Weight in

water [gl

0.1899

0.64203

0.2260

0.7635

7.8

12.4

Specimen 1 Coating Specimen 2

Fig. 7.16. Specimens for ad hesion tests.

axial force on the Unit-O-matic machine with 25 kN load cell. The force at which the fracture of

the bonding occurred was recorded by a calibrated recorder. Bonding strength was then

caicuiated by using the force recorded and the surface area of the fracture. Results are presented

in Tables 7.4. and 7.5. for specimens sprayed with the conical and with the curvilinear noule,

respectively. Four specimens sprayed by each noule were tested, and three of each were used

to calculate the bonding strençth. The specimens sprayed with the conical noule al1 fractured

within the layer of coatinç, while the specimens sprayed with the curvilinear noule fractured

within the layer of adhesive.

Table 7.4. Results on Adhesion Tests - Specimens Sprryed with Conical Nonle.

Specimen

1

2

- - - - - -

Average: 18.6

- - -

3

Tensile strength

[ ~ l r n r n ' ]

24.1

17.3

Remark

Coaiing failed

Corting failed

14.3 Coating failed

Table 7.5. Results on Adhesion Tests - Specimens Sprnyed with Curvilinerr Noale.

Specimen

1

2

-- - - --

Average: 23.3

- - -

3

From Tables 7.1 and 7.5, it is evident that the coatings sprayed with the curvilinear n o d e

had much better bonding strength. The average strençth for the specimens sprayed with the

conical nozzle was 19.6 ~lrnrn'. The specimens sprayed with the cuMlinear noule had higher

bonding strength than the adhesive strensth of the epoxy. The average value of 23.3 Nlrnrn',

represents the tensile strençth of the adhesive. This value is slightly under the strençth specified

by the manufacturer. AI1 we can Say about the bonding strength of the coatings is that they exceed

this value. In order to measure it, stronçer adhesive is needed.

Tensile strength

[N/mm2]

19.0

24.6

Typical fracture cross-sections are presented in Figures 7.17. and 7.18, smooth surface

of the detached epoxy, and the fracture within the coating (sprayed with the conical nozzie),

respectively. These tests are also in agreement with the metalloçraphy and the porosity tests.

Insuficient melting when sprayinç with the conical noule, resulted in microstructure

irregularities, cavities, and embedded spherical particles. Funher on, this resulted in higher

porosity and lower bonding strength of the coatinç. Coatings sprayed with the curvilinear noule

are expected to be supenor in one more area, and that is in the quantity of oxides in the coared

layer. Better plasma flow parameters, and lower fraction of the oxygen throughout the entire flow

domain, are expected to reduce the oxidation which is always present in an APS process. Tests

on the quantity of oxides in the coatinçs are not performed here and they remain to be done in

the future. However, this is another parameter of the APS sprayed coatings where the curvilinear

noule is expected to be superior compared to the conical one.

Rernark

Epoxy failed

Epoxy failed

26.4 Epoxy failed

Fig. 7.17. Cross-section of the specimen sprayed with the curvilinear noale.

Fig. 7.18. Cross-section of the specimen sprayed with the conicrl nozzle.

8. CONCLUSIONS AND RECOMMENDATIONS

A detailed study of an Atmosphenc Plasma Spray (APS) process is presented in this work.

Emphasis were put on the ças shrouded nozzles, which is one of the ways to improve the quality

of the coatinçs sprayed by APS. Beinç a very complex problem, study of the APS process

required combined approach, theoretical and experimental. By using both in this work, the

following contributions were made in the field of thermal plasma processing.

1) Utilizing the current knowledçe in the fields of thermal plasma, numencal fluid flow

and heat transfer, and panicle dynamics, a mathematical mode1 was established for parametric

study and numerical simulations of an APS process.

2) An enthalpy probe was desiçned and manufactured. Parallel measurements of the

stagnation pressure in thermal plasma jet were done with the desiçned probe and with an

uncooled ceramic probe. Results were utilized to examine the systematic error in stagnation

pressure measurements due to thermal boundary layer surrounding the probe tip. In addition, a

detailed numerical analysis on the fiow around the probe tip was carried out, and a cornpensating

alporithm was established for the above error.

3) Detailed numerical smdy of the plasma flow around the water-cooled probe was used

to examine the systematic error in enthalpy measurements. A compensating algorithm is

established for this error.

4) Experimental study of the thermal plasma jet, emerçing from a DC spraying gun was

performed by usinç the enthalpy probe and a dynarnic (movinç) Pitot-probe. Also, detailed

numencal calculation was perfonned by using two modifications of the mathematical model,

parabolic a d ellipiic. ;-\n improved power-law scheme is proposed here, based on the dynamic

measurements of stagnation pressure at the spraying gun outlet cross-section. This approach

brings more certainty in the definition of plasma profiles at the iniet of the caiculation domain.

5) Using the established mode!, a detaiied parametric study was carried out on the fIow

field inside the gas shrouded nozzie, and on the resulting free plasma jet. The above mentioned

diagnostics tools were used to verifL the results. Based on the andysis of the streamlines inside

the standard conical nonle, a new design of the gas shrouded noule, with curvilinear walls is

proposed and manufactured.

6) A detailed pararnetric study was perfonned on the plasma jet - shrouding gas

interactions, and on the protection to the plasma jet against the mixing with surrounding air. Two

modes of shrouding gas injection were investigated, through a series of small injection ports

(exiaing on the commercial Sas shrouded noule), and through a continuous slot. In suppon of

the above analysis, an experimental study on the gas shrouded plasma jet was carried out.

7) Practical sprayinç tests were performed with two different nozzie designs. A few tests

on the obtained coating quality were performed, including: porosity tests, adhesion tests, and

metalloçraphy tests. The results were used to correlate the quality of the coating to the plasma

parameters yielded by the ças shrouded noules.

M e r performinç the above tasks, and anaiyzing the contributions made, several

conclusions could be extracted. The conclusions may be related to three distinct areas:

a) experimental work and methods.

b) rnodelling work,

c) gas shrouded n o d e performance.

Mon of the experirnental work done was based on the water-cooled enthalpy probe, that

was custom-designed for this panicular rvork. It proved to be a reliable diagnostic tool, with an

acceptable margin of error. Compensations for the known systematic enors were included in the

processing of the data, topether with two new tems: 1 ) systematic error in stagnation pressure

measurernent due to themai boundary Iayer around the probe tip, and 3) systematic error in

enthalpy measurement. The first error has not been adequately investigated in the past. The

existing correction terms were based on theoretical analysis and were overestimating the above

error. Correction te- suggested in this work is in good agreement with the experirnents (paralle!

rneanirements with cooled and uncooled probes), and it yields much more reasonable values of

the above error.

The second error is related to the enthalpy measurements, and it is a consequence of the

assumption of identical extemai heat transfer from the plasma to the probe during the two stages

of probe operation. Numerical analysis performed in this work showed the extent of the

systematic error introduced with the above assumption. Suggested compensating algorithm is

believed to improve the accuracy of the measurements.

Another diagnostic tool that was used in this work was a dynamic (moving) Pitot-probe.

It proved to be a handy, easy-to-use tool for quick scanning of the stagnation pressure profiles.

Its accuracy largely depends on the design of the probe, the design and accuracy of the pressure

transducers used, and the techniques for processinç the data. The accuracy of the method can be

significantly improved by properly choosinç the above parameters. It can çive valuable

information in the plasma jet re-ions where the enthalpy probe cannot be used.

In the rnodelling pan of the work. two types of models were used to simulate the plasma

jet, parabolic and elliptic. The parabolic mode1 was found to yield systematically higher values of

the plasma flow parameten. Experimental results were much closer to the values predicted by the

elliptic model. The main reason for this discrepancy is the fact that the parabolic model cannot

account for large scale air entrainment and mixinç in the initial portion of the jet. Recent works

in the fieid suggested that this large scale mixing is the mode of interaction between the jet and

the surroundhg atrnosphere in this region, rather than turbulent difision. The elliptic model also

gave very good predictions of the recirculating zones and air entrainment wit hin the gas shrouded

nonles. Its predictions are in relatively good agreement with the experirnental results. Part of the

model responsible for particle dynamics, has alço given reliable results on the particle trajectories,

velocities and temperature histones.

Performance of the ças shrouded nozzies have been examined by parallel use of two

different noule desiçns, conical and curvilinear. Both, experimental results and model

predictions, suggest that the cu~l inear noule gives much better temperature and argon fraction

profiles. This is due to cold air entrainment within the novle that could not be avoided by the

conical noule. Aiso, the outlet velocity profile yielded by the curvilinear n o d e had much better

shape for panide injection.

Anaiysis of the shrouding gas interaction with the plasma jet showed that the injection

throuçh sixteen pons does not -ive an adequate protection to the plasma jet. An alternative to

this mode of injection was through a continuous dot. This mode of injection brouçht some

improvements in the plasma temperature, and argon fraction, but certain radial cornponent in

injection velocity prevented it ftom performinç as the mode1 predictions indicated. It is, however,

believed that by a proper design of the injection chamber. the above problems could be eliminated.

Spraying tests that were performed by using the two noules, indicated siçnificant

differences in the iron-aluminide coating quality. It is found that the coatinçs sprayed with

curvilinear nonle have lo wer porosi y, better bo nding strength, and better microstnicture. These

dEerences could be addressed to bener plasma flow parameters, significantly higher temperature

and argon fraction. and slightly hi~her velocity. A combination of significantly improved

temperature distribution. and similar velocity distributions, resulted in much improved particle

heating in case of the curvilinear nozzle. Similar velocities in the free jet region mean that the

residence tirne of the particles is approximately the sarne for two nozzies. At the sarne time, much

higher temperature in the case of curvilinear noule, results in much better particle heating and

their complete melting. This is believed to be the main reason for obvious differences in the

coating quality.

Based on the above conclusions, here are some recornmendations for the hture work:

1) Systematic error in stagnation pressure measurements by an enthalpy probe could be

investigated in more detail. haiysis in this work is done for a single probe with certain diarneter

ratio. This analysis could be extended to several probe diarneter ratios, so more generd correction

factors could be suçgested.

2) Systematic error in enthalpy measurement needs detailed experimental investigation.

One way would be to design a more robust probe, with separate cooling circuits for the internai

and the extemal surface of the probe. The other way would be to use the standard probe design,

but adjusted to allow for changes in gas flow rate in a much wider range.

3) An improvernent in the shrouding ças injection and the protection to the plasma gas

could be made by proper design of the injection chamber with a slot. Detailed experimental

analysis of such an injection port is needed to confirm the advantages predicted by the model.

4) More tests on the coatings obtained by two noules are needed to examine the content

of oxides. Curvilinear nozzie is significantly reducing the content of oxygen throughout the jet

and the resulting coatinçs should be much better in that regard.

5) Further irnprovernents to the curvilinear noule design could be made by trying to

eliminate some shoncomings discovered in this work. For example, particle injection parameters

could be improved in order to avoid sorne of the material buildups on the nozzle walls. Aso,

different cu~linear noules csuid be tested, with different shapes, lençths, initial diffuser angle,

etc.

REFERENCES:

M-Mi~chner, C. H.Kmger, Jr., Partially lonized Gases, John Wiley & Sons Inc., 1992.

H-Herman, Advanced hlaterials and Processes, Vo1.38., No. 1, pp 59 & 84, 1990.

D.C.Schram, G.M.W. Kroesen, and J.C.M. de Haas, in "High-Temperature Dust Laden Jets", Eds Solonenko and Fedorchenko, pp 329, 1989.

H.D.Steffens, and M.Weve1, Recent developments in Vacuum Arc Spraying, Froc. of National Thermal Spray Conference, Ed D.L.Houck, Cincinnati, Ohio, 1988.

D.A.Jaçer, D.Stover. and 1V.S. Schlump, Hiçh Pressure Plasma Spraying in Controlled Atmosphere u p to Two Bar, Proc. of Int. Thermal Spray Conference, Orlando, Florida, pp 69., 1992.

W-Maiiener, and D.Stover, Plasma Spraying of Boron Carbide using Pressure up to Two Bar, Proc. of Int. Thermal Spray Conference, Anaheim, CA pp 291, 1993.

Y.C.Lee. Modellinç Work in Thermal Plasma Processing, Ph.D. Thesis, University of Minnesota, 1 984.

A.H.Dillawan, J.Szekely, J.Batdorf, R-Detering, and B.C.Show, Plasma Chem. and Plasma Process., Vol. 1 O, NO.^., pp 32 1, 1990.

Y.C.Lee, and E.Pfender, Plasma Chem. and Plasma Process., Vo1.5, No.3, pp 2 1 1, 1985.

C.H.Chang, Numerical Simulation of Alumina Spraying in an Arçon-Helium Plasma let, Proc. of Int. Thermal Spray Conference, Orlando, Florida, pp 793, 1992.

J.H.Harrinçton et ail., Method and Apparatus for Shielding the Effluent from Plasma Sprayinç Gun, U.S.Patent No. 4,12 1,082, 1978.

R.T.Srnyth, Method and Apparatus for Flame-Spraying Coating Matenal ont0 a Substrate, U.S.Patent No. 4.12 1,053, 1978.

R.A.Antonia, and R. W.Bilger, J. Fluid. Mech., V0l.6 1, pp 805, 1973.

R.A. Antonia, and R. W.Bilger, Aeronaut. Q., Vo1.26, pp 69, 1974.

H.O.hwar, and J.A.Weller, Water Power, Vo1.21, pp 2 14, 1969.

JArendt, H.A..Babcock, and J.C.Schuster, Proc. A.S.C.E. Hydraul. Div., Vo1.82, pp 1038, 1956.

S-Beltaos, and NRajaratnam, Proc. Cm. Hydraul. Conf, Edmonton, 1973.

L. J.S.Bradbury, and J.RiIey, I. Fluid. Mech., Voi.27, pp 33 1, 1967.

W.Forstal1, and A.H.Shapiro, I. Appl. Mech., pp 399, Vol. 1, 1950.

Y-Kobashi. Proc. 2" Japan Natl. Congr Appl. Mech., pp 223, 1952.

RLandis, and -4.H.Shapiro. The Turbulent Mxing of Coaxial Gas Jets, in "Heat Transfer and Fluid Mechanics Instniments, Stanford Univers. Press, Stanford, California, 195 1.

J.F.Maczynski. J. Fluid. Mech.. VOIX, pp 597, 1962.

A-Nakano, Cryogenics. Vol.34, pp 1 79, 1994.

M.Murakami, Cryogenics. Vol.19, pp 1 133, 1989

H-Eroçlu, J. of Eng. Gas Turbines and Power, Vol. 114, pp 768, 1992.

E.Villermaux, and E.J.Hopfinger, J. Fluid. Mech., Voi.263, pp 63, 1994.

E-R-Subbarao, and B.J.Cantwel1, 1. Fluid. Mech., Vo1.245, pp 69, 1992.

N-Rajaratnam, Turbulent Jets, Elsevier Pub. Co .. Amsterdam-Oxford-New York, 1 * ed.. 1976.

J.O.Hinze, Turbulence. McGraw-Hill Pub. Co., New York, NY, 2"' ed., 1975.

B .E. Launder. and D. B. Spalding, The Numerical Cornputations of Turbulent Flows. Imper. Collese of Science and Technology, NTIS, 1973.

RClifl, J-RGrace, and M.E. Weber, Bubbles, Drops and Panicles, Acadernic Press, 1973.

C.T.Crowe, Gas-Particle Flow, in "Pulverized Coai Combustion and Gasification, Ed. Smoot and Pratt, Plenum Pub. Co., 1979.

Y-C-Lee, and E-Pfender, Plasma Chem. and Plasma Process., Vo1.7, No. 1, pp 1, 1987.

S. A-iMorsi and AI. Alexander, I. Fluid hlechanics, Vol.55, pp 193, 1972.

I.S-Shuen, L.D.Chen, and G.M.Faeth, rUChE I., Vo1.29, pp 167, 1983.

W.E.Ranz and W.R.Marshal1 Jr., Chem. Eng. Prog., Vol. 48, No.3, pp 14 1, 1952.

W.E.Ranz and W.R.hIarshal1 Ir., Chem. Eng. Prog., Vol.48, No.4, pp 179, 1952.

P-Barkan, and A.hl.Whitman, M M Journal, Vo1.4, No.9, pp 1691, 1966.

A AVoropaev. V.M. Goidfarb. .\.V.Donsky, S .V.Dresvin, and V. S.Klubnikin, Thermal Physics at High Temperarures (in Russian), Vo1.4, No.3, pp 464, 1969.

P. S tefanovic, Dynamic Method for Stagnation Pressure Measurements in High Temperature Flows, Mast ers Thesis. University of Belgrade, Yuçoslavia, 1 987.

P.Pavlovic, P. S tefanovic. .M.Jankovic, S. Oka: "Contact Methods for Diagnostics of Therrnai Plasmas", Journal de Physique, FASC 18, Colloque NoS., pp.28 1-289, CS- IWO.

T.P.Mac!ean. and P. Schagen. Electronic Imagine, Academic Press, 1979

Mhiasri. Construction of an Electronic Imaging System for Plasma Spray Processing, Masrers Thesis. University of Toronto. 19%.

J.Grey, P.F.Jacobs, and MP.Sherman, Rev. Sci. Instrum., Vol.33, pp 7 , 1962.

J.Grey, Rev. Sci. Instrum.. Vol.34. pp S. 1963.

M-Brossa, E.Pfender. Plasma Chem. and Plasma Process., Vol.8, No. 1 ., pp 75. 1988.

.A.Capetti. and E.Pfender, Plasma Chem. and Plasma Process., Vo1.9, No. 1 ., pp 329, 1989.

P. S tefanovic, P. Pavlovic, and SI. Jankovîc, Proc. of the 9'"nt- Syrnp. on Plasma Chemistry, (ISPC-9) [UPAC, Pupmchiuso. Italy, Vol. 1 ., pp 3 14, 1989.

J-RFincke, W.D. Swank, and D.CHagçard. Plasma Chem. and Plasma Process., Vol. 13, No.4, pp 5 79. 1993.

I.RFincke, S. C . Snyder, and W. D. S wax&, Rev. Sci. Instrum., Vol.64, No - 3 , pp 7 1 1. 1993.

W.L.T.Chen, J.Heberlein. and E.Pfender, Plasma Chem. and Plasma Process., Vol. 14, NO.^., pp 3 17, 1994.

S.V. Dresvin, AV-Donskoi, V.M.Goldfarb, and V.S.Klubnikin:"Physics and Technology of Low-Temperature Plasmas", Iowa State university Press, h e s , 1977.

H.A.Becker, and A.P.G.Brown, I. of Fluid Mech., Vo1.62, pp 84, 1974.

AVoropaev, S.V.Dresvin, and V.S.Klubnikin, Thermal Physics at High Temperanires, (in Russian) Vo1.7, No.+ pp 633, 1969.

C-R-Dean, Aerodynamic Measurements, iWT Press, Boston, 1963.

F-Homrnan, and ZAgnew, Math. Mecech., Vol. 16, No.3 , pp 1 53, 1936.

C. W.Hurd, K.P.Chesky, and ..\.P. S hapiro, Trans. ASME, Vo1.75, pp 253, 1953.

V.P.Shoulter, and G. 1-Bleyker, Applied hfechanics, No. 1, pp 16 1, 196 1

1-E-Campbell, High Temperature Technology, John Willey Pub. Co., New York, 1959.

D.L.Smith, and S. WChurchill, S. W.Col1ege of Eng.,University of Michigan, Tech. Rep. ORA Project, 1965.

J. Mostaçhimi, and E. Pfender, Proc. ISPC-11, IUPAC, Ed. I.Harry, 1, 321, 1993.

A.L.Hare:, Proc ISPC-2, M A C , G.2 2, 1977.

FLUENT V1.2 User's Guide. Fluent. Inc. Lebanon, New Hampshire, 1994

E-Ower, and R. C. Panhurn. The hleasurement of Air Row, Pergamo Press, O.dord, 1 966.

G.N.Abramotich, Turbulent Jets of .Air, Plasma, and Red Gas, Consultants Buureau, New York, 1969.

AH-Dillawari, and J. Szekely, Plasma Chem. and Plasma Process., Vol. 7, No.3, pp 3 17, 1987.

V-P-Chyou, and E-Pfender, Plasma Chem. and Plasma Process., Vo1.9, NO.^., pp 29 1, 1989.

M. Jankovic, D.hfilojevic, and P.S tefanovic, Journal de Physique, Fasc 1 8, Colloque No. 5, pp 229, C5- 1990.

J-D-Rarnshaw, and C-H-Chang, Plasma Chem and Plasma Process., Vol. 12, No.3, pp 299,

J.D.Rarnshaw, and C.H.Chang, Plasma Chem. and Plasma Process., Vol. 12, No.3, pp 299, 1992.

S.V.Patankar, Numerical Heat Transfer and Fluid Flow, McGraw Hill Book Co., 1980.

EPfender, J.R.Fincke, and R-Spores, Plasma Chem. and Plasma Process.,Vol. 1 1, No.4, pp 529, 1991.

I.RFincke, W.D.Sw& and D.C.Hasgard, Proc. of National Thermal Spray Conference, Anaheim CA, pp 49, 1993.

S-Russ, E.Pfender, and P J. Strykowski. Plasma Chem and Plasna Process., Vol. 14, No.4, 1994.

preBFC VIO, User's Guide. Fluent. Inc.. Lebanon. New Hampshire, 199 1

M. Jankovic, and J. Mosraghimi, Plasma Chern. and Plasma Process., Vol. 15, No.4, pp 607, 1995.

F.Lana, and P L.Viollet, Proc. of the 8" Int. Symp. on Plasma Chemistry, (ISPC-8) iWPAC, Tokyo, lapan, pp 3 1. 1957.

F.Lana. and F.Kassabji, Proc. of the 9' Int. Symp. on Plasma Chemistry, (ISPC-8) m A C , Tokyo, Japan. pp 170, 1957.

E-Fleck, Y.C.Lee, and E.Pfender, Proc. of the 7" Inr. Syrnp. on Plasma Chemistry. (ISPC-7) IUPAC, Eindhoven, Netherlands, pp 1 1 13, 1985.

F.P. Incropera. and D P DeWitt, Fundamentais of Heat and Mass Transfer. Wiley, New York, 1990.

Ençineered Materials Handbook - Ceramics and Glasses, ASM International, 199 1.

M. Vardelle. AVardeile, G. Delluc, PFauchajs, and C-Trassy. in "Dust Laden Jets", Eds Solonenko and Fedorchenko. pp 299, 1989.

A. VardelIe, M. Vardelle, P.Fauchais, P. Proulx, and M. I.BouIos, Proc. of Int. Thermal Spray Conference, Orlando, FLA pp 513, 1992.

M.Jankovic, J.hlostaghimi, and J.O.Noça, Proc. of Int. Sym. Developments ad Applications o f Ceramic and hietal rüloys, Quebec City, Quebec, pp 457. 1993.

Y.M.Lee, and R..A.Berry, Proc. National Thermal Spray Conference, .Anaheim CA, pp 67, 1993.

SG- 100 Manual. Miller Thermal Inc., Appleton. Wisconsin, 1992.

Standard Test Mettiod for Density of Giass by Buoyancy, ASTM C693-73, Vol. 15-02.

Standard Tesr Method for Adhesion or Cohesive Strength of Flame Sprayed Coatinps, ASTM C633-79, V01.02.05.

H.S.Carslaw, and I. CJaeger, Conduaion of Heat in Solids, Odord Press, Glasgow. 1 967.

LG-Currie, Fundamental biechanic of Fluids, LMcGraw-HiIl, New York, 1993.

S.V.Patankar. and D.B.Spalding, Heat and Mass Transfer in Boundary Layers, Intenext Books, London, 1972.

R.E.Sonntaç, and G.J.Van Wylen, Fundamentals of Statistical Thermodynamics, John Wiley & Sons, New York. 1965.

TRANSPORT EQUATIONS FOR THE FLUID FLOW

The following equations have to be solved when rnodelling thermal plasma jets:

- Conservation of mass

where p is the density of the ças, and is the velocity component in j" direction.

- Conservarion of rnornentum

where r,, is the srress tensor. p is the static pressure. The stress tensor is siven by

where p is the molecular viscosity, and p, is the turbulent viscosity. It is given by

171

where C, is a constant. k is the kineric energ of turbulence, and E is the dissipation of kinetic

energy of turbulence.

The standard k-E mode! of turbulence was used to close the system of conservation

equations. Two additional conditions were the equation for the conservation of kinetic energy of

turbulence k and its dissipation rate E:

- Consemation of kineric energ of turbulence:

- Conservation of dissipation of kinetic energ of turbulence:

where C , , C, are empirical constants'30'. o, and o, are "Prandtl" numbers governing the

turbulent difision o f k and E. G, is the rate of production of kinetic energy of turbulence(30'..

au au. au. J

Gk = PL- + )1. axi a ~ . a~

J J

Since an arçon piasma jet emerging into the arnbient air is considered, two additional

equations must be solved: conservation of rnergy and conservation of chernical species.

- Conservation of energy:

where h is the enthalpy of the gas mixture, oh is the "Prandtl" nurnber governing the energy

difision, J, is the flux of species 1. and S, is the volumetnc radiative loss from the plasma.

- Conservation of chemicai species:

where m, is the mass fraction of species Z, J,., is the difisive mass flux of species I in the i"

direction, and S, is the net rate of production/destniction of species 1 per unit volume due to

c hemical reaction. Since the difision of air into the argon pIasma was considered as a binary

diffusion problem, this term was zero. The diffusive mass flux is ~ i v e n by

(A. 10)

where 0, is the Schmidt nurnber

Thermophysical and transport propenies of the arçon-air rni,xture were obtained by the

mie of mixtures. For example. the enthalpy of the mixture was calculated as

APPENDLY B:

COEFFICIENTS a,, a2, AND a, IN EQUATION FOR DEUG FORCE COEFRCIENT

APPENDLK C:

DC SPMYING GUN SI'STE3I

Spraying Gun SG-100 from Miller Thermal is a DC plasma generator designed to work

at powers of up to 100 k W [t consists of a light weight housing and the interchangeable

electrodes for multimode operation. Depending on the anode-cathode configuration, it can

operate with nominal power of eirher 40 kW or 80 kW, and three different piasma gas Bow

regimes, from subsonic to supersonic. [ts actual operating power and the gas ffow parameters

depend on the balance between four independent circuits mentioned in the previous text.

Electrical systern:

- 80 kW power supply, Glenn Products.

- Water-coded electrode leads, Flex-Cable

- Hiçh frequency arc starter.

- Controls and indicators on the control panel.

Power wpply is 80 kW Glenn Products. designed to gve DC output of either 90 V or 180

V open circuit voltage. Maximum load voltage is either 80 V or 160 V, with the comesponding

maximum current of 1000 A or 500 A The input voltage is 460 V, three phase, 60 Hz. Electrode

leads, connectinç the power supply and the Gun, are made of copper. They are well insulated and

water-cooled. The high frequency arc staner is a custom asrembled unit, connected parallel to

the Gun. Arcinç that occurs on the sparkin- gaps of the starter, creates hiçh frequency, and high

voltage siçnal that initiates the arc between the cathode and the anode. Controls and indicators

on the control panel. relevant for the electricai system are: a) analog readouts for operating

voltage and current of the Gun, b) power supply ON and OFF buttons, c) arc starter button, d)

potentiorneter for choosing the operating current of the Gun.

Cooling water system:

- Water pump, Paco, 7 5 HP,

- Water tilters, Filtrine, with replaceable filter cartridçes,

- Flowmeter "Thru View", E M , for water flow rates 0-25 GPM,

- Flow switch, Transamerica Delaval, 5 GPM shut-off,

- Differential temperature transducer. Delta-T Co.,

City water is used for cooling purposes. Ir passes through the water filters before going

to the pump. The flow srvitch is installed to protect the Gun from overheating and possible

damage, if the water tlow falls beIow 5 GPM. Differential temperature transducer gives the

temperature difference of the water at the inlet and the outlet of the gun. This measurement is

necessary for calculation of the heat Iosses IUso, therrnocouples are provided to measure the

increase in the cooling water temperature through the elecrrode leads. Indicators and controls on

the conno1 console, relevant for the cooling water system, are: a) water pump ON-OFF switch,

b) indicator lamp that lights when the water purnp is ON. c) indicator lamp that iights when the

water flow is below 5 GPM. and the corresponding interlock is activated, d) readout for the

ternperature transducer

Cas systern:

- Argon sas bottles,

- Rotameter on the main _ras line. FischerkkPoner, flow rates 0-2 scfm of air,

- Rotameter on the shroudin~ Sas line, Dwyer, flow rates 0-100 scfh of air,

- Pressure sases. Pacific Scientific, pressure 0-100 psig.

Gas system has nvo independent gas lines, main gas and the shrouding ças. The gun cm

operate with or without the shrouding Sas, but it cannot operate without the main gas. Gas flow

interlock is installed to protect the çun from operating with the low gas flow rate. It shuts down

the power supply at flow rates lower than 7 scfh at 100 psig. This limit is well below any

anticipated flow rates throuçh the system dunng the reçular operation. Indicators and controls

on the control console, relevant for the ças system, are: a) ON-OFF valve on the main gas line,

b) flow control valve on the main ças line, c) flow switch on the main gas line that controls the

gas interlock, d) indicator lamp that lights when the gas flow rate is too low and the

corresponding interlock is activated,

Powder feeding system:

- Powder feeder, Sankyo Dengyo, mode1 MFHV-2, with adjustable feedrate,

- Rotameter on the carrier ças line, Dwyer, flow rates 0- 100 scfh,

Sankyo Dengyo powder feeder is a flexible feeding unit with the rotating table and the two

scrapers, coarse and fine. Adjustinç the distance of the scrapers to the rotating table determines

the feedrate. Also, rotation speed of the table may be adjusted for continuous change in the

feedrate. On the other hand, the injection velocity of the particles is a function of the camer ças

80w rate, only. The powder feeder is pressunzed in order to allow for the pneumatic transport

of the powder. Indicators and controls on the control console, relevant for the powder feeding

system, are: a) ON-OFF swi tch thai activates control valve on the carrier gas line, and starts the

rotating table of the feeder, b) indicator lamp that Iiçhts when the particle injection is on.

DESIGN PARAMETERS OF DYNA3IIC PITOT-PROBE SYSTEM

D. 1 Dynamic characteris tic of the mensuring system

Dynamic behaviour of the measurine system c m be best described by observing a stepwise

input function and the system response fiinction, both presented in the Figure D. 1 . We can see

that the system response function has a form of amortized oscillations around the constant value

of the input function. The system response fbnction may be disfigured by amplitude or by

fiequency, the first one resultinç in an error in absolute value of the measured signal, and the

/ / i(

I - - Stepwise input function 1

I l

I 1 1 --- - System reponse function 0.0 i

time [SI Fig. D. 1. Input function and system response function.

second one renilting in a phase shifl of the recorded sigai. Typical error in free jet measurements

is to record a non-syrnmetric profile of the stagnation pressure, in perfectly axisymmetric jet.

The dynamic characteristic of the measuring system is a complicated function that

descnbes the system response funcrion, and its distortion From the input function. There are

numerous mathemarical models"" that c m predict dynamic charaaenstic of the measuring system

for vanous input functions. Their analysis is beyond the scope of this work, so oniy a bnef

parametnc analysis will be presented here.

The dynarnic Pitot-probe measuring system consists of the probe, the pressure transducer,

and the electronic cornponents that connect the transducer and the data acquisition board.

Furthermore, the above system can be divided to the pneumatic and the electronic part. The

pneumatic part consists of the probe itself and the small chamber in front of the sensitive

membrane inside the pressure transducer Today's electronic components, which are in use in data

acquisition, are very fast and their response time is not crirical for the above measurements. This

lads us to a conclusion that the dynarnic charactenstic of the entire system will be only as good

as the dynamic characteristic of its weakest componenr, the pneumatic part of the system.

The pneumatic part of the measurinç system is schematically presented in Figure D.I . Irs

entire volume consists of volume C L (Pitot-tube of diameter d and lençth 4, and volume C: (the

chamber in front of the transducer membrane, heiçht h and diameter dl). In desiçning the probe

and choosinç the pressure transducer, it is very important to get the proper volume ratio C',/&.

For measurements in thermal plasmas. where the çradients of stagnation pressure may be very

aeep, it is important to have the system with good dynamic characteristic. It should be capable

of recording the profile of the stagnation pressure without significant distortion. Since thermal

plasma jets are turbulent, with pulsations in velocity, temperature and stagnation pressure, it is

not desirable to have a meamring system too sensitive. It should be capable of recording the basic

pressure signal without senous deformation, whiie it should remain insensitive to turbulent

pulsations of velocity and pressure. This means that for signal Eequencies of D200 Hz (frequency

Fig. D.Z. Schernatic of the pneumatic part of the measuring system.

of the turbulent pulsations) the rneasurins system performs intesration and yields the time-

averaged values of stagnation pressure.

In order to achieve the above requirernent. it is re~ornmended'~' that the volumes V, and

& are of the same order of masnitude (C;/I> < IO), and are very srnail (-10" m3). The

differential pressure transducer used, Ornera 112PC, had a volume & = 3x10-* m'. The probe is

made out of staidess steel tubing wi th outside to inside diameter ratio 2.Y 1 -0 mm. By mounting

the transducer close to the probe outlet, and by choosing the short probe, the overall length of

the pneumatic part is minimized. The resultinç volume of this part of the pneumatic part was

V, = 9 . 4 ~ 1 0 * ~ mJ, thus fulfilling the above requirernent for the C',/IL ratio.

D.2. Minimum velocity of the probe movement

The exposure time of the probe should be smaü enough in order to avoid overheating and

meiting of the probz tip. As a first approximation, heating of the probe c m be treated as one

dimensional heat conduction with constant extemal heat flux. The problem is schematically

presented in Figure D.3., where we can see that the stagnation heat flux of q, is heating the tip of

the probe. The Iength of the probef is exposed to the constant heat flux of kq;"), where k is a

constant with sugçested value k = 0.25. It is assumed that there is no further change in

temperature at x = I (dT/ax = 0).

Under these assumptions the one-dimensionai heat conduction equation becorne~(~')

Fig. D.3. Schematic of the dynamic Pitot-probe heating.

Time [sec]

Fig. DA. Heating curves of the probe tip.

where AT is the change in the probe tip temperature, Ar is the time interval, Fo = ctAr/lz is the

Fourier number. ci is the average thermal difisivity of the stainless steel SS 2 16 in the

corresponding temperature întewal. C, is the average specific heat capacity of the SS 3 16. and

p is its density.

It is possible now to calculate the heating curves for different values of the sta~nation heat

flux that act upon the probe tip. Results are presented in Fig. D.4. By using the obtained curves.

it is easy to determine the exposure time of the probe rip, so it does not reach the melting point.

The meltinç point of the stainless steel is represented by a dashed horizontal line (T= 1670 K).

Thermal plasma flows are known for very hiçh values of stagnation heat flux (q, = 10 hfW/mL).

When recording the stapation pressure in the potential core of the jet, the exposure time has to

be very short (-0.1 sec) Typical radial dimension of the jet in this region is about 10 mm, which

182

yields the value of the minimum probe velocity of Wp = 0.1 m/s, approximately. It is expected

that this velocity be sufficient for the downstream parts of the jet. with an increased radius, but

signifïcantly decreased values of qr However, the dynamic behaviour of the probe bas to be tested

for possible distortions of the recorded pressure signal. before proceeding to the measurernents.

D.3. Experimental test of the chosen dynamic Pitot-probe system

There are numerous mathemarical models for predictinç the dynarnic characteristic of the

dynamic Pitot-probe measurincr - rystem. Their mutual charactenstic is rhat they are not hiçhly

accurate, and are used pnmarily during the desien - stage of the measunng system. There is still

no alternative to the experimental testing of the actual measuring system, since it yields much

more reiiable information on the recorded signal distortion. The problern with both, analytical and

experimental methods of tesring the dynamic Pitot-probe measuring system, is that the input

Elapsed time [msec]

Fig D.5. Recorded voltage output of the pressure trnnsducer.

signal is generally an unknown function. In experimental approach various devices are used to

simulate the input signal. based on the previcus knowledge of the flow field. hlso the system

response function is recorded and the cornparisons could be made.

The approach used in rhis work was to record the stagnation pressure profile of the cold

argon jet. The velocity of the dynamic Pitot-probe was equal to the value that will be used in

thermal plasma measurements, IT = 0.1 mis. It was necessq to use a high sampling rate, 1000

& to obtain a representative profile of the stagnation pressurp. Recorded voltage output of the

transducer is presented in Figure D 5 We can see that the electrical noise of the system cannot

be avoided with such a hiph sarnpiing rate. By averaging 5-6 successively recorded profiles, the

measurement uncertainty can be reduced.

ïhe observed cold jet was also scanned by using a point-by-point method and using the

same probe and transducer. The profile obtained was compared with the profile recorded by the

dynarnic Pitot-probe method Calculared velocity profües are presented in Figure D.6. Agreement

- 100 - - - stntic Pitot-probe (m=3.37 g/s) - - - dynamic Pitot-probe (m=3.32 g/s) m

\

E 80 - - - r i CI .- I - - -

- -

1 d

diameter [mm]

Fig. D.6. Pnrsllel dynnmic and stntic Pitot-probe measurements.

betrveen the recorded profiles iss very sood Velocity profiles were integrated in order to obtain

the total m a s flow rate of the argon. They are compared with the value measured by a calibrated

rotameter, rn = 3.20 ç/s. Both rnethods are within 5% of what is considered to be the accurate

value of the mass flow rate. Having used the same probe for both measurements, the eEect of

systematic error in stagnation pressure rneasurements related to the probe dimensions, the

viscosity of the fluid, the pressure gradients. the inclination angle, etc., is eliminated to a certain

eaent. The difference between the two recorded stagnation pressure profiles is a consequence

of only the probe rnovinç in the dynamic method. There is no systematic distortion of the

recorded pressure signal.

Extrapolation to the thermal plasma measurements can be made in a sense that the

measuring system is not expected to behave differently. The argon fl ow rate used for the coid

measurements was 3 2 ç/s (compared to 1 ç/s in thermal plasma), in order to produce the level

of stagnation pressure similar to the one in plasma jet. However, the level of stagnation pressure

is expecîed to be higher in the plasma. and the profile to be recorded is expected to have steeper

gradients. Nevenheless. these obvious differences are not expected to change the dynamic

behaviour of the measuring sysrem, and to introduce any serious disti~urernent of the recorded

profiles.

APPENDIX E:

DERIVATION OF EXPRESSION FOR ERROR LY 3IEASUREhIENT OF DYNAMIC

PRESSURE BY A CVATER-COOLED PITOT-PROBE

The distribution of plasma temperature in the thermal boundary layer around the probe

tip is given by

where 6 is the boundan: . laver - thickness It is assumed that in the isothermal case. velocitv in t

boundary layer changes as

Distribution of veloclty is presented in Figure E. 1 We can see that the curve of acrual

velocity (obtained by numerical simulation), and the curve represented by Equation (E.2) are in

oreement. relatively good a,

The change of pressure in the boundary Iayer, for the isothermal c u n e , is given by

Axial coordinate [mm]

Fig. E.I. Velocity distribution in the boundary Iayer.

It is assumed that the total pressure in rhe boundary layer rernains constant.

and

M e r substitutinç the pressure p. from Equation (E.3)- and the velocity U, €rom Equation (E2),

into Equation (E.4). and after performinç the denvation, the hnction f(y/6) becomes

The values of velocity on the non-isothermal curve and on the isothermal curve, are

related to each other in a way sirnilar to the temperature distribution (Equation E. 1)

Since the pressure is proportionai to the square of velocity (p-U'), the values of the

pressure on the non-isothermal curve could be expressed as follows

In order to estimate the error of the stagnation pressure measurement, it is necessary to

perform t h e inteeration dong the isothemal and non-isothemal curve, within the domain of

interest P O - 6 or p=p,-p ,-,s,, and p=p,-p ,,, ). For isothermal curve we have

Pr- im dp. (sot Pr- isor - - - 4 1 2

pal - = -v*

P Pa 2

The integation is performed assuming that the gas is ideal and incompressible, (p=p(T)).

For non-isothermal cume. after substituting for dpnlJc2, from Equation ( E 7). and afier performing

the integration, we can write

For the most probable case r n = ~ 2 , Equation (E.9) reduces to

The error in dynamic pressure measurement Lp,, defined by the equation(4.20), may be

obtained by subtracting the equations (E.8) and (E. 10)

The above equation represents rhe absolute enor in dynamic pressure measurernents due to the

temperature gradient in boundary layer surrounding the probe tip. Funlier simplification can be

made by introducine a factor 9, defined by the Equation (4.22)

where Ap,-,, is the stagnation pressure rneasured in an isothermal case. According to the

experiment with water-cooled and an uncooled probe the difference between and p,-,, is

lower t han 10%. In order to simpIiS, the equation (E. 1 1)- as a first approximation we may

assume

Pt-nisot - Pa Pt- i m t - P, = 5

Then, equation (E. 1 1 ) reduces to equation (4.2 1 )

(E. 1 4 )

The assumption made in Equarion ( E 13) introduces cenain error in calculation of the error of

measurement by Equation ( E 14). In order to avoid that, it is necessary to perform an iterative

calculation according to the following algorithm:

1 ) Assume that the isothemal and non-isotheml vaiues of the stagnation pressure are equd -

Pr-uat - P,-num

2 ) Calculate 9 = p,,s,,, - p,,

3 ) Calculate 5 frorn the Equation (1.33), by using 'rp, =

4) Calcuiate Ap, from the Equation (E. 14).

9 Calculate = *,-,, + *M. 6) Repeat steps 3) - 5 ) untill convergent solution for is achieved. In srep 4) use the

Equation (E. 1 1 ) insread of Equation ( E II).

CALCULATTON OF TEMPERATURE FROM THE MEASURED ENTEULPY

In order to calculate the temperature of plasma, it is necessary to know the composition

of the gas. In this work. s simplified approach for determining the composition of plasma gas is

used. Plasma is trested as bina- mixture of arson and air; the later is considered as a sin Je

component gas, and therefore maintains the standard composition of atmospheric air. The above

assumption allowed for caiculation of argon mass fraction. by simp[y measunng the content of

oxyçen in the exhaust gas.

The enthalpy of the mixture is piven by the following

m h ( T ) + (1 .4 r .-l r

Dependence of enthalpy on temperature is known and tabulated for arçon and air. Calculation of

temperature is based on iterative procedure, where the plasma temperature is guessed initially,

and then adjusted through a series of iterations until the Equation (F.2) is satistied.

This approach is used previously in enthalpy probe rneasurernent~(~~', but it introduces

certain error in temperature calculation. The air entrained by plasma is heated rapidly. Diatornic

oxyçen and nitrogen molecules fiorn air are dissociated and are reacting with each other forming

nitrogen-oxide (NO). Equilibrium analysis of air cornpo~i t ion~~~~, shows that the nitrogen-oxide

(NO), is present in the mixture within the temperature range of 2000-5000 K. It has a maximum

fraction of approximately 4% at temperature of 3000 K. The enthalpy probe has significant

quenching ability, due to a very rapid cooling of plasma ças during the aspiration stage. It is likely

to erpect that the molecular oxygen and nitroçen will be completely recovered, considering the

kinetics of dissociation reaction in both directions. On the other hand, the content of nitrogen-

oxide is dependant on the quenching rate, and it is reasonable to expect its presence in the exhaust

ças at room temperature. By negfecting the presence of nitrogen-oxide in the exhaust gas, cenain

error is introduced in the calculation of arçon fraction by using the Equation (F. 1). Also, certain

error is introduced by neglecting the energy used for formation of NO molecules, and not

including it in the Equation (F.2) The result of the above is a slightly hieher calculated

temperature.

It is very dificult to estimate the content of nitrogen-oxide in the exhaust gas without

performing a precise composition analysis. If we assume a "frozen chemistry" with respect to the

nitroçen oxide, which means extremely high quenching rate by the probe so the content of NO

remains intact dunng the aspiration, it is possible to estirnate the maximum possible error in

temperature calculation This analysis is performed for typical temperature and arson fraction

distribut ion within the free plasma jet. acknowled-ing that the probe was used to measure the

temperature within the range of 2000-6000 K. Results are given in the following table as an error

in temperature calculation. versus the plasma temperature.

It is evident that the error reaches its maximum at about T=3000 K, where also nitroçen-

oxide has its maximum content in air, while it is almost neçligible for temperatures higher than

5000 K. The error presented in the above table represents maximum possible error, caiculated for

a "frozen chemistry" with respect to nitrogen oxide. In real measurements this e m r wdl be lower,

because a "frozen chemistry" extreme is very rarely fùlfilled. Having that in mind, we may

conclude that the approach used in this work of measuring only the content of one component

Corn the gas mixture, Qves reasonable results of cdculated temperature. Estimated error is very

low in the reçions with h i ~ h e r temperatures (4000-6000 K), and it is well within uncenainty of

the rnethod ar lower temperatures (T<3000 K). However, for more precise measurements, it is

necessas, to perform a complete anaiysis on the composition of plasma gas by using more

sophisticated methods (mass spectrometry for example).

APPENDIX G:

CALIBRATION CURVES FOR hIICRO-ORIFICES

1 1 O 100 1000

Pressure drop [Pa]

Fig. G. 1. Cdibrntion curves for micro-orifices.

APPENDIX H:

HEAT TRINSFER COEFFICIENT FROAI PROBE WALL TO TBE COOLING

IVATER

Enthalpy probe is made of three pieces of tubine that form two very narrow annular

passages for cooling water. In order for probe to be cooled effectively, the flow rate of the

cooling water has to be rnaxirnized. SIaximurn fl ow rate obtained for the enthalpy probe used in

this work \vas rn, = 19.8 -S. Convective heat t r ade r coefficient from the probe walls to the

cooling water c m be calculated based on the following analysis. Standard procedure in this area

is to establish an hydraulic diametei", d,, based on the area of the cross-section available for the

flow, A , and on the wetted perirneter P

Reynolds number for the tlow inside the cooling passages. and the Prandtl number for cooling

water can be now calculated as

w ~ H V R e = - and Pr = - v a

Nusselt number can be caiculated from the following empirical formula(79', for hlly developed

turbulent flows in pipes

Convective heat transfer coefficient is a function of Iocal Nusseit number

In the above equations u, v, and K represent thermal difisivity, kinematic viscosity and

thermal conductivity of the cooling water, respectively. Cooling passages of the probe have

hydraulic diameters of 0.69 mm and 0.74 mm, resulting in different velocities and Reynolds

numbers of the cooling water. However. for the sake of simplicity, an average convective heat

transfer coefficient is caiculated, h = 33 k ~ / r n ' K . The average measured temperature of the

cooling water is T, = 290 K.

LISTING OF THE PROGMRI FOR CALCULATION OF PLASMA JET

PARAMETERS

program probe C

c... ..calculation of temperature and velocity of plasma jet c.. . . . from measured enthalpy, stagnation pressure and composition

dimension r(30),ent(3O),dp(30).sm(4,3O),rhoar(43),rho~(43), 1 rhoo2(43),rhohî(43),visar(43),visn?(43),viso2(43), 3 vish2(43), har(43),hn2(43),ho2(43), hh2(43),cpar(43), 3 cpn2(43),cpo2(43),cph2(43), h(4),vis(4),q(4),rho(4) logicai lpro open(S,file='probe.inp',status='old') open(1 O,file='probe.out',status='oldr) open( 14,file='prop.dat',status='oId')

c.. . . . reading rneasured parameters.. . . . . . . . . . . . . . . . . . . . . . -. . .

read(5,13) press do 15, i=1,30 read(5,I 1) r(i).ent(i),dp(i),(srn(j.i), j= 1.4) if(r(i).eq.9999.) go to 16

15 continue 16 l=i- 1

write(6,*) 1 close(5)

c.. . . .readinç gas propenies - corresponding to 300, 600, . .lî6OO K read( 14, *) read(l4,*) (cpar(j), j= 1.43) read(l4,*) read( 14. *) (cpotG), jS1.43) read(l4, *) read( 14. *) (cpn2G). j= 1.43) read(l4, *) read(l4,*) (cphZ(j), j= 1.43) read(l4, *) read(l4, *) (rhoar(j), j= 1 $3)

read( 1 4, *) read(l4,') (rhoo2(i), j= 1 ,43) read( 14, *) read(l4, *) (rhonl(j), j= 1.43) read(l4, *) read(l4,*) (rhoh2(j), j= 1.43) read(l4, *) read(l4,*) (visar(j), j= 1-43) read(14, *) read(l4, *) (viso2(j), j= 1,43) read(l4, *) read(l4, *) (visn2(j), j= 1 $3) read(l4, *) read(l4, *) (vishx), j= 1.43) close(l4)

c. .. ..tabulating the values of ças enthalpy ............ har(0)=0. ho2(0)=0. hn2(0)=0. h hZ(O)=O. cpar(0)=0. cp02(0)=0. cpn2(0)=0. cph2(0)=0. do 12, i= l,43 har(i)=har(i- l )+(cpar(i- I )+cpar(i))* 150. hoî(i)=ho2(i- 1 )+(cpo2(i- 1 )+cpo?(i))* 150. hn2(i)=hn2(i- 1 )+(cpnî(i- 1 )+cpn?(i))* 150. hh?(i)=hh?(i- 1 )+-(cphl(i- 1 )+cphl(i))* 150.

12 continue c.....calculation of flow parameters

write(l0,3 1) do 17, i=l,i

c.. . ..calculation of total temperature.. ................. ]pro=. tme. det= 1000. write(6,*) det tes=300. write(6,*) det

1 8 h( l )=prop(tes, har) h(2)=prop(tes, h o 3 h(3)=prop(tes, hn2) h(4)=prop(tes. hhî)

write(6, *) det s h=O. write(6,') det do 19, j=l,4

19 sh=sh+sm(j,i)*h(j) write(6.843) i,sh,ent(i),det

843 fomat(t2,i3,x,fl0.0,x,flO.O,x,flO.3) if((abs(sh-ent(i))/ent(i)).le.0i) 1 ) go to 90 if(1pro) go to 80 if(sh.gt.ent(i)) go to 85 det=-det/ 10. lpro= m e . go to 85

80 iflsh.it.ent(i)) go to 85 det=-det/ 1 0. Ipro=.false.

85 tes-estdet go to 18

90 tt=tes c.. . . - caiculation of Stream temperature.. . . . . . . . . . . . . .

t=tt c... . .calculation of components and the mixture properties.

30 rho( 1 )=prop(t,rhoar) rho(2)=prop(t,rhoo2) rho(3)=prop(t,rhon2) rho(.l)=prop(t,rhohî) rhop=O. do 20, j 4 . 4

20 rhop=rhop+sm(j,i)*rho(j) vis( 1 )=prop(t,visar) vis(2)=prop(t,viso3) vis(~)=prop(t,visnl) vis(4)=prop(t,vish2) visp=O. do 21. j=I,J

2 1 visp=visp+sm(j,i)*vis(j) cp( 1 )=prop(t.cpar) cp(2)=prop(t,cpo2) cp(3 )=prop(t.cpn2) cp(4)=prop(t,cpa cpp=o. do 22, j= 1.4

22 cpp=cpp+sm(j,i)*cp(i)

c.. .. .calculation of velocity.. ............................ u=sqrt(2. *dp(i)/rhop) reno-7i*rhop*O.O~72/visp u=sqrt(2. *dp(i)*( 1 .-6./reno)/rhop)

c.. .. .correction for corn pressibili ty ........................ skap= 1 ./( 1 .-press/rhop/t/cpp) c=sqrt(skap* presshhop) smah=u/c if(smah.le.0.2) go to 34 u=sqrt(2. *dp(i)/rhop/( 1 .+smah*smah/4.))

c.. . ..stream temperature.. ................................... 34 ts=tt-u*u/cpp/?.

if(abs(ts-t)/t.le.O.Oj) go to 25 t=ts

go to 30 output of overall results.. . . . . . . . . . . . . . . . . . . . . .

write( l0,32) r(i), ts,u.(sm(j,i), j= 1.4) continue ....................................................

format(t3,f7.2~ l3.f9.O, t25,flfl0,t35,4(f5.3,3x)) fomat(l,t3,fl.O,/) format(t2,'RADIAL PROFILESt./t S,'r[rnm]'.t 1 3 ,'TF]',t2?,

end

dimension table(<)

slop=(table(i+ l )-table(i))/3 00. prop=table(i)+slop* delt retum end

fùnction temp(h 1 .table) C

dimension table(43)

do IO, i=1,43 if(h 1 .ge. table(i)) go to 1 1

10 continue I l l=i

delt=h 1 -tabIe(l) slop=300./(table(l+ 1 )-table(1)) temp=float(l)*300.+slop*delt return end

APPENDLY J:

Air properties: (viscosity thermal conductivity K, specific hert crpacity C,, volumetric

radiation sink term SR, and enthalpy h)

Argon properties: (viscosity thermal conductivity K, specific heat cnpncity C,, volumettic

radiation sink term SR, and enthalpy h)

T(K)

1000

p(kg/m sec)

535.e-5

w ( ~ / r n K)

4.27e-2

Cp(JkgK)

520

S@/m3)

O

h( J/W 5.2e5

APPENDIX K:

PROPERTTES OF IRON-ALUb:tGVIDE POWDER

IRON (Fe):

Density : p = 7570 kg/m3

Melting point: Tm,, = 1810 K

Boiling point: T, = 2923 K

Latent heat of fusion: L, = 266.5 kJkg

Specific heat capacity Cp(J/kgK) and thermal conductivity K OV/mK):

Specific heat capacity of liquid Fe: C, = 824 JkgK

XLUMNUM (Al):

Density : p = 2702 kçirn'

Melting point: T,,,, = 93 3 K

Boiling point: T,, = 2740 K

Latent heat of hsion: L, = 395.3 W k g

S pecific heat capacity C,(J/k-/K) and thermal conductivity K (W/mK):

Specific heat capacity of liquid Al: C, = 1088 J/k&

IMAGE EVALUATION TEST TARGET (QA-3)

APPLIED IMAGE. lnc 1653 East Main Street - S.; Rochester. NY 14609 USA -- --= Phone: 71 61482-0300 -- - - Fax: 71 61288-5989

O 1993. Appiied Image. Inc.. Ali R~ighS Reserved