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DUST EROSION PERFORMANCE OF CANDIDATE MOTORCASE THERMAL PROTECT -ETC(U)MAR 80 D H SMITH DNAO01-79-C-0179

UNCLASSIFIED PUA-TR-1473-O0-05 DNA-5286F NL

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i ¢ DUST EROSION PERFORMANCE OF CANDIDATE0 MOTORCASE THERMAL PROTECTION

g MATERIALS

D. H. Smith

Prototype Development Associates, Inc.

1740 Garry Avenue, Suite 201

Santa Ana, California 92705

10 March 1980

Final Report for Period 1 January 1979-1 October 1979

CONTRACT No. DNA 001-79-C-0179

APPROVED FOR PUBLIC RELEASE;DISTRIBUTION UNLIMITED. 7. ,

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REPORT D MENTATION PAGE ... I) ' .srk I.ro, ,I D I RA . . .F R.L N GOVT ACCESSION NO.. I *,T. A'A, Or, NhMFIF r

JST OSION PERFORMANCE OF.ANDIDATE MOTORCASE Final epart.THERMAL PROTECTION M MATER1 Jan P-1 Oct 79

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9 PE RFRMING OkCANIZ ATION NAME AND Ao -"- DIUN PAM M I A

Prototype Development Associates, Incorporate1740 Garry Avenue, Suite 201 Sur N99QAXA1410-06Santa Ana, California 92705 ,_. .11 (CONTROLLING OFFICE NAM AND ADDRESS ,, _ MaDirector 1 '1 ) 0Mrt9 JDefense Nuclear AgencyWashington, D.C. 20305 -M-_

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This work sponsored by the Defense Nuclear Agency under RDT&E RMSS Code

B342079464 N99QAXAI41006 H2590D.

ErosionMaterialsMotorcaseTest Results

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A study was conducted to evaluate the erosion performance of candidate motor-case thermal protection materials for advanced missiles. Available data werecompiled and evaluated and empirical expressions were developed to describethe erosion performance of two of the leading candidate materials (VAMAC 15Jand Kevlar-epoxy). These expressions then were applied to predict the flightresponse of these two materials for two design flight trajectories and asimulated freestream dust environment. Finally, a number of available ground

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UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

20. ABSTRACT (Continued)

test facilities were evaluated for use in performing erosion tests of materialsfor ascent flight. Recommendations were made for the optimum facilities toaccomplish different types of test objectives.

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(Mien Dlat. Entered)

PREFACE

The work described in this report was conducted by Prototype Development

Associates, Inc. (PDA), Santa Ana, California, for the Defense Nuclear Agency (DNA)

under contract number DNAOl-79-C-0179. Captain A.T. Hopkins was the DNA Contracting

Officer's Representative. The technical effort at PDA was performed under the direc-

tion of Mr. M.M. Sherman, Program Manager. Mr. D.H. Smith served as the Principal

Investigator. Important contributions to the effort were provided by Messrs. J.L. Schmidt

and J.E. Dunn of PDA's technical staff. PDA also is indebted to the following indivi-

uuals who provided valuable assistance and cooperation in obtaining and interpreting

the data contained herein: Mr. A.W. Zimmerman (TRW), Mr. G.P. Johnson (MDAC),

;;r. G.H. Burghart (SAI), Mr. H.F. Lewis (AEDC), and Dr. W. Barry (The Aerospace Corp.).

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TABLE OF CONTENTS

Section Page

Preface 1

List of Illustrations 4

List of Tables 6

Conversion Table 7

1.0 Introduction and Summary 9

2.0 Facilities 11

2.1 Continuous Dust Erosion Tests 11

2.1.1 Facility Description 11

2.1.2 Test Conditions 13

2.1.3 Particles 13

2.1.4 Model Descriptions 15

2.1.5 Tare Data 15

2.2 Pebble Impact Tests 16

2.2.1 Facility Description 16

2.2.2 Pebbles 18

2.2.3 Model Description 18

2.3 Salvo Dust Erosion Tests 18

3.0 Data Correlation 21

3.1 VAMAC 15J Dust Erosion Correlation 21

3.1.1 Shock Layer Effects 21

3.1.2 Debris Shielding 22

3.1.3 Heating 22

3.1.3,1 Kinetic Energy Deposition 22

3.1.3.2 Convective Heating 24

3.1.4 Particle Velocity 32

3.1.5 Correlation 34

3.1.6 Applicability to Salvo Data 37

3.2 Kevlar-Epoxy Dust Erosion Correlation 37

3.3 VAMAC 15J and Kevlar-Epoxy Pebble Impact Correlation 41

3.3.1 VAMAC 15J 41

3.3.2 Kevlar-Epoxy 42

2

jTABLE OF CONTENTS- (Continued)

Section Page

4.0 Flight Predictions 45

4.1 Environment 45

4.2 In-Vacuo Erosion 46

4.3 Shock Layer Effects 46

4.4 Wall Temperature Effects 50

4.5 Pebble Impact Predictions 50

5.0 Recommendations for Future Testing 55

5.1 Arc-Jets 55

5.2 Powder Guns 56

5.3 Ballistic Ranges 56

5.4 Rocket Sleds 59

5.5 Rotating Arms 59

5.6 Facility Recommendations 61

5.7 Recommendations for Future Testing 62

References 63

Appendix A - Data 65

A-1 ENEC Materials 67

A-2 Motorcase Materials 71

A-3 Shroud Materials 113

A-4 Shroud Nosetip Material 137

A-5 Salvo Particle Data 139

Appendix B - Assessment of Shielding of Erosion in Regionsof High Potential Flux 147

B-1 Introduction 148

B-2 Analytical Method 148

B-3 Derivation of Dimensionless Parameter 151

Nomenclature 153

Distribution List 155

1 3

LIST OF ILLUSTRATIONS

Figure Page

1 Schematic view of AEDC Dust Erosion Tunnel 11

2 DET test cabin and model positioning system 12

3 Wedge model holder and sting support for DET tests 15

4 DET model 16

5 SAI pebble test facility and projectile velocity measuring systems 18

6 Shock layer effects in the DET 23

7 Probability of incoming particle colliding with debris in DET 23

8 Kinetic energy method comparison: 4-deg angle 25

9 Kinetic energy method comparison: 4-deg angle 261mn




13 Kinetic energy method comparison: 14-deg angle 3014 Kinetic energy method comparison: 30-deg angle 31

15 Convective heating in DET 32

16 Convective heating model comparison (po = 300 psi) 33

17 AEDC run 3 data trace 33 J.18 Influence of surface temperature on erosion 35 V

19 Influence of velocity on erosion 3520 Influence of impact angle on erosion 36

21 VAMAC 15J erosion data correlation evaluation 37

22 Comparison of VAMAC 15J salvo test erosion data with DET correlation

(velocity effect) 38

23 Comparison of VAMAC 15J salvo test data with DET correlation

(particle diameter effect) 38


(angle effect) 39


(MgO data) 39

26 Influence of impact angle on Kevlar-epoxy erosion 40

27 Influence of velocity on Kevlar-epoxy erosion 41

28 Kevlar-epoxy erosion data correlation evaluation 42

29 Kevlar-epoxy 20-degree pebble impact data 43

30 Kevlar-phenolic 6-degree pebble impact data 43


4

LIST OF ILLUSTRATIONS - (Continued)

Figure Page


33 Design trajectories 45

34 VAMAC 15J motorcase erosion (Trajectory A) 47

35 VAMAC 15J motorcase erosion (Trajectory B) 47

36 Schematic of vehicle shock layer 48

37 Influence of shock layer on motorcase erosion 49

38 Motorcase surface temperature histories 52

39 Crater depth history 53

40 Particle impact parameters in Bell rotating arm facility 60

A-l DET models with qaps and holes 83

B-l Debris shielding geometry 149

1 5

LIST OF TABLES

Table Page

1 Dust cloud characteristics for p0 1,000 psi, h° 0 500 Btu/Ibm 14

2 TARE data 173 Effect of temperature on flight erosion predictions 53

4 Multiple particle impact ground simulation facilities 57

5 Erosion facilities recommendations 61

A-1 ENEC metal model DET data 68

A-2 ENEC carbon-carbon model DET data 69 4A-3 VAMAC materials 72

A-4 Viton materials 75

A-5 Tungsten-bearing resin (TBR) materials 77

A-6 Other materials 79

A-7 Material constituents 81

A-8 DET notes 84

A-9 Motorcase material DET data 85A-10 Pebble test notes 105A-ll Motorcase material pebble test data (Feb - Apr 1979) 109

A-12 Shroud materials identification 114

A-13 Shroud program composite materials process summary 117

A-14 DET test notes 118

A-15 Shroud material DET data 119 2.

A-16 Pebble test notes 128

A-17 Shroud material pebble test data 129

A-18 Shroud nosetip DET data 138

A-19 Salvo particle data 140

6.

6r

Conversion factors for U. S. customary to metric (SI) units of measurement.

To Convert From To Multiply By

angstrom meters (m) 1.000 000 X E -10atmosphere (normal) kilo pascal (kPa) 1.013 25 X E +2bar kilo pasc~l (kPa) 1.000 000 X E +2barn meter (m) 1.000 000 X E -28British thermal unit (t~ermochemical) joule (J) 2 2 1.054 350 X E +3cal (thermochemical)/cm § mega joule/m (MJ/M) 4.184 000 X E -2calorie (thermochemical)§ joule (J) 4.184 000calorie (thermochemical)/g§ joule per kilogram (J/kg)* 4.184 000 X E +3curie§ giga becquerel (G~q)t 3.700 000 X E +1degree Celsiust degree kelvin (K) t = to + 273.15degree (angle) radian (rad) 1.745 319 X E -2degree Fahrenheit degree kelvin (K) t = (top + 459.67)/1.8electron volt§ joule () 1.602 19 X E -19erg§ joule () 1.000 000 X E -7erg/second watt (W) 1.000 000 X E -7foot meter (m) 3.048 000 X E -1

foot-pound-force joule 3 (J)3 1.355 818gallon (U. S. liquid) meter' (m') 3.785 412 X E -3inch meter (m) 2.540 000 X - -2jerk joule (J) 1.000 000 X E +9joule/kilogram (J/kg) (radiationdose absorbed)§ gray (Gy)* 1.000 000kilotons§ terajoules 4.183kip (1009 lbf) newton (N) 4.448 222 X E +3kip/inch (ksi) kilo pascal (kP) 2 6.894 757 X E +3ktap newton-second/m (N-s/m 2 ) 1.000 000 X E +2micron meter (m) 1.000 000 X E -6mil meter (m) 2.540 000 X E -5

mile (international) meter (m) 1.609 344 X E +3ounce kilogram (kg) 2.834 952 X E -2

pound-force (lbf avoirdupois) newton (N) 4.448 222pound-force inch newton-meter (N.m) 1.129 848 X E -1pound-force/inch2 newton/meter (N/m) 1.751 268 X E +2

pound-force/foot2 kilo pascal (kPa) 4.788 026 X E -2pound-force/inch (psi) kilo pascal (kPa) 6.894 757pound-mass (Ibm 2avoirdupois) kilogram (kg) 2 2 4.535 924 X E -1pound-mass-foot3 (moment of inertia) kilogram-meter3 (kg-m3) 4.214 011 X E -2pound-mass/foot kilogram-meter (kg/m ) 1.601 846 X E +1rad (radiation dose absorbed)§ gray (Gy)* 1.000 000 X E -2roentgen§ coulomb/kilogram (C/kg) 2.579 760 X E -4shake second (s) 1.000 000 X E -8slug kilogram (kg) 1.459 390 X E +1torr (mm Hg, 00 C) kilo pascal (kPa) 1.333 22 X E -1

*The gray (Gy) is the accepted SI unit equivalent to the energy imparted by ionizing radi-

ation to a mass of energy corresponding to one joule/kilogram.iThe becquerel (Bq) is the SI unit of radioactivity: 1 Bq = 1 event/s.fTemperature may be reported in degree Celsius as well as degree kelvin.§These units should not be converted in DNA technical reports; however, a parentheticalconversion is permitted at the author's discretion.

7

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8

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SECTION 1.0

INTRODUCTION AND SUMMARY

Advanced missiles may have to survive ascent flight through an erosive free-stream dust environment which would impose potentially severe performance constraints

on the various external protection materials (EPMs). This requirement has resulted

in a number of test programs designed to evaluate candidate materials for this ap-

plication by obtaining data for use in deriving analytical expressions for erosion

performance predictions.

Since the dust that could be encountered ranges in size from microscopic parti-

cles to pebbles nearly an inch in diameter, tests of both continuous dust erosion and

single pebble impacts have been conducted. The tests were performed by McDonnell-Douglas

Astronautics Company (MDAC); TRW, Inc.; and Science Applications, Inc. (SAI), at facili-

ties operated by the Arnold Engineering Development Center (AEDC) and by SAI.

Included in the various ground test programs were candidate materials to provide

external thermal protection for the vehicle shroud, extendible nozzle exit cone (ENEC),

and motorcases. This report contains a compilation (Appendix A) of all the available data

from these test programs. In addition, studies were performed to define the erosive envi-

ronment that will be experienced by the motorcases during flight and to derive analytical

expressions to predict the flight response of some of the primary candidate motorcase

materials.

One group of materials of particular interest for motorcase protection consists

of ethylene/acrylic elastomers with the trade name VAMAC. Several types of VAMAC have been

considered which differ in details of their manufacturing processes and in the relative

amounts of components and additives, such as carbon black. At the time that the analyses

reported herein were performed, the formulation of most interest was desionated VAMAC 15J by

MOAC. The available data for this material were examined and an empirical expression was derived

to predict its erosion response in freestream dust environments. This correlation is

shown to represent the upper bound of the data bases, from both the AEDC and the SAI testfacilities. A correlation of dust erosion data for Kevlar-epoxy, the basic motorcase ma-

terial, also was derived; and Kevlar-epoxy was found to ha - erosion resistance similar

to that of VAMAC 15J. A correlation was obtained for the impact of large pebbles on both

VAMAC and Kevlar-epoxy, and it was concluded that the deepest crater expected in flight

would be less than 0.015-inch deep.*

*This conclusion is based on the available data and will be evaluated further in a systemproof test to be performed in the Holloman rocket sled facility under a separate contract.

9

TI

An evaluation of the expected flight erosion environment was conducted, and

it was found that, depending on the trajectory, the shock layer will reduce motorcaseerosion by 30 to 60 percent and will prevent any particles smaller than 200 to 600p in.diameter from impacting the surface. In light of these analyses, facilities for further

booster ascent flight erosion testing were evaluated, and the following facilities were

recommended:

* AEDC Dust Erosion Tunnel

* Bell Aerospace Rotating Arm

0 SAI Powder Gun

* Sandia Laboratories or Holloman AFB Rocket Sled

r

10 S

SECTION 2.0FACILITIES

Data from three types of erosion tests were evaluated during this program:1) continuous dust erosion tests, 2) pebble impact tests, and 3) tests employing several

sequential salvos of small dust-size particles. The continuous dust erosion tests were

conducted at the Dust Erosion Tunnel (DET) at the Arnold Engineering Development Center

(AEDC) near Tullahoma, Tennessee. Both of the other two types of tests were performed

at the Science Applications, Inc. (SAI) Electro-Optics and Impact Laboratory in Santa Ana,

California. These facilities are described in this section. A full listing of the test

data is given in Appendix A.

2.1 CONTINUOUS DUST EROSION TESTS

2.1.1 Facility Description

The DET is a continuous-flow, arc-heated wind tunnel located in the Engine Test

Facility (ETF). High-pressure air supplied from the von Karman Facility (VKF) high-pres-

sure air system is heated in a 5 MW arc heater. Dust particles are injected upstream of

the nozzle throat and aerodynamically accelerated in a low-expansion-rate hypersonic noz-

zle. A multiple-mount model positioning system with nine stings is enclosed in a test

cabin and injects models into the tunnel flow. An exhaust connection is provided through

a diffuser to the ETF exhaust plant. The tunnel is water-cooled. Schematics of the tun-

nel and model positioning system are shown in Figures 1 and 2 (from Reference 1).

CONTROLROOM

DUST INJECTION SECTION TESTCABINARC & MIXING SECTION

DC POWER

(NOZZLE TH ROAT1

SUBSONICINfj EXHAUST

DIFFUSER ISO LATION.~

C

Figure 1. Schematic view of AEDC Dust Erosion Tunnel.

MODEL POSITIONING SYSTEM TEST CABIN

TUNNEL EXIT SPECIMEN INNOZZLE TEST POSITION WNO

!S E

CABIN-ACCESS DOOR

L SPECIMEN IN STOWED POSITIONINDEXING MECHANISM

Figure 2. DET test cabin and model positioning system.

Controls for the dust dispenser and the model positioning system are located in

a control room along with all recording and inoication equipment necessary to evaluate the

arc heater and tunnel test condition parameters. Instrumentation for recording tunnel and

model parameters consists of 36-channel oscillographs and several strip chart recorders.

Pyrometers and many types of high-speed motion-picture cameras with frame speeds up to

5000 fps are available for model observation. Front surface temperatures of the earlier

shroud specimens were obtained with an infrared pyrometer which responds to temperatures

in the range from 230°F to 8000F. The backfaces of some of the models used in this program

were instrumented with one or more thermocouples. Facilities for pre- and post-test photo-

graphing and weighing of the erosion specimens are provided. Other equipment required for

the conduct of the tests were screens to sieve the particulate.

A variety of equipment has been used to characterize the dust cloud in the DET

test cabin. This equipment includes a laser holographic system, a laser doppler velocim-

eter, impact bars, and cloud bars. The current program relied primarily on prior calibra-

tions of the dust environment. However, supplementary data were obtained with impact bars,

and holographic runs were made at one point during the present tests to provide an accurate

calibration of the facilities. A detailed description of the DET and its calibration is

contained in Reference 1.

12

i. S;,

2.1.2 Test Conditions

Erosion tests for the external protection materials (EPMs) were conducted in

the DET using two different chamber pressures and three different particle sizes. Since

the particles are accelerated by the air flow, this provides six possible impact veloci-

ties, although only four of the combinations were actually used.

A calibration program, described in Reference 2, obtained holographic data on

650-micron and 50-micron (nominal diameter) particles for the 1,000 psi chamber pressure

condition. These data were used in that program to define statistically equivalent clouds

of uniform diameter spherical particles having the same overall particle density and av-

erage values of mass/particle, kinetic energy/particle, and kinetic energy/mass as the

actual clouds. Table 1 summarizes the results of that study. Where possible, statisti-

cally equivalent particle parameters are listed in this report. This required adjusting

the freestream particle concentrations reported in References 3, 4, and 5 because particle

concentration is a derived quantity based on the total mass flow of particles divided by

the particle velocity. Since no holography was done for the 300 psi chamber pressure con-

dition, the particle velocities listed for those tests were obtained with the following

expression:rVAT Eq (1,000 psi)]

V (300 psi) = VNOMINAL (300 psi) 1 VNOM (1,000 psi) (1)

= 2,140 ft/sec

Since no holography was done for the 200-micron nominal diameter particles at

any condition, nominal values of the particle diameter and velocity are listed for those

tests. However, whenever possible, it is important to use the statistically equivalent

velocity rather than the nominal velocity to correlate DET erosion data. If the mass loss

ratio is assumed to be of the form G - k V2, then the value of k derived for 650-micron

particles using the nominal velocities will be 50 percent higher than that derived using

the statistically equivalent velocity.

Because no calibration data for the conditions of the ENEC and shroud nosetip

tests were available, nominal conditions are listed for those tests.

2.1.3 Particles

The particles used for all the DET tests reported herein were produced by crush-

ing 98- to 99-percent pure fused cubic MgO crystals. The resulting particulate then was

washed with alcohol and screened several times to obtain a batch of particles with sizes

concentrated near the desired nominal size. The particles are irregular both in shape

it and in size.

13

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2.1.4 Model Descriptions

All of the flat test specimens were 2-inch diameter discs which were mounted in

wedge-shaped model holders, as illustrated in Figure 3. The specimen retainer surrounding

the test specimen was made of the same materials as the 2-inch disc to avoid edge effects

and to get a one-dimensional mass loss. The backface of the test sample materials of each

test specimen was instrumented with one thermocouple at the center of the disc, as shown

in Figure 4. The model holders support two test specimens, and each model holder is

sting-mounted to one of the nine struts of the model positioning system.

The hemisphere models had a diameter of 3 inches and a nominal thickness of

0.050 inch. The backface of each hemisphere was instrumented with two thermocouples lo-

cated side-by-side near the model stagnation point. Each hemisphere was sting-mounted

to one of the nine struts of the model positioning system.

A. ~

r___ ' ,_______ ! . ~

t -C 8" OVERHEAD CAMERA STRUT -

~CL 8" HOLOGRAPH WINDOW (REF) WINDOW (REF) tH20

NOTE: ALL DIMENSIONS IN INCHES

Figure 3. Wedge model holder and sting support for DET tests.

2.1.5 Tare Data

Tare data obtained in these tests are summarized in Table 2 (from Reference 6).

If it is assumed that tare sample weight change is due primarily to outgassing, contami-nation, and handling, then tare weight change may be only a weak function of material.

The standard deviation of the weight change for all of the samples taken together is

15

0.055 gram. Comparing this value to the weight losses measured for the erosion tests,

it is found that the accuracy for all tests performed at impact angles of 9 degrees or

*greater should be very good. However, the 4-degree impact angle data are generally

questionable.

-~ THERMOCOUPLEJUNCTION

20VAMAC 15Jf" 2.0- - - - BOND

- EPOXY-GLASS

Figure 4. DET model.(.

2.2 PEBBLE IMPACT TESTS

2.2.1 Facility Description

The pebble impact experiments were conducted in the Science Applications, Inc.

(SAI) Electro-Optics and Impact Laboratory located in Santa Ana, California. The launcher

used in this test program is a powder gun consisting of a variable volume powder chamber

to which launch barrels of various sizes can be attached on one end and a 30/06 rifle

action mechanism mounted on the opposite end. A plastic diaphragm separates the powder

chamber and the launch barrel. The operating sequence is to place a sabot holding the

pebble and the diaphragm in the breech of the barrel, secure the powder chamber, place

a custom loaded 30/06 rifle cartridge into the gun, and finally fire the gun with an

electric solenoid.

The primary instrumentation used in the tests is a light screen system for mea-

suring projectile velocity. With this system, time is measured by counting the pulses of

a very accurate electronic clock. Two screens are placed five feet apart to sense the

passing of the projectile. As the projectile passes over the first screen, a signal is

I

Table 2. TARE data.

.2Reference 6: Po 1,000 lb/in

A = 40 sec

= 9 degrees

Weight Chan ge,* Am(g)

Run 5A Run 6AMaterial Name ho = 552 Btu/lb ho = 493 Btu/lb

Ke/VAMAC 0.014 0.005

VAMAC 0.039 -0.023*

Alternate VAMAC 0.105 0.010

Ke/VITON 0.043 -0.035*

VITON 0.039 -0.028*

Ke/TBR 0.008 -0.053*

TBR 0.007 -0.026*

* Negative indicates weight gain.

Reference 4: Run 9

Po = 992 lb/in 2

ho = 507 Btu/lbm

Material Name Angle At Am(deg) (sec) (g)

TBR II 4 40 0.105

TBR II 9 60 0.140

KePVF/.75 PVF 9 60 0.075+0.25 E NOV

p

Avg = 0.025

2.055 480 05IN K;) 168

17

sent to command an electronic device to start counting the pulses. When the projectile

passes the second screen, a signal is sent to stop the pulse counting and to convert the

pulse count number into a velocity reading. The velocity is then displayed on a digitalreadout. To preclude the possibility of a false command due to the shock wave which pre-

A. cedes the projectile, a backup system of paper screens containing conductive wires is

employed to ensure accurate velocity measurement. A schematic of the velocity measuring

systems is shown in Figure 5.

LIGHT SCREENS

Q BAFFLES C

PROJECTILEAND SABOT' SHOCK1HAE

W VE PAPER SCREENS HEATER

EnGEGUNII

Figure 5. SAI pebble test facility and projectile velocity measuring systems.

2.2.2 Pebbles

Spherical pebbles made from Tonalite, a type of granite from a core sample taken

near Cedar City, Utah, were used for most tests on this program, although a few shots were

fired with glass spheres.

2.2.3 Model Description

The samples tested were rectangles, typically 6-inches square, although other

sizes were also used. Some samples were bonded to substrates simulating the motorcase

and interstage skirt structure, while others had no back surface support.

2.3 SALVO DUST EROSION TESTS

The salvo dust erosion tests are performed by SAI in essentially the same manner

as the pebble impact tests except that the salvo tests are conducted inside an evacuated

tube, and the paper screens that provided the pebble test backup velocity data are not

used. A number of small particles (weighed and counted) is placed in the sabot and fired

18

K at the target. The sample is then removed from the apparatus and weighed. This procedure

is typically repeated at least four times for each sample, and each measurement representsa data point. Since the mass loss on a single shot is very small, each test sample has an

identical tare sample used to determine weight change due to other effects, such as out-

gassing and water absorption. The test and tare samples are stored together, placed in

the test vacuum chamber at the same time, and weighed at the same times. The reported

weight losses from each shot actually are the differences between the test sample and the

tare sample weight changes.

F|

19

77 7

fill

20

I

SECTION 3.0

DATA CORRELATION

Both the dust erosion and the pebble impact data were correlated during this

program. A number of tests of different varieties of EPMs have been conducted at the

DET. At the time of this study, the majority of the data were for a formulation de-

signated VAMAC 15J. Therefore, based on these data, an expression to predict the

flight erosion of VAMAC 15J was derived.

A second material that was evaluated in this effort is the Kevlar-epoxy

motorcase material itself, since erosion protection can be provided by simply increasing

the motorcase thickness. This would probably be the least expensive approach, although

it could result in a substantial weight penalty. An erosion correlation for this ma-

terial also was derived from DET data.

During ascent, the materials may encounter debris varying in size from micro-

scopic dust to pebbles nearly an inch in diameter. It has been shown analytically that

the mass fraction of large pebbles is so small that they account for relatively little

of the erosion mass loss. This conclusion does not preclude the possibility that a few

impacts by large pebbles could cause deep craters that would be a threat to the sur-

vival of the vehicle, even though the total mass removed is small due to the small num-

ber of these craters. Therefore, crater depth correlations were derived for both

VAMAC 15J and Kevlar-epoxy based on impact data obtained at SAI with spherical granite

pebbles.

3.1 VAMAC 15J DUST EROSION CORRELATION

Useful correlations of measured erosion data require accurate knowledge of

both the particle impact parameters (particle diameter, impact velocity, and impact

angle) and the target material conditions (surface temperature and internal temperature

distribution). A brief study was performed to evaluate these parameters for the wedge

test models and the DET test conditions used in the subject test programs. The study

considered: 1) the effects of the wedge shock layer on the particle velocity and impact

angle, 2) the possible surface shielding effect of debris from upstream particle impacts,

3) the influence of kinetic energy deposition on the surface heat flux, and 4) the

effects of variations in particle size and freestream concentration on impact velocity.

3.1.1 Shock Layer Effects

A two-dimensional analysis was conducted of particles traveling through the shock

layer of the DET wedge model holder. Various combinations of particle velocity and size

21

were evaluated. Since the change in gas velocity across the wedge shock is relatively

small, the principal effect of the shock layer is to turn the particles; however, this ef-

fect was found to be negligible for particles greater than 10 microns in diameter. Figure

6 shows the computed turning angles experienced by a range of particle sizes traveling

through the shock layer of a 14-degree half-angle sharp wedge.

3.1.2 Debris Shielding

A study of debris shielding on flat plates has resulted in a simple analytic

technique that has been used to define a non-dimensional parameter for evaluating the onset

of shielding effects. Both the analytic technique and the non-dimensional parameter are

described in Appendix B. The analytic technique was used to evaluate one DET run for each

of the two particle sizes used. The results are shown in Figure 7, and it can be seen that

the probability of shielding is negligible in both cases.

3.1.3 Heating

No direct measurements of kinetic energy deposition are available for the mate-

rials tested, and convective heating has not been calibrated for the 300 psi chamber pres-

sure test condition. Fortunately, the models tested in the program described in Reference

4 had thermocouples installed, as shown in Figure 4. The responses of these thermocouples

were used to evaluate both kinetic energy deposition and convective heating.

3.1.3.1 Kinetic Energy Deposition

Kinetic energy deposition was evaluated using data from tests run with 50-micron

particles, since kinetic energy deposition is proportional to ':locity cubed and the 50-

micron particles are traveling approximately 40 percent faster than the 650-micron particles.

The principal analytic tool used in this study was the PDA Ablation Conduction and Erosion

(PACE) code. This code solves the one-dimensional heat conduction equation for multiple

materials, including convection, radiation, independent external and/or internal heat flux,

erosion, ablation, and internal decomposition. For these analyses, constant material prop-

erties were used, and no ablation or decomposition was considered. Material properties

used are listed below:

Thickness Density Conductivity Specific Heat

Material (inch) (lb/ft") (Btu/ft-sec-°R) (Btu/lb-°R)

VAMAC 15J 0.18 81 0.000083 0.40(Reference 3)

Epoxy-glass 0.05 118 0.000069 0.25

22

PARTICLE~14 DIAMETER (M):

5025

C-, -- 12.5

Dn - 6.25

5 13- 3.12

wU P0 =1,000 PSI

wi h 450 BTU/LBC-) 140

z 1.56

12

caEROSION -

wU SAMPLE-j POSITIONzI

<00 0.5 1.0 1.5 2.0DISTANCE FROM SHOCK (INCH)

Figure 6. Shock layer effects in the DET.

0.025-

P0 = 1,000 PSI

ho =450OBTU/LB

0.020- 0 9z2 ~50 t PARTICLES

0UU- 0.015-

co

c0.0100

0.005-650.L PARTICLES__

- EROSION -

SSAMPLEr

0 POSITION0 2 4 6 8

DISTANCE FROM LEADING EDGE (INCH)

Figure 7. Probability of incoming particlecolliding with debris in DET.

23

In Reference 4, it was shown that good agreement with the response of the ther-

mocouples in two models was obtained by assuming a kinetic energy accommodation coefficient

(CKF) of 0.7 sin e, resulting in an energy deposition rate due to particle impacts of:

0-6= 62.4 x 106 I1/2 p V3 sine (2)KE= (32.2) (778) KE p

8.7 x 1 0- 0 p V3 sin 2 e

ppin which p_ and V p are dust density (g/m3 ) and velocity (ft/sec), respectively, and e is

impact angle. In this study all of the models tested with 50-micron particles were ana-

lyzed both with the above kinetic energy deposition expression and with no kinetic energy

deposition. The results are compared to the measured thermocouple responses in Figures 8

through 14. Several conclusions are evident from these figures.

" Predicted and measured temperatures generally agree well,

indicating that the material properties and the convective

heating model are accurate.

* The predictions using Equation 2 appear to match the mea-

sured data somewhat better than the predictions with no

kinetic energy deposition.

" The differences between the two sets of predictions are

too small to provide a firm definition of the kinetic

energy deposition.

* Since no difference at all is observable between the two

sets of predictions for either the 4-degree wedge data

(due to the sine-squared dependence) or the 30-degree

wedge data (due to the short test times), no conclusions

on angular dependence can be drawn.

3.1.3.2 Convective Heating

Convective heating in the DET has been calibrated for the 1,000 psi chamber pres-

sure condition (Reference 1). These data are shown in Figure 15, along with the calculated

kinetic energy heating for two typical test conditions.

Initial calculations for the 300 psi test condition were made using the 1,000 psi

heating modified by the square root of the pressure to reflect the Reynolds number depen-

dence of laminar convection. This substantially underpredicted the observed temperature

histories, and it was found that the best agreement was obtained using:

(300 psi) = 0.91 q (1,000 psi) (3)

24

200 I -

I ______ _DUST

Oz 4- _ OUT

1 6 0 -° ... .- -___P_____ __ REDICTIONS - - -/

"

""TO

40A 4-iI

10

INI

~80C

I-.-I

.J

4010 20 30 40 50 60

TIME (SEC)

200 _ _ _ i __

160 _____________ _____ UST OUT

I ~ ~ C~ HAS NO EFETI

0 1C_I.-

10 20 30 40 50 60

TIME (SEC)

Figure 8. Kinetic energy method comparison: 4-deg angle.

25

S 4

200 1_ _~

N DUST

160 _7------- -'~-_ _ _ _ _

I ~~PREDICTIQIS _____

120,I -

I, . . . . ._ _... . . . .. . ..- . . -. -.. ... . .

4 0-

LU -

0-15 20 25 30 35 40

TIME (SEC)

200 , I

DUST OUT

IN O 4V

160 I I _ _ ___ _--

PREDICTIONSLL. 'KE HAS-NO-EPtCT) -

120CCI

80

LUI

37 42 47 52 57 62TIME (SEC)


26

9* C ~KE0.si0C.U __

N

LUJ

LL 120LUJ

130 1S0 1,10 190 210 1)31-

TIME (SEC)

20DUST OUT_

S20 7__ ____ 01__ __LUE

LU

60 ___ ___

0 ____ ____ ___

130 150 170 100 210 230

TIME (SEC)


27

200

200N r* __ _ _ _ _ _ _ _PREUTCTTr5-T- -

16_ =9 CKE 0.7 sin 0 1

LJ-1... 0- =,- ---,- -- -- ___ ___-_.

Luj 00____ __

40

100 1 !0 120 1I 140 10TIME (SEC)

200 -

I6 Flo- 9__ - - __- CK~ 0.7 sine0 -

I N CKE z=0

I .OUT-120 - -- 1..._0___-_ _-_---- --.--.---- --'-'-__

LJU

. 0

.. 40 . . ...... . . .. . .. . - -. ___ -

0 ..... ._

100 110 120 130 140 ISO

TIME (SEC)

Figurell. Kinetic energy method comparison: 9-deg angle.

28

:<:.. .. . ' '" - -- ,,-- ' '- ' -'-,'M, . . ., . .. . . .. d J '-r -. ... " , -- ",- - -- - - , ,,L .. .- .. ....5.

.-,,

* 4KE 0.7 sin -

LJ

Wi~ 120 -__ ___ ______ ______ ___ __

S80 _

10 20 30 40 50 60TIME (SEC)

0 14' PREDICTION!

160 IN ____ -___ $ .7 sin ___

_~K __ _ _

(9J12

0UU

<U

80

F- 4 -DUST

40 1___1

10 20 30 40 50 GOTIME (SEC)


29

200 ______ ______ -OUT

I IN D~ )__ _ ___-.____- ST

160 6 4 _ _-_ _ __ _

CD ___ __ __

120

Uj A0 NO- ___ _ _ _ ___ _

PLEU _

_ _

152 25 TIME33

2 0 0- _ _ _ -_ _ _ _ _ _ _ _ _ _ _ _ _

D ST OUT

I GO10 - IN

0~

37 42 45257 62TIME (SEC)


30

___________ ___v.---- 30" c HAS NH

L L

,I 1 -- - I

I-- I-. . . .. .

4-

-______- -____ ...

85 !89 :3 197 201 225

TIME (SEC)

200 -I-

, OI ]

#I; -30' P-- -- -' --. . .

CK HAS NO EFFE t '

40 o -IN

185 189 ___Y20 i , '_

TIME (SEC)


31

10P = 1,000 psi

ho0 = 450 Btu/lb

-- CONVECTION (REFERENCE 1)

KINETIC ENERGYVp 2,940 ft/sec

P =1.0 g/ m3

5

P .5 gm 3

0 10 20 30

IMPACT ANGLE (DEG)

Figure 15. Convective heating in DET.

The temperature history shown in Figure 16 for the AEDC Run 7 (TRW Series, Ref-

erence 4) compares a measured thermocouple history to predictions using the above two meth-

ods. The relatively high heating for 300 psi probably is due to turbulence. The tunnel

wall turbulent boundary layer grows to the tunnel centerline at 300 psi, but does not at

1,000 psi. All further analyses of 300 psi tests were done using the above equation for

heating.

AEDC Run 3 (TRW Series) was found to be anomalous. Figure 17 shows that the pre-

dictions significantly underpredict the temperature rise. Reference 7 indicated that some

300 psi runs in the MDAC series also appeared to experience very high heating (these runs

were not reported in the MDAC test report). It was concluded at that time that ice forming

in the airflow measurement venturis caused the facility control electronics to malfunction.

Run 3 has not been included in any of the following correlations.

3.1.4 Particle Velocity

The conclusions described in this section used the statistically equivalent par-

ticle velocities discussed in Section 2.1.

32

-p 0 3P0 psi PRDCT S

"20 - --,~O

___~'1 T_ _

I __7 _ _T-

I- _____ --- 'TIME, SEC_

00010111213

2401O 1

80

100 114 128 142 !56 !7C

TIME, SEC

Figure 17. AEDC run 3 data trace.

33

3.1.5 Correlation

A seven-step procedure was used in the data correlation:

1. Calculate surface temperature histories for all models

using observed mass loss ratios (constant during run)

for each model.

2. Plot mass loss ratio (G) versus predicted surface tem-

perature during erosion.

3. Obtain function f(T) to describe the effect of temper-

ature on mass loss.

4. Plot G/f(T), using observed G and predicted f(T), versus

velocity to obtain velocity dependence.

5. Similarly, plot G/[f(T) • velocity function] versus im-

pact angle to obtain impact angle dependence.

6. Repeat Step 1 using erosion model derived in Steps 2

through 5.

7. Plot predicted G's versus observed G's to evaluate model.

The results of Steps 1 through 3 are shown in Figure 18. Each of the surface

temperature range bars shown represent the range from the lowest to the highest surface

temperature predicted for a single test sample during the erosion period. The two func-

tions shown as dashed lines both were used in attempting to correlate the mass loss data,

and the results are shown in Figure 19. The temperature function f2(T) was selected be-

cause the resultant velocity variation is more credible than that resulting from f1(T).

The squared dependence on velocity was chosen even though it does not fit the 50-micron

particle data well. This was done for several reasons:

* The function selected is an upper bound.

* It will be shown in Section 4.0 that the majority of

the flight erosion for the erosion-critical Tra-

jectory A occurs below 3 kft/sec, in the velocity ranqe

where the squared dependence gives best agreement with

the data.

The poor correlation of the 50-micron data may be due

to some other parameter (such as particle size) that

cannot be varied independently.

34 k

0.6

,1) = 90" +s //0.5 j @DNOM = 650]I

0.4 NOM = 50ti

0.3 -

"-'J f2(T) , "- --

0.2 - a-00

f2(T)

0.1

0II I

0 100 200 300 400

SURFACE TEMPERATURE RANGE (OF)

Figure 18. Influence of surface temperature on erosion. 7901325

0= g

SYMBOL Po (PSI) DNOM(,U)

0 1000 650

0 300 650+ 1000 50

G G

f(T) fl (T) NT) f2 IT)

0.4 - 0.4G V2 GV2

f ~ V2

0.3 0.3 '

4-

0.2 - 0.2 +

0 + 0

0.1 1 1 I 0.1 I I2 4 6 1 2 4 6

Vp (KFT/SEC) VP (KFT/SEC)

7901324

Figure 19. Influence of velocity on erosion.

35

4

The mass loss data then were corrected for both temperature and velocity, and

are plotted against impact angle in Figure 20. It is noted that the correlation is very

poor for the 30-degree data. However, it will be shown in Section 4.0 that this is notcritical, since less than 15 percent of the erosion predicted for Trajectory A occurs

at impact angles above 15 degrees.

15

SYMBOL Po (PSI) DNOM ; S

O 1.000 6500 300 650

+ 1.000 50

100

/0N /

oC / o~

0e 0

01 0 20 .0

IMPACT ANGLEtIDEG)7901319

Figure 20. Influence of impact angle on erosion.

The resultant expression for the erosion of VAMAC 15J is:

G = 1.15 x 10 - 7 V 2 [1 + 2.5 x 10- 5 (T-150) 2 ] f(a) (4)

with a kinetic energy accommodation coefficient (see Equation 2) of:

C KE = 0.7 sine0 (5)

where f(e) is a tabular function shown graphically in Figure 20. Erosion for all of the

DET tests was then calculated using Equations 4 and 5, and the predicted and measured mass

losses were compared in Figure 22. The agreement is actually somewhat better than might

be expected from Figures 20 and 21. The reason for this is that the assumed temperature

dependence tends to limit the erosion; i.e., as erosion increases, the surface temperature

drops, thereby decreasing G.

36

100.0

SYMBOL P. (PSI) DNOM(/)

• 1000 650

10 300 650

+] 10.0

1.0 00 /

+o

. .......0.15 X 10 7V/

1.17 X 10 7V

2f2 (flf)

0 0 '1o TARE

PERFECT CORRELATION

1 ld TARE

0.01 I I I

0.01 0.10 1.00 10.00

MEASURED MASS LOSS (GRAM)7901327

Figure 21. VAMAC 15J erosion data correlation evaluation.

It was found that by multiplying the constant in Equation 4 by 1.15, the resultant

correlation, also shown in Figure 21, represents an upper bound to all DET data. This cor-

relation is selected as the final expression recommended for conservative design predictions:

G = 1.35 x 10-7 V2 [1 + 2.5 x 10-5 (T-150)2] f(e) (6)

3.1.6 Applicability to Salvo Data

Following the development of the above correlation, salvo erosion data were ob-

tained on several VAMAC materials. These data are compared to the predictions of Equation 5

in Figures 22 through 25, and the correlation is seen to be conservative in almost every

case.

3.2 KEVLAR-EPOXY DUST EROSION CORRELATION

The DET data reported in Reference 4 are correlated here as a function of velocity,

impact angle, and particle size. Due to the relatively limited data base it was impossible

to estimate the effect of surface temperature.

The effect of impact angle is shown in Figure 26. These data have been fit mathe-

matically by the straight line:

G = G90 + 0.0353 (e - 9) (7)

37

7 I

1.2

1.35 X 10-7 V 2 f2 (TMfO) /; ),~~ T 200oF./

T 70°F0.8

2I- S

<0

0< t-J•

1650/ GLASS0.4 0 =

200

SYMBOL TEMPERATURE (OF) '1

0 70

0 150U 200

00

0 2000 4000 6000 i 'IMPACT VELOCITY (FT/SEC) 7901326

* gure 22. Comparison of VAMAC 15J salvo test erosion datawith DET correlation (velocity effect).

1.01.35 x 10-7 V2 F2 (T) f (6)

/ ,:)o i

F-

o9G LASS-J O2 V =3000 FT/SEC

0 = 20 °'

1,000 2,000 3,000 4,000

PARTICLE DIAMETER- A7901323 i. h

Figure 23. Comparison of VAMAC 15J salvo test data withDET correlation (particle diameter effect).

38

1.2

1.35 X 10- 7 V2 f 2 (T) f(0)

0.8 f2 (T) = 1.0

MASS LOSS RATIO 165011 GLASSV = 3000 FT/SEC

0.4

AVG OF 12 DATA POINTS

0 1 1

0 100 200 300

TARGET INCIDENCE ANGLE7901328

Figure 24. Comparison of VAMAC 15J salvo test datawith DET correlation (angle effect).

1.2 SAIMO DATA 1 1.35 x 10-O V2 F2 (T) f (0)

V = 3,000 FPS

0= 200 T 2000 F

o T= 70°F T =70°F

I"E T = 2000]F

0.8

W0

I-

-J('3

0.4 0

g0 0

0 1 1 - - I

0 1,000 2,000 3,000 4,000

PARTICLE DIAMETER-u7901322

Figure 25. Comparison of VAMAC 15J salvo test datawith DET correlation (MgO data).

39

... . . . . . ". .- .l- . I T

2 SYMBOL P0 DNOM

(PSI) ( )

0 1000 650

0 300 650

+ 1000 so

0403 0

0

0-0

C 15

0 5 10 15

IMPACT ANGLE, 8 (DEG)

Figure 26. Influence of impact angle on Kevlar-epoxy erosion.

in which G is mass loss ratio, and o is impact angle in degrees. Note that some of the

scatter in Figure 26 is due to the fact that different velocity data are plotted together.

To eliminate the effect of impact angle, the data were then divided by the above

function, evaluated for the appropriate impact angle, and the results are plotted in Figure

27 as a function of velocity. A particle size dependence is suggested by the fact that the

2,140 ft/sec data and the 2,950 ft/sec data (all 6 50V particles) are well fit by a velocity-

squared curve, while the 4,125 ft/sec data (50p particles) not only do not fall on that

curve, but actually show generally lower erosion than the 2,950 ft/sec data. To describe

this data in a simple manner, the velocity-squared curve shown in Figure 27 was fit through

the 6 50p data, and the difference between the value of that function evaluated at 4,125

ft/sec and the average of the 50v data was used to derive the following particle sizefunction:

G - 0.21 + 0.0018 D (8)

65011

in which D is particle diameter in microns. Note that the actual diameters for the two par-

ticle sizes were determined to be 4 38 p and 94p, as discussed in Section 2.1. These latter

values were used to derive Equation 8.

40

3

SYMBOL IMPACT ANGLE2 (DEG)

<0< 0 14

2L<2

00z II

C

1000 2000 3000 4000

VELOCITY, V (FT/SEC)

Figure 27. Influence of velocity on Kevlar-epoxy erosion.

Combining the impact angle, velocity, and particle size functions yields the ex-

pression for the erosion mass loss of Kevlar-epoxy:

G = 0.26 x lO-7 V2 (1 + 0.04 e) (I + 0.0086 D) (9)

Erosion rates for all of the tests used in developing this correlation were then

calculated with this model, and the predicted and measured mass loss ratios are compared

in Figure 28. Equation 9 is seen to correlate the data reasonably well.

3.3 VAMAC 15J AND KEVLAR-EPOXY PEBBLE IMPACT CORRELATION

Pebble impact data for VAMAC 15J and Kevlar-epoxy are presented in References 3

and 5, respectively. These data were obtained using the Science Applications, Inc. (SAI)

28mm smooth-bore powder gun and machined sperhical tonalite granite pebbles.

3.3.1 VAMAC 15J

The majority of the VAMAC pebble data were obtained for VAMAC samples which were

reinforced with Kevlar or graphite fibers in addition to the carbon black contained in

all VAMAC materials. However, since the data indicate that the fibers may actually de-

grade erosion resistance, only the unreinforced VAMAC 15J was considered here. Unfor-

tuantely, the mass losses in the pebble impact expression for this material is derived

partially from the correlation of the DET data for room temperature specimens:

41

G = 1.35 x 10- 7 V2 F(e) (10)

in which f(e) is the graphical function shown earlier in Figure 21.SYMBOL P0 DNOM

(PSI) (F)

0 1000 650

0 300 650

2 3000 650

0 0o_

0

C-

CO0 0

temslosathceter of suhacae:n-iesoaltemxmmcae et

w

o. PERFECTa. CORRELATION

(d) is:

d = G RDsin (11)

$

in which D is pebble diameter, and p and p-are pebble and target densities, respectively.

3.3.2 Kevlar-Epoxy

In contrast to the VAMAC 15J samples, Kevlar-epoxy samples lost significant mass

in the pebble impact tests. Very little data are given in the references for Kevlar-epoxy;

however, there is a large amount of data on Kevlar-phenolic. It was expected that Kevlar-

epoxy and Kevlar-phenolic would have similar erosion properties, and the following data

evaluation shows this is the case. Consequently, the correlation was actually performed

using Kevlar-phenolic data.

42

The impact data are shown in Figure 29 for Kevlar-epoxy and in Figures 30 through

32 for Kevlar-phenolic. To eliminate particle diameter as a parameter, the crater depth

was non-dimensionalized by the particle diameter. The locl failure mechanism associated

with break-through is different from that associated with impact damage to a thick specimen.

Since the actual motorcase is several times thicker than the impact samples, only data for

particles that did not break through the sample are shown.

0.4 0

CORRELATION(EQUATION 9)

Cr 0.3

uJ

0 0.2uJt.U _j

< SYMBOL D INCH)

0 0.380. 0 0.62

00

0 1 2 3

VELOCITY (KFT/SEC)

Figure 29. Kevlar-epoxy 20-degree pebble impact data.

0.4

0 0LSYMBOL W(INCH)

I

0 0.38I0.3 6 0.62]

a 0 CORRELATION

0.2 (EQUATION9)

o. 0.0

0 •0 I 11 2 3

VELOCITY (KFT/SEC) 7901700

Figure 30. Kevlar-phenolic 6-degree pebble impact data.

43

• .- - - . __ i - - - . ... .... " .... . . .. _- - .. ... .. . . 4

7'

0.4 0

S0.3 0

0 - CORRELATION0.2 (EQATIN ~SYMBOL D(INCH)

rr0 0.38CL 0.1 0 0.62

0 10

12 3

VELOCITY (KFT/SEC)

Figure 31. Keviar-phenolic 12-degree pebble impact data.

0.4

uORRELATION

U= 0.3 (EQUATION 9)

Cr 0.0

0.2 SYMBOL WINCH)0 0.3

0: 0 0.62

0

V1 2 3

VELOCITY (KFT/SEC) 7901699

Figure 32. Keviar-phenolic 30-degree pebble impact data.

44

SECTION 4.0

FLIGHT PREDICTIONS

The erosion of VAMAC 15J was predicted for two trajectories (Section 4.1)

and one atmospheric dust profile, using the temperature-dependent erosion model described

in Section 3.1. Erosion was calculated both with and without the influence of the shock

layer on the particles. The shock layer is calculated to reduce erosion by 30 percent on

one trajectory and by 50 percent on the other trajectory. Erosion also was calculated withand without the effect of material temperature in the erosion model. When the temperature

function is set equal to 1.0, the erosion predicted for the two trajectories is reduced by

4 percent and by 30 percent relative to the nominal predictions for the two trajectories.

Pebble impacts for both VAMAC and Kevlar-epoxy were evaluated, and no craters

deeper than 0.010 inch were predicted.

No debris shielding analyses were performed for flight because the debris shield-

ing analysis currently does not have a collision model. The smallest particles in theflight dust profile specified are so numerous that virtually every incoming particle will

collide with one or more of them. Consequently, the limiting analysis performed for the

DET tests, which assumed all equal-sized particles, is not applicable to the flight case.

4.1 ENVIRONMENT

Motorcase erosion calculations were performed for two trajectories, which are

designated as A and B. Trajectory 3 includes the effects of worst-case winds. Figure 33illustrates both trajectories. The dust profile (identical for both trajectories) is

defined in Reference 3.

60.0 TRAJECTORY A 60.0 TRAJECTORY B

50.0- T 50.0ww

U 40.0- U~ 40.0- TIME

.VL IT < LCT

w0 w

10 . I 0.0~

>LL Li

30.0 V :30.0 VELOCITYUJ -0 0 _O

DOW 20.00 3. 40 o 6~ o~oWo20.0 .7 : ....WZ ,U 2W

10.0 0a 10.0 V 0

0.01 0n00.0 10.0 20.0 30.0 40.0 50.0 60.0 0.0 10.0 20.0 30.0 40 .0 50 .0 60 .0

ALTITUDE (KFT) ALTITUDE (KFTI

Figure 33. Design trajectories.

45

4.2 IN-VACUO EROSION

The in-vacuo erosion predictions (i.e., the effects of the shock layer are ig-

nored) are shown in Figures 34 and 35 for the two trajectories. To show the influence of

particle size, the predictions are subdivijed !int particle size ranges that produce

roughly equal erosion increments for Trajectory A. Trajectory A clearly is

the more severe with respect to erosion. The principal reason for this difference is the

difference in the angle-of-attack histories. Because of the angular dependence used in

the erosion model, the predicted erosion rate varies approximately as the square of the

impact angle. Consequently, even though the angle-of-attack (AOA) persists much longer

in Trajectory B, the higher average AOA prior to 40,000 ft altitude in Trajectory A

produces more than twice the total erosion predicted for Trajectory B.

4.3 SHOCK LAYER EFFECTS

An approximate analysis was performed (Reference 8) to estimate the effects of

the shock layer on the trajectories of the impinging dust particles. The analysis was

restricted to the windward meridian and used a tangent-cone procedure (Figure 36) to de-

scribe the shock wave shape. The shock shapes on the three-angle shroud were superimposed,

with the intersection points determined from Mach-line projections. The flowfield in each

region was based on a tangent-wedge calculation, with a pseudo-wedge angle defined by the

tangent-cone shock angle. Two-dimensional trajectories then were computed for the par-

ticles by neglecting crossflow deflection and vehicle roll effects. The particle drag

coefficients were based on the data correlations in Reference 9 for smooth spheres.

This procedure was designed to provide a conservative estimate of the actual

particle erosion, since each approximation tends to underpredict the deflection of the

particles away from the body. A partial exception to this rule is the use of the tangent-

cone shock approximation which overpredicts the shock standoff distance on the windward

meridian (although this is offset to some extent by overpredicting the streamline turning

effects). However, for the trajectory times of most importance; i.e., when the angle-of-

attack is less than 5 degrees, the tangent-cone shock shape approximation is most accurate.

Particle trajectories were computed over the axial region from the end of the

shroud to the end of Stage One for both trajectories. Figure 37 shows typical results

for the two trajectories, and leads to the following observations:

For Trajectory A:

1. Aerodynamic shielding in the shock layer reduces erosion on

the windward meridian from 0.026 inch to 0.017 inch.

46

PARTICLE SIZERANGE IMMI

NO SHOCK 0 TO 0.2

SLAYER

o " 0.2 TO I

w I TO2

F-~ TO 4

/;'i,4 TO 20

00 10.0 20,0 3M. 40.0 50.0 60.0 70,0

ALTITUDE (KFT)

1 2 3 4

VE LOCITY (KFT/SEC)

Figure 34. VAMAC 15J motorcase erosion (Trajectory A).

Cl

q

zCN

UJ

UI

a:

-JPARTICLE SIZE

RANGE(MM)

o0 TO 0.2

42 TO 2

0T0

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

ALTITUDE (KFT)

I I I I I I I1 2 3 4

VELOCITY (KFT/SEC)

Figure 35. VAMAC 15J motorCse erosion (Trajectory B).

47

CN

000 0

LLJ

LU0

LI

Q/)

C-

< 0 )F- a)

0zujF- -

0><<- 0-A 4 L

.1:2: 0 Cj

C~) -J 4-

NOIIVIS:2 IVO

48c

L.-. TRAJECTORY B

0.01 -4-I-AU

-o* SHOCK LAYER

(0.003)

Ci 0

z

o TRAJECTORY A

cc)

LUj 0.03

<-40 IN-VACUO

(0.026)

0.02

SHOCK LAYER(0.017)

0.01

0 20 PARTICLETO 20 TO 2 4 4 DIAM-mm

200i 1mm 2 mm 4mm 20 mm

Figure 37. Influence of shock layer on motorcase erosion.

49

-4

2. Particles smaller than 10001 contribute less than 13 percentof total erosion.

3. Essentially all erosion occurs at velocities less than 3000 ft/sec.

For Trajectory B:

1. Aerodynamic shielding in the shock layer reduces erosion on

the windward meridian from 0.009 inch to 0.003 inch.

2. Particles smaller than O000u contribute less than 7 percent

of total erosion.

3. Ninety percent of the erosion occurs at velocities less than

3000 ft/sec.

Thus, the shielding effect produced by aerodynamic deflection of particles in

the shock layer produces a significant reduction in predicted motorcase erosion depth for

both trajectories; although the effect is much greater for Trajectory B because of

its smaller, longer duration angle-of-attack history. Future design analyses should ac-

count for these shock layer effects, although it may be necessary to develop improved

techniques to describe the flowfield and particle interactions over the complex body

shapes of interest. The results also indicate that ground test erosion programs should

concentrate mostly on particles larger than lOOO0 and on impact velocities below 3000

ft/sec.

4.4 WALL TEMPERATURE EFFECTS

The motorcase surface temperature histories predicted for the two trajectories,

including the calculated effects of heating due to particle kinetic energy deposition, are

shown in Figure 38. Erosion histories were calculated both with the temperature dependence

function f2 (T), described earlier in Section 3.1, and with the temperature function set

equal to 1.0 (i.e., no material temperature dependence). The results of those calculations

are compared in Table 3.

4.5 PEBBLE IMPACT PREDICTIONS

The maximum crater depth histories were calculated for both VAMAC 15J and Kevlar-

epoxy using the erosion models described in Section 3.3. Because the angles-of-attack at

the low altitudes where pebbles may be encountered are much larger for Trajectory A

than for Trajectory B, only Trajectory A was evaluated. The results are shown in

Figure 39. Peak crater depths occur at different altitudes for the two materials

due to the different angular dependence functions used. Since f(e) used in the VAMAC 15J

50

correlation is approximately proportional to sin e, the VAMAC 15J crater depth is approxi-

mately proportional to sin 0 squared, while the Kevlar-epoxy crater depth is correlated by

sin e to the first power. This difference in angular dependence may be due partly to the

use of DET data to predict VAMAC 15J crater depths. However, it should be noted that com-

parison of the Kevlar-epoxy data and the VAMAC 15J data from the DET indicates that the

mass loss of Kevlar-epoxy actually is less sensitive to impact angle than is the mass loss

of VAMAC 15J.

The maximum crater depths expected for the trajectory and particle size distri-

butions analyzed are 0.009 inch for VAMAC 15J and 0.013 inch for Kevlar-epoxy. These

craters are not expected to pose a hazard to the vehicle.

51

600 TRAJECTORY B

END EROSION

00

S200

0 1 20 30 40 50 60 70

ALTITUDE (KFT)

12 3 4VELOCITY (KFT/SEC)

600 TRAJECTORY A

o400XwN

njI-NwN

200 END EROSION END EROSION--X(SHOCK LAYER (IN-VACUOSHIMELDING CALCULATION)CALCULATION)

0L L

0 10 20 30 40 50 60 70ALTITUDE (KFT)

1 2 3 4 5VELOCITY (KFTfSEC)

Figure 38. Motorcase surface teripprature histories.

52

Table 3. Effect of temperature on flight erosion predictions.

Shock Surface PredictedTrajectory Layer Temperature Erosion

Effects Function (inch)

IA No 1.0 0.025dINo f 2(T) 0.026

IYes 1.0 0.0165

Yes f 2(T) 0.0173

B No 1.0 0.0063

No f 2(T) 0.0095

Yes 1.0 0.0029Yes f 2(T) 0.0034

15

KEVLAR-PHENOLIC-- VAMAC 15J10

w

C.)

x

00 10 20 30 40 5

ALTITUDE (KFT)

Figure 39. Crater depth history.

53

54

- i iC

SECTION 5.0

RECOMMENDATIONS FOR FUTURE TESTING

A study has been performed to evaluate several existing facilities for use in

performing erosion tests of candidate external thermal protection materials. The evalu-

ation considered such factors as flight simulation capability, performance characteriza-

tion, flexibility of test conditions, and cost. As a result of this study, it is

recommended that material screening tests and relative performance comparison tests be

conducted in the Bell Aerospace Corporation rotating arm facility and in the Dust Erosion

Tunnel (DET) at the Arnold Engineering Development Center (AEDC). Tests to obtain de-

tailed information for development of analytical erosion models should be performed at

the Bell rotating arm facility and at the Science Applications, Inc. (SAI) powder gun

facility. Finally, materials/system performance verification tests should be conducted

using a rocket-powered sled (e.g., at Holloman AFB or at Sandia Laboratories, Albuquerque).

Five basic types of facilities were considered: particle-seeded arc-jets, pow-

der guns, ballistic ranges, rocket sleds, and rotating arms. A summary of facility capa-

bi' -s is shown in Table 4. The relative advantages and limitations of each type of

facility are discussed in the following paragraphs.

5.1 ARC-JETS

Several particle-seeded arc-jets currently are used for reentry erosion testing

including the AEDC High Enthalpy Ablation Test (HEAT) facility, the Avco 10 MW facility,

and the AEDC DET. However, the only such facility that can produce the desired particle

velocities without unacceptably high convective heating (for ascent flight simulation),

is the DET. The DET has the further advantage of being able to provide essentially con-

tinuous flow. Tests at conditions producing very low erosion rates can be conducted suc-

cessfully by extending the test duration until measurable mass losses have been achieved.

The principal disadvantage of the facility (shared by all particle-seeded jets) is that

calibration of the particle environment (particle size, velocity, and distribution) is

very difficult and time consuming. The particles appear to break up during injection, so

that the effective particle size can only be determined accurately by holography. Parti-

cle velocity is proportional to the particle size (since the particles are drag-acceler-

ated by the gas stream), as well as to the gas flow conditions (enthalpy and chamber

pressure). In principle, almost all conditions of interest can be simulated in the DET;

however, in practice it is very difficult to vary any single particle or flow parameter

independently. Consequently, testing has primarily been conducted at only a few cali-

brated conditions.

55

Because of the difficulties associated with calibrating the particle impact con-

ditions and in varying individual test parameters, the DET is not generally satisfactory

for tests supporting the development of analytical erosion models. However, since a large

number of samples can be tested in a single run, DET tests are relatively inexpensive and

the facility is well suited for material screening tests and for obtaining material per-

formance comparisons.

5.2 POWDER GUNS

The mass removed by the impact of a single particle at ascent fliqht condi-

tions is so small that it is generally less than the tare mass change due to handling the

sample. Therefore, with the possible exception of tests with large pebbles, single par-

ticle impact tests are generally impractical for ascent erosion studies. Consequently,

SAI has developed a multiple particle salvo test in which a number of particles are

launched simultaneously. The particles initially are contained in a sabot which is accel-

erated by a powder gun. A typical test sequence consists of impacting the sample with

four (or more) salvos of particles and weighing the sample after each salvo. Each salvo

is considered to be a data point for purposes of computing the approximate test cost

listed in Table 4.

This technique has been found to be reasonably effective and to have the

advantages that particle size and velocity, as well as target temperature, can be varied

independently and measured accurately. The principal disadvantages are: 1) due to the

sharp reduction in mass loss with impact angle, the tare mass change can introduce sub-

stantial errors at low impact angles and velocities, and 2) model temperatures are limited

to the range in which no permanent material degradation occurs.

5.3 BALLISTIC RANGES

Ballistic ranges are widely used for reentry erosion testing for two reasons:

1) no other type of facility can duplicate high performance flight velocity and aerody-

namic heating simultaneously, and 2) no other type of facility can produce hypersonic im-

pacts by snowflakes and water droplets. The principal disadvantages of ballistic ranges

are high cost, short test time, and the difficulty of obtaining accurate in-flight mea-

surements of the mass loss.

Unfortunately, the features that make ballistic ranges attractive for reentry

are of minor importance for ascent flight applications. The principal advantages for

ascent flight testing are that the particle environment can be controlled accurately, and

the impact velocity can be determined accurately. In addition, it often is possible to

recover the models for accurate measurements and examination.

56

Table 4. Multiple particle impact ground simulation facilities.

PARTICLE PARTICLE PARTICLE

APPLICATION FACILITY MDEL SIZE VELOCITY SIZE DENS ITy

(ft/sec) (vm) (gm/.3

)

-AEDC RANGE G- 2.5" Diameter 400 18000 0.2 1 1 0.1 * 2 (average)

Guided Rail Track Flat, Cone or Dust concentrated Increase to 6

SCREENING with Dust Shakers Pyramid in 120 '3 inch cur- possible Sitains. Actual density=30 tims averagedensity.

-AEDC OFT- 2" - 4" 2000 - 5500 0.05 - 2.0 1 - 30

SCREENING Arc-Heated Tunnel Flat, Wedges, Conewith Injected Par-ticles

-HOLLOMAN-

SCREENING Supersonic Sled 14" x 24" Wedge to 4200 Unlimited. "2

Piercing Dust Loaded 7ly 1 - 3Nets 7" Diaeter Cone to 8000 Used to date

SYSTEM VERIFICATION -SANJIA ROCKET SLI-

18" Diameter 0 . 3500 Unlimited TBDOR SCREENING 8" Diameter 6500

*Tests proposed to

simulate flyout pro-file.

SCREENING ND IMPACT -BELL AERO- Typical: 1000 at 1 atm 0.001 - 2.0 Average density low.

THEORY Whirling Am with 8 square inch 3000 at 0.1 atm Dust concentrated in

Out r an o'l I pound maximum single jet.ust or Rain No,zles including holder

IMPACT THEORY -SAI POWDER GUN- 6" Square 500 -5000 Unlimited N/A

Multiple Particle

Salvos

57..

TICL. PAR'ICLE TEST FACIL ITY TEST COST PER COST PERIMlI MATETIALS Ot RAT ION STAIUS FREQUENCY TEST DATA POINT

(ave'age) 800 Feet Operational l-2/Day $2,000 - $2.000 -to 6 490 4.000 4,000

Si 02 (7 Models/Week)

. 30 600 sec Maximum Operational I - 2/Week $5.000 - 1 250-

M90 10 sec Typical 08 - 36 Models/Week) 7,000 350

Al 2 0 3

Sia-month lead time 1/week $40.000 500

2 Y for test program $S5,000with dust nets

000 to 2/ek$15,000 -1.0

ANY 3,000 feet Dust nets now 2/Week 20,000 $.000

$3,000

density low. Rain and Hours Operationalenftrated in Dust Cost for tests up to Cost for tests up to

jet. st environment 4-5Day500 ft/seccalibration required 2,500 5t/se $00 it/25

200 200

t S ANY Operational 25Shots/Day 20 200-$IS

5.4 ROCKET SLEDS

From a facilities comparison standpoint, rocket sleds essentially are very large

ballistic ranges. In comparison to ballistic ranges, however, cost per model is reduced

in most cases because the sleds are large enough to mount many models. Test times sub-

stantially longer than those achieved in ballistic ranges are achieved by using longer

particle fields, although the high acceleration and deceleration of the sled typically

cause large velocity changes during the period of erosion. This fact can be an advantage

in designing a system verification test, although it can complicate the use of the data

for erosion model development.

To date, most rocket sled dust tests have employed dust nets. These are finenylon nets with particles bonded to them. However, in a recent test program, shakers were

developed which are mounted over the track to provide a uniform free-falling dust environ-

ment to provide improved simulation of flight conditions.

5.5 ROTATING ARMS

A rotating arm facility consists of a long counterbalanced arm that can be ro-

tated to achieve high tip speeds. Rotating arms typically operate in sub-atmospheric

chambers to reduce air drag on the arm. Such facilities at both Bell Aerospace Corporation

and Sandia Laboratories have been investigated; however, only the Bell facility appears

capable of duplicating an ascent flight environment. The Bell facility is designed

for model speeds up to 3,000 ft/sec, although in its most commonly used configuration; only

2,500 ft/sec can be achieved. Provisions for both rain and dust erosion exist; however,

tests to date have been primarily rain erosion, and the dust dispensing system is unsophis-

ticated and not well calibrated. The dust is introduced into a near-sonic airstream by a

metering unit and injected down and into the path of the model. The dust velocity relative

to the model is the vector sum of the dust and model velocities. This will have a very

minor effect on impact velocity (typically 3 percent) but will affect model holder design.

The most commonly used model holder mounts two 2-inch square flat models on

either side of a wedge with a horizontal metal leading edge. This holder design has the

disadvantage that particle impact angle is strongly affected by particle injection veloc-

ity, as shown in Figure 40. This is a serious disadvantage because particle injection

velocity is not only difficult to measure accurately, but is also a function of particle

size and type. To avoid this problem, a new model holder with a vertical leading edge

should be designed. As shown in Figure 40, impact angle is almost independent of particle

injection velocity with this holder design except at very high particle velocities. The

models are clamped to the holder with metal strips. Mass loss of these strips can provide

a mass loss reference for each model.

59

-. . . - .. . " "

*

I

APPARATUS MODEL HOLDERS SYMBOL

DUST

MODEL VELOCITY = 2500 FT/SEC .

MODEL

INCIDENCEANGLE (DEG)

1515

-,,15

10 10 '|I

S0-0,, 200 35

CC

PARTICLE VERTICAL VELOCITY (FT/SEC) .

Figure 40. Particle impact parameters in Bell rotating arm facility.

60

This facility can provide very long run times and has the potential of dupli-

cating the flight velocities and particle size regime with accurately deter-

mined impact velocities. Due to the low absolute velocity of the particles in this

facility, they can be trapped edsily to measure dispersion patterns and flow rates and to

evaluate particle break-up. In addition, the cost per model may be lower than at any of

the other facilities. This facility has two disadvantages: 1) to achieve this capability,

a calibration program is required to characterize the dust field; and 2) its velocity re-

gime is only of limited interest to the reentry missile community. However, the velocity

regime may be applicable to erosion tests of many tactical missile materials. Although

it is ideal for motorcase material testing, it cannot simulate the peak erosion conditions

on the shroud.

5.6 FACILITY RECOMMENDATIONS

Based on the evaluations summarized in the preceding section, recommendations

have been made for the selection of erosion test facilities for developing and character-

izing materials for external thermal protection of a missile system during ascent

flight. The selections reflect the different types of test objectives and simula-

tion requirements such as: 1) screening and evaluation of materials for different vehicle

locations, and 2) establishing data bases for developing analytical erosion models. The

recommendations are listed in Table 5 and are discussed briefly in the following paragraphs.

Table 5. Erosion facilities recommendations.

APPLICATION MATERIAL VARIABLE RANGE RECOMMENDED FACILITYCATEGORY

SCREENING MOTORCASE MATERIAL -- BELL ROTATING ARMSHROUDCOMPOSITE MATERIAL DET

SHROUDMETALLIC MATERIAL DET

IMPACT VELOCITY 0 - 2500 fps BELL ROTATING ARMTHEORY ANDTERIND AIMPACT ANGLE 0 - 90 degEROSION ALLMODEL PARTICLE SIZE 0 - 2.0 mmDEVELOPMENT PARTICLE MATERIAL --

VELOCITY 2500 - 5000 fps SAI POWDER GUNALL PARTICLE SIZE -2.0 mm

TARGET TEMPERATURE ROOM TEMP

SHROUD COUPLED HEATING ANDMETALLIC CONTINUOUS EROSION -- DET

SYSTEM PROGRAMMED VELOCITY,VERIFICATION PARTICLE SIZE AND

IMPACT ANGLE HISTORY -- ROCKET SLED

- -1

The Bell Aerospace rotating arm facility potentially offers a unique erosion

capability for the motorcase ascent environment at a very low cost per sample. It is

recommended that a pilot program be initiated to calibrate this facility and to obtain

preliminary erosion data. Following this program, the Bell facility should be used as

the primary facility for screening motorcase materials and for the impact theory and

erosion model development tests that fall within its range of capabilities. The SAI

powder gun should be used as an alternate facility for this latter purpose and for other

impact theory and erosion model development tests, particularly those requiring higher

impact velocities. The DET is recommended for materials screening tests and for all

tests of shroud metallic and composite materials. Rocket sleds are best suited for sys-

tem and materials performance verification tests.

Finally, it is recognized that many other facilities are available for per-

forming material erosion tests. The present study was limited in scope and therefore

considered only those facilities believed to be of most interest for ascent flight

erosion problems. Consideration of other test facilities, along with a more detailed

examination of the facilities evaluated herein, can be accomplished at a later date

if warranted by subsequent design studies and system performance analyses.

5.7 RECOMMENDATIONS FOR FUTURE TESTING

The following recommendations are made concerning erosion testing of MX motor-

case insulation materials:

* More data should be obtained at velocities below 2,500 ft/sec.

If these data are obtained in the DET, the particle cloud should

be surveyed using holography.

* No data should be obtained at impact angles in excess of 20 degrees.

* DET models with wedge angles greater than 9 degrees should not be

pre-heated. Higher dust concentrations should be used (since debris

shielding has been found not to be a problem) to allow shorter test

times and, thereby, lower surface temperatures.

62

REFERENCES

1. Lewis, H. F., et al., "Description and Calibration Results of the AEDC Dust

Erosion Tunnel," AEDC-TR-73-74, May 1973.

2. Lewis, H. F., "DNA MX Material Evaluation Test," AEDC-TSR-78-P35, 20 September

1978.

3. Spangler, P. S., et al., "Advanced Booster Propulsion System Hardening Program

Final Draft Report,"MDAC. Unpublished.

4. Zimmerman, A. W. and J. W. Nienberg, "Results of Dust Erosion Tests for MX

Validation," TRW Vulnerability and Hardness Laboratory, 79.4735.9-02, January

1979.

5. Kong, S. J., "Interim Technical Report on Ranking of Shroud Alternate Materials,"

MDAC. Unpublished.

6. Spangler, P. S. (MDAC), personal communication with D. H. Smith (PDA),

13 February 1979.

7. Johnson, G. P. (MDAC), personal communication with D. H. Smith (PDA).

8. Dunn, J. E. (PDA), letter to Capt. A. T. Hopkins (DNA), 20 September 1979.

9. Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, New York, 1960.

10. Johnson, G. P., "DET/Track G Test Summary," Advanced Missile Flyout Survivability

Programs Review," SAMSO/NAFB, 13-14 June 1979.

11. Spangler, P. S., "Advanced Booster Hardening Technology Program Fourth Monthly

Progress Letter," DNAO01-79-C-0135, June 1979.

12. "Advanced Booster Hardening Technology Program - 4ardcopy of Viewfoils," MDAC,

Contract DAO01-77-C-0135, 16 October 1979.

63

I

,a

.a t

64r

r 64

APPENDIX A

DATA

65

i'I

APPENDIX A

DATA

Erosion data for materials for four sections of an advanced missile vehiclewere gathered. These sections are:

1. Extendible Nozzle Exit Cone (ENEC).

2. Motorcase.

3. Shroud.

4. Shroud nosetip.

To simplify cataloguing the many materials considered, the numbering system used by MDAC

in Reference 3 has been adopted. The materials are identified by a four-digit number:

Digit Meaning

I Material Application:

I. ENEC

2. Motorcase

3. Shroud

4. Shroud nosetip

2 Base Material Number

3, 4 Material Variation Number

The material descriptions and data from the DET and pebble impact tests are given

in Sections Al through A4 for the four sections of the vehicle considered. The salvo par-

ticle impact data for all materials are given in Section A5.

66

A-I. ENEC MATERIALS

Two types of ENEC materials were tested: metals and carbon-carbons. The metal

samples were all NblOHf, with the following coatings:

Sample Coating

Ml None

M2 HfO2

M3 Silver-moly enriched silicide

M4 Aluminide

M5 Hafnium-modified silicide

The carbon-carbon materials were provided by Aerojet Solid Propulsion Company and

the specimens were machined by MDAC.

DET test data for the ENEC materials are listed in the following tables. Sample

thickness changes during testing are listed for the metal models, while the more conven-

tional mass losses and mass loss ratios are listed for the carbon-carbon models.

67

LC C LO C) LO LO LO LO C C3 C C LO LO CM C) C CLA CD LA " C) CMj r- CMi m LO C) m w) C M .- CiC Ln

LA -- - C C C ) CM C1 CM CM cl) CM 1: C C.- c.-

LU LA C c CMC C CMj 40 ko CD C C CMj 00 a) a)CD

4J L9 CM k9 Oi- O) a a C ) a) 0 A k9 a C a - r- 19 LALA ~ LA LA LA 'r - - LA LA :: r -j LA r LA z~ * 0

f- WD - a) a) LA LA' %0 (D M 00Ca) C C~jM M

44 L LA LA t.0 to LA LA ko LA LA LA LA CD C C C C C C C

ID D -- p - --I' CD LA- In____o

LA CCAD A _

C ) C) LAo

~0 _ _ _ __O_

4-

L U C _ _ _ _ _

- 0 C) ----- No.-

o - A

2 , -i Cn - _ D__ -40-IIa) a)t____CD I ~ CCL 0ID

Co j _ _ _ __ _ _ _ _

~~~~-~~ bA-______-_ _ _ _ _ _ _ _ ________

- I -Q.

w I)-o _ _1 _ _ _ _ _ _

ujj

0- -. )- -i

-J:Ln Q)

DC - ____ ___ _ __ ____

I LA6A

06L

(D a, CIJ r-. .K- - aC'. c'j m CJ . - C M C CM

%D0 L. n N an m~ m an m anC3 - or- 00.- r-. tD - men Lr) -

an .- . a CM CM - 4 40 41

-. m mm) m C)3 an C) C)

zr a n I n 'I*-0- .~

-- N. n r-. an * CD -co

.0 anLo -ca

(0

-

an C) C

*0

CI -- p

oo

fa C)

CU.

C6

A-2. MOTORCASE 'ATERIALS

Materials designed to protect the motorcase, as well as the Kevlar-epoxy

motorcase material itself, are described in Tables A-3 through A-7. One series of DET

tests evaluated VAMAC 25 models with gaps and holes. Figure A-l shows the model geome-

tries. Some pebble impact test models employed 2024 T-6 aluminum isogrid substrates.

The isogrid panel was machined from a plate, resulting in a 0.038-inch thick skin stif-

fened by 0.5-inch deep by 0.064-inch thick ribs in a pattern of equilateral triangles,

all having leg lengths of 3.5 inches.

Tables A-8 and A-9 list the DET test data, and Tables A-10 and A-lb list pebble

impact data for the motorcase materials.

71

-D(C) -x

cc cc

C, C, CCC

EC X: -.-. C

C-:>(4C>

-x~~~~~ ~i -C-r- Z z :

C,, c) C: )C ,C, C , 0 C

- c - - -CD D- -- - - - - -

err, C)

CD Li C) M < CD ML)iZC)CD C

LiC CD (0C C- Lo cl to to Li' zr C)

C) C) ~ i CCcc C)

7~~~~C C)~7 C - - 7a c

-4-4 -C CC)

COli V C 0'o m4 .jD -2 ! L2 4

C C)C) -72

2q

N C)Ln

LLULUJ cJ N

- riIC

LnU

V)

ra LW C NJ)

Lo LA

C)

uj V)

=3- -Ux N-i N- <-

C)

aC)

o) o Lo LA

M 4-3:~ C D

<) U- ) lV)<[ LA J

< =.

<LU

-O -n U L"

CC

Ln LUJ

C)

.D C > LO CD NO-OC

F - LC

CD0 LA C A A

NJi m LUi

CD~ LAix L.) LU

cc CD -: LU2

N -i

LU L - LA LL

r 2 C' LA o

ii

o cr . ~

73J ~ LU~

Table A-3. VAMAC materials - (Continued).

Materials tested in DET.

REFERENCE OTHER COMMENTSNUMBER DESIGNATIONS

2129 VAMAC 17 HEAVY DAMAGE

2130 VAMAC 28C 34.7 VOLUME PERCENT T5R

2131 VAMAC 28D 34.7 VOLUME PERCENT LCI1O

2132 VAMAC 18217-32LC LOW CARBON

2133 15 PERCENT VAMACSPONGE

2134 25 PERCENT VAMACSPONGE

2135 VAMAC 25HERCULES

2136 VAMAC 32LC 100 PARTS VAMAC, 20 PARTSCARBON, 4 PARTS ADDITIVES

2137 MM2 MM2 - VAMAC - 151A

2138 MM3 MM3 - VAMAC - 151B

2139 MM4 MM4 - VAMAC - 151B

2140 MMl HERCULES KEVLAR MMI -

VAMAC - 151A

7j

74

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75

Table A-4. Viton materials - (Continued).

MATERIALS TESTED IN DET MARCH 1979

REFERENCE OTHER COMMENTSNUMBER DESIGNATION

2214 100 VITON + 15 XC-72 (BY WEIGHT)

2215 100 VITON + 30 XC-72 (BY WEIGHT)

MATERIALS TESTED IN DET DECEMBER 1978

2216 34.7 VOLUME PERCENT TBR

2217 VITON 28P 34.7 VOLUME PERCENT LCI1O

2218 VITON MOSITES

PEBBLE IMPACT TEST MATERIALS FEB - APR 1979

2219 WHITE VITON

76

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Table A-5. Tungsten-bearing resin (TDR) materials (Continued).

Materials tested in DET.


2313 TPR 3 (504N-54) HITCO ADVANCED EPS MATERIAL

2314 TBR 3 (504N-55)

2315 TBR 3 (504N-56) I2316 TBR 3 (504N-57)

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79

Table A-6. Other materials -(Continued).

MATERIALS TESTED IN DET


2002 KEVLAR-EPOXY STAGE 3 MOTORCASE MATERIALMOTORCAS E

2402 NBR 68

2403 NBR 69

2404 NBR-19709-6A (60/40)

2405 NBR-19709-6B (75/25)

2406 NBR-19707-7 020 VINYL

2501 KPN ROCKETDYNE

2502 HERCULES KEVLAR 49 FIBERS PERPENDICULARTO FLOW

2503 HERCULES DOME LARGE STRIPWRAP I

2504 AEROJET INNER INNER PLY HELICAL WRAP

2505 AEROJET OUTER OUTER PLYr

2506 ROCKETOYNE

2507 MM5 MM5-ROYACRIL 9,30 USCM 252

2508 HERCULES KEVLAR

2509 ROYACRIL 25 ROYACRIL z25 19709-13

2510 EPDM 1 EPOM NECP-19709-9A (80/20)

2511 EPOM 2 EPDM-19709-2B

PEBBLE IMPACT TEST MATERIALS

2132 LOW CARBON LOADINGVAMAC

2133 VAMAC SILICA CARBON REPLACED BY 95 PARTSCABOSIL MS-7-4 PER 100 PARTSV AMA C

30

Table A-7. Material constituents.

REFERENCE DESCRIPTION SOURCENUMBER

4.01 NBR B. F. Goodrich Aerospace and Defense Products(Nitrile butadiene 500 South Main Streetrubber) Akron, Ohio 44318

per Air Force Specification 67A60754

4.02 Viton B DuPont Company(Ethylene acrylic Elastomer Chemical Departmentelastomer) Wilmington, Delaware 19898

4.03 Viton B-50 Same as Viton B

4.04 VAMAC B-124 Same as Viton B

4.05 VAMAC VMX 5067 Same as Viton B

4.06 MT-NS Carbon black R. T. Vanderbilt Company30 Winfield StreetEast Norwalk, Connecticut 06855

4.07 SAF Carbon black Cabot Corporation(Vulcan 9) Carbon Black Division

Boston, Massachusetts 02110

4.08 SRF Carbon black Same as SAF Carbon black(Sterling S-1)

4.09 Diak #1 Same as Viton B

4.10 DPG Same as Viton B(Diphenylquanidine)

4.11 MDA Same as Viton B(Methyl dianiline)

4.12 MgO (Magolite D) C. P. Hall Company444 Alaska AvenueTorrance, California 90503

4.13 Kevlar-epoxy motorcase Hercules Incorporatedsegments Systems Group

Post Office Box 98

Magna, Utah 84044

4.14 Graphite-epoxy McDonnell Douglas Astronautics Company5301 Bolsa AvenueHuntington Beach, California 92647

4.16 Special carbon Celanese ResearchLCIO, LC20, LC37 Post Office Box 1000

Summit, New Jersey 07901

81

Table A-7. Material constituents -(Continued).

REFERENCE DESCRIPTION SOURCENUMB ER

4.17 Carbon Fiber "High Modulus Modmor MorganReinforcing Carbon, Morganite Modmore, Ltd.Type IV" Buttersea Church, London, England

4.18 Graphite fiber KGF 200, Kureha Carbon FiberCF-01 Kureha Chemical Industry Company, Ltd.

Tokyo, Japan

4.19 Kevlar 49 CS 800 finish Fiberglass Reinforcements, Inc.14530 South AnsonSanta Fe Springs, California 90670

4.20 Chemlock C-328 bond Hughson ChemicalsDivision of Lord CorporationErie, Pennsylvania

4.21 Bostik 1142 adhesive Bostik DivisionUSM CorporationBoston StreetMiddleton, Maine

4.22 Bostik 1107P primer Same as Bostik 1142

4.23 PVF (Polyvinyl formal)--

4.24 EpNor (Epoxy noralac)--

4.25 DOTG--

(diorthotolylguanidine)

4.26 ISAF Carbon black

4.27 FEF Carbon black--

(ASTM designation N550)

82

MODEL WITH STRAIGHT GAP

F LOWDIRECTION

0.14 VAMAC 25[ !///./A. . . T7_z (TYPICAL)

0.05, 0.15

MODEL WITH ANULAR GAP

0.125

MODEL WITH HOLE

Figure A-1. DET models with gaps and holes.

83

a,. * - ..... .. . ... .... *~ 'L . .. ... ... ..

N

Table A-8. DET notes.

1 - QUESTIONABLE - TARE SAMPLES IN RUN 3 CHARRED AND LOST SUBSTANTIAL MASS IN

20 SECONDS.

2 - QUESTIONABLE - HIGH MASS LOSS.

3 - QUESTIONABLE - MASS LOST DURING CLEAR AIR TIME (LAYERS PEELED OFF BY

SHEAR/AEROHEATING).

4 - QUESTIONABLE - FRONT EDGE OF RETAINER MATERIAL PEELED UP SO AS TO SHIELD SAMPLE.

5 - SAMPLE DIAMETER QUESTIONABLE DUE TO EROSION/THERMAL DEGRADATION AROUND EDGE OF

2-INCH DISC.

6 - QUESTIONABLE - HIGH MASS LOSS AND ERODED THROUGH.

7 - SPECIMEN WAS A TRAPEZOID RATHER THAN A 2-INCH DISC SURROUNDED BY A TRAPEZOIDAL

RETAINER. G VALUES AY BE HIGH DUE TO EDGE EFFECTS.

8 - PRE-DAMAGED SPECIMEN.

9 - QUESTIONABLE - RESULTS INCONSISTENT WITH OTHER RESULTS FOR RUN.

10 - SINGLE LAYER LOST DURING CLEAR AIR TIME.

11 - QUESTIONABLE - LAYERS BEGAN PEELING OFF BEFORE MODEL WAS ON CENTERLINE.

12 - MASS LOSS CALCULATED FOR 2.00-DIAMETER SPECIMEN.

13 - NO HOLOGRAPHIC CALIBRATION FOR THIS CONDITION. NOMINAL PARTICLE SITE AND PARTICLE

VELOCITY CALCULATED BY AEDC LISTED.

14 - EROSION FOR ALL MODELS ON THIS RUN APPROXIMATELY HALF THAT SEEN ON OTHER RUNS.

84

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A-3. SHROUD MATERIALS

Candidate shroud materials including titanium are described in Tables A-12and A-13. Tables A-14 and A-15 list the DET test data, while Tables A-16 and A-17

list the pebble impact data.

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117

Table A-14. DET test notes.

1 - QUESTIONABLE - TARE SAMPLES IN RUN 3 CHARRED AND LOST SUBSTANTIAL MASS IN

20 SECONDS.

2 - QUESTIONABLE - HIGH MASS LOSS.

3 - QUESTIONABLE - MASS LOST DURING CLEAR AIR TIME (LAYERS PEELED OFF BY

SHEAR/AEROHEATING).

4 - QUESTIONABLE - FRONT EDGE OF RETAINER MATERIAL PEELED UP SO AS TO SHIELD

SAMPLE.

5 - SAMPLE DIAMETER QUESTIONABLE DUE TO EROSION/THERMAL DEGRADATION AROUND EDGE

OF 2-INCH DISC.

6 - QUESTIONABLE - HIGH MASS LOSS AND ERODED THROUGH.

7 - SPECIMEN WAS A TRAPEZOID RATHER THAN A 2-INCH DISC SURROUNDED BY A TRAPEZOIDAL

RETAINER. G VALUES MAY BE HIGH DUE TO EDGE EFFECTS.

8 - PRE-DAMAGED SPECIMEN.

9 - QUESTIONABLE - RESULTS INCONSISTENT WITH OTHER RESULTS FOR RUN.

10 - SINGLE LAYER LOST DURING CLEAR AIR CIME.

11 - QUESTIONABLE - LAYERS BEGAN PEELING OFF BEFORE MODEL WAS ON CENTERLINE.

12 - MASS LOSS CALCULATED FOR 2.00-DIAMETER SPECIMEN.

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136

A-4. SHROUD NOSETIP MATERIAL

Several three-inch diameter, 0.05-inch thick metal nosetips were tested in the

DET. The nosetips were made of stainless steel. Inconel, or titanium. Most of the nose-

tips experienced melt-through at the stagnation point before the end of the test. The

data are summarized in Table A-18.

137

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A-5. SALVO PARTICLE DATA

A large body of data was obtained on VAMAC 25 for varying surface temperature,

particle material and size, and impact velocity and angle. In addition, screening data,

all at the same set of conditions, were obtained for 25 other materials. These data are

all listed in Table A-19. Material samples were all provided by McDonnell Douglas

Astronautics Company, and information regarding the materials tested may be obtained from

that source.

139

Table A-19. Salvo particle data.

Particle

Run No. Material Type Size T Angle Velocity G/-

790612-09 Vamac 25 MgO 2.0 RT 20 3075 .12-10 3000 .20-11 3000 .21

-12 3075 .15-13 3000 .32 .216/.062-14 3075 .23-15 3000 .18-16 3000 .26

-17 3000 .27790611-01 3.0 2770 .06

-02 2950 .10-03 2950 .20-04 2950 .20-05 2950 .06 183/.094-06 2950 .12 3

-07 2950 .29-08 2820 .28-09 2820 .21-10 3075 .31

790530-16 Glass 1.65 2500 .062700 .092080 .03

790604-01 2000 .03-03 1900 .16-04 1950 .18 .109/.064

790605-03 2500 .17-04 1800 .08

-06 2220 .11

790606-05 2700 .245-06 2800 .487-07 3010 .381-08 3075 .479 .441/.179

-09 3010 .531

790607-01 3200 .22-02 3400 .742

790530-01 4370 .46-05 4160 .29-06 4510 .32-09 4350 .42 .473/.150-10 4100 .39-11 4670 .67-13 4450 .54-14 4180 .69

140

Table A-19. Salvo particle data - (Continued).

Particle'

un N. Mt er-ll Type Size T Angle Velocity G

79061 3-C0 Vamat W'' Glass 1.65 RT 20 3050 .34-02 3000 .30

-03 3000 .33-04 3000 .26 329/.052-06 J 3000 .42

-07 3050 .27-08 3000 .36-09 3000 .35

790524-05 0.325 4360 .5790706-01 1.65 9 2825 .04

-02 3300 .03-03 3000 .08-05 3200 .06-06 3200 .06-07 3200 .04-08 3200 .07 .058/.018-09 3200 .06

-10 3100 .07-12 3100 .09-14 3200 .05-15 3375 .04

790705-01 MgO 0.65 2180 .14-02 2940 .22-03 2700 .16-04 2800 .21-05 2575 .19-06 2700 .19 .186/.025-07 2700 .20-08 2600 .21-09 2250 .16-10 2450 .18-11 2500 .19

790716-02 200 20 2800 .40790716-01 Glass 1.65 2800 .67790713-04 MgO 0.65 3200 .4179071 3-03 Glass 1.65 2800 .4379071 3-01 2900 .9279071 3-02 150 2900 .49790619-09 RT 4925 .83

-10 5000 .63 745/.087-11 4900 .79 4-12 4900 .73

790618-01 0.325 3000 .26-02 3050 .12-03 3050 .17-04 3000 .12-05 3000 .12 159/.052-06 2850 .19-07 3000 .18-08 2500 .11

141---- . -- --- -

I{-.

Table A-19. Salvo particle data -(Continued).

Particle

Run No. Material Type Size T Angle Velocity G /

790618-09 Vamac 25 Glass 1.65 RT 20 4500 .28-10 I4925 .33j-11 5100 .76-12 I5200 .72 .639/.232-13 5500 .75)

79061 9-01 5400 .77-02 -5000 .86

790614-12 0.50 3050 .19~-14 3000 .27 .227/.04

79061 5-02 1 13050 .22~790612-04 MgO 0.65 3000 .20)

-05 I 3000 .191K-06 I3000 .18) .188/.008

-07 3000 .191-08 V 13075 .18)

790605-09 Glass 1.65 1600 .03-10 1700 .01-12 11600 .02

790606-02 V 11100 .06790830-02 K/EA9332-1 MgO 0.65 400 3000 2.267790830-01 K/LlOO-1 I ]3000 .875790829-02 N0WEX 438EP 3000 2.215790829-01 KEVLAR/CIBA V 2440 .736

11

142

1 .4


All at 200, RT, 1.0 mm Glass

Run Number Material Velocity C G c

0790815-07 T300, Lol, Item 4 3000 .726-08 2980 .696-09 2960 .887 .792 .127-10 2980 .632-11 2980 .964-12 2980 .844

0790815-01 T300, Hil, Item 4 2980 .642-02 2980 .677-03 2980 .738-04 2980 .669 .732 .105-05 2980 .931-06 2980 .735

0790814-04 R-2051AI, Item 3 2980 .374-05 3080 .529-06 3000 .906-07 2850 .927-08 2960 .892-09 3290 .724 .771 280-10 3200 1.118 .-11 3200 .305-12 3200 .659

079081 3-01 329K, Lol, Item 2 2565 .071-02 2760 .082-03 3240 .054-04 3079 .464-05 2980 .214

0790814-01 2980 .288 .426 .217-02 2950 .775-03 2900 .389

0790810-01 329K, Hi2, Item 2 3015 .411-02 3030 .298-03 3105 .140-04 3030 .360-05 3000 .596-06 3030 .739

0790809-01 Kevlar 353, Hil 3030 .526-02 | 3030 .289-03I 3100 .640 .488 .128-04 3015 .465-05 3030 .521

0790809-06 Kevlar 353, Lol 3030 .238-07 I 3225 .492 490 .231-08 3050 .796 4-09 3030 .435

0790716-04 P1 700 PS 3000 .20-05 | 2800 .21-06I 3125 .15 .260 .114-07 3200 .44-08 2825 .30

143



Run Number Material Velocity G G

0790711-01 KE PVF .75 PVF + .25 EP .312-02 3300 .487-03 .659-04 3100 .770-05 3200 .721-06 3200 .680-07 ---- 1.006 .821 .111

0790712-01 3200 .850-02 ---- .903-03 3100 .820

0790703-12 KE PVF .75 PVF + .25 EP 3300 .668-13 Composite 3300 .956 /-14 1 3400 .513-15 3400 1.220

0790703-08 Kevlar Phenolic Composite 3300 362-09 I 3300 :587 (o)i-10 3300 815-11 3300 1.022

0790629-17 KETBR Composite 3200 .522-18 I 3200 1 211 >1

0790702-01 1 3200 1.0160790629-14 KE/EA 9323 3000 .418

-15 3400 .394-16 3225 .625

0790703-16 3400 .7500790803-03 3070 .816

-04 3240 1.327-05 3370 .966 .916 .222

-06 3090 .722 I-07 3020 .912

0790629-07 KE/ADX 3130 3200 .185-08 ---- .139-09 3200 .353-10 3200 .544

0790806-01 3125 .419-02 3075 .610 .701 .269-03 3000 1.197-04 3150 .745-05 3050 .688

0790629-01 TBR - Carbon Filled 3225 .403-02 3100 .309-03 3200 .457 .-04 3200 .623 .424 .128-05 3200 .485-06 3100 .268

0790628-10 TBR - Unfilled 2700 .300-11 ± 3000 .430-121 3200 .418

144

Table A-19 Salvo particle data - (Continued).



0790628-13 TBR - Unfilled 3000 .601-14 3200 .670-15 3300 .384 .527 .136-16 3375 .378-17 3010 .600

0790628-03 .75 PVF + .25 EP Res. 3200 .117-04 3000 .148-05 3250 .131-06 3250 .198-07 3350 .229-08 3250 .371 263 .076

-09 3100 .2540790703-04 CIBA Epoxy 3300 .338

-05 3300 .398-06 3300 .720-07 3300 .777

0790801 -01 3320 1 .041-02 3070 .244 .694 .268-03 3170 .589-04 3170 .646

0790802-01 3170 .874-02 3060 .682

-03 3120 1.014-04 3170 1.007

0790702-07 KE/EA 9332 Comp. 3300 .064-08 3375 .087-09 3300 .136

0790703-01 ? .202-02 3300 .262-03 3225 .574

0790807-01 3000 .167 .314 .174-02 3030 .167-03 3225 .400

0790702-02 KE/L-100 Comp. 3225 .055-03 ---- .168-04 3300 .615-05 3300 .117-06 3300 .505

0790892-05 3080 .223-06 3240 .348 366 .178-07 3100 .215 .-08 3070 .634

0790803-01 3160 .524-02 3080 .360

0790629-11 KE 759 EP Comp. 2477 .294-12 3300 .416 (0)1-13 3000 1 .000

145

4x




0790626-01 HYSOL ADX 3130 3000 .184-02 .037-03 3000 .453-04 3010 .322-05 3100 .354-06 3100 .362 .378 .046-07 3100 .426-08 3100 .426

0790622-04 HYSOL EA 9323 3200 .391 \-05 2900 .374-06 3200 .432-07 2809 .410 .507 .190-08 2800 .566-09 3200 .461-10 2850 .912

079(621-09 HYSOL EA 9309 ER 2600 .161-10 3000 .290-11 2700 .207 .-12 2750 .293 .263 .064-13 2700 .310-14 2700 .318

0790620-01-02 2600 .156-03 2700 .185-04 2850 .133-05 2600 .229-06 2700 .121-07 3185 .302

0790621-01 2850 .280-02 ---- ---- .177 .073-03 2750 .045-04 ---- .098-05 '700 .125-06 2600 .214-07 2600 .221-08 2600 .193

146

_ _ A)

APPENDIX B

ASSESSMENT OF SHIELDING OF EROSION

IN REGIONS OF HIGH POTENTIAL FLUX

147

APPENDIX B

ASSESSMENT OF SHIELDING OF EROSION

IN REGIONS OF HIGH POTENTIAL FLUX

B-1. INTRODUCTION

Particle erosion of missiles has been the subject of a great deal of study and

testing. For much of the testing, particularly in ballistic ranges and rocket sled facil-

ities, it is desirable to compress the particle density. In doing this, there is a possi-

bility that rebounded particles and debris (referred to herein simply as "debris") from

upstream locations will collide with incoming particles and effectively shield downstream

locations on the test sample. A simple method of assessing the probability of debris

shielding on a flat plate has been developed. This method has been used to derive a dimen-

sionless parameter that can be used to determine whether or not shielding is probable.

B-2. ANALYTICAL METHOD

The analysis was performed for a flat plate* at some angle-of-attack (e) to the

flow, moving at a velocity, Vp, through the particle field. The following assumptions were

made to allow the prediction of the onset of shielding:

Assumptions:

1. Debris particles are all of the same size and density.

2. All incoming particles impact the surface.

3. Debris particles do not collide with one another.

4. The debris leaves the surface at an angle equal to the

angle of incidence of the incoming particles.

5. The debris layer depth is much less than its length.

The principal task in predicting shielding is the calculation of the concentra-

tion of debris in the path of an incoming particle. For the situation under evaluation,

this reduces to simply the calculation of the transit time of debris from the leading edge

of the surface to the point under examination (see Figure B-1). This can be shown by the

following argument: assume that the surface in front of the point under examination is

2divided into equal segments of area, (AX) . Each segment produces a streamtube of debris.

Due to assumptions 2 and 3, all streamtubes are identical. Consequently, the debris in

streamtube volume element, v2' in the second streamtube is identical to that in v 2 in the

first streamtube. is identical to and similarly, each volume element in the tube

*If the impacted surface is a cone or a yawed cylinder, debris shielding will begin at

higher particle densities than predicted by this method, due to the effects of streamlinedivergence.

148

. . ._._._._._._._

PARTICLE FLUX IN

v

p

\0ui AX SIN 6

PARTICLE PATH

AX

s 1stAX STREAMTUBE

NvAX , H

11TUBE

I , , '\\ I,- ,

N./ r 2

NN lNAX \TUBE

\ r TUBE

AX .v, I..-

AX-

F\. ire -1. Debis shilding ,noetry

149

J

is matched by an identical element in the first streamtube. If the debris layer length ismuch greater than its height, the number (N) of debris particles along the path of an in-

coming freestream particle (tube 6) is approximately equal to the number in tube C which

has been shown to be equal to the total number in the first streamtube.

(Mass flux per unit surface area) AX2 (1 + G) tL

(Mass of debris fragment)

where tL is the transient time from X = 0 to X L.

So: N 6 p. AX2 sin e (1 + G) Vp tL (Al)

Pd T Dd3

The transit times to each station L are obtained by solving the following equation

numerically:

L = (Ve -VOX) tL -l/B zn[(Ve Vox) BtL + 1] (A2)

in whichPe CDA d

B = Cd (A3)

Assuming that the residual kinetic energy is equally shared by the debris:

V p2 (0 - C)V x = KE+ G•cos e (A4)ox 1 + G

From statistics, the probability that an incoming particle collides with debris is

E

p = 1 e~- (A5)

where E = Total cross sectional area of debris in Tube B

Area of Tube 6

N Aeff

so E X- (A6)AX2 sin e

where Ae is the effective cross section area of a single debris particle. Since Equation

(5) is based on incoming particles of infinitesimal size, the diameter of the incoming

particle is superimposed upon that of the debris particle, so:

Aeff = (Dd + D) 2 (A7)

150

.- .,

Substituting Equations (1) and (7) into (6):

3p. (Dd + Dp )2 (1 + G) Vp tLd 3 (A8)

Pd Dd3

B-3. DERIVATION OF DIMENSIONLESS PARAMETER

A dimensionless parameter is derived such that if the parameter is less than one,

the probability of an incoming particle striking a debris fragment is less than 10 percent.

The expression for the probability of such a collision [Equations (5) and (8)] is straight-

forward with the exception of the transit time. Consequently, the principal task in the

derivation of the dimensionless parameter becomes the identification of an explicit func-

tion for the transit time. Using the conservative assumption that the debris initial ve-

locity is zero, the expression for the debris displacement is:

X = Ve t - I/B kn (B Ve t + l) (A9)

The problem then is to find a function f(X) such that f(X) > t for all X. A two-branched

function for f(X) is found. The first branch uses:

f(X) K (X 2 (AID)Ve R

K is evaluated from the requirement that for all X:

X < Ve f(X) - I/B tn [B Ve f(X) + 1] (All)

Substituting for f(X) and multiplying through by B:

1 1

XB < K(XB) - Zn [K(XB)Y + 1] (A12)

Now let1

K(XB) = (A13)

which yields:

1 <2n + (A14)

K2

Over the range 0 < < 1, the right hand side is a minimum at c = I and has a value of

1 tn(2). Thus

1

K2 < 0.307 (A15)

~151,

That is, the function selected is always less than t as required, as long as

i K >

> 1.81 (A16)

For the second branch of the function, let:

XKf(X) =V- (A17)

e

Substituting for f(X) in Equation (11) and multiplying through by B yields:

XB < XKB - in (XKB + 1) (A18)

This branch will be valid over the range:

1

= K(XB)7 > 1 (Ag)

Substituting the value from Equation (16) for K yields

XB > 0.307 (A20)

Substituting Equation (20) into Equation (18) and solving yields

K > 3.26

Since a 10 percent probability of collision corresponds to an exponent E of 0.1,

the shielding parameter can be stated:

P < 0.1 if:30p _ (Dd 2 (1 + G) Vp f(X)

+ Dr2 p < 1.0

(d Dd3

f(X) 181 (XB)2 (XB < 0.307)Ve

f(X) = 3.26 X (XB > 0.307)e

A152

NOMENCLATURE

(Applicable to main text and appendices)

SYMBOL MEANING UNITS

A Cross section area ft2

B Particle deceleration parameter defined in Equation A3 ---

CD Drag coefficient

CKE Kinetic energy accommodation coefficient

D Diameter ft

e Base of natural logarithms ---

E Exponent defined in Equation A6

G Erosion mass loss ratio (mass removed/impacting mass) ---

h Enthalpy Btu/lbm

L X distance to station under analysis ft

M Mass Ibm

N Number ---

p Pressure lbf/in 2

P Probability ---

Heat flux Btu/ft2-sec

tL Transit time from X = 0 to X = L sec

T Temperature deg F

V Velocity ft/sec

X Streamwise coordinate ft

GREEK

p Density 1bm/ft 3 .

e Impact angle deg

SUBSCRIPT

Freestream

d Debris

e Edge of boundary layer

eff Effective

NOM Nominal

o Initial

p Impacting particle

t Target

X Streamwise component

* Except freestream particle density, p_ is given in "conventional" units of g/m

153

154

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