HHeeaatt && PPoowweerr EEnnggiinneeeerriinngg

242  © Metallurgical and Mining Industry, 2010, Vol. 2, No. 3

UDC 669.18:533.694.6

Modeling of Gas Powder Flow in Nozzles of Gunned Lance

A. K. Kharin1, P. S. Kharlashin2

1 OJSC “Ilyich Iron & Steel Works of Mariupol” 1 Levchenko St., Mariupol, 87504, Ukraine

2 Pryazovskiy State Technical University 7 Universitetskaya St., Mariupol, 87500, Ukraine

Engineering method of calculation of one-dimensional double-speed flow of gas suspended matter in the nozzles of gunned lance was developed. The solution of set of differential and algebraic equations enabled to calculate the change of static pressure, velocity of carrier gas and powder, volume fraction of hard phase along the cylindrical nozzle as well as distribution of these parameters in the outlet section. Keywords: GUNNED LANCE, DOUBLE-SPEED FLOW, EQUATION OF MOTION, NOZZLE

Introduction Torch torkret process of refractory surface is

a standard production operation in the repair of local zones of 160-ton converter lining in oxygen-converter plant of JSC “Ilyich Iron & Steel Works of Mariupol”. Durability of refractory coat varies within 2-7 smelting operations.

The experience gained at the integrated iron-and-steel works showed that quality of slag lining essentially depends on lance design and multicomponent jet flow. This section of torkret process theory is researched not enough.

Calculation procedure of gunned lance with three levels of gas mixture flow is described in [1]. The disadvantage of the method is usage of one-speed model of gas mixture flow in the lance, and calculation method for two-phase nozzles is not presented at all.

The purpose of present research is to improve the calculation procedure of gas-dispersion two-phase flow in the cylindrical nozzles of gunned lance and determine the effect of diameter of δ particles, their density ρ2 and volume fraction ε2 of hard phase on the distribution of gas-dynamic properties along the two-phase nozzle and in the nozzle outlet section.

Results and Discussion Mathematical model of separate flow in

two-phase nozzles The system of equations of quasione-

dimensional two-phase flow in double-speed approach includes, first of all, equation of joint movement of phases [2] and equation of one phase movement. For example, for carrier gas this differential equation will be as follows:

sing1112Fw1Fdx

dp1

dx

1dw1G

(Eq. 1) In the calculations there are also used

equations of: – condition for gaseous phase

p=ρ1RT1 (Eq. 2)

– continuity for gaseous phase and powder in the dispersed flow

1w111G (Eq. 3)

2w222G (Eq. 4)

The following symbols are accepted in

equations 1-4 and further: m1, m2 – rate of gas-

carrier and powder; f/1m1G ,

f/2m2G - relative rate of gas and powder,

HHeeaatt && PPoowweerr EEnnggiinneeeerriinngg

© Metallurgical and Mining Industry, 2010, Vol. 2, No. 3  243

kg/(s·m2); f - nozzle are, m2; D – nozzle inside diameter; δ - equivalent diameter of powder particles, m; w1, w2 -phase velocities, km/s; p - static pressure, Pa; Т - static temperature, K;

1m/2m - mass concentration of powder,

kg/kg; 1 , 2 - volume fraction of gas and hard

phase; η - dynamic coefficient of viscosity, Pa·s; ν - kinematic coefficient of viscosity, m2/s; F1w, F12 – wall friction force of gas and force of interphase interaction, N/m3; ρ1, ρ2 – density of gas and powder, kg/m3; R - gas constant, J/(kg·К); g - gravity acceleration, m/s2; α - canting angle of nozzle, deg. Indexes mean the following parameters: 1 - gas-carrier, 2 - powder particles, 12 – gas mixture, i - i component in the mixture.

It is accepted in the model that impurity is monodispersed and equations are for horizontal fixed nozzle, axis х is directed along the nozzle.

Closing ratios Summand F12 appearing in equation 1 is a

force that characterizes intensity of interphase interaction calculated by equation:

12 1 2 1 2 1 2

3/

4 DF C w w w w

(Eq. 5)

where aerodynamic drag factor is determined with

account of concentration 2 as:

n2

210DCDC

(Eq. 6)

In (6) coefficient 0DC depending on

Reynolds' number /1/)2w1w(12Re was calculated in the same way as in publication [3]. Flow structure coefficient is within n = 2.25-4. Loss of momentum of gas and particles was calculated by formula:

D2/2iwiiiiwF (Eq. 7)

Nozzle wall friction coefficient of gas was

determined as:

0,237 11 1 10,0032 0, 221 32Re Re

v/D1w1Re (Eq. 8)

Loss of momentum of dispersion phase ζ2 due to wall impact was defined as in [3].

Boundary conditions At the entry to lance (х = 0), the temperature

of gas and dispersion impurity element were Т1 = Т0, Т2 = b t  Т0. Since steady-state flows of phases m1, m2 were set, phase velocity and inlet pressure were not defined. It is necessary to set only dynamic lag factor:

2 1 0/ 1

xw w

(Eq. 9)

Initial data Equivalent diameter of one of cylindrical

nozzles was D = 20 mm, its length l = 100 mm. The rate of carrier gas (N2) was Vc = 360 m3/h and remained constant at all conditions. The rate of refractory powder changed within the range m2 = 150-600 kg/min. Concentration μ = 20- 80 kg/kg corresponded to this ratio between gas and powder. Particle drag coefficient was accepted as f =1.3 (for a sphere f = 1). Diameter of particles was δ = 0.03-0.4 mm, their density was changed in the range ρ2 = 2000-5000 kg/m3. We will remind that the true density of, for example, MgO is ρ2 ≈ 2790 kg/m3, chrome-magnesite brick ρ2 = 2900 kg/m3, Al2O3 - ρ2 = 3770 kg/m3.

Analysis of obtained results As follows from Figure 1а, static pressure р

along the length of cylindrical nozzle is distributed non-uniformly – it drops sharply towards the outlet section. Such pressure behavior was experimentally confirmed in [3].

We will notice that if pressure of gas mixture in the lance is 0.2-0.7 MPa, the nozzle always works at supersonic pressure difference and static pressure pcr ≈ ≈0,56pо in the outlet cross-section at any values of μ, δ, ρ2 . It was determined that all other things being equal, the finer grinding of powder (less δ), the higher pressure p at the entry to nozzle. This results from the fact that, for example, decrease of δ from 0.4 to 0.03 mm (in 13.3 times) at the same rate of m2

leads to increase of contacting area between particles with carrier gas in 177 times. With reference to this example, growth of gas mixture resistance to motion in the nozzles is a natural physical process. But the more diameter of particles δ, the smaller volume they occupy in gas-dispersion flow. For example, at the same charge of powder m2 increase in diameter δ from 0.03 to 0.05 mm leads to decrease

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References

P. S. Kgicheskaya i

o. 1, pp. 107-1P. S. Kharkogo Universi

Yu. M. Kuzneder Injection igiya, 1991, 16

eived March

Mining Indu

e of particle vsize δ at diffe

n of pressurhard phase, ding on the hown as a resermined thafect on gas-dance.

Kharlashin, NGornorudnay

109.* lashin, A. Kiteta, 2009, Netsov. Gas Dyin Molten Me60 p.*

*

h 03, 2010

150

140

130

120

110

100

90

80

70

0

w2, m

ustry, 2010, V

velocity w2 (-)erent density

re, density ovolume fracparticle siz

sult of researat particle didispersion f

N. O. Chya Promyshl

K. Kharin. No. 19, pp. 73-ynamics of Pr

Metal, Chely

Published in R

0.03 0.1

m/s

Vol. 2, No. 3

and volume of particles ρ

of gas-tion of ze and ch. ameter

flow in

hemeris. lennost,

Vestnik -78.*

rocesses yabinsk,

Russian

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246  © Metallurgical and Mining Industry, 2010, Vol. 2, No. 3

Antonov Yu. G. ................................................. 207 Ayupova T. A. .................................................. 203 Bedarev S. A. .................................................... 230 Belov B. F. ....................................................... 180 Bezdetny I. A. ................................................... 220 Bryukhanov A. A. ............................................. 215 Buga I. D. .................................................. 180, 207 Cecho L. ............................................................ 193 Dergach T. A. ................................................... 220 Dolzhanskiy A. M. ............................................ 203 Dyomina E. G. ................................................. 207 Fedyaev D. I. .................................................... 230 Grekov S. V. ..................................................... 186 Grinev A. F. ...................................................... 177 Hajduk D. .......................................................... 193 Hepke М. .......................................................... 215 Horsky J. ........................................................... 193 Hovhannisyan A. M. ......................................... 225 Khamkhotko A. F. ........................................... 186   Kharin A. K. ..................................................... 242 Kharlashin P. S. ................................................ 242 Kozerema M. M. ............................................... 236 Kutsova V. Z. .................................................... 203 Levchenko G. V. ................................................ 207

Malich N. G. .................................................... 236 Medinskiy G. A. .............................................. 207 Nefedyeva E. E. ................................................ 207 Nosochenko O. V. ............................................ 180 Oshovskaya E. V. ............................................. 230 Parenchuk I. V. ................................................ 180 Petrov A. F. ....................................................... 186 Prikhodko E. V. ................................................ 186 Raudensky M. ................................................... 193 Rodman D. ........................................................ 215 Rodman М. ....................................................... 215 Romanova G. S. ................................................ 230 Sargsyan L. E. .................................................... 225 Severina L. S. ................................................... 220 Shaper М. ......................................................... 215 Shtepa V. P. ...................................................... 236 Solovy A. V. ..................................................... 236 Stoyanov P. P. .................................................. 215 Togobitskaya D. N. ........................................... 186 Trotsan A. I. ...................................................... 180 Yeron`ko S. P. .................................................. 230 Yurkov S. K. ..................................................... 220 Zilberg Yu. V. ................................................... 215