mixtures. The rate of turbulent combustion of rich mixtures was greater than that for weak mixtures having the same values of u n. This is due to diffusion-thermal instability [8].

The addition of water can be used to reduce the concentration of the oxides of nitrogen in the exhaust gases from the combustion of alcohols. This should increase the volumetric power. The use of alcohols in engines does not require any major alterations to the fuel injection system. The data indicates that, compared with the combustion of gasoline, the concentration of the oxides of nitrogen will be slightly reduced and the concentrations of the oxides of carbon and hydrocarbons will remain at about the same level.

It is well known that methanol can be decomposed into hydrogen and the oxides of carbon on catalysts, which do not contain precious metals, at relatively low temperatures. The combustion of such mixtures has been studied by [9]. Even with partial decomposition of the methanol, the use of weak mixtures is feasible right down to the idling state of the engine.

LITERATURE CITED

I. O.L. Gulder, Combust. Sci. Technol., 33, No. 1-4, 179 (1983). 2. O.L. Gulder, Combust. Flame, 56, No. 3, 261 (1984). 3. A.S. Sokolik, V. P. Karpov, and E, S. Semenov, Fiz. Goreniya Vzryva, ~, No. i, 61

(1967). 4. V.P. Karpov and E. S. Severin, Fiz. Goreniya Vzryva, 14, No. 2, 33 (1978). 5. B. Lewis, in: Selected Combustion Problems (AGARD), Butterworth (1954). 6. S. Vuititski, T. Lezhanski, et al., Arch. Combust., 2, No. 3-4, 149 (1982). 7. V.P. Karpov, Fiz. Goreniya Vzryva, 18, No. i, 130 (1982). 8. V.P. Karpov and E. S. Severin, Fiz. Goreniya Vzryva, 16, No. i, 45 (1980). 9. V.P. Karpov and E. S. Severin, Fiz. Goreniya Vzryva, 1-8, No. 6, 38 (1982).

COmbUSTION OF A TURBULENT SUPERSONIC NONISOBARIC HYDROGEN

JET IN AN ACCOMPANYING SUPERSONIC AIR FLOW

S. I. Baranovskii, A. S. Nadvorskii, and V. A. Perminov

It is of great practical interest to study the supersonic combustion of gas jets. One approach to the solution of this problem is to use simplified Navier--Stokes equations. This system allows flow of boundary-layer type to be calculated, as well as compression and rare- faction waves. Since the Cauchy problem for the given system is correct in supersonic flows, it is possible to use the march method, which is widely applied in calculating supersonic inert nonisobaric jets and also the combustion of supersonic jets; see [i, 2], for example. Experimental investigation of the reacting jets may be found in [3].

It is necessary to study the influence of heat liberation on the static pressure and processes in the mixing layer. It is also important to establish the influence exerted on the mixing by the cotraveling characteristic and the density ratio in the external flow and in the jet (parameters characterizing the mixing intensity for inert jets) in combustion con- ditions. These questions are investigated in the present work. Note that some of them were considered in [!, 2].

Consider an axisymmetric supersonic turbulent jet of hydrogen issuing into a cotrave!ing supersonic jet of air (Fig. i). The gas is assumed to be viscous and heat conducting. A diagram of the flow is shown in Fig. !.

The mathematical model differs from [4] in that the presence of chemical reaction is present. The basic equations are as follows

MOSCOW,

August, 1986. 1985 �9

Translated from Fizika Goreniya i Vzryva, Vo!. 22, No. 4, pp. 14-18, July- Original article submitted March 12, 1985; revision submitted August 28,

0010-5082/86/2204-0399512.50 �9 1987 Plenum Publishing Corporation 399

Air {

H'2 i

Fig. i

P/Pa P/#a

I~ 12 7 ~ ....

,Z ,

1,04

2 4 r/r a

0 20 40 x/ r a F ig . 2

i

0,9 |

o,~ I { 50 40 5o x / ~

Fig. 3

Fig. I. Flow diagram: i) external density discontinuity; 2) boundary of mixing layer; 3) streamlines leaving the edges of the nozzle; 4) reflected density discontinuity; 5) suspend- ed density discontinuity.

Fig. 2. Distribution of static pressure along symmetry axis (a) and its profile in the cross section x/r~ + l0 (b).

Fig. 3. Distribution of the longitudinal velocity componemt along the axis. Here and in Figs. 3-6, the continuous curve~ correspond to results for a burning jet and the dashed curves to those for a frozen jet.

.~ (p.r~) + ~@r~ = o, (l) au Ou t a [ ~Su'~ ap

~ . ~o .~ ~ ( ~ . , . ~ , ~,, (2)

ah . oh , a / ~ , ~ ah ~

i a t au . / l t ' ~ O K (3) + 7 ~ tt 1 - - ~ u ~ "v l'yK . ~ J ~r + - - hj ,

a! a! t 0 {Pc ~Of~ (4)

Here, u, v a r e the p r o j e c t i o n s o f t h e v e l o c i t y on the x and r a x e s ; p, d e n s i t y ; p, p r e s s u r e ; = 0, p l a n e c a s e and a ~ 1 t h e a x i s y m m e t r i c c a s e ; ~e, e f f e c t i v e v i s c o s i t y ; h , t o t a l e n t h a l p y ;

K, kinetic energy of turbulence; Oh, aj, effective Prandtl and Schmidt numbers; hi, enthalpy of the j-th mixture component; and

W}I~ W H ] = mr& + mr~ + ~ mH~o + - - H2~ Wo H moll

is the mass fraction of hydrogen-containing elements. The Launder--Jones two-parameter K--E model of turbulence is used

~, = ~, + ~, (K, E)= ~ + C,pKVE,

~K~_

400

u-U, l

0,6

0,2 , ,

I"~:~ 0 ~ 0,8

Fig. 4

4~--+--- }!.,, is. I ! ~ . / i -4

0 0~ 0,~ q Fig. 5

Fig. 4. Dimensionless-velocity profile inside the mixing layer in the cross section x/ra = 22: the dash-dot curve corresponds to the Schlichting curve.

Fig. 5. Profile of turbulent viscosity and static tempera- ture inside the mixing layer in the cross section x/r a = 22.

mN 2

0,4

0,2

u / . o [ ; , I

0 0,5 1,0 r/r a . 9 10 ~0 ~ / r a

Fig. 6 Fig. 7

Fig. 6. Nitrogen,concentration profile in the cross section

x/r a = 22.

Fig. 7. Distribution of the longitudinal velocity component

along the axis.

o-~ ----- Pr + Prt~

~*_~ I*~ + Sc-7 ~ ~' Sc-- 7 ~ -- ~ -- Oj

~e ~tt

(~E GE '

(6)

where Pl, Pt are the laminar and turbulent viscosity; C~, CI, C2, Sc t, Prt, OK, and o E are the standard constants of the turbulence model [4].

Combustion is modeled by four equilibrium chemical reactions occurring in the hydrogen-- air mixture

H2 ~ H + H, m~_h/m~ = K, (p, T), (7)

0 ~ 0 + 0 , moJmg=K~(p,T) , (8)

OH-~::O + H, moH/(rnom~i) =K.~(p, T), (9) H~O ~ OH + H, mH2o/(moI~mH) ---- K 4 (p, T). (10)

401

TABLE i. Initial Data for Calculations

P a r a m e t e ~

Ia, K M (t lie

295i 5902 552 27~

1,65 4,68 3,4.i0 a 2,2. lO 6

0,72 0,36 3,23 1 '61

V erslon

o90. 552

3,:~1 6,9. iO a

0,36 3,28

2951 276

2,34 i , l . 10 ~

0,72 t ,6i

2951 27t}

2,34 l A, 10 ~

0,72 1,6i

Note~ m = Ue/Ua, n = Pe/0u, N = Pc/Pc, Te = I132~ ue = 2108 m/see, Me = 3, N = 2. In version 5, the chemical reac- tion is frozen.

It follows from the assumption of an identical diffusion rate of all the gases that

Wo W o . (l l)

It is known that the heat liberation at finite reaction rates is larger than that ob- tained taking account of the kinetic mechanism of chemical reaction, but in the given case upper bounds on the influence of combustion on the flow structure are of interest.

In the model of combustion adopted, seven chemical components are taken into account: H, O, OH, H20 , Ha, 02, and N~. Nitrogen is assumed to be neutral; the other components are calculated by solving Eqs. (4) and (7)-(11). For closure of the model, thermal and caloric equations of state are added to the system

p = p B T / W z , W~ = mdWt ,

h = y.j h~(T) m~ + (u ~ + v2)/2 + K. i = 1

In the initial cross section, the distribution of the velocity components, pressure, and temperature components is specified, and the initial conditions for h, K, E are specified. The boundary conditions of symmetry are imposed at the axis, The upper boundary is chosen so that the external discontinuity is in the calculation region, which allows all the variables at the upper boundary to be assumed equal in an unperturbed homogeneous external flow. The system in Eqs. (1)-(6) is written in Mises coordinates and solved by a finite-difference method [4]. In Figs. 2-6, the results of calculation for a theoretical hydrogen jet with parameters Ue = 2108 m/sec, u u = 2591m/sec, Ma= 2.34, M e = 3, Te = 1200~ Ta= 276~ Re = 1.2.10e; here and below, the subscript a denotes parameters at the nozzle outlet aperture and e denotes parameters in the external flow.

Increase in pressure at the axis (Fig. 2a) results in heat liberation as a result of chemical reactions; further undulatory change in pressure is explained by the total action of heat liberation and interference of compression and rarefaction waves reflect- ed from the jet boundary. Ignition leads to the formation of a strong shock wave propagating in the direction of the accompanying flow; the maximum increase in static pressure is 25%.

To study the influence of combustion on mixing, two calculations are performed with the same initial parameters, but four equilibrium chemical reactions occurring in the hydrogen-air mixture are modeled in the first case, while in the second the chemical reaction is frozen (which is achieved experimentally by replacing hydrogen by helium or air by nitrogen).

As is evident from Fig. 3, the combustion significantly increases the range of the jet; see also [2]. On the one hand, this result decreases the turbulent viscosity, because of the drop in density on combustion; on the other hand, there is expansion of the burning jet on account of increase in static pressure, which leads to a large distance (in comparison with the frozen jet) of the mixing layer from the symmetry axis.

It follows from [5] that the dimensionless velocity profile inside the mixing layer of the nonisobaric turbulent jet is well described by the Schlichting curve. However, this refers only to the case where the gases involved are homogeneous and inert, The profile of

402

the dimensionless excess velocity in the cross section x/r a = 22 as a function of the self- similar coordinate ~ = y/6 is shown in Fig. 4, where d is the width of the mixing layer; y is the coordinate measured from the internal boundary of the layer. It is assumed that at the upper boundary of the mixing layer u = u, = 0.9 u e + 0.I ua; at the lower boundary, u = us = 0.9 u a + 0.i u e.

Combustion leads tO great filling of the velocity profile, Note that, in the case of a frozen jet, the velocity profile is poorly described by the Schlichting curve. For the same cross section, the dependence of the turbulent viscosity and static temperature .on the coor- dinate n is shown in Fig. 5. Chemical reaction decreases the turbulent viscosity by a factor of three in comparison with a frozen jet; this is explained both by the lower de~sity value and by the kinetic energy of turbulence (the influence of combustion on K was also studied in [2]).

Concentration profiles of nitrogen are shown in Fig. 6; in the given model, nitrogen serves as the passive impurity. Increase in pressure as a result of combustion leads to large (up to 20%) expansion of the jet; this, in turn, changes the range of the latter, as well as other parameters.

With the aim of studying the influence of the cotravelling parameter and the density ratio in the external flow and in the jet, five different calculations are performed (Table i). The boundary layers inside and outside the nozzle are not taken into accoun1~. In the initial cross section, a narrow layer in which the parameters vary linearly from their values at the nozzle cross section to the values in the external flow is specified. The boundaries of the mixing layer are determined from the nitrogen concentration. Calculations show that the density ratio, as for inert jets, influences mixing, changing the position of the lower boundary of the layer and having practically no influence on the position of the upper boundary. This is because there is a flame front of temperature around 2500~ (at n = 3.23 and 1.61) close to the upper boundary.

The axial velocity is plotted in Fig. 7 for'all five calculations (Table I). Curve 1 lies above curve 4 (although n is higher), since the large temperature in the jet: leads to more intense combustion and hence to increase in pressure at the axis. This, in turn, leads to stronger expansion of the jet, i.e., the mixing layer is removed farther from the axis and as a result the axial velocity increases.

Thus, heat liberation as a result of combustion may lead to significant (up to 25%) in- crease in static pressure and considerable decrease in turbulent viscosity, causing an increase in range of the jet and deterioration of mixing. The profile of dimensionless excess velocity in the mixing layer of the reacting jet is not described by the Schlichting curve.

i. 2.

3. 4.

.

LITERATURE CITED

O. M. Kolesnikov, Uch. Zap. TsAGI, 13, No6 6, 49 (1982). V. I. Golovichev, in: Gas Dynamics of Combustion in a Supersonic Flow [in Russian], ITPM~ Novosibirsk (1979). R. V. Jenkins, NASA-CR-146346 (1976). S. I. Baranovskii, A. S. Nadvorskii, and V. A. Perminov, in: Jet Flows of Liquids and Gases [in Russian], Novopoiotsk (1982), part II. I. M. Karpman and V. D. Traskovskii, Mekhn. Zhidk. Gaza, No. I (1981).

403