INVESTIGATION OF THE COMBUSTION STRUCTURE OF HYDROGEN JETS IN A SUPERSONIC AIR STREAM

U.K. Zhapbasbayev, Z.A.Mansurov Al-Faraby Kazakh National University, 480078, Almaty, Kazakhstan

e-mail: nich7@kazsu.kz There are given the data of calculated theoretical research of diffusive combustion of flat

supersonic hydrogen jets in a hypersonic stream, received by Navier-Stock’s parabolic equations, closed by one-parameter –model of turbulence and multistage mechanism of hydrogen oxidation. The regularities of combustion, depending on the operating parameters, are discussing. The influences of air stream structure and the ways of fuel feed to the length of inflammation delay and to the quantity of hydrogen burnout level have been defined.

)( ωlk −

Introduction. The research of hydrogen combustion in hypersonic flows presents great

difficulties both in theoretical and experimental plan. Theoretical research is complicated by the fact that the regularities of combustion at supersonic speeds are defined by the intensities of turbulent exchange processes, chemical reaction velocities in a stream and by the influence of gas dynamic effects accompanying heat release. Thus, each from the listed factors may essentially influenced on combustion process. It's almost impossible to carry out full-scale experiments in laboratory conditions for Mach numbers of a stream . 5>M

There are some experimental and calculated theoretical researches of combustion in supersonic jet streams ( ) [1 – 8]. They show the multistage of chain reactions [1,2], inflammation delay of hydrogen-air mixture [3 - 5], necessity of the account of pulsation concentration to the velocity of chemical transformations [4, 5] and gas-dynamic mechanism influence on combustion [6, 8].

3<M

The detailed experimental data on a turbulent structure of supersonic shift streams have allowed to study the regularities of turbulent mixing [9] and to evaluate the use of modern models of turbulence for their description. In particular, a less expressed anisotropy character of turbulence in the mixing area of two supersonic streams has been revealed [9]. In accordance with experimental data [9], the conducted calculated theoretical analysis of different isotropic models of turbulence allowed to reveal that one–parameter )( ωlk − -model of turbulence satisfactorily describes main regularities of mixing area of two supersonic streams [10].

Supersonic combustion with shocks has been investigated in [10,11] and the influence of shock waves on inflammation and mixing processes has been found out. As experimental data show [3,8], hydrogen jet mixing with air co-flow is one of the most important factors to organize hydrogen combustion. In this connection, discovering of mixing mechanism depending on various dynamic, thermal, kinetic and geometric conditions has a great importance for practice. However, it is necessary to state that, unfortunately, there is no sufficiently full idea, both in qualitative and quantitative sense, about the influence of shocks on turbulent condition of a stream – its thin structure, as well as on chemical reactions proceeding at supersonic velocities.

In experimental researches of diffusion hydrogen combustion in non-calculated supersonic jet of high-enthalpy air there has been revealed the alternation of the areas of intensive combustion with the areas of combustion delay, caused by gas-dynamic flow structure [8]. In particular, the influence of different ways of fuel feed to the length of inflammation delay of hydrogen has been pointed out. The registration of OH radical radiation by flare length has allowed evaluating combustion intensity and completeness [8]. The alternation of a zone of intensive combustion with a zone of delayed combustion may influence on the working process efficiency during the organization of supersonic hydrogen combustion in combustion chambers and needs detailed study.

In this connection, the authors of the given paper aimed to show that the attraction of PUNS system in combination with approved models of hydrogen oxidation turbulence and

kinetics may give more full notion on the regularities of supersonic hydrogen jet system combustion in co-flow hypersonic air stream.

The results of calculated theoretical researches of diffusive combustion of supersonic plane hydrogen jet system in co-flow hypersonic stream are given below.

Mathematical model of a stream. There is considered the supersonic combustion in the

field of turbulent mixing of supersonic plane hydrogen jets system with hypersonic air stream. Hydrogen jet is running out in parallel or under a small angle θ into hypersonic air stream from flat slots with the height , disposed at the distance from each other (see Fig.1). The axis 1h 3hOX is directed along a plane of stream symmetry and the axis OY is perpendicular to it. The strip with the width L, limited by planes of symmetry, may be isolated as the system of flat jets is periodically repeated, and the solution of the problem in this field may be considered by substituting of rejected part with conditions of symmetry along boundary planes.

The stream in a whole field is supposed to be supersonic, the gas is considered to be viscous, heat conducted, chemically reacting and stream condition – to be turbulent.

The system of parabolic equations of energy, continuity, substance and angular momentum equation written in a matrix form can be used to describe an averaged stream. Turbulent two-dimensional motion of gas mixture is described by the system of parabolic time-average Navier-Stock’s equations.

( ) WHSyy

GxF rrr

rr

++∂∂

=∂∂

+∂∂ (1)

Where ( )[ ],,,,, 2iuCupEuvpuuFF ρρρρρ ++=

rr

( )[ ],,,,, 2ivCvpEpvuvvGG ρρρρρ ++=

rr

[ ],,0,0,0,0 iWWW &rr

=

,,32

21

Pr,

34,,0

22

⎥⎦

⎤⎢⎣

⎡

∂∂

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+∂∂

∂∂

∂∂

=y

CScy

vy

uye

yv

yuSS i

t

tt

t

ttt

µµ

µγµµ

rr

.0,,0,0,0 ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

= ∑ yC

hSc

HH i

ii

t

tµrr

Here are considered next symbols: - longitudinal and transversal components of velocity,

vu,p - pressure, ρ - density, e -specific internal energy, -concentration of substance in

a mixture, -specific enthalpy of i -component of a mixture, iC

ih tµ - coefficient of turbulent dynamic viscosity, - turbulent analogues of Prandtle and Schmidt numbers, which are

tt Sc,Pr

.9,0,Pr =tt ScThe equation of ideal gas state is written in the next form:

,RTp ρ= (2)

Where ∑=i i

io m

CRR , is a molecular mass of – component of mixture, – an universal

gas constant.

im i 0R

Complete energy is the next:

∑ ∫ ∑+++=

i

T

T iiivii ChvudTcCE

0

022

2 (3)

Where , - are, accordingly, heat of formation and thermal capacity per unit volume of i –component of mixture.

0ih vic

Wilke formula [12] is used to calculate thermal physical properties of hydrogen air mixture. Dependence of a thermal capacity coefficient on temperature is taken as a polynomial of the forth degree [12].

The coefficient of turbulent dynamic viscosity tµ is determined by one-parameter -model of turbulence. )( ωlk −

klCt ωω ρµ = (4) The kinetic energy of turbulence k is determined by the equation:

ω

ρρρµ

∂∂µ

∂∂µ

∂∂

∂∂ρ

∂∂ρ

lkC

yk

yScyu

yk

yykv

xku d

t

ttt

23

2

−∂∂

∂∂

+⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛=+ (5)

The constants of model take the meanings: .0.1,09.0 == dCCω All the quantities formed the system of equations (1) – (5), are dimensionless.

Coordinates yx, are referred to , components of velocity and 1h u v are referred to ,

density 1U

ρ to 1ρ , pressure p to specific internal energy e to the coefficient of

turbulent viscosity

,211Uρ ,2

1U

tµ to 111 hUρ , kinetic energy of turbulence k - to . 21U

In non-auto model jet streams there has been found out the expression to determine , conformed to the experimental data [13].

ωl

,

max

minmax

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂−

=

yu

uulω (6)

Where , are, accordingly, maximum and minimum meaning of longitudinal

velocity, and

maxu minu

max⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

yu – maximum meaning of partial derivative of longitudinal velocity in the

given section. The velocity of hydrogen combustion in the air is described by multiply staged

mechanism, enclosed 9 reversible chemical reactions, where 6 active substances H, O, OH, H2O, O2, H2 [14] participate:

H+O2 OH+O,O+H2 OH+H, H2+OH H+H2O OH+OH O+H2O, H2+M H+H+M, H2O+M OH+H+M (7) OH+M O+H+M, O2+M 2O+M, H2+O2 2OH

Detailed quantitative information about these elementary reversible chemical reactions and about their constants can be found in [14].

The influence of alternation effects on the quantity of averaged velocities of elementary chemical reactions has been taken into account with the help of modified model of Spigler’s immiscibility [15, 16], which approximately determines a dampening influence of concentration pulsation on the velocity of chemical reactions. The determination of reaction velocities, considering immiscibility, reduces to substitution of constants of velocities of j reactions in

forward ( ) and return ( ) directions to jfk j

bk ( )jf

jf Uk −1 , ( )j

bj

b Uk −1 where the levels of

immiscibility and are expressed through averaged concentration meanings of components and their root – mean –square pulsations [16]

jfU j

bU

( ),2,1== jUU jjf { } ( ),9,...,3,1,min 21 =+= jUUU j

f

,jf

jb UU = ( ,2,1,0,

233,0max 22

22

=⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+

−= j

ZZ

Ujj

jjj ξ

ξ ) (8)

22 1

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂=

yZ

lScc

j

tj ω

ω

ξ

Where is, accordingly, the concentration of chemical elements H and O. )2,1( =jZ j

Though this model is considered to be the most simplified, however, its using brings to the best agreement of calculation results and results of experiments [15,16]. Boundary conditions of equations’ system (1) –(8) in initial section at has the following form:

0=x

a) In jets ,cos1 θ=u θsin1 =v Or ,cos1 θ=u θsin1 −=v ,

1=ρ , ,1

21

1

γRMC

e v= ,21uCk k= ;1ii CC = (9)

b) In stream

,11

22

1

22 TR

TRMMu = ,02 =v ,

22

11

RnTRT

=ρ ,11

21

22

γRTMTC

e v= ,22uCk k= .2ii CC =

In the planes of symmetry ,0=y Ly = the next symmetry conditions are given

.0,0 ====== vyk

yC

ye

yyu i

∂∂

∂∂

∂∂

∂∂ρ

∂∂ (10)

The system of equations (1) – (8) together with the boundary conditions (9), (10) is solving by numerical method. Finite–difference expressions of the convective terms and terms with pressure gradients in a longitudinal direction have been got with left-hand differences because of positive own meanings of Jacobean matrix UFA ∂∂= , and in a transverse direction – with differences “against stream”, considering the sign of own meanings of Jacobean matrix

UGB ∂∂= by the scheme of splitting of stream vectors [17, 18]. The terms, describing viscous voltages of a shift and heat stream, have been received by central differences. The difference analogues of the equation of mass conservation, angular momentum equation and energy are solving jointly by the method of matrix pass [19]. The approbation of numerical calculation method of the system of gas dynamic equation is given in [10]. Solution of the equation of concentration of active substances’ transformation in general iterative process is separately from the main system. Recommendations [2] have been taken into account during integration of chemical kinetics equation.

The problem of outflow of pre-wall plane hydrogen jet into supersonic stream in accordance with the experiments conditions [3] has been considered to verify generalized mathematical model of hydrogen combustion. Combustion of pre-wall sound jet of cool hydrogen , injected through a slot in the wall of air dynamic pipe with the height

=4 mm into supersonic stream of heated air (( KT 2541 = )

1h 44,22 =M , KT 12702 = ) has been investigated in [3]. A tangential hydrogen injection has been carried out at static pressure, which is approximately equal to a static pressure of running stream ( ). The composition of airflow was consisted of oxygen, steam and nitrogen: =0,266, =0,256, =0,478. The profiles of temperature, molar concentration of H

25 /10 мHP =0

2OC 02OHC 0

2NC2, O2 reagents and combustion products of H2O

in an output section of combustion chamber ( )89/ 1 =hx have been measured. The zone of combustion has been determined by a maximum meaning of molar concentration H2O.

Instead of sticking condition, slip conditions have been set up in the calculations, mind that boundary conditions don’t essentially effect on the length delay of hydrogen ignition and on the pressure distribution along the wall in thin boundary layer. As it is shown in the figure 2, the distributions of temperature (see Fig.2,a) and concentration of hydrogen, oxygen and steam molecules (see Fig.2,b) at an output section of the canal are satisfactorily described by experimental data [3]. Beginning coordinate of the ignition ( )45/ 1 =hx and monotonic pressure growth down the flow are well agreed with the experiment. Pressure quantity at output section

exceeds the meaning in the point of ignition to 20%. ( 89/ 1 =hx )Discussion of calculation results. The main operating parameters of the stream are non-

calculation degree 21 ppn = , Mach’s number of the jet and the stream , jet 1M 2M

temperature and stream temperature , coefficient of excess air -1T 2T α , angle of jet outflow - θ . The effect of operating parameters to mechanisms of ignition and combustion has been investigated in the numerical experiment. Calculation conditions are given in the Table.

Figure 3 shows the calculation results for combustion of a supersonic hydrogen jet in the

concurrent supersonic airflow, the initial parameters of the flow correspond to regime 1. It is

readily seen that ignition of the hydrogen-air mixture starts at a distance from the

point the jet starts exhausting. The ignition delay makes the hydrogen jet mix with the airflow,

producing a homogeneous reacting mixture, which does not ignite because the jet temperature is

relatively low. Mixing of the cold jet with the hot flow results in an increase in hydrogen-air

temperature up to 900K, thus providing kinetic conditions required for chain chemical reactions

to proceed. Weak disturbance waves emerging at the nozzle edge are reflected from the flow

boundary, which stimulates the ignition of the reacting mixture (see Fig.3,a). The drastic increase

in temperature in the flame front (see Fig.3,b) results in the pressure increase and formation of a

shock wave (see Fig.3,a). The zone of elevated pressure accounts for the occurrence and

propagation of disturbance waves. The disturbance waves propagating from the flame front are

reflected from the flow boundary and, interacting with each other, from a wave structure with

compression and expansion zones separated by oblique shock waves (see Fig.3,a).

100/ 1 =hx

The distribution of OH hydroxyl concentration shows the formation of the combustion-front

surface (see Fig.3,c). It is very noticeable during the distribution of an oxygen concentration (see

Fig.3,d) and H2O steam concentration (see Fig.3,e). The flame-front surface has a complex

configuration. Its internal part is distributing on a homogeneous mixture and is closed because of

complete oxygen combustion in this zone. Unburned part of the fuel jet reacts with oxygen

contained in the flow at a barrel-shaped surface. But its external part is spreading on mixing

layer. The combustion heightens the temperature and the pressure, generates heat Mach waves,

which form a wavy structure of the stream by interacting with gas-dynamic waves, caused by

non-calculation of jet outflow. Received isolines distribution of hydroxyl concentration is in

correlation with a wavy structure of gas-dynamic area. It should be noticed that received

calculation data are in a qualitative agreement with the results of experiments on diffusive

hydrogen combustion in non-calculated regimes of supersonic jet outflow [8].

Oxygen mixed with the hydrogen jet reacts completely in the front part of the flame front (see

Fig.3,d). Later, the oxygen concentration decreases closer to the flame surface, and there is

absolutely no oxygen in the internal part of the plume. H2O steam concentration is distributed in

the whole volume of internal part of the flame (see Fig.3,e).

It should be noticed that the length of ignition delay is strongly extended (practically in 4 times)

in comparison with the case when the composition of the stream mixture consists of oxygen,

steam and nitrogen (see regime 2, Table). Figure 4 shows the field of OH hydroxyl

concentration for regime 2. As is seen from this figure, ignition begins at a distance 22=x from

jet exhaustion. The drastic decrease in the induction-zone length can primarily be attributed to

the increase in the air-to-fuel ratio from α =1,22 to α =2,41 and to the presence of water vapor,

water being an active component triggering chain reactions.

Mach waves, spreading from the flame front, reflect from the flow boundary and, interacting

between themselves, form a wavy structure with the zones of compression and rarefaction,

separated by oblique shock waves (see Fig. 4,a).

The influence of active particles on ignition of the reacting mixture is well known from

numerous experimental and theoretical studies [20]. To confirm this commonly known fact, we

performed calculations with parameters corresponding to regime 3 (see Table). In this regime

there is monatomic oxygen with the initial concentration in the composition of

the flow mixture. In this case, the flow contains atomic oxygen, which is an active component

and triggers the chain reaction of oxidation of the hydrogen-air mixture. Ignition starts at a

distance (see Fig.5,a). As compared with the basic regime 1 (see Table), the length of

ignition delay is decreased in 3,3 times.

000025,0=oOC

30=x

The length of ignition delay can be decreased by the way of feed of the hydrogen jet under the

angle into the stream on the account of intensification of a cool fuel mixing with a hot flow of

oxidizer. The pattern of distribution of hydroxyl OH concentration, corresponding to the regime

4 (see Table), is given in the figure 6. It is shown that the ignition begins earlier at a running jet

side than in a shady side 75=x 120=x , caused by a transverse convective fuel mixing with the

oxidizer (see Fig.6,a). It is easy to notice that an oblique flame front of hydrogen airy mixture is

laid under an angle to the flow direction and the angle of the position of the oblique flame front

is approximately equal to the angle of feed of plane hydrogen jet. In the first cell the diffusive

flame front has a non-symmetrical form (see Fig.6,b) and further a cellular structure of the flame

front is little differed from the form, corresponding to co-flow jet feed (see Fig.3,c).

Conclusions The obtained calculation data reveal wave structure of the flow and describe laws of diffusion

burning of unmixed gases in non-isobaric mode of injection of the plane supersonic hydrogen jet

system into a concurrent supersonic air flow.

If there are active particles, combustion is initiated in the mixing zone. The diffusion plume has a

cellular barrel-like shape in accordance with the wave flow structure resulting from hydrogen

combustion. With increasing air-to-fuel ratio (α =2,41), combustion is completed within the

calculation domain. The data obtained on the flame-front structure are in good qualitative

agreement with the theory of diffusion combustion of no mixed gases [20,21].

REFERENCES 1 Bayev V.K., Golovichev V.I., Tretiakov P.K., Garanin A.F., Konstantinovsy V.A., Yasakov V.A. Combustion in a supersonic stream // Novosibirsk: Nauka, 1984. 2 Meshcheryakov E.A., Sabelnikov V.A. The role of the mixing of kinetics in the decreasing of heat-isolation at supersonic combustion of non-mixed gases in the increased canals// Combustion, Explosion, and Shock Waves.1988. V.24. № 5. 3 Burrows M.C., Kurkov A.P. Supersonic combustion of hydrogen in a vitiated air stream using stepped-wall injection// AIAA Paper. 1971. № 71-721. 9 p. 4 Sinkha N., Desh S.M. Calculations of supersonic streams in the canals in the presence of combustion, carried out by the solving of Navie-Stocks parabolised equations//AIAA Journal. 1988. №7. pp. 48-60. 5 Kolesnikov O.M. Influence of the concentrations pulsation on the ignition of a hydrogen pre-wall jet in a supersonic stream // Combustion, Explosion, and Shock Waves.1985. V.21. №1. pp. 53-58. 6 Kopchenov V.I., Lomkov K.E. Numerical research of the intensification of supersonic combustion and profiling of combustion chamber, accounting non-balanced effects in three-dimension raising. Air-dynamics of high velocities. Fazis. 1997. № 1, pp. 43-52. 7 Eklund D. R., Stouffer S.D., Northam G.B. Study of a supersonic combuster employing swept ramp fuel injectors // J. Propulsion Power. 1997. V.13, No 6. pp. 697-704. 8 Vorontsov S.S., Zabaikin V.A., Pikalov V.V., Tretiakov P.K., Chugunova N.V. The research of the structure of diffusion hydrogen jet in supersonic high-enthalpy air stream// Combustion, Explosion, and Shock Waves. 1999. V.35. № 5. 9 Gobel S.G., Datton J.K. Experimental research of turbulent layers of the mixing in a pressed gas // AIAA Journal. 1991. № 2. pp. 48-59. 10 Zhapbasbayev U.K., Makashev E.P. Gas-dynamic structures at supersonic hydrogen combustion in the system of plane jets in a supersonic stream // J. Appl. Mech. and Tech. Physics. 2001. V.42, №1 . pp.25-32. 11 Tabejamaat S., Ju Y. and Niioka T. Numerical Simulation of Secondary Combustion of Hydrogen Injected from Preburner into Supersonic Airflow // AIAA Journal. 1997.Vol.35. №9. 12 Rid R., Prasnits J.,Sherwood T. Gas and fluid peculiarities // Leningrad: Chamistry.1982. 13 Krasheninnikov S.Yu. Calculation of axially symmetric swirling and nonswirling turbulent jets // Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza. 1972. №3. 14 Dimitrow V.I. The Maximum Kinetic Mechanism and Rate Constants in the H2-O2 System. React. Kinetic. Lett., 1977. V.7. №1. 15 Spiegler E., Wolfsntein M., Manheimer-Timnat Y. A model of unmixedness for turbulent reacting flows//Acta Astronautica. 1976. V.3. №3-4. pp. 265-280. 16 Gromov V.G., Larin O.B., Levin V.A. Turbulent hydrogen combustion in a pre-wall jet, elapsed в into supersonic air stream//Combustion, Explosion, and Shock Waves. 1987. V. 23.№ 6, pp.3-9. 17 Steger J.L. and Warming R.F. Flux Vector Splitting of the Inviscid Gas Dynamics Equations with Application to Finite Difference Methods//Journal of Computational Physics.1981.V.40, april. pp. 263-291. 18 Thomas J.L., Walters R.U. Relaxation schemes with the differences against the stream for Navie-Stocks equations // AIAA Journal.1988. №2. 19 Anderson D.A., Tannehil J.C., Pletcher R.H. Computational Fluid Mechanics and Heat Transfer. N.Y.: McGraw-Hill, 1984. 20 Basevich V.Ya., Kogarko S.M., Dinaburg E.I. and Kamenostskaya S.L. Combustion and stabilization of hydrogen flame in an axially symmetric flow// Combustion, Explosion, and Shock Waves. 1968. v.4. №2, pp. 220-230. 21 Vulis L.A., Ershin Sh.A. and Yarin L.P. Fundamentals of the Gas-Plame Theory. Leningrad: Energiya, 1968.

Table

Regime parameters Regime 1 Regime 2 Regime 3 Regime 4 1M 1,8 1,8 1,8 1,8

2M 3,0 3,0 3,0 3,0 KT ,1 254 254 254 254 KT ,2 1270 1270 1270 1270

α 1,22 2,41 1,22 1,22 θ , deg. 0 0 0 30

n 0,7 0,7 0,7 0,7 0

2HC 1,0 1,0 1,0 1,0 0

2OC 0,232 0,232 0,232 0,232 0OHC 0 0 0 0 0

2OHC 0 0,1 0 0 0HC 0 0 0 0 0OC 0 0 0,000025 0 0

2NC 0,768 0,668 0,767975 0,768

0x

h3

h3

h1

L

y

Fig.1 Schema of the Flow

Fig.2. Temperature distribution and volume concentrations in the section: 89/ 1 =hx

points – experiment [3], dash curves - calculations [5], continuity curves – the authors’

calculations.

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

0.000 0.002 0.003 0.005 0.006 0.008 0.009 0.011 0.013 0.014 0.016 0.017

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

ya)

b)

c)

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

0.000 0.019 0.039 0.058 0.077 0.097 0.116 0.135 0.154 0.174 0.193 0.212 0.232

d)

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

0.000 0.022 0.044 0.066 0.088 0.110 0.132 0.155 0.177 0.199 0.221 0.243

e)

c)

Fig. 3. Calculation results for combustion of a supersonic hydrogen jet in a concurrent supersonic air flow: a) isobars, b) isotherms, c) the field of OH concentration, d) the field of

concentration, e) the field of concentration. 2O OH 2

50 100 150 200 250 300 350 400x

0.0

25.5

51.0y

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

0.000 0.002 0.003 0.005 0.007 0.009 0.010 0.012 0.014 0.016 0.017 0.019 0.021

a)

b)

Fig. 4. Calculation results for combustion of a supersonic hydrogen jet in a concurrent supersonic air flow: a) isobars, b) the field of OH concentration.

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

a)

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

0.000 0.002 0.003 0.005 0.006 0.008 0.010 0.011 0.013 0.014 0.016 0.017

b)

Fig. 5. Calculation results for combustion of a supersonic hydrogen jet in a concurrent supersonic air flow: a) isobars, b) the field of OH concentration.

50 100 150 200 250 300 350 400x

0.0

25.5

51.0y

a)

50 100 150 200 250 300 350 400x

0.0

25.5

51.0

y

0.000 0.002 0.003 0.005 0.006 0.008 0.009 0.011 0.012 0.014 0.015 0.017 0.018

b)

Fig. 6. Calculation results for combustion of a supersonic hydrogen jet in a concurrent supersonic air flow: a) isobars, b) the field of OH concentration.