Brief Communication

Effect of Confinement in High-Speed Reacting Mixing Layer

DEBASIS CHAKRABORTY,*† H. S. MUKUNDA, and P. J. PAULDepartment of Aerospace Engineering, Indian Institute of Science, Bangalore 560 012, India

INTRODUCTION

High Mach number mixing layers play an im-portant role in the development of supersoniccombustor ramjet (scramjet) engines. The mix-ing of air and fuel is hindered by both shortercombustor residence time and by stability ofsupersonic shear layer relative to subsonic coun-terpart. Although many experimental and com-putational investigations were carried out forsupersonic free shear layer [1–5] and confinedshear layer [6–9], the effect of lateral confine-ment on supersonic mixing layer is not clearlybrought out. The fundamental difference in thedevelopment of turbulence in the mixing layerand wall boundary layer can affect the structureof the flow and the growth rate of mixing layersignificantly. Chakraborty et al. [9] have per-formed two-dimensional direct numerical simu-lation (DNS) for high-speed confined reactingshear layer with finite rate chemical kineticswith seven species and seven reactions. Argu-ments have been provided for treating two-dimensional calculation using the work of Luand Wu [8], Zhuang et al. [10], Farouk et al. [7],and others who have conducted computationalstudy of the compressibility of high-speed mix-ing layer and shown that two-dimensional sim-ulation is satisfactory for confined mixing layer.Good comparison of experimental wall pressuredistribution with DNS results obtained was con-sidered the basis of further investigations.

In this work, the effect of lateral wall confine-ment on the growth and structure of supersonicreacting mixing layer has been studied by con-ducting DNS study for free shear layer andcomparing these results with the DNS results ofconfined shear layer.

ANALYSIS

In order to understand the combustion processinside the scramjet combustor, DNS is per-formed for the confined supersonic reactingmixing layer as it contains all the fundamentalprocesses involved in supersonic combustion ina confined environment. The results of the DNScalculations for the H2/air confined supersonicmixing layer are given in the earlier work of thepresent authors [9]. The simulation is per-formed for the hypervelocity mixing layer exper-iment of Erdos et al. [6]. In this experiment, thesecondary stream (H2) comes in contact withthe primary stream (air) at the edge of thesplitter plate in an enclosed test section of size535 mm 3 25.4 mm. The schematic experimen-tal setup for which the computations were car-ried out is presented in Fig. 1. The Machnumber and the temperature of the two streamsare 3.99 and 2400 K (air) and 3.09 and 103 K(H2) respectively. The convective velocity is3000 m/s and the convective Mach numbers are0.85 and 0.82 referred to H2 and air streamsrespectively. The free shear layer experimentsof Clemens and Mungal [11] suggest dominantthree-dimensional effects for this convectiveMach number range and have been supportedby linear instability analyses [12, 13] which haveshown that oblique disturbances become moreand more unstable as convective Mach numberexceeds 0.6. However, Tam and Hu [14] andZhuang et al. [10] have shown that, for laterallyconfined mixing layers, the most unstable modeis the lowest order two-dimensional mode. Theprincipal point made in these papers is that thecoupling between the motion of the shear layerand the channel acoustic wave produces a newinstability mechanism in the supersonic rangewhich originates from the wall confinement andis different from the classical Kelvin-Helmholtz

*Corresponding author. E-mail: mukunda@cgpl.iisc.ernet.in†Scientist/Engineer, Aerodynamics Division, VSSC, Thiru-vananthapuram.

COMBUSTION AND FLAME 121:386–389 (2000)0010-2180/00/$–see front matter © 2000 by The Combustion InstitutePII S0010-2180(99)00154-6 Published by Elsevier Science Inc.

instability. Zhuang et al. [10] have shown thatthe bounded two-dimensional modes are ingood agreement with the experiments of Pa-pamoschou and Roshko [15]. Lu and Wu [8]have performed two-dimensional simulationsfor a mixing layer with a convective Machnumber as high as 1.77 citing the work of Tamand Hu [14] who studied the effect of confine-ment on the shear layer development in super-sonic streams. These studies have shown thattwo-dimensional simulation is satisfactory forconfined mixing layers.

Two-dimensional simulations by Liou et al.[5] have been shown to capture the majorfeatures of supersonic free shear layer for thehigher convective Mach numbers also. Further,Shin and Fergizer [16] demonstrated that heatrelease makes the dominant mode two-dimen-sional even in the high Mach number region andconcluded that the most unstable mode forreacting flow is two-dimensional even if theinstability mode is three-dimensional (oblique)for the nonreacting case. So the role of large-scale structure in the development of supersonicreacting mixing layer is very important and canbe understood from two-dimensional simula-tion. Effect of lateral confinement on the

growth of the supersonic reacting mixing layer isinvestigated by comparing the two-dimensionalDNS results of free and confined cases.

The details of the computational procedureare available in Ref. [9]. Two-dimensionalNavier-Stokes equations along with species con-tinuity equations are discretized by a fourth-order spatial and second-order temporal com-pact scheme [17, 18]. The chemistry modelincludes six reacting species H2, O2, H2O, OH,H, O and nonreacting species N2 and sevenreaction mechanisms [17]. The species HO2 andH2O2, important in ignition are not included inthe mechanism. This is because the presentstudy is aimed at examining the effect of lateralconfinement on the growth rate of supersonicmixing layer. The grid structure has 1000 gridpoints of 0.3 to 0.8 mm size along the length of535 mm, while the smaller size is arranged nearthe inflow plane to capture initial developmentof the mixing layer. There are 101 grid points inthe cross stream direction with fine grid (of size0.09 mm) near the interface, and the grid isexponentially stretched in the far field regiontoward upper and lower boundaries. Grid inde-pendence of the results was established by com-paring spatial profiles with different grids andalso by analyzing the spectral content of fluctu-ations of the flow parameters.

Application of the boundary conditions forthe free shear layer problem differs from theboundary conditions for the confined case [9].The solid walls (both upper and lower) for theconfined case is replaced by free surface bound-

Fig. 1. Schematic representation of experimental setup of Erdos et al. [6] for which computations were done.

TABLE 1

Inflow Parameters for Reacting Mixing Layer

Species u, km/s T, K M p, MPa Re/mm

H2 2.4 103 3.09 0.021 1,600Air 3.8 2,344 3.99 0.021 22,000

387CONFINEMENT IN A HIGH-SPEED MIXING LAYER

aries. The conditions at free surfaces are ob-tained by solving Riemann conditions. On theinflow streams is imposed a velocity fluctuationover a range of frequencies at a total rmsintensity of 0.3% of the mean velocity (SeeTable 1 for Pa stream parameters.). This fre-quency range allows the mixing layer to grow asmay happen in reality. The outflow boundaryconditions are obtained by second-order extrap-olation and are considered satisfactory for thisproblem dominated by supersonic flow.

RESULTS AND DISCUSSION

As in the earlier study [9], the computationswere performed for three sweep times—onesweep for clearing the flow field and two moresweeps to collect statistical information and alsoto check on the statistical invariance of thecalculation. One sweep of calculation is taken asthe time the flow takes to cross the axial lengthof flow domain (535 mm) with its convectivevelocity. After the attainment of statisticalsteady state, velocities, density, and the speciesmass fractions are gathered at all radial pointsof few axial locations at each time step over onesweep duration to enable statistical analysis.

The mean profiles of axial velocity (u) anddensity (r) at various axial locations are firstcalculated from the stored time series data ofDNS. Two different estimates, namely shearlayer thickness (b) and momentum thickness(u), were made from these mean profiles forcalculation of shear layer width. The shear layerthickness (b) is defined as the distance of thetransverse locations where the value of u(u 2ua)/(ua 2 ub)u is 0.9 and 0.1, where ua and ub

are the velocities of upper and lower streams.Perhaps a better physical representation of

the local width of the mixing layer is provided bythe momentum thickness (u) defined by

u 5 E2`

` r

rau*~1 2 u*! d y (1)

where u* 5 (u 2 ub)/(ua 2 ub).Calculated shear layer thickness and momen-

tum thickness for confined and free shear layersare compared in Fig. 2. It is clear that thegrowth rate is more for confined shear layer

compared to free shear layer. Adverse pressuregradient present in wall boundary layer ismainly responsible for the enhanced growthrate of the confined shear layer. Moreover, it isalso clear from the figure that up to a distanceof 300 mm from the splitter plate, the growthrates for both cases follow the same trend andonly beyond that distance the two differ. For theconfined mixing layer case, as the flow proceedsdownstream, the mixing layer starts comingcloser to the boundary layer and there is mutualinterference. Further downstream these two lay-ers merge into one another and it is difficult todistinguish between the two. At the farthestdownstream location, the width of shear layerfor the confined case is about 130% more thanthat of free shear layer.

The mean mass fractions of H2O and OHspecies were compared for both cases in Fig. 3at the axial locations of 100 mm, 300 mm, and500 mm. It is clear from the figure that up to adistance of 300 mm the reaction zone for boththe free and confined shear layers is limited tothe mixing layer region. Further downstream,for the confined case, because of merging of themixing layer and wall boundary layers the reac-tion zone for the confined case extended up tothe lower wall and it is about 5% more than thefree shear layer reaction zone. Higher temper-ature in the wall boundary layer of the confinedflow aids reaction and causes this broader reac-tion zone.

Fig. 2. Comparison of the shear layer growth between theconfined and free reacting mixing layer of H2–air.

388 D. CHAKABORTY ET AL.

CONCLUSIONS

The effect of lateral confinement on the growthand structure of hypersonic reacting mixinglayer has been studied by comparing DNS re-sults of confined and free shear layers for thesame inflow parameters. It is observed thatbecause of the presence of adverse pressuregradient in the wall boundary layer, the growthrate of the confined mixing layer is much greatercompared to the free shear layer, although thegrowth rates of the two follow the same trenduntil there exists distinct mixing layer and wallboundary layer. The presence of higher temper-ature in wall boundary layer causes a broaderreaction zone for the confined case compared tofree shear layer.

The authors would like to express their sincerethanks to Dr. V. Adimurthy of VSSC, Thiruvan-anthapuram for the support provided for carryingout this work.

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Received 22 February 1999; revised 3 August 1999; accepted18 October 1999

Fig. 3. Comparison of mean profiles at various axial locations for confined and free mixing layers (a) H2O mass fraction, (b)OH mass fraction.

389CONFINEMENT IN A HIGH-SPEED MIXING LAYER