Compressibility and finite-rate chemistry influence on reactive shear layers development

MCS 8 C¸ es¸me, Izmir, Turkey, September 8-13, 2013 COMPRESSIBILITY AND FINITE-RATE CHEMISTRY INFLUENCE ON REACTIVE SHEAR LAYERS DEVELOPMENT Pedro J. Mart´ ınez Ferrer, Guillaume Lehnasch and Arnaud Mura [email protected] Institut Pprime - UPR 3346 - CNRS - ENSMA - Universit´ e de Poitiers BP 40109, 86961 Futuroscope, France Abstract The shear layers growth rate is known to be altered by compressibility and heat release effects. On the one hand, for increasing levels of compressibility, there is indeed a decrease in pressure fluctuations leading to a reduction in pressure-strain terms, which is responsible for the decrease in growth rate. On the other hand, previous numerical simulations showed that the main influence of the thermal expansion is to reduce the magnitude of the vorticity within the vortex cores and reaction zones, while the baroclinic torque generates alternate regions of positively and negatively signed vorticity at the braids and vicinity of vortex cores. The combination of the two effects favors the diffusion of the vorticity field as well as its attenuation within the vortex core, which results in lower growth rates of sheared layers. Such insights were mostly gained from the consideration of temporally developing mixing layer analyses that relate the longitudinal spatial coordinate to time via the introduction of an artificial average velocity across the layer. In this case, the flow becomes symmetric with respect to its development axis, and it does not distinguish between the fluids from the two streams with different velocities. The analysis of both compressibility and heat release is revisited here by considering numerical simulations of spatially-developing high speed reactive shear layers for different convective Mach number values including the influence of finite rate chemistry effects. The evolution of the vorticity thickness growth rate is analysed in detail in the light of the turbulent kinetic energy and enstrophy budgets. If the use of global single step chemistry tend to support previous findings, that were obtained from temporally developping mixing layer simulations, the conclusions presently drawn from the consideration of finite rate chemistry effects throught the use of detailed chemical kinetics are different. Finally, these investigations are further extended to the consideration of shocked (reactive) mixing layers, a situation significantly less documented in the literature. Introduction Numerical simulations of high-speed reactive shear layers already concentrated a large amount of research efforts, see for instance [1, 2], and the interest in such reactive flow conditions has been, to a large extent, motivated by the development of airbreathing vehicles able to cruise at hypersonic speeds. Most of the aforementioned works dealt with temporally developing turbulent reactive mixing layers and often considered either single-step chemistry or infinitely fast chemistry. Numerical simulations of spatially-developing high speed mixing layers were much seldom reported in the literature and mainly devoted to inert situations [3, 4]. The amount of computer resources needed to obtain an equivalent resolution is indeed greater for spatially growing layers but they display some important differences with temporal simulations. In spatially-developing mixing layers, events that occur downstream can influence the flowfield upstream, whereas in temporally developing layers, no event can affect the flow at previous times. Moreover, in contrast with temporally developing layers, entrainment rates of fluid from the two streams are not necessarily the same. In the present work, direct numerical simulations of spatially-developing shear layers are performed for reactive conditions, and including a detailed description of molecular transport also. Figure 1, which reports a numerical Schlieren superimposed with temperature iso-lines at a convective Mach number value Mc=0.8, pro- vides a typical example of the results that may be obtained from the two-dimensional numerical simulation of a mixing layer developing between vitiated air and hydrogen mixture streams 1. Figure 1: Temperature iso-contours superimposed on numerical Schlieren of the pressure field. Transport equations and numerical methods The present numerical study is carried out with a multicomponent compressible and reactive flow solver. Special attention is paid to the competition that may exist between molecular diffusion and chemical kinetics as well as complex flowfield structures that may feature shock and expansion waves. We therefore consider the compressible Navier-Stokes equations written for a reactive multicomponent mixture characterized by the conservative vector q=�ρ,ρu1,ρu2,ρu3,ρet,ρY1,...,ρYα,...,ρYNsp �t, where ρdenotes the density, uiare the components of the velocity vector, pis the pressure, etis the total energy, Yαis the mass fraction of the αth species (α=1,...,Nsp) with Nsp the total number of chemical species. The corresponding system of conservative equations is supplemented with the ideal-gas equation of state p=ρRT/W, with Rthe universal gas constant and Wthe molecular mass of the mixture obtained from W−1=�Nsp α=1 Yα/Wα. The specific heat capacities at constant pressure and enthalpies for each species are expressed as polynomial forms of the temperature involving a series of coefficients determined from the JANAF databases. The j-component of the heat flux is evaluated from Jj=�Nsp α=1 ρYαVα,j (hα+RT˜χα/Wα)−λ∂T/∂xj, where λis the thermal conductivity of the mixture and ˜χαis the rescaled thermal diffusion ratios of the αth species, which is defined in such manner that DαβXβ˜χβ=θα, with αand β∈[1, ..., Nsp]. In the previous expression, θαand Dαβ denote the thermal diffusion vector and diffusion matrix, respectively, while Xβdenotes the βth species molar fraction. The j-component of the molecular diffusion flux is represented by ρYαVα,j =−�Nsp β=1 ρ˜ Dαβ (dβ,j +(Xβ˜χβ/T)∂T/∂xj), with dβ,j =∂Xβ/∂xj+(Xβ−Yβ)∂ln P/∂xj, where ˜ Dαβ is the flux diffusion matrix formed by the flux diffusion components YαDαβ. All the transport coefficients mentioned above, i.e., ˜ Dαβ, ˜χβas well as the volume and shear viscosity κand µare evaluated using the general purpose fortran library EGLIB [5]. The solver handles detailed chemical kinetics as described through Nrelementary reaction steps involving Nsp chemical species �Nsp α=1 ν� α,jMα��Nsp α=1 ν�� α,jMα,j=1,...,Nr, where Mαis the chemical symbol for the αth species, while ν� α,j and ν�� α,j denote the stoichiometric coefficients. The resulting chemical source terms are given by ˙ωα=�Nr j=1(ν�� α,j −ν� α,j)qj with qj=kfj �Nsp α=1 [Xα]ν� α,j −krj �Nsp α=1 [Xα]ν�� α,j , where kfj and krj denote the forward and reverse rate constants of the jth elementary reaction, respectively, and [Xα]is the molar concentration of the αth species. The treatment of the inviscid component of the transport equation for the conservative vector relies on the seventh-order accurate Weighted Essentially Non-Oscillatory (WENO7) recon1Note that (eddy) shocklets are visible in Fig. 1, and their presence has been also evidenced in the threedimensional numerical simulations we conducted under the same conditions. struction of the characteristic fluxes [6]. In practice, the numerical solver uses a seventh-order accurate centered finite difference scheme, and the application of the WENO7 scheme is conditioned to a smoothness criterion which involves the local values of the normalized spatial variations of both pressure and density [7]. The viscous and molecular diffusion flux functions are determined using an eighth-order centered difference scheme. The temporal integration is performed using the Strang splitting technique: the non-reactive part of the equations is integrated in time thanks to an explicit third-order TVD Runge-Kutta algorithm [8] while the chemical production rates are calculated by solving a stiff system of Ordinary Differential Equations (ODEs) with the general purpose solver VODE [9]. Further details about the numerical methods as well as an exhaustive verification of the solver are provided in references [7, 10]. Table 1: Inlet stream conditions retained for inert and reactive numerical simulations. Global chemistry Detailed chemistry Fuel stream Oxidizer stream Fuel stream Oxidizer stream P(Pa) 94232.25 94232.25 94232.25 94232.25 T(K) 545.0 1475.0 545.0 1475.0 ρ(kg/m3)0.354 0.203 0.354 0.203 YH2(−)0.05 0.0 0.05 0.0 YO2(−)0.0 0.278 0.0 0.278 YH2O(−)0.0 0.17 0.0 0.17 YH(−)- - 0.0 5.60 ×10−7 YO(−)- - 0.0 1.55 ×10−4 YOH (−)- - 0.0 1.83 ×10−3 YHO2(−)- - 0.0 5.10 ×10−6 YH2O2(−)- - 0.0 2.50 ×10−7 YN2(−)0.95 0.552 0.95 0.55 Flow configuration and numerical setup The parameters characterizing each inlet stream are determined from previous experimental and numerical studies, see for instance references [11, 12, 13] which are related to supersonic combustion ramjet (Scramjet) conditions. In these studies, hydrogen is the reference fuel because of its high level of energy per unit weight and shorter ignition delays. For instance, in the experimental study conducted by Miller et al. [11], the fuel stream is composed of hydrogen diluted with nitrogen (or helium) while the oxidizer stream corresponds to vitiated air obtained from combustion operated between hydrogen and air in a pre-chamber. The levels of heat release reached in this experiment were not large enough to induce significant changes in the large scale development of the reactive shear layer, which remains very similar to those previously reported for inert cases at the same level of compressibility. As the present study aims at investigating such heat release effects in high speed shear flows, the retained inlet flow conditions, presented in Table 1, slightly differ from those previously considered in [11]. We will denote by GC the simulations based on the global single step chemistry while DC will refer to simulations performed with a detailed chemistry representation. Conditions at chemical equilibrium are determined from a preliminary study in order to settle the radical mass fraction values in the vitiated air stream, see Table 1, the influence of which is far from being negligible [11]. From this preliminary study, we also determined the adiabatic temperature at equilibrium as well as the auto-ignition times. Figure 2(a) reports the temperature at equilibrium as a function of the mixture fraction z, i.e., a passive scalar defined to be unity in the fuel inlet stream and zero in the oxidizer inlet stream. It is compared to the values associated with other inlet streams conditions that were previously considered in the literature: Miller et al. [11], Cheng et al. [12] and Sekar et al. [13]. The corresponding data can be used to obtain a rough estimate of the maximum levels of temperature that may be obtained within the shear layer and associated heat release. On the one hand, in the configuration of Miller et al. [11], the adiabatic temperature at equilibrium remains lower than the vitiated air stream temperature. On the other hand, in the configurations of Cheng et al. [12] and Sekar et al. [13], heat release is clearly more pronounced. Finally, our configuration appears as an intermediate case featuring a maximum temperature of 2400 K in the vicinity of the stoichiometry (zst =0.41) and, therefore, levels of heat release are expected to produce significant changes in the large scale development of the shear layer. T(K) 0 500 1000 1500 2000 2500 3000 0 0.2 0.4 0.6 0.8 1 Present mixture Sekar et al. (1990) Cheng et al. (1994) Miller et al. (1998) z(−) (a) t(µs) 10 100 1000 0 0.2 0.4 0.6 0.8 1 DC, pure air DC, vitiated air GC z(−) (b) Figure 2: Adiabatic temperature level at equilibrium (a), and self-ignition time scale (b), for different values of the mixture fraction. Figure 2(b) provides the self-ignition delays for the mixture considered in this work. Results associated with global chemistry (GC) have been obtained by using the single step global reaction of Marinov et al. [14] while those associated with detailed chemistry (DC) are based on the chemical reaction mechanism of O’Conaire et al. [15] featuring 21 elementary reactions steps and 10 species. As expected, the shortest ignition time values are obtained from the global reaction mechanism. However, the comparison of the results obtained with either a pure air or a vitiated air oxidizing stream confirms that the presence of chemical radicals significantly shortens the self-ignition delay, and also enlarges the flammable domain. The inlet mixtures that have been considered above, see Table 1, will be used to specify the boundary conditions of spatially-developing numerical simulations of both inert and reactive mixing layers. The corresponding numerical simulations will be conducted for different levels of compressibility characterized by convective Mach number values Mc=0.35,Mc=0.70 and Mc=1.10. In the case Mc=1.1, two-dimensional numerical simulations did not lead to the destabilization of the shear layer. This confirms the conclusion of linear and nonlinear stability analyses, which indeed show that, as the convective Mach number increases, the most amplified modes are no longer two-dimensional and become three-dimensional with perturbations propagating with an angle θrelative to the (x1,x 2)plane. This behavior has been also assessed for compressible reactive mixing layers [16]. In practice, despite the growth in computing performance, parametric DNS investigations with detailed transport and chemical kinetics description still remain limited by computational resources. The present study is therefore restricted to two-dimensional numerical simulations, which have already been shown to accurately portray the characteristic large-scale rollup and vortex-pairing processes. Implications of chemistry-induced heat release on these processes are thus expected to be meaningfully addressed with such numerical simulations. The main conclusions obtained herein indeed concern the large-scale development of shear layers, i.e., under the principal influence of the large eddies resulting from the Kelvin-Helmholtz primary instability. Such characteristics are clearly less sensitive to three-dimensional small-scale dynamics. Finally, it is noteworthy that the insights gained from these two-dimensional numerical simulations have been confirmed from the results of two distinct three-dimensional numerical simulations of reference, which have been conducted for Mc=0.35 under inert conditions, and Mc=0.70 with detailed chemistry under reactive conditions. In all cases to be investigated, the two inlet streams remain supersonic. The velocity in the oxidizer inlet stream is increased to reach the desired value of the convective Mach number, while the velocity in the fuel inlet stream is kept barely larger than the speed of sound. The initial vorticity thickness, δω,0, is adjusted to maintain the same value of the initial Reynolds number Reω,0=640for all the simulations. Numerical simulations are conducted in a computational domain with dimensions L1×L2=350δω,0×80δω,0for Mc=0.35 and L1×L2=350δω,0×122δω,0for Mc=0.70. These computational geometries are respectively discretized with N1×N2= 1739×369 points and N1×N2= 1739×403 points. Mesh stretching is applied in both directions of space. In the transverse direction, the grid size ∆x2=0.168δω,0 is maintained constant from the center of the domain to x2=±20δω,0. A slight stretching is also applied along the longitudinal direction from the beginning of the computational domain, where ∆x1=0.40δω,0, to x1=150δω,0where a constant grid size ∆x1=0.168δω,0is set. In any case, the maximum grid size values conform with those retained in the direct numerical simulations conducted by Fu and Li [3] and the extent of the computional domain is sufficient to allow for the shear layer development [4]. Finally, the simulations are initialized with an hyperbolic tangent profile for the streamwise velocity component, temperature and species mass fractions [1]. A Dirichlet boundary condition is applied at the inlet while non-reflecting conditions are set at the outlet, bottom and top of the domain. A random perturbation is superimposed on the transverse velocity component within a gaussian spot centered at (x1,x 2)=(4δω,0,0) to trigger the destabilization of the mixing layer. Spatially-developing shear layers analysis Figure 3 shows the instantaneous structure of the inert and reactive shear layers for two convective Mach number values. The top inlet stream is associated with fuel injection and the bottom with oxidizer injection. The structure corresponding to the inert case at Mc=0.35 (I-2D-0.35) shows a certain level of coherence with three (approximately) equidistant ellipticalshaped vortices in the domain x2/δω,0∈[200,350]. As the convective Mach number value is increased, the flowfield structure becomes more distorted and the coherence evidenced in the previous case is no longer observed. For the reactive cases, two different flow structures can be observed depending on the retained reaction mechanism. With the detailed reaction mechanism of O’Conaire et al. [15], the flow field structure remains similar to the one of the inert cases. Heat release levels are present on the fuel lean side, delineating the high temperature regions. These regions are continuous at Mc=0.35 (DC-2D-0.35) and become isolated spots at Mc= 0.70, suggesting that the influence of heat release is less important in this case. With the global reaction mechanism of Marinov et al. [14], the shear layer is more severely affected by heat released, whatever the level of compressibility. Low density fluid in the mixing region results in a shift of the unstable mode to lower wave numbers (longer wavelengths). Indeed, when single step chemistry is retained, the largest part of heat release occurs in the early development of the shear layer, which explains why there are only few traces of heat subsequently released further downstream, where almost all hydrogen and oxygen have already been converted into combustion products. Table 2 reports some quantitative confirmations of the qualitative observations discussed above. The vorticity thickness δωis defined as δω=∆U |∂�u1�f/∂x2|max ,(1) where ∆U=U1−U2. Operator �·�refers to Reynolds average while the same operator with index f, i.e., �·�f, denotes Favre average. Primes and double primes indicate the corresponding fluctuations. It can be seen that the vorticity thickness growth rate, given by η−1dδω/dx1with η=(U1−U2)/(U1+U2), is greater in inert cases. Significantly lower values of the growth rate are obtained with global chemistry, which features the shortest ignition delays and also the largest heat release levels. With a detailed chemical kinetics description, the same tendency is observed at Mc=0.35. However, the growth rate value reached at Mc=0.70 is very close to the one previously found under inert conditions, see Table 2, which is confirmed by the flowfield structures displayed in Figs. 3(b) and 3(d). Heat release levels become indeed lower at higher levels of compressibility when using detailed kinetics, whereas the opposite trend is observed with global single-step chemistry. The results obtained here with detailed chemical kinetics contrast with those issued from several numerical simulations conducted in similar conditions under the fast chemistry assumption which did not evidence the same effects. (a) I-2D-0.35 (inert, Mc=0.35). (b) I-2D-0.70 (inert, Mc=0.70). (c) DC-2D-0.35 (detailed chemistry, Mc=0.35). (d) DC-2D-0.70 (detailed chemistry, Mc=0.70). (e) GC-2D-0.35 (global chemistry, Mc=0.35). (f) DC-2D-0.70 (global chemistry, Mc=0.70). Figure 3: Fields of the normalized temperature c=(T−Tmin)/(Tmax −Tmin)superimposed with iso-lines of heat release for the inert and reactive spatially-developing shear layers. Figure 4 provides the normalized growth rate values. Results obtained for inert conditions are found comparable with standard data available from the literature [16, 17, 18, 19]. Here, the reference growth rate δ� ihas been obtained from the preliminary simulation of an inert and incompressible air-air mixing layer, which is not presented here just for the sake of conciseness. The values of the Reynolds number, Reω=Reω,0δω/δω,0, reached at the location x1=300δω,0, where most of the data post-processing will be performed, are also comparable to those associated with previous numerical investigations conducted in similar conditions [1, 2, 20]. Table 2: Results obtained from inert and reactive spatially-developing shear layers. The Reynolds number is computed at x1=300δω,0. Cas η−1dδω/dx1Reω I-2D-0.35 0.143 6421 I-2D-0.70 0.133 8247 DC-2D-0.35 0.103 5158 DC-2D-0.70 0.129 7884 GC-2D-0.35 0.049 3735 GC-2D-0.70 0.031 4638 δ�/δ� i(−) 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Dimotakis (1991) Debbischop & Bonnet (1993) Hall et al. (1993) Day et al. (1998) Langley exp. curve Fu & Li (2006) I-2D CD-2D CG-2D Mc(−) Figure 4: Normalized growth rates vs. Mc. Figure 5 illustrates the budget of the turbulent kinetic energy (TKE) for each simulation as a function of x2/δω. The TKE transport equation is given by D(�ρ�k) Dt=−�ρ��Rlk ∂�ul�f ∂xk�−�ρ��1 �ρ��τ� lk ∂u�� l ∂xk �� −1 2 ∂ ∂xk �ρu�� lu�� lu�� k+2p�u� lδlk −2τ� lku�� l�+�p�∂u�� k ∂xk �+�u�� l��∂�τlk� ∂xk −∂�p� ∂xl�. (2) The first contribution in the RHS of the above equation is the production term �ρ�P. It is followed by the dissipation rate �ρ��, the transport term T, the pressure dilatation contribution Π, and the mass flux coupling term Σ[20]. As shown in Fig. 5, for the present set of two-dimensional numerical simulations of inert and reactive mixing layers, the most important contributions to the TKE budget are the production and transport terms, �ρ�Pand T. Their levels get reduced as the convective Mach number Mcis increased or heat release is present, a behavior similar to the one observed for the vorticity thickness growth rate. This tendency is even more pronounced for the simulation conducted with global chemistry at Mc=0.70. The influence of compressibility and heat release on the shear layer growth rate is further investigated by studying the enstrophy transport equation D�ωiωi� Dt=2�ωiωj ∂ui ∂xj �−2�ωiωi ∂uj ∂uj �+2�eijkωi 1 ρ2 ∂ρ ∂xj ∂p ∂xk �+2�eijkωi ∂ ∂xj�1 ρ ∂τkm ∂xm��.(3) The four terms appearing in the RHS of Eq.(3) describe, respectively, vortex stretching, volumetric expansion (or compression), baroclinic torque and viscous effects. The dilatation and baroclinic mechanisms are strictly zero in constant-density flows. Volumetric dilatation may occur when the density decreases due to heat release and, since the term ∂uj/∂xjis positive for expanding flows, the quantity −ωiωi∂uj/∂xjis associated with a possible enstrophy reduction mechanism. Finally, the baroclinic torque represents the generation (or destruction) of vorticity induced by the differential fluid accelerations that result from non-aligned pressure gradients and density gradients. -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 -3 -2 -1 0 1 2 3 〈 ρ 〉P 〈 ρ 〉 ε T Π Σ x2/δω(−) (a) I-2D-0.35. -0.002 -0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 -3 -2 -1 0 1 2 3 〈 ρ 〉P 〈 ρ 〉 ε T Π Σ x2/δω(−) (b) DC-2D-0.35. -0.002 -0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 -3 -2 -1 0 1 2 3 〈 ρ 〉P 〈 ρ 〉 ε T Π Σ x2/δω(−) (c) GC-2D-0.35. -0.004 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 -3 -2 -1 0 1 2 3 〈 ρ 〉P 〈 ρ 〉 ε T Π Σ x2/δω(−) (d) I-2D-0.70. -0.002 -0.0015 -0.001 -0.0005 0 0.0005 0.001 0.0015 0.002 -3 -2 -1 0 1 2 3 〈 ρ 〉P 〈 ρ 〉 ε T Π Σ x2/δω(−) (e) DC-2D-0.70. -0.00025 -0.0002 -0.00015 -0.0001 -5e-05 0 5e-05 0.0001 0.00015 0.0002 0.00025 0.0003 -3 -2 -1 0 1 2 3 〈 ρ 〉P 〈 ρ 〉 ε T Π Σ x2/δω(−) (f) GC-2D-0.70. Figure 5: TKE cross-stream budget evaluated at x1=300δω,0for inert and reactive spatiallydeveloping mixing layers. Quantities are made non dimensional with ∆Uand δω. Figure 6 displays the last three terms of the RHS of Eq.(3) for Mc=0.35 and Mc=0.70. Whatever the level of compressibility, baroclinic torque, which contributes to the production of enstrophy, and viscous diffusion, which contributes to its destruction, are the most important terms in the enstrophy budget of inert and reactive mixing layers 2. The dilatation term plays a less important role in the destruction of enstrophy whereas the vortex stretching mechanism is not represented in such two-dimensional numerical simulations. At Mc=0.35, the heat release decreases the amplitudes of dilatation, baroclinic torque and viscous diffusion terms. At Mc=0.70, there is no clear reduction of these terms in the reactive case using detailed kinetics compared to the inert case. This also explains why the growth rates are very similar for this two configurations (I-2D-0.70 and DC-2D-0.70). Moreover, the levels of enstrophy production (baroclinic torque) when using detailed chemistry are higher when compressibility increases, see Figs. 6(b) and 6(e), thus enhancing the shear layer growth rate. Nevertheless, the use of a global reaction mechanism at Mc=0.70 results in the lowest values of the production/destruction terms involved in the enstrophy budget. Finally, it is also worth noting that, in reactive cases at Mc=0.35, these terms display an asymmetry for negative values of the transverse coordinate. The corresponding locations area is associated with the fuel lean side, where combustion occurs, see Figs. 3(c)–3(f). 2Note that this will not be necessarily the case for three-dimensional numerical simulations, where vortex stretching may compensate the viscous diffusion term. -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 -3 -2 -1 0 1 2 3 I-2D-035 DC-2D-035 GC-2D-035 x2/δω(−) (a) Dilatation, Mc=0.35. -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -3 -2 -1 0 1 2 3 I-2D-035 DC-2D-035 GC-2D-035 x2/δω(−) (b) Baroclinic torque, Mc=0.35. -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 -3 -2 -1 0 1 2 3 I-2D-035 DC-2D-035 GC-2D-035 x2/δω(−) (c) Viscous diffusion, Mc=0.35. -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 -3 -2 -1 0 1 2 3 I-2D-070 DC-2D-070 GC-2D-070 x2/δω(−) (d) Dilatation, Mc=0.70. -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 -3 -2 -1 0 1 2 3 I-2D-070 DC-2D-070 GC-2D-070 x2/δω(−) (e) Baroclinic torque, Mc=0.70. -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 -3 -2 -1 0 1 2 3 I-2D-070 DC-2D-070 GC-2D-070 x2/δω(−) (f) Viscous diffusion, Mc=0.70. Figure 6: Enstrophy budget for the inert and reactive naturally developing mixing layers, computed at x1=300δω,0. Quantities are made non dimensional with ∆Uand δω. Shocked spatially-developing shear layers The above results confirmed that mixing between fuel and air streams under highly compressible conditions is inherently slow. However, since shock waves (SW) are present inside the intake and combustor of Scramjet engines, shock wave impingement may provide an attractive method to enhance mixing. In this last section, we report numerical simulations of both inert and reactive shear layers interacting with steady oblique shock waves. U1 U2 x1 x2 1 2 3 4 5 6 0 Figure 7: Sketch of the SW mixing layer interaction geometry. 0: splitter plate; 1: SW generator; 2: incident SW; 3: shear layer; 4and 6: reflected SW; 5: transmitted SW. Figure 7 provides a schematic view of the flow configuration. The fuel (top) and oxidizer (bottom) inlet stream properties remain strictly the same as those considered in the above cases and, therefore, values gathered in Table 1 still hold. The initial Reynolds number value is kept to 640 and the convective Mach number is set to Mc=0.48. The computational domain size is L1×L2=275δω,0×120δω,0and is uniformly discretized in space using N1×N2= 1638×717