Finite-rate chemistry effects in turbulent hypersonic boundary layers: A direct numerical simulation study

The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasiadiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully developed turbulent conditions using a five-species, chemically reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inlet of the computational domain, both simulations are initiated in the laminar flow region and the flow is let to evolve up to the fully turbulent regime. Modal forcing by means of localized suction and blowing is used to trigger laminar-to-turbulent transition. The high temperatures reached in the near-wall region including the viscous and buffer sublayers activate significant dissociation of both oxygen and nitrogen. This modifies in turn the thermodynamic and transport properties of the reacting mixture, affecting the first-order statistics of thermodynamic quantities. Due to the endothermic nature of the chemical reactions in the forward direction, temperature and density fluctuations in the reacting layer are smaller than in the frozen-chemistry flow. However, the first- and second-order statistics of the velocity field are found to be little affected by the chemical reactions under a scaling that accounts for the modified fluid properties. We also observed that the Strong Reynolds Analogy remains well respected despite the severe hypersonic conditions and that the computed skin friction coefficient distributions match well the results of the Renard-Deck decomposition extended to compressible flows.

Figure 1

Isosurfaces of $Q$-criterion, colored with the local values of ${\mathrm{O}}_2$ mass fraction for the CN case. The entire computational domain is displayed, along with a zoom on the laminar-to-turbulent transition region.

Figure 2

Wall distributions of the skin friction coefficient $C_f$ as a function of ${\mathrm{Re}}_x$. ($–––$), CN case; ($––––$), FR case. The black dash-dotted line denotes the laminar correlation $C_f^{\text{lam}}$.

Figure 3

Instantaneous visualizations of the normalized streamwise velocity in a $x\text{−}z$ plane for FR case (top) and CN case (bottom) at $y\approx 4.5{\delta }_{\text{in}}^{*}$ (corresponding to $y^{+}\approx 30$ at $\widehat{x}=5100$). The spanwise white solid lines denote the blowing-and-suction forcing location; the dashed lines mark the position of the first peak of $C_f$, and the dash-dot lines indicate the streamwise position at which ${\mathrm{Re}}_{\tau }=185$. The spanwise direction is stretched for better visualization.

Figure 4

Streamwise evolution of averaged dynamic viscosity $\overline{\mu }$ (a) and thermal conductivity $\overline{\lambda }$ (b) at the wall, normalized with respect the constant values of the FR case. ($–––$), CN case; ($––––$), FR case.

Figure 5

Streamwise evolution of the averaged mass fractions ${\overline{Y}}_n$ at the wall for species ${\mathrm{O}}_2$, NO, O, and N. ${\overline{Y}}_{{\text{N}}_2}$ is not shown being outside the $y$-axis bounds.

Figure 6

Wall-normal profiles of the van Driest-transformed streamwise velocity (a) and of the normalized mean temperature (b) at ${\mathrm{Re}}_{\tau }=185$. ($–––$), CN case; ($––––$), FR case.

Figure 7

Wall-normal mean profiles of viscosity and thermal conductivity (a), specific heat capacity at constant pressure (b), Prandtl number (c), and specific heat ratio (d) at ${\mathrm{Re}}_{\tau }=185$. ($–––$), CN case; ($––––$), FR case.

Figure 8

Wall-normal evolution of mean Lewis number (a) and Schmidt number (b) at ${\mathrm{Re}}_{\tau }=185$, for the chemically reacting simulation, in inner scaling.

Figure 9

Wall-normal profiles of the average Damköhler number (a), species mass fractions (b), and species Damköhler number ${\text{Da}}_n^I$ at ${\mathrm{Re}}_{\tau }=185$. In panel (b), ${\mathrm{N}}_2$ is not shown, being $Y_{{\text{N}}_2}>0.25$.

Figure 10

Wall-normal profiles of Reynolds stresses (a) and of the normalized r.m.s. temperature (b), at ${\mathrm{Re}}_{\tau }=185$. ($–––$), CN case; ($––––$), FR case.

Figure 11

Wall-normal profiles of r.m.s. mass fractions (b) at ${\mathrm{Re}}_{\tau }=185$ for the CN case.

Figure 12

Correlation coefficient between $u^{\prime \prime }$ and $T^{\prime \prime }$ without total temperature correction (a) and with total temperature correction (b), at ${\mathrm{Re}}_{\tau }=185$. ($–––$), CN case; ($–.–.–..$), SRA estimation.

Figure 13

Wall-normal profiles of the turbulent Prandtl number for CN case, at ${\mathrm{Re}}_{\tau }=185$. ($–––$), CN case; ($–.–.–..$), SRA estimation.

Figure 14

Normalized turbulent transport of species mass fractions in the streamwise (a) and wall-normal (b) directions; normalized turbulent diffusion fluxes in the streamwise (c) and wall-normal (d) directions, at ${\mathrm{Re}}_{\tau }=185$.

Figure 15

Wall-normal profiles of the turbulent Schmidt number for CN case, at ${\mathrm{Re}}_{\tau }=185$. The horizontal dashed-dotted line denotes the SRA estimation.

Figure 16

Premultiplied spanwise spectra $k_z{E}_{vv}/u_{\infty }^2$ (a), $k_z{E}_{uu}/u_{\infty }^2$ (b) and $k_z{E}_{TT}/T_{\infty }^2$ (c) for the chemical nonequilibrium simulation, at ${\mathrm{Re}}_{\tau }=185$.

Figure 17

Streamwise evolution of skin friction coefficient ($–––$) superposed with Renard-Deck decomposition (symbols) (a) and contribution of each term of Eq. (28) (b) for the chemical nonequilibrium case.

Figure 18

Distribution of two-point correlations in the spanwise direction, at ${\mathrm{Re}}_{\tau }=185$: $\alpha =u$, at $y^{+}=10$ () and $y^{+}=150$ (); $\alpha =\rho$, at $y^{+}=10$ () and $y^{+}=150$ (). (a) CN case; (b) FR case.

Figure 19

One-dimensional energy spectra in the spanwise direction, at ${\mathrm{Re}}_{\tau }=185$ : $\alpha =\rho u^2$, at $y^{+}=10$ () and $y^{+}=150$ (); $\alpha =T$, at $y^{+}=10$ () and $y^{+}=150$ (). (a) CN case; (b) FR case.