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Numerical strategy to perform direct numerical simulations of hypersonic shock/boundary-layer interaction in chemical nonequilibrium

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Abstract

Literature regarding hypersonic shock/boundary-layer interaction is mostly restricted to calorically perfect gases, even though this condition is far from reality when temperature rises. High-temperature effects alter physical and transport properties of the fluid, due to vibrational excitation and gas dissociation, and chemical reactions must be considered in order to compute the flow field. In this work, a code for hypersonic aerodynamics with reactions using parallel machines (CHARLIE) is described and a numerical methodology is developed to perform direct numerical simulations of shock/boundary-layer interaction in chemical nonequilibrium. The numerical scheme and the characterization of non-reflecting boundary conditions are addressed. Results show that the flow properties differ considerably if chemical reactions are taken into account. A direct numerical simulation of a shock interacting with a turbulent boundary layer in the hypersonic regime with high-temperature effects is also presented for the first time.

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Acknowledgements

This work was supported by the Air Force Office of Scientific Research (Grant FA9550-16-1-0385) and performed using HPC resources at the University of Maryland (DeepThought2) and the Maryland Advanced Research Computing Center (MARCC).

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  1. P. S. Volpiani

    Present address: ONERA, The French Aerospace Lab, 8 Rue des Vertugadins, 92190, Meudon, France

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  1. Department of Mechanical Engineering, University of Maryland, College Park, MD, 20742, USA

    P. S. Volpiani

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Appendices

Appendix 1: Numerical scheme coefficients

See Tables 4 and 5.

Appendix 2: Thermo-chemistry validation

In order to validate the thermo-chemistry implementation, a mono-dimensional methane-air laminar flame was simulated at equivalence ratio \(\phi =0.83\) and compared with the AVBP solver solution [68]. A two-step reduced chemical mechanism for the methane oxidation presented in [69] was used in both runs:

$$\begin{aligned} \mathrm {CH_4} + 1.5\mathrm {O_2}&\longrightarrow \mathrm {CO} + 2 \mathrm {H_2O} \end{aligned}$$
(42)
$$\begin{aligned} \mathrm {CO}+0.5 \mathrm {O_2}&\longleftrightarrow \mathrm {CO_2} \end{aligned}$$
(43)

The corresponding reaction rates are modeled using Arrhenius laws:

$$\begin{aligned} q_{1}&=A_1 T^{\beta _1}\exp {\left( \frac{-E_\mathrm{a1}}{RT} \right) } \left( \frac{\rho Y_{\mathrm {CH_4}}}{W_{\mathrm {CH_4}}}\right) ^{n_{\mathrm {CH_4}}^1} \left( \frac{\rho Y_{\mathrm {O_2}}}{W_{\mathrm {O_2}}}\right) ^{n_{\mathrm {O_2}}^1} \end{aligned}$$
(44)
$$\begin{aligned} q_{2}&=A_2 T^{\beta _2}\exp {\left( \frac{-E_\mathrm{a2}}{RT} \right) } \left[ \left( \frac{\rho Y_{\mathrm {CO}}}{W_{\mathrm {CO}}}\right) ^{n_{\mathrm {CO}}^2} \left( \frac{\rho Y_{\mathrm {O_2}}}{W_{\mathrm {O_2}}}\right) ^{n_{\mathrm {O_2}}^2} \right. \nonumber \\&\quad \left. -\frac{1}{K_\mathrm{e}} \left( \frac{\rho Y_{\mathrm {CO_2}}}{W_{\mathrm {CO_2}}}\right) ^{n_{\mathrm {CO_2}}^2} \right] \end{aligned}$$
(45)

where pre-exponential factors, activation energies, and model exponents are summarized in Table 6; \(K_\mathrm{e}\) is the equilibrium constant for the second reaction.

The reference viscosity is \(1.8405\times 10^{-4}\) kg/(m\(\cdot \) s), the reference temperature 300 K, and the exponent for the power law 0.6759. The domain of length 1.6 cm was discretized in 400 equally distributed points.

Figure 20 compares the spatial evolution of mass fractions profiles, temperature, and heat capacity at constant pressure with the reference simulation. The agreement is excellent, validating the numerical implementation.

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Volpiani, P.S. Numerical strategy to perform direct numerical simulations of hypersonic shock/boundary-layer interaction in chemical nonequilibrium. Shock Waves 31, 361–378 (2021). https://doi.org/10.1007/s00193-021-01018-6

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