Prediction of aerothermal characteristics of a generic hypersonic inlet flow

Abstract

Accurate prediction of aerothermal surface loading is of paramount importance for the design of high-speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shock-wave/turbulent boundary layer interaction at Mach 8.3. High Reynolds numbers ($Re_L \approx 11.6 \times 10^6$ based on free-stream conditions) and the presence of cold walls ($T_w/T_\circ \approx 0.26$) leading to large near-wall temperature gradients necessitate the use of wall-modeled large eddy simulation (WMLES) in order to make calculations computationally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using a standard LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including three-dimensionality in the mean, shock/boundary layer interactions, and flow separation. We demonstrate that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes.

Appendix A. Statistical and grid convergence

In this section, the statistical and grid convergence of the main quantities of interest are investigated.

1.1 A1. Averaging time convergence study

As shown in Fig. 26, increasing the time averaging interval by 8 flow through times does not affect the pressure and mean surface heat flux statistics, and hence, these key quantities of practical interest are considered statistically converged.

Fig. 26

Streamwise distributions of the time-averaged a surface pressure and b surface heat flux on the flat plate at $z/L_r = 0$. WMLES denotes the result reported in Fig. 9 and WMLES2 denotes the solution averaged in a time interval, which is 8 flow-through times longer than that of WMLES

1.2 A2. Resolution sensitivity study

A higher-resolution simulation with 143M cells was carried out. This mesh is generated by refining the near-wall region of the mesh with 70M cells (as described in Table 1). As shown in Fig. 27, the results from both resolutions are generally within the experimental uncertainty bars of measured wall pressure. The heat flux predictions upstream of $x/L_r=190$ are improved with the finer mesh. In terms of the flow structure, as shown in Fig. 28, the shape of the predicted separation bubble from the higher resolution agrees with the experimental sketch better. Further mesh refinements, especially in the vicinity of the separation bubble may improve the predictions. However, given the intrinsic uncertainties in the prescription of inflow conditions, and the higher cost of more refined computations, we did not carry out additional simulations with finer grid resolution. As remarked earlier, the LES results are always going to be grid dependent, but do converge to DNS in the limit of very fine grids. Here, we have demonstrated the level of accuracy that can be expected at affordable cost.

Fig. 27

Streamwise distributions of the time-averaged a surface pressure and b surface heat flux on the flat plate at $z/L_r = 0$. The results from WMLES with 70M cells and WMLES mesh 2 with 143M cells are reported for comparisons. Also plotted are the uncertainty bars reported from the experiment

Fig. 28

Distribution of the total pressure $\overline{P_\circ }/\overline{P_{\circ ,\infty }}$ on a transverse y–z plane at $x/L_r=183.2$. b Denotes the experimental result and is adapted from the Fig. 11(a) of [25]. a, c denote the WMLES results from the mesh with 70M cells and 143M cells, respectively