Reducing turbulence- and transition-driven uncertainty in aerothermodynamic heating predictions for blunt-bodied reentry vehicles

Turbulent boundary layers approximating those found on the NASA Orion Multi-Purpose Crew Vehicle (MPCV) thermal protection system during atmospheric reentry from the International Space Station have been studied by direct numerical simulation, with the ultimate goal of reducing aerothermodynamic heating prediction uncertainty. Simulations were performed using a new, well-verified, openly available Fourier/B-spline pseudospectral code called Suzerain equipped with a ``slow growth'' spatiotemporal homogenization approximation recently developed by Topalian et al. A first study aimed to reduce turbulence-driven heating prediction uncertainty by providing high-quality data suitable for calibrating Reynolds-averaged Navier--Stokes turbulence models to address the atypical boundary layer characteristics found in such reentry problems. The two data sets generated were Ma[approximate symbol] 0.9 and 1.15 homogenized boundary layers possessing Re[subscript theta, approximate symbol] 382 and 531, respectively. Edge-to-wall temperature ratios, T[subscript e]/T[subscript w], were close to 4.15 and wall blowing velocities, v[subscript w, superscript plus symbol]= v[subscript w]/u[subscript tau], were about 8 x 10-3 . The favorable pressure gradients had Pohlhausen parameters between 25 and 42. Skin frictions coefficients around 6 x10-3 and Nusselt numbers under 22 were observed. Near-wall vorticity fluctuations show qualitatively different profiles than observed by Spalart (J. Fluid Mech. 187 (1988)) or Guarini et al. (J. Fluid Mech. 414 (2000)). Small or negative displacement effects are evident. Uncertainty estimates and Favre-averaged equation budgets are provided. A second study aimed to reduce transition-driven uncertainty by determining where on the thermal protection system surface the boundary layer could sustain turbulence. Local boundary layer conditions were extracted from a laminar flow solution over the MPCV which included the bow shock, aerothermochemistry, heat shield surface curvature, and ablation. That information, as a function of leeward distance from the stagnation point, was approximated by Re[subscript theta], Ma[subscript e], [mathematical equation], v[subscript w, superscript plus sign], and T[subscript e]/T[subscript w] along with perfect gas assumptions. Homogenized turbulent boundary layers were initialized at those local conditions and evolved until either stationarity, implying the conditions could sustain turbulence, or relaminarization, implying the conditions could not. Fully turbulent fields relaminarized subject to conditions 4.134 m and 3.199 m leeward of the stagnation point. However, different initial conditions produced long-lived fluctuations at leeward position 2.299 m. Locations more than 1.389 m leeward of the stagnation point are predicted to sustain turbulence in this scenario.