Session X16: Supersonic and Hypersonic I

Supersonic wall turbulence at high Reynolds numbers

We perform a Direct Numerical Simulation of supersonic turbulent boundary layer flow up to Re_τ=5500, considering a Mach number of 2 and adiabatic wall. 

This allows us to approach an asymptotically high–Reynolds number state, capturing flow features that are not visible at lower Reynolds numbers.

In particular, the presence of a true log-layer enables us to assess important aspects such as the outer peak of the velocity variance, scaling of velocity spectra and the intensity of very-large-scale motions.

We expect the present data to highlight the effect of compressibility at high Reynolds numbers by comparing them with recent high Reynolds DNS of low speed flows [Pirozzoli et al., JFM, 2021].

Moreover, the comparison with different flow cases at high Re is relevant in assessing common features, as well as flow specific ones.   

Development of a wall model for chemically-reacting turbulent hypersonic boundary layers

The numerical prediction of aerodynamic drag and heat transfer on high-Mach flight vehicles poses a significant computational challenge owing to the presence of multi-scale flow features such as turbulence, shock waves, and activation of thermochemical processes. To that end, the development of wall models capable of representing the correct reacting boundary layer dynamics at a reduced computational cost is crucial. The current work presents and evaluates a generalization of the wall model of [Griffin et al., JFM, 2023] (GFM model), accounting for finite-rate chemistry and multicomponent diffusion in reacting hypersonic boundary layers. The formulation is then evaluated a priori with direct numerical simulations of chemically-reacting turbulent boundary layers at Mach numbers of 7 and 10, comparing the predictions of velocity, temperature and mass fraction profiles, as well as the wall shear stress τ_w and heat flux q_w. Preliminary analysis demonstrates significant improvements relative to the classical equilibrium wall model when applied to compressible wall-bounded flows with strong wall-cooling.   

Direct numerical simulations of hypersonic shock-turbulence interactions

We present the results of shock-turbulence interactions in hypersonic flows using direct numerical simulation (DNS) and linear interaction analysis (LIA). The DNS calculations are conducted with the HTR solver at various turbulent Mach numbers. These results are compared with linear theory by solving the unperturbed problem using the in-house chemical equilibrium code Combustion Toolbox. Subsequently, the perturbed problem comprising weakly isotropic vortical disturbances is solved using LIA. The study focuses on how dilatational energy ahead of the shock influences the Reynolds stress components. Additionally, we examine the effect of vibrational excitation on turbulence amplification by using two thermodynamic models: calorically perfect gas and calorically imperfect gas with frozen chemistry.   

Stagnation enthalpy effects on a hypersonic turbulent compression corner flow

Very high gas temperatures, which activate several thermochemical processes, are a typical feature of hypersonic flows. In this study, we investigate the effects of stagnation enthalpy on a turbulent boundary layer that flows over a cold isothermal compression corner. The analysis is carried out numerically by performing direct numerical simulations with the Hypersonic Task-based Research (HTR) solver (Di Renzo et al., Comp. Phys. Comm. 255, 2020). The main parameters of this fundamental configuration, including free-stream Mach number, wall-cooling, and free-stream stagnation enthalpy, are varied systematically in several calculations to highlight the response of the flow field. Moreover, both calorically perfect and imperfect gas models are taken into account in the mathematical formulation of the problem to highlight the effects of vibrational excitation on the flow dynamics. The variations of the skin-friction coefficient, wall heat flux, Reynolds analogy factor, and pressure fluctuations will be described in this talk while highlighting the importance of high-temperature effects on hypersonic turbulence.   

Free-stream disturbance receptivity and amplification at hypersonic speeds by adjoint Green’s function

Transition to turbulence in the boundary layer on hypersonic vehicles in flight is difficult to infer from wind tunnel tests or at reasonable computational cost.

A new physically motivated scaling for transition location on blunt cones in tunnel tests is shown to collapse several experimental datasets in the absence of transition reversal. This scaling supports transient growth as the transition mechanism, even when approaching the sharp limit, contrary to traditional wisdom. 

The discrepancy between transition in flight and in tunnel tests is addressed by answering the question of how fluctuations in the free-stream are transported into the boundary layer and amplified on a blunt cone. The receptivity and amplification of a disturbance that arrives at a point near transition is directly computed by way of the adjoint Green’s function. The adjoint Green’s function provides a quantitative account of all possible linear receptivity and amplification mechanisms in a way that is agnostic to a particular choice of free-stream disturbance field.   

Passive Control of the Aero-Optics of a Supersonic Shear Layer

When a planar wavefront passes through a compressible shear layer, density gradients lead to the refraction and warping of the wavefront. Particularly in the presence of density fluctuations, this phenomenon can be a hindrance to the preservation of the wavefront. In this study, we measure the shear layer created through boundary-layer separation on a backward-facing step within a Mach 2.8 freestream. Within the first phase of this study, measurements are obtained using stereoscopic particle image velocimetry (SPIV) to quantify the incoming boundary layer upstream of separation along with the shear layer itself. Quantities of interest include the boundary layer thickness, the shear layer thickness, and Reynolds stresses. With these data, passive flow control devices can be properly sized, with planned experiments including wavefront measurements to quantify the aero-optic health of the shear layer.   

Aeroacoustics and vorticity assessment for a highly-heated, supersonic aerospike nozzle jet

Large Eddy Simulations (LES) are deployed to characterize the effect of temperature on the various terms of the time-averaged vorticity equation for a supersonic aerospike nozzle jet. It is known that convection of vortices through the shock-cell structure formed in a non-ideally expanded jet generates sound propagating into the far-field. In the meantime, higher jet temperature ratios are also strongly affecting sound generation. This study allows to describe the effects of jet temperature on the different vorticity equation terms and hence to shed new light on the underlying mechanisms for sound generation. It is found that the vorticity transport term is the strongest in the annular region of the jet indicating strong dynamic effects responsible for sound generation. In the cold case, the vorticity transport term is highest at the location of the separation bubble whereas at higher temperature ratios, it is stronger at the outer annular shear layer. A further distinction of the tilting and stretching terms due to compressibility and velocity gradients shows that stretching effects are dominating in the vicinity of the annular nozzle outlet. The tilting term is dominating the vorticity dynamics further downstream in the jet. Finally, the baroclinic term grows in intensity with increasing temperature ratio.   

Assimilation of wall-pressure measurements in high-speed boundary layers using a Bayesian-ML approach

Assimilation of wall-pressure measurements in high-speed flows was previously successfully demonstrated using ensemble variational (EnVar) techniques, for flat plate boundary layers (Buchta & Zaki, J. Fluid Mech., 916, A44, 2021) and flow over a slender cone (Buchta et al. J. Fluid Mech., 947, R2, 2022). The EnVar technique is accurate, does not require an adjoint algorithm, and can be adopted with any forward model. However, success is highly dependent on the choice of the initial estimate of the unknown control vector. In this study, we develop a global optimizer for data assimilation using a Bayesian approach coupled with deep operator networks (DeepONets). Bayesian optimization minimizes the loss function by progressively incorporating measurements obtained from new estimates. A Gaussian process regression (GPR) is adopted as an estimator of the loss function, for which we adopt an ensemble of DeepONets. Performance is assessed in the context of high-speed boundary layer undergoing transition due to subharmonic resonance of planar and oblique instability waves. Using our combined Bayesian-DeepONet algorithm, the dominant frequency and phase difference between the 2D and 3D waves are estimated with satisfactory accuracy and efficiency.   

Development of an Open-Source MHD Capability and the Efficacy of a Magnetic Dipole Control System for Atmospheric Entry

This study assesses the effectiveness of using a translating and rotating magnetic dipole for increased performance and rotational control of a reentry vehicle by implementing magnetohydrodynamic (MHD) physics into Computational Fluid Dynamics (CFD) software. Lorenz force and joule heating source terms were added to both SU2 and Kestrel using conductivity calculated by a modified Gupta-Yos model. Both CFD programs used a two-temperature rigid rotator and harmonic oscillator thermochemistry model with 11-species reacting air in laminar flow with a non-conductive and non-catalytic body. Baseline solution grid independence was verified using stagnation line temperatures, electron densities were compared with the NASA RAM-C II experiment to verify the chemistry, and shock standoff distance ratios were verified with experimental, theoretical, and numerical data. The study shows that a rotated or off-center dipole can increase drag and lift while also providing control moments and demonstrates the possibility of its use for flow control. Additional studies will look at how vehicle design and dipole location can improve the efficacy of a MHD control system.   

Catalysis and Dissociation Effects on Hypersonic Boundary Layers Structure over Small Defects

Nonequilibrium aerodynamics can significantly impact flow field characteristics and gas-surface interactions, particularly in relation to material ablation for Hypersonic flows. Defects on ablative surfaces pose a significant challenge in Hypersonic flows due to the mixed hyperbolic-elliptic characteristics of the viscous-inviscid interaction. Modeling their effect on separation and catalytic recombination is necessary to improve the understanding of flow-reaction coupling over damaged ablators. This study aims to compare the dissociation effects of air in nonequilibrium on surface geometry with a defect present in representative hypersonic flow field conditions. Both the boundary layer impact and the ablation thermo-chemistry changes are taken into account. An analytical approach based on the Triple Deck Theory (TDT) of boundary layer response to localized defects was used, and the results are compared to numerical methods and schemes modeled in SU2. A custom-configured Carbon-air mixture was created using Mutation++ that includes Catalytic recombination and gas surface interaction models. Results show that separation in high Mach number flows is a complex phenomenon with a single separation region transitioning to multiple bubbles before supporting unsteady breathing. The recirculation significantly affects the transport of atomic species from the dissociation layer to the surface.   

Parametric DNS Study of Coolant Materials for Transpiration Thermal Protection Systems Along Hypersonic Leading Edges

Recently there has been increasing interest in hypersonic flight systems, but the practical use of these systems remains limited primarily by the enormous heat loads present during atmospheric hypersonic flight. Transpiration thermal protection systems (TPS) can be used to combat large incident heat fluxes in a manner similar to ablative processes. However, transpiration TPS utilize vaporization of a replenishable liquid coolant and so experience no surface degradation. As such, transpiration TPS are reusable and capable of maintaining sharp geometries during operation. The goal of this study is to evaluate the cooling capability of transpiration TPS considering a variety of flight conditions and coolant properties. A parametric study of metal and metal oxide coolants was conducted using 3D DNS studies and self-similar 2D boundary-layer solutions. The boundary-layer solutions assumed frozen flow, while the DNS studies investigated the effects of thermochemical non-equilibrium and chemical interactions. With the results of this study suitable coolant materials may be determined for given flight conditions. Hence, a step is taken towards attaining reusable thermal protection systems for sharp leading edges with greater speed, maneuverability, and efficiency than is currently possible.   

Non-intrusive reduced-order modelling of coupled fluid-material physics at ablating interfaces

Designing thermal protection systems for atmospheric reentry requires simulating the coupled physics of a (possibly ablating) reacting solid and a super/hypersonic flow. The computational bottleneck is often the computational fluid dynamics solver, which, in the presence of severe CFL constraints, is orders of magnitude more expensive than the material response solver. While we can afford to compute the material response using the governing equations, the computational cost of solving the fluid dynamics equations must be reduced by developing reduced-order models that capture the behavior of the fluid in response to the material dynamics.

We develop reduced-order models for the fluid dynamics using a novel, non-intrusive paradigm. Inspired by the form of projection-based reduced-order models, we seek reduced-order tensors as well as bases for the test and trial subspaces by minimizing the error between ground-truth observations and the predictions provided by the reduced-order model. The domain of the optimization problem is a product manifold of several Euclidean spaces (as many as the number of tensors we wish to fit) with a Grassmann manifold and a Stiefel manifold. The optimization can be performed non-intrusively in the sense that the gradient of the cost function with respect to the parameters does not require quering the full-order fluid dynamics solver. The resulting models are demonstrated on the Mach-2 flow over an ablating wedge.