Session ZC15: Supersonic and Hypersonic II

Wall-cooling and compressibility effects on high-speed turbulent boundary layers

Aerodynamic drag and heat transfer on high-speed boundary layers are highly influenced by the free-stream Mach number and surface temperature. These two parameters strongly affect the near-wall dynamics, weakening the coupling between velocity and temperature fields that is often leveraged in reduced-order models. In this study, we analyze a numerical database to quantitatively describe Mach number and wall cooling effects in high-speed zero-pressure-gradient turbulent boundary layers using Direct Numerical Simulation. To investigate the individual effect of each parameter, three free-stream Mach numbers (from 2 to 6) and four wall temperature conditions (from adiabatic to very cold walls) are explored, while Re_τ remains fixed. The present database is designed to shed light on the coupling between momentum and temperature fields, with emphasis on the choice of the diabatic parameter Θ [Zhang et al., JFM, 2014] to recover the same flow dynamics at different Mach numbers. Additional analysis on the effect of Mach number and wall-cooling on turbulence anisotropy and separation of turbulence scales allows us to provide a novel view on the physical mechanisms that underlie similar behaviour in certain aspects, while different in others.   

Computational analysis of the interaction of particles with the shock structure surrounding hypersonic aerial vehicles

When hypersonic aerial vehicles re-enter the atmosphere they encounter rain droplets, mist, fog, meteoroids, and ice crystals present in precipitating clouds. An impact with these minute objects at such high speeds can cause significant/catastrophic damage to the vehicle's outer surface. Liquid droplets also tend to disintegrate into smaller droplets and create a mist that can further damage the vehicle. The distribution of particles of various diameters encountering a shock and the droplet deformation that follows - which are both crucial for estimating the impact event is not well-understood. To this end - the present study produces a DNS-like Euler-Lagrangian (EL) coupled, compressible, density-based solver with the Clift-Gauvin particle drag model (best performance for high-speed flows) to produce a comprehensive statistical analysis of the positions and conditions of particles of different diameters. The understanding gained from this study is intended to form the foundation of future CFD of isolated raindrops and ice crystals. The simulations are based on a double-wedge geometry with conditions encountered at 20 kilometers altitude with a large number of particles in the range of 1 to 1000 microns considered.    

Quantitative background-oriented schlieren (BOS) analysis of density fields around supersonic projectiles using two optical flow techniques

Optical flow is an image processing technique that measures intensity shifts between image pairs. The Horn-Schunk and Lucas-Kanade algorithms were used to produce background-oriented schlieren (BOS) images of supersonic conical projectiles. The optical flow processing methods are compared to each other and other BOS image processing methods for quantitative measurements of the density field around the projectiles. The Horn-Schunk analysis is shown to more accurately reproduce the sharp density jump across the shock wave and had less background noise. Both optical flow methods cause some artificial spreading of the shock wave appearance and density rise which is related to the local averaging of pixel intensities in the image processing analysis. The BOS processing methods show accuracy similar to quantitative schlieren but are limited by the pixel resolution of the images. The reconstruction of the density field requires the application of an Abel inversion to account for the path integration of the light ray deflection through the conical flowfield. Several methods for computation of the inversion are considered and compared. The calculated density fields are compared to the theoretical Taylor-Maccoll conical flow profile.   

The generation and modeling of freestream disturbances from hypersonic boundary layers: A resolvent perspective

Turbulent boundary layers (TBL) formed on the walls of hypersonic experimental facilities generate acoustic disturbances which radiate into the freestream (i.e. the test section) and disrupt the measurements conducted within the test section and in the near-wall region (Duan et. al.; Journal of Spacecraft and Rockets 56.2 (2019): 357-368). Hence, accurate theoretical models for the acoustic disturbances generated by TBLs are necessary to account for the impact of the freestream disturbance field on transition studies and experimental designs. In this work, we model the connection between the freestream disturbance field and near-wall generation mechanisms using the resolvent analysis applied to a hypersonic TBL.   

Unsteady Surface Pressure Fluctuations Due to Surface Deformations on an Airfoil in a Uniform Mach 6 Flow

Hypersonic vehicle control fins experience pressure and thermal loads which cause steady and unsteady surface deformations. The aerodynamic response to the unsteady deformations must be characterized and are often approximated by local piston theory, which bases the pressure response on a local inviscid steady state. However, this methodology does not incorporate the effects of viscosity, mostly through the presence of a boundary layer, as well as the influence of flow complexities, such as multiple adjacent deforming surfaces. In this work, deformation of single and tandem surfaces on a representative airfoil geometry in a Mach 6 freestream is forced based on linear beam theory, with a range of beam modes considered. The unsteady aerodynamic response predicted by local piston theory, two-dimensional versions of boundary element theory, Euler-based CFD, and Navier-Stokes-based CFD at different Reynolds numbers are compared and discussed.   

surface instabilities at ablating interfaces

Ablating surfaces are often used in hypersonic applications as a thermal protection system. Numerical simulations of the interaction between the hypersonic flow and the ablating surface have a tendency to develop high wavenumber surface instabilities. In this work, the nature of the instabilities is investigated through numerical simulation of both a simplified model and the fully nonlinear coupled ablation system. In order to understand the nature of the instability, a simplified model of the linear inviscid flow over an isothermal (linear) porous ablator subject to small surface perturbations is studied. In the simplified model, the surface recession rate is proportional to the absolute value of the gas velocity at the surface. This is a representation of the well-known B' approach to surface ablation. Despite the fluid and porous material dynamics both having been linearized, the presence of the absolute value in the interface model still introduces a nonlinearity. Studying this semi-analytical system numerically shows the system to be unstable with amplification in the highest wavenumbers that are numerically represented.Moving to the full ablation system with nonlinear coupled physics, the supersonic flow over an ablating flat plate with a blunted leading edge is simulated. The results show the same type of behavior observed in the simplified model, where high wavenumber structures start developing along the surface. It is then demonstrated, that in both problems considered, the use of a low-pass filter can successfully mitigate the growth of the high wavenumbers.   

Dependence of wall-pressure measurements on precursor perturbations in hypersonic boundary layers

To maximize the utility of measurements in hypersonic flows, we interpret sensor data with the aid of the equations that govern their dependence on precursor events. Specifically, the adjoint Navier-Stokes equations are used to evaluate the sensitivity of a sensor to upstream perturbations. Particular attention is placed on the domain of dependence (DOD) of wall-pressure measurements, and we report results at Mach 4.5 for boundary layers over flat plates and slender cones in the transitional regime. In backward time, the DOD retreats upstream from the sensor location, taking the form of a wavepacket that splits into two parts: one that propagates into the free stream and the second that remains within the boundary layer. The latter part amplifies as it advects upstream, with most of its energy being concentrated near the boundary-layer edge. The sensitivity to different disturbances, e.g. upstream temperature versus velocity fluctuations, is contrasted as well as the DoD for sensors within the pre-transitional and transitional boundary layers. The introduced framework paves the way for a richer interpretation of sensor data and improved design of measurements in high-speed flows.   

Direct numerical simulation of a strongly reacting turbulent hypersonic boundary layer in chemical nonequilibrium

The combined presence of leading-edge shock waves together with near-wall viscous dissipation activates several high-enthalpy effects in hypersonic boundary layers, including both vibrational excitation and molecular dissociation. With chemical processes proceeding at finite rates, on time scales comparable to that of turbulent mixing, the thermodynamic fluctuations introduced by eddy motions result in significant interaction between the thermochemical and hydrodynamic fields. In order to further characterize this turbulence-chemistry interaction, we present a direct numerical simulation of a reacting high-Mach turbulent boundary layer undergoing significant chemical activity. Leading-edge effects and the resultant near-wall recombination layer are considered with a five-species chemical mechanism. The direct numerical simulation demonstrates that the breakdown to turbulence is accompanied not only by the expected increase in heat flux, but also by a considerable variation in the chemical composition within the boundary layer. Implications for reduced-order modeling of turbulent reacting hypersonic boundary layers are assessed, and a detailed analysis of the closure problem for the modeling of subgrid chemistry in the context of large-eddy simulation is presented.   

The effects of large temperature variations on compressible flow over a heated cylinder

Flow over a cylinder with large temperature variations between the solid surface and the fluid flow is a strongly coupled heat transfer and fluid dynamics problem that arises in a variety of engineering applications. It is crucial to resolve all scales in the vicinity of a cylinder with direct numerical simulations (DNS) to comprehend the aerodynamics and heat transfer more accurately. This work studies the compressible flow over a heated cylinder with various temperature ratios between the cylinder surface and freestream flow at different Reynolds and Mach numbers using DNS. The representation of the cylinder boundary conditions is achieved by adding a ghost cell immersed body method to an in-house GPU-based Cartesian grid solver. Results from two-dimensional DNS show that an increase in the temperature ratio leads to a rise in the mean of the drag coefficient but a stabilization in its fluctuations. Moreover, increasing the Mach number decreases the heat transfer rate between the cylinder surface and fluid flow. We will also present the aerodynamic characteristics of the flow from the perspective of flow separation, vortex strength, shedding, and formation length.