High-enthalpy, hypersonic compression corner flow

In the fundamental configuration studied here, a steady hypersonic free stream flows over a thin sharp aligned airfoil or flat plate with a leading-edge shock wave, and the flow field in the shock layer (containing a viscous and an inviscid layer) is steady laminar and two-dimensional, for a perfect gas without real and high-temperature gas effects. The viscous and inviscid layers are analysed and computed simultaneously in the region from the leading edge to the trailing edge, including the upstream-influence effect present, to determine the interactive flow throughout the shock layer and the positions of the shock wave and the boundary-layer edge, where matching is required. Further theoretical analysis of the shock layer helps to explain the computational results, including the nonlinear breakdown possible when forward marching against enhanced upstream influence, for example as the wall enthalpy increases towards its insulated value. Then the viscous layer is computed by sweeping methods, for higher values of wall enthalpies, to prevent this nonlinear breakdown for airfoils including the flat plate. Thin airfoils in hypersonic viscous flow are treated, for higher values of the wall enthalpies and with the upstream-influence effect, as are hypersonic inviscid flows, by modifying the computational methods used for the flat plate. Also, the behaviour of the upstream influence for bodies of relatively large thickness, and under wall velocity slip and enthalpy jump for flat plates, is discussed briefly from a theoretical point of view.Subsequent to the present work, computations based on the Navier–Stokes and on the parabolized Navier–Stokes equations have yielded excellent and good agreement respectively with the present predictions for large Mach and Reynolds numbers.

In this work, a transition process in a hypersonic flow over a cold-wall compression ramp is studied using direct numerical simulation (DNS) and global stability analysis (GSA). The free-stream Mach number and the Reynolds number based on the flat-plate length are 7.7 and $8.6 \times 10^5$ , respectively. The shock-induced pressure rise causes the boundary layer to separate on the flat plate, forming a separation bubble around the corner. Without introducing any external disturbances, the DNS captures the transition to turbulence downstream of flow reattachment. The DNS results agree well with the experimental data as well as theoretical predictions. To uncover the intrinsic instability in the flow system, GSA is employed to investigate the three-dimensionality of the two-dimensional base flow. Several stationary and oscillatory unstable modes are revealed, which result in spanwise periodicity inside and downstream of the separation bubble. The GSA and DNS results indicate that the intrinsic instability of the flow system triggers the formation of streamwise counter-rotating vortices and boundary-layer streaks near reattachment. The downstream transition to turbulence starts from the breakdown of the streamwise vortices and streaks. Moreover, the second harmonic of the most unstable global mode and a broadband low-frequency unsteadiness occur in the saturated flow, which has a significant influence on the transition process. In summary, the present study demonstrates a transition process in a hypersonic compression-ramp flow as a result of the intrinsic instability of the flow system.

Numerical simulation of compression corner flows at Mach number 9

Hypersonic near-continuum flow over a flat plate with micro-scale roughness is studied using the kinetic direct simulation Monte Carlo method on roughness module configurations with different relative roughness (h) values and roughness densities (RN) under a matrix of freestream parameters (Mach number Ma∞, Reynolds number Re∞, temperature T∞, and Knudsen number Kn∞). An open-source Stochastic PArallel Rarefied-gas Time-accurate Analyzer code, which enables Cartesian grid adaption and efficient parallelization, is utilized for the rough-plate flow simulations. Flowfield analysis reveals that the local patterns inside the roughness modules evolve starting from closed (two vortices) via transitional ultimately to open (one vortex) by an increase in h, with co-existing shrinkage of high-density zones and attenuation of density peaks. The surface quantities are significantly influenced by the flowfield characteristics, and a local association between the peak heat flux and the peak pressure is identified. Non-dimensional peak heating and pressure correlation laws for the local peak heat flux and pressure coefficients in terms of two length-scale transformations are proposed, enabling the capture of local heating and pressure extrema on rough plates with varying h and RN conditions under different Ma∞, Re∞, and T∞ parameter values. The peak heat flux and pressure coefficients can be described by analogous correlating equations expressed by first-order-polynomial or power functions. An increase in the rarefaction degree (Kn∞) deviating from the near-continuum regime causes the correlation laws to fail.

Effect of Knudsen Layer on the heat transfer in hypersonic rarefied gas flows

A hypersonic laminar flow over double wedges with a fixed forward angle of 15° and varied aft angles is studied using computational fluid dynamics and global stability analysis (GSA) at a free-stream Mach number of 12.82 and a total enthalpy of 21.77 MJ/kg. The specific total enthalpy is high enough to trigger evident vibrational excitation and air chemistry. To assess the effects of thermal and chemical nonequilibrium, three different thermochemistry models of air are considered, including frozen, thermal nonequilibrium, and thermochemical nonequilibrium gases. Two-dimensional base-flow simulations indicate that the onset of incipient and secondary separation is insensitive to the inclusion of thermochemistry, although the size of the separation region is substantially reduced. GSA is then performed on the base flows and identifies a three-dimensional stationary global instability beyond a critical aft angle, which is also insensitive to thermochemical nonequilibrium. The criterion of the global stability boundary established for the supersonic flow over compression corners in a calorically perfect gas in terms of a scaled deflection angle [Hao et al., “Occurrence of global instability in hypersonic compression corner flow,” J. Fluid Mech. 919, A4 (2021)] is, thus, extended to high-enthalpy conditions.

A generalized reference enthalpy formulation for the skin friction, heat transfer and radiation-equilibrium temperature distributions over aerodynamic surfaces in attached hypersonic / hyperenthalpic flow is proposed. The formulation, which has been extensively employed in various forms by numerous investigators in the perfect gas regime, has also been recently demonstrated to provide adequate estimates of the heat transfer distribution in thermochemically active high enthalpy flow conditions when coupled to thermochemically active Euler solutions. It is now used to reveal the relevant similitude parameters for viscous effects in hypersonic flow, and the importance of the temperature distribution across the boundary layer and of the temperature-viscosity relation. It is shown that, although reproduction of the flight total flow enthalpy as well as surface temperature is the obvious solution for full viscous simulation in (perfect gas) hypersonic flow, the hot surface testing requirement and, in a number of practical applications, also the hot flow requirement may be relaxed with reasonably small error that can be of the same order as the measurement accuracy in present-day hypersonic testing. This similitude error, however, may increase significantly in cases exhibiting strong viscous/inviscid interaction or when the laminar-turbulent transition process becomes important. In this respect, alternative full simulation solutions, which are less demanding in terms of reproduction of the high levels of flight freestream and surface temperature or even Reynolds number, are discussed.

SummaryThis paper describes an experimental study of the interaction between a hypersonic flow and a transverse jet which issues radially from a slender conical model. Measurements in the region far upstream of the jet show qualitative agreement with free interaction analyses, while downstream a film cooling effect appears to reduce the heat transfer rate substantially. The effect of changes in Reynolds number, jet pressure ratio and mass flux is examined and compared with similar phenomena caused by fixed disturbances such as compression corners. The shape of the interaction shock wave is found to agree with the predictions of the second-order blast wave theory. Finally a correlation is found between the boundary layer separation length and a local mass flux parameter.

The two-dimensional Reynolds averaged compressible Navier-Stokes equations are solved using MacCormack's second-order accurate explicit finite difference method to simulate the separated transonic tur- bulent flowfield over an airfoil. Four different algebraic eddy viscoisity models are tested for viability to achieve turbulence closure for the class of flows considered. These models range from an unmodified boundary-layer mixing-length model to a relaxation model incorporating special considerations for the separation bubble region. Results of this study indicate the necessity for special attention to the separated flow region and suggest limits of applicability of algebraic turbulence models to these separated flowfield. each of these studies the time-dependent Reynolds averaged Navier-Stokes equations for two-dimensional compressive flow are used and tur- bulence closure is achieved by means of model equations for the Reynolds stresses. Wilcox1'2 used a first-order accurate numerical scheme and the two equation differential tur- bulence model of Saffman 12 to simulate the supersonic shock boundary-layer interaction experiment of Reda and Mur- phy 13 and the compression corner flow of Law.14 Good quan- titative agreement with the Reda and Murphy data was ob- tained, but only the qualitative features of the compression corner flow were well simulated. Using a more sophisticated second-order accurate numerical scheme, Baldwin3'4 con- sidered both the two equation differential model of Saffman and a simpler algebraic mixing-length model to simulate the hypersonic shock boundary-layer interaction experiment of Holden.15 He found the more elaborate model of Saffman to yield somewhat better results than the algebraic model, but at the cost of considerably more computing time. Good quan- titative agreement with experiment was not obtained with either model. Following Baldwin's approach all subsequent investigations have been performed using the more rigorous second-order accurate numerical scheme of Mac- Cormack.17'18 Deiwert5'6'11 considered an algebraic mixing- length model to simulate the transonic airfoil experiment of McDevitt et al. 16 while Horstman et al. 8 used a similar ap- proach to simulate their hypersonic shock boundary-layer ex- periment on an axisymmetric cylinder. In each of these studies, while qualitative features of the flows were described well, good quantitative agreement with experiment in the in- teraction regions was not obtained. Using a relaxing turbulence model Shang and Hankey7 simulated the compression corner flow of Law, and Baldwin and Rose10 simulated the flat plate flow of Reda and Murphy. In each of these studies the relaxing model was found to per- form significantly better than the simpler algebraic model and, according to Shang and Hankey, provided significantly better comparisons with measurements than were obtained by Wilcox using the two equation differential model of Saffman. In each of these studies it was essential that the full Navier- Stokes equations be considered to describe the viscous- inviscid interaction and the elliptic nature of separating-

Oblique shocks and expansion waves are commonly found in aerospace applications such as wings and nozzles. These types of shocks change the properties of the flow, thus causing changes in the lift, drag, and/or heat transfer. Hypersonic flow is important to study as its impacts are significant. In this thesis, computational fluid dynamics (CFD) is utilized to characterize the physics of the flow. Parametric studies of the Mach number and turning angle were conducted. Simulations included both inviscid and viscous flows to demonstrate the effects of boundary layer on flow properties. The majority of the viscous flows were focused on the compression corner where the boundary layer started growing. The simulations produced evidence of flow separation at high turning angles. In addition, the boundary layer turned the flow upward at an angle, causing an oblique shock before reaching the corner. This phenomenon is known as shock-shock interaction. A turbulent flow developed a boundary layer faster than a laminar flow and can delay the separation of the flow. In general, the boundary layer can offset the properties of the flow, and a part of this study was performed to obtain the percentage difference and then use it as the correction factor for the offset.

Two-Dimensional Shock Structure in Transonic and Hypersonic Flow

This paper presents the effect of blowing (transpiration flow) on hypersonic flow over a flat plate at different flow regimes. The investigation involves the study of the interaction between the free stream flow of argon gas at Mach 5 and transpiring gas introduced at the fluid–solid interface. The freestream Knudsen number considered for the present analysis are 0.002, 0.01, 0.05, and 0.25, extending from continuum to rarefied through transitional flow conditions. Flow simulations are performed using the open source particle-based direct simulation Monte Carlo (DSMC) solver called Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA). In the DSMC framework, the transpiring gases are introduced as jets with specified velocity, number density, and temperature uniformly throughout the surface in the direction normal to the surface. The variation in flow field properties, such as density, temperature, and velocity with and without transpiration, is studied. The influence of rarefaction on surface heat flux distribution is studied at different flow Knudsen numbers. Furthermore, the effect of introducing the transpiring gas at different densities into the flow field is investigated and its impact on the surface heat flux is discussed. It is interesting to note that in certain cases, the heat flux actually increases locally as a result of the interaction between transpiring gas and freestream flow.

A new very high-order finite-difference method for linear stability analysis and bi-orthogonal decomposition of hypersonic boundary layer flow

Experiments are reported in which the heat flux distribution near a single circular, sonic transverse jet on a flat plate exposed to a hypersonic (Mach 6.7) freestream flow was quantitatively measured using thermochromic liquid crystals. The freestream conditions were such that the boundary layer growth on the plate ahead of the jet was laminar. The results indicate that the interaction of the jet with the freestream flow created a complex flowfield with regions of separation and reattachment which caused localised enhancements to the heat flux upstream and to the side of the jet, the magnitudes of which were sensitive to both jet plenum pressure and jet gas composition.

A numerical study is presented which investigates, through direct numerical simulation (DNS) of the Navier-Stokes equations, the characteristics of supersonic/hypersonic boundary layers over porous surfaces. Two different configurations are considered, namely a Mach 6 flow over a flat plate with periodic porosity in both the streamwise and spanwise directions, and a shock-boundary-layer-interaction (SBLI) case at Mach 2 with a localized porosity layer. The method used to carry out the numerical simulations consists of a 6th-order hybrid weighted-essentially-non-oscillatory/central-differencing (WENO-CD) scheme, which provides high numerical stability in the regions of strong gradients, while minimizing the numerical dissipation in smooth regions. A validation of the numerical code, by comparison with other high-order non-hybrid DNS codes is presented for both the configurations, as well as a grid convergence study. The effects of Reynolds number and wall cooling on the flow characteristics in the pore region and on the acoustic waves radiated by the pores are analyzed for the periodic porosity case. The role of a porosity region localized at two different streamwise positions along the flat plate on the bubble length, the mean flow features and the wall pressure is investigated for the SBLI configuration, and compared to the case of smooth wall. The results show the capabilities of the high-order finite-volume-based Cartesian-grid hybrid method in carrying out high-resolution simulations with relatively low computational cost, thus demonstrating its effciency andversatility for the DNS of multiscale hypersonic flow configurations over porous surfaces.