Hypersonic Flow Research Articles

State-to-state dynamics and machine learning predictions of inelastic and reactive O(3P) + CO(1∑+) collisions relevant to hypersonic flows

The state-to-state (STS) inelastic energy transfer and O-atom exchange reaction between O and CO(v), as two fundamental processes in non-equilibrium air flow around spacecraft entering Mars’ atmosphere, yield the same products and both make significant contributions to the O + CO(v) → O + CO(v′) collisions. The inelastic energy transfer competes with the O-atom exchange reaction. The detailed reaction mechanisms of these two elementary processes and their specific contributions to the CO relaxation process are still unclear. To address these concerns, we performed systematic investigations on the 3A′ and 3A″ potential energy surfaces (PESs) of CO2 using quasi-classical trajectory (QCT) calculations. Analysis of the collision mechanisms reveals that inelastic collisions have an apparent PES preference (i.e., they tend to occur on the 3A′ PES), while reactive collisions do not. Reactive rates decrease significantly when the total collision energy approaches dissociation energy, which differs from the inelastic process. Inelastic rates are generally lower than the reactive rates below ∼10 000 K, except for single quantum jumps, whereas the reverse is observed above ∼10 000 K. In addition, by combining QCT with convolutional neural networks, we have established neural network (NN)-STS1 (inelastic) and NN-STS2 (reactive) models to generate all possible STS cross sections. The NN-based models accurately reproduce the results calculated from QCT calculations. In this study, all calculations have been focused on analyzing collisions at the ground rotational level.

An improved continuum model for hypersonic thermal nonequilibrium flow in the near-continuum regime

In this work, the rarefied Couette flow of diatomic gases with thermal nonequilibrium effects is investigated by the direct simulation Monte Carlo (DSMC) method, and a macroscopic computational model is developed to consider the local rarefaction effects for diatomic gases in the near-continuum regime. The nonlinear transport properties of the diatomic gases are studied, indicating that effective viscosity and effective translational thermal conductivity in the shear nonequilibrium state are affected by translational nonequilibrium effects, which obey the same laws for both monatomic and diatomic gases. The transport coefficients of internal energy modes are affected by both translational nonequilibrium and internal energy relaxation, therefore, the effective rotational and vibrational thermal conductivities are related to the effective viscosity through a modified Eucken relation that accounts for internal energy relaxation. Conclusively, effective constitutive relations are newly established as a function of the shear nonequilibrium parameter and the modified Eucken factors for thermal nonequilibrium flows, and these are integrated into the macroscopic two-temperature model. Subsequently, it is assessed in the simulation of hypersonic flows over flat plates and cylinders at various Knudsen numbers. The results show that the surface shear stress and heat flux obtained by the proposed model agree well with the DSMC results, indicating significantly improved performance compared to the conventional Navier–Stokes two-temperature model for hypersonic flows in the near-continuum regime.

Effect of near-wall distance on velocity slip and temperature jump conditions in hypersonic rarefied gas flows

In nonequilibrium slip and jump conditions, normal gas velocity and temperature gradients are used to calculate the gas slip velocity and temperature at the surface, respectively. Gökçen et al. (Computational fluid dynamics near the continuum limit, AIAA Paper No. 87-1115, 1987, and Gökçen and MacCormack, Nonequilibrium effects for hypersonic transitional flows using continuum approach, AIAA Paper No. 89-0461, 1989) stated that the tangential velocity and temperature of the gas molecules before a collision with the surface could be interpreted as the macroscopic tangential velocity and temperature of the gas molecules at the so-called near-wall distances auλ and aTλT away from the surface, respectively. The coefficients au and aT are the order of unity. In the present work, new forms of the slip and jump conditions are proposed by modifying the Gökçen slip and jump conditions to include the coefficients (au, aT). Numerical investigations are comprehensively conducted to determine the numerically proper values (au, aT) for the hypersonic rarefied gas flows. Cases such as the circular cylinder in cross-flow and sharp and blunted leading edge wedge are considered in the present work, with nitrogen as the working gas. The simulation results show the significant effects of the coefficients (au, aT) on the accuracy of the slip velocity and surface gas temperature predictions, and the values of au = 1.2 and aT = 1.1 show good agreement with the direct simulation Monte Carlo data.

Validity of Stokes' hypothesis for near-continuum hypersonic flows

The alternative interpretation of Stokes' hypothesis provided by Buresti [Acta Mech. 226, 3555–3559 (2015)] is investigated by an analysis of a near-continuum, hypersonic flow of oxygen over a double cone obtained from a large-scale direct simulation Monte Carlo computation. We show that for molecular oxygen, which has comparable bulk and shear viscosity coefficients, the difference between mechanical and thermodynamic pressure is negligible throughout most of the flow. This result justifies neglecting viscous stresses in the normal stress tensor associated with fluid particle dilatation, as is often done in continuum descriptions of compressible flows. The violation of the revisited Stokes' hypothesis was only observed in highly nonequilibrium regions of the flow (shocks and strong expansions) and wherever non-continuum effects become significant. For nonequilibrium flows of gases with large bulk viscosity relative to their shear viscosity, the revisited Stokes' assumption may still breakdown and requires further investigation.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory for Hyperthermal Collisions in the O2+O2 System.

Interactions between oxygen molecules play an important role in atmospheric chemistry and hypersonic flow chemistry in atmospheric entries. Recently, high-quality ab initio potential energy surface (PES) of the quintet O4 was reported by Paukku et al. [J. Chem. Phys. 147, 034301 (2017)]. 10543 configurations were sampled and calculated at the level of MS-CASPT2/maug-cc-pVTZ with scaled external correlation. The PES was fitted to a many-body (MB) form with the many-body part described by the permutationally invariant polynomial approach (MB-PIP). In this work, the PIP-Neural Network (PIP-NN) and MB-PIP-NN methods were used to refit the PES based on the same data by Paukku et al. Three PESs were compared. It was found that the performances differ significantly in the O+O3 region as well as in the long-range region. Therefore, additional 1300 points were sampled, and the efficient compressed-state multistate pair-density functional theory (CMS-PDFT) was used to calculate the electronic structure of these 1300 points and 10543 points by Paukku et al. Then, a completely new quintet PES was fitted using the MB-PIP-NN method. Based on this PES, the quasi-classical trajectory (QCT) approach was used to reveal all possible reaction channels for hyperthermal O2-O2 collisions.

Transonic, supersonic, and hypersonic flow of rarefied gas into vacuum through channels with a forward- or backward-facing step

Transonic, supersonic, and hypersonic flow of rarefied gas into vacuum through channels with a forward- or backward-facing step

Navier-Stokes characteristic boundary conditions for high-enthalpy compressible flows in thermochemical non-equilibrium

This fundamental study presents Navier-Stokes characteristic boundary conditions (NSCBCs) for high-enthalpy hypersonic flows in thermochemical non-equilibrium. In particular, the relevant locally one-dimensional inviscid (LODI) relations are derived within a two-temperature framework for high-enthalpy hypersonic flows undergoing finite-rate thermochemical processes, including air dissociation and vibrational relaxation. Using these LODI relations, a set of NSCBCs are proposed and later demonstrated in canonical test cases, including the interaction of homogeneous isotropic turbulence with a shock wave subject to high-enthalpy thermochemical non-equilibrium effects.

Relaminarization effects in hypersonic flow on a three-dimensional expansion–compression geometry

This experimental work explores the flow field around a three-dimensional expansion–compression geometry on a slender cone at Mach 8 using high-frequency pressure sensors, high-frame-rate schlieren, temperature-sensitive paint, shear-stress measurements and oil-flow visualizations. The $7^\circ$ cone geometry has a hyperbolic slice which acts as an expansion corner and suppresses the disturbances present in the upstream boundary layer. Downstream of the cone-slice corner, high-frequency boundary-layer disturbances attenuate in all cases. Under laminar conditions, second-mode instabilities from the cone diminish and lower-frequency second-mode waves develop on the slice at a frequency commensurate with the increased boundary layer thickness. For fully turbulent cases, the boundary layer over the slice shows evidence of a two-layered nature with a turbulent outer region and a near-wall region with strong attenuation of high-frequency disturbances and reappearance of lower-frequency instability waves. When a downstream compression ramp is added to the slice, the expanded boundary layer shows enhanced susceptibility to separation such that separation is observed at a $10^{\circ }$ deflection, which is smaller than expected for turbulent conditions. For a $30^{\circ }$ ramp, boundary-layer separation occurs further upstream where the heat flux contours show a decrease in heating that is characteristic of a transitional separation. These results demonstrate the effect of relaminarization caused by an upstream expansion on a subsequent shock-wave/boundary-layer interaction.

Inflatable aerodynamic decelerators for CubeSat reentry and recovery: Surface properties

In this investigation, Direct Simulation Monte Carlo Method is used to compute the surface properties of inflatable aerodynamic decelerators (IAD) applied for the reentry, recovery, and reuse of cubeSats. Surface properties calculation is of fundamental importance for flexible thermal protection system materials selection that withstand the harsh reentry environment. Furthermore, simulations are extremely important to detect possible hot spots at the IAD before design and flight. In this work, three IAD configurations are exposed to a rarefied hypersonic flow with freestream conditions that correspond to those found at reentry conditions at 105 km altitude. All geometries are assumed to be axisymmetric and have a maximum radius of 0.3 m from the center line to the shoulder edge. The main differences between the geometries are the angle between the IAD and cubeSat body and the IAD curvature for geometry 3. According to the results, all IAD geometries are effective in protecting the cubeSat during the reentry phase. It is shown that the IAD geometry has a significant influence on the heat transfer, pressure, and skin friction coefficient distribution over the flexible heat shield. The maximum heat transfer coefficient computed for geometry 1, 2, and 3 is 0.90, 0.97, and 0.84, respectively.

Compressible FSI of elastic spikes for drag reduction under hypersonic flow

In this study, a new fluid structure interaction (FSI) algorithm is developed for the aerodynamic-elasticity problem, aiming to address the coupling problem between compressible fluids and deformable solid structures. To verify the feasibility of the proposed model, a two-dimensional cantilever panel case under shock waves was conducted. Our numerical results present good consistency with the data from literatures. Furthermore, the validated FSI algorithm is applied on an elastic spike under compressible hypersonic flow. The complicated interaction between the fluid and solid structure under various spike geometry sizes and materials were revealed in respect of the spike deformation, pressure, temperature, and flow fields distribution. The main findings show that the spike deformation largely affects pressure and temperature on the blunt, the aerodynamic drag and lift force, indicating the necessity of FSI. For the spike diameters and lengths, it is found that larger spike diameters and shorter spikes benefits for deformation reduction, thereby minimizing fluctuations in aerodynamic drag force. For spike materials, spikes with larger elastic moduli and lower densities are preferred for the drag reduction. Thus, the proposed FSI model can accurately predict flow fields around and deformations for elastic spikes and offer guidance for drag reduction design in aerospace engineering.

Imaging focused laser differential interferometry.

Focused laser differential interferometry (FLDI) is an important diagnostic for measuring density fluctuations in high-speed flows. Currently, however, high dynamic range FLDI is limited to photodiode measurements. In order to spatially resolve multiple locations within complex flows, we present a novel, to the best of our knowledge, refractive-optic imaging FLDI concept that not only produces two-dimensional images without scanning but also reduces the measurement noise floor of those images. To demonstrate this concept, a 33 × 33 grid of FLDI points is first generated using a microlens array. Then, the beams are split and recombined using two polarized Mach-Zehnder interferometers to maximize flexibility in beam separation and optimize signal sensitivity. Next, the FLDI points are collected slightly out of focus on a high-speed camera in order to increase the number of pixels n per FLDI point, thereby reducing noise floor by n. Finally, an under-expanded jet with a characteristic screech at 14.1 kHz is tested with the imaging FLDI setup, showing clear barrel and reflected shock features as well as spatially varying turbulence densities. Overall, this unique concept enables the creation of reduced-noise-floor, two-dimensional FLDI datasets for the study of supersonic and hypersonic flows.

Sub-filter-scale shear stress analysis in hypersonic turbulent Couette flow

Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

State-to-state study of non-equilibrium recombination of oxygen and nitrogen molecules.

Rapidly cooled mixtures are of interest for several applications, including hypersonic flows due to the presence of strong cooling temperature gradients in regions such as hypersonic boundary layers and expanding nozzles. There have been very few studies of rapidly cooled mixtures using the high-fidelity rovibrational databases afforded by abinitio potential energy surfaces. This work makes use of existing rovibrational state-specific databases to study rapidly cooled mixtures. In particular, we seek to understand the importance of thermal non-equilibrium in recombining mixtures using both rovibrational and vibrational state-to-state methods for oxygen and nitrogen molecules. We find that although there is significant non-equilibrium during recombination, it is well captured by the vibrational state-specific approach. Finally, we compare the global recombination rate computed based on the state-specific recombination rate coefficients and the global recombination rate computed based on the time local dissociation rate coefficient, which is reversed using the principle of detailed balance. The local dissociation rate coefficient is computed by weighting the state-specific dissociation rate coefficients with the state-specific distribution of energy states. We find a large difference between these rates, highlighting a potential source of errors in hypersonic flow predictions.

Sensitivity Analysis of Ionization in Two-Temperature Models of Hypersonic Air Flows

Plasma generation in hypersonic flows is analyzed using a two-temperature model of nonequilibrium air. The uncertainties in electron number density predictions are assessed for flow scenarios that correspond to both strongly shocked and strongly expanded flows, and the dependencies of the calculated uncertainties on individual input parameters are quantified. Ionization levels behind 5 and 7 km/s normal shocks are found to be most sensitive to the associative ionization reactions producing O2+ and NO+ in the region of peak electron number density, with nitric oxide kinetics dominating the uncertainty downstream. The higher levels of ionization behind a 9 km/s shock are found to strongly depend on the electron impact ionization of atomic nitrogen as well as the charge exchange between N2+ and N. Recombining flow scenarios depend on many of the same processes that influence the shocked flows, with the notable addition of the reassociation reaction O++N2↔NO++N, which is responsible for large uncertainties in electron number density in net recombining flows. The results provide valuable insight into the typical magnitude of uncertainty associated with plasma formation predictions in hypersonic flows and identify the parameters that should be targeted in efforts to reduce those uncertainties.

Effect of surface radiation on the stability of hypersonic flat plate boundary layer

Transition of hypersonic boundary layer flow is an important problem in aerodynamic research. To obtain the natural transition position using the flow stability analysis method, it is necessary to analysis the neutral curve and the perturbation growth rule. Accurate calculation of the basic flow is the basis and prerequisite for stability analysis. This paper proposes that surface radiation should be considered in the analysis of hypersonic boundary layer flow stability due to the high temperatures at the vehicle surface caused by aerodynamic heating. In order to obtain the influence of surface radiation on the flow stability, we assume that the surface satisfies the energy balance and the gas satisfies calorimetrically perfect gas properties. To simplify the analysis, gas radiation has been neglected. The boundary layer analysis of a hypersonic flat plate with and without radiation has been performed by a combination of flow stability theory and direct numerical simulation. It is found that high temperature radiation on the surface causes energy to transfer outwards. The results showed that surface temperature decreases along the streamwise direction and is no longer an adiabatic surface temperature. Instability interval decreases and the maximum growth rate increases. The range of the instability region expressed in dimensionless frequency values moves to lower frequency as the Mach number increases. Maximum growth rate shows a tendency to increase and then decrease as the Mach number increases.

Crossflow Instability on a Swept Fin–Cone with Variable Nose Bluntness in Mach 6 Flow

Experiments and computational analysis have been conducted to study instabilities in the boundary layer over a swept fin–cone geometry in hypersonic flow. Experiments were carried out at the United States Air Force Academy’s Mach 6 Ludwieg Tube. Infrared thermography was employed to assess the surface temperature distribution, particularly the thermal striations on the fin that indicated a crossflow-dominated transition. Increasing the unit Reynolds number increased heating and moved the crossflow-transition front closer to the fin leading edge. Stability analysis based on the linear parabolized stability equations identified unstable stationary crossflow modes across the range of tested unit Reynolds numbers, and the most amplified disturbances were found to have wavelengths of 2–4 mm. The experimentally observed thermal striations were analyzed and found to have initial wavelengths of 2–5 mm but eventually formed higher-amplitude structures with a wavelength of approximately 10 mm. Discrete roughness elements of different diameters and spacings were implemented near the fin leading edge. Boundary-layer transition onset was found to be delayed with a subsequent lowering of the fin surface heating, with discrete roughness elements having a wavelength of 13.33 mm.

Hypersonic boundary layer over a flat plate with slip and shear nonequilibrium effects

Near-space hypersonic vehicles could encounter significant rarefied nonequilibrium effects during the flight through atmosphere, which largely influence the gas-surface momentum and heat transfer. In this paper, hypersonic boundary layer over a flat plate with velocity slip, temperature jump, and shear nonequilibrium effects is theoretically considered. The slip boundary conditions and nonlinear transport relations are embedded into the boundary-layer equations to describe the flow. Local similar solutions are derived, and key parameters for characterizing slip and shear nonequilibrium effects are determined. The velocity-slip and temperature-jump effects are determined by [(2−σu)/σu]Mae/Rex and [(2−σT)/σT]Mae/Rex respectively, and the shear nonequilibrium effect is characterized by Mae2/Rex. The obtained boundary-layer solutions are compared with the Navier–Stokes solutions for a Mach 4.5 slip flow, and the results of Direct Simulation Monte Carlo for a Mach 10 rarefied flow, good agreements are achieved. The separate and combined effects of velocity slip, temperature jump, and shear nonequilibrium on boundary-layer solutions and momentum/heat transfer are clarified. The results show that both the slip and shear nonequilibrium effects cause the boundary layer to become thinner and decrease the skin friction and Fourier heat conduction. However, with including sliding friction, the total heat flux might even increase as the slip degree increases. These results provide valuable insight into the boundary-layer characteristics of hypersonic near-continuum flows.

Numerical study on drag and heat flux reduction induced by a counterflowing jet for rarefied hypersonic flow over a blunt body

This paper focuses on the drag and heat flux reduction induced by a counterflowing jet located on the leading edge of the blunt body head in rarefied hypersonic flows using the direct simulation Monte Carlo method. Flow structures in the flowfield, such as detached shock wave, Mach disk, contact surface, jet layer, and recompression shock wave, are all weakened gradually with the increase in the freestream altitude, and they eventually disappear at the altitude of 90 km. The increase in the jet pressure provides a great drag reduction by up to 53% when it increases from 800 to 1600 Pa, but the proportion of drag on the blunt body head to the total drag is only affected slightly by the jet pressure. A noteworthy finding is that further increasing jet pressure almost have no effect on heat flux variation when it is larger than 1200 Pa. On the whole, jet temperature has a quite weak influence on both flow structures and drag, while heat flux on the blunt body head is closely related to jet temperature. The results suggest that jet temperature should vary with that of blunt body surface, and moreover, the optimal jet temperature should be moderately lower than the wall surface temperature. In addition, increasing freestream altitude can provide excellent performance of drag reduction, but it causes non-monotonic variation of heat flux. In view of this, it is worth noting that heat flux on the blunt body head actually increases with altitude when the blunt body is in a severely rarefied atmospheric environment, such as the altitude H > 70 km.

Predicting lift and drag coefficients during hypersonic Mars reentry using hyStrath

During hypersonic reentry, a spacecraft experiences several different fluid flow regimes, which usually require the application of different software frameworks to simulate the respective regimes. This study aims to evaluate the hyStrath library for predicting aerodynamic lift and drag coefficients of complex three-dimensional (3D) geometries during hypersonic Mars reentry, using flight data of the Viking 1 mission as reference. A range of altitudes (h=30−140 km) and Mach numbers (M=13−24) where flight data is available is considered, covering the rarefied, transitional, and continuum fluid flow regimes. The hyStrath library contains a set of modified solvers and state-of-the-art thermophysical and chemistry models within the framework of OpenFOAM, dedicated to modeling high-enthalpy hypersonic flow problems. Depending on the flow regime, the computational fluid dynamics solver hy2Foam or direct-simulation Monte Carlo solver dsmcFoam+ are employed in the study. Because hyStrath is based on OpenFOAM, it allows the use of an unstructured adaptive mesh refinement approach for arbitrary geometries. We obtain excellent results throughout all investigated flow regimes and Mach numbers with an average deviation of 1.5% and 2% from the measured lift and drag coefficients, respectively. The applicability of the framework for accurately modeling both rarefied and continuum Mars reentry problems of complex 3D geometries such as the Viking capsule is demonstrated.

Investigation of the influence mechanism of hypersonic flow field environment on thermionic emission efficiency

Electron Transpiration Cooling (ETC) is a novel thermal management method that utilizes thermionic emission to cool the leading edge surface of a hypersonic vehicle. Establishing a thermionic emission model that accounts for the hypersonic flow field environment is imperative for accurately predicting the thermal protection efficiency of ETC. A thermionic emission dual-sheath model was established, considering the impact of hypersonic non-equilibrium flow field particle parameters on thermal electron emission. The virtual cathode threshold was obtained through numerical analysis, considering the influence of particles parameters and surface thermoelectric material parameters in a non-equilibrium flow field. Distribution of sheath potential and particle number density in plasma sheath region were performed at a range of conditions. Thermionic emission efficiency approached 80 % as the plasma ion density was 5 × 20 m−3 and the work function was 2 eV. The results showed that plasma ions have different degrees of neutralization effect on thermal emission electrons depending on the flow field and surface material characteristics, ultimately causing varying surface thermionic emission efficiency.