Nonequilibrium Hypersonic Flows Research Articles

Assessment of the Influences of Numerical Models on Aerodynamic Performances in Hypersonic Nonequilibrium Flows

Assessment of the Influences of Numerical Models on Aerodynamic Performances in Hypersonic Nonequilibrium Flows

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.

Influence of Gas-Surface and Gas-Gas interactions on the energy accommodation coefficient in non-equilibrium hypersonic gas flows

Accurate accommodation coefficients are crucial in predicting aerodynamic force and heating in hypersonic rarefied flows. This study employs molecular dynamics simulations to investigate the characteristics of non-equilibrium hypersonic flow and its impact on the energy accommodation coefficient (EAC). Our findings reveal that the non-equilibrium gas flow in the gas-surface interaction region comprises an equilibrium subsonic flow, an incident hypersonic flow, and its reflected counterpart. Gas-surface and gas–gas interactions occur simultaneously as gas atoms incident toward the solid surface, with the latter enhancing the EAC by altering the ratios of collision types. Overall, an increase in the ratios of trapping-desorption and permanent-adsorption collisions enhances the EAC at the interface. Results indicate that the number density of the subsonic flow determines the transition from immediate-reflection collisions to trapping-desorption collisions, while the ratio between the potential well depth and the internal energy of the subsonic flow determines the occurrence of permanent-adsorption collisions. These findings disclose the influence of the gas-surface and gas–gas interactions on the atomic collision types and EAC in a hypersonic flying interface, providing valuable insights for predicting the aerodynamic heating in rarefied gas flow.

Can vibrational pumping occur via O2–N2 collisions in nonequilibrium vibrationally excited air?

The occurrence of vibrational pumping in air under nonequilibrium conditions is investigated as this phenomenon is not considered in the design of the current phenomenological models. It is shown that pumping can only happen during de-excitation and when the translational temperature is below around 1000 K. O2 is the molecule that would get pumped, and pumping will not occur when the initial equilibrium temperature is greater than around 1200–1600 K due to the formation of enough O to extinguish pumping via the O2–O vibration–translation reaction. The limiting initial temperature can be increased to around 2000 K if a nonequilibrium initial condition is considered. In cases where pumping does occur, constant–volume reactor simulations showed pumping of ≈5%. Nozzle simulations representative of that in hypersonic wind tunnels are conducted for an equilibrium temperature of 1100 K at the throat; pumping of up to around 10 K (≈1%) can be observed. It can be suggested that constant–volume reactors generally overestimate the manifestation of thermochemical nonequilibrium-associated phenomena and are a better zero-dimensional analogy for the relaxation process in flows with large length scales and no further expansion after an initial rapid expansion. After examination of the uncertainties of the most important rates used in the simulations, one may suggest that the current results correspond to the upper bound for the magnitude of pumping. It may be concluded that pumping is unimportant for practical intents and purposes in nonequilibrium hypersonic flows, and phenomenological models need not be able to recreate this phenomenon.

Effect of equilibrium constant for carbon dioxide recombination in hypersonic flow analysis

An equilibrium constant is an important parameter in regard to determining the backward reaction rate constant in chemical kinetics modeling for a hypersonic flow. Three common approaches for the equilibrium constant determination are based on the partition function, Gibbs free energy, and the experimental reaction rate measurement. The present study conducted a computational fluid dynamics (CFD) analysis with different equilibrium constant formulations in a thermochemical nonequilibrium hypersonic flow in order to study the influence of the equilibrium constant in carbon dioxide flow during the Martian entry. The equilibrium constant for the carbon dioxide molecule dissociation differs from one method to another among the reactions that are considered in the carbon dioxide flow. Three different flow conditions, which are based on the experimental data that is provided in the literature, are considered in the detailed comparison analysis using CFD. The variation of the flow properties in terms of pressure, temperature, and mass fraction along the stagnation line is compared for different cases of the equilibrium constant computation. The results that are obtained from the present study confirm that the equilibrium constant influences the numerical computation in the thermochemical nonequilibrium flow especially for the non-catalytic wall boundary condition.

Numerical Investigation on the Jet Characteristics and the Heat and Drag Reductions of Opposing Jet in Hypersonic Nonequilibrium Flows

We adopted the transient numerical method for the simulation of an ELECTRE vehicle with an opposing jet at an altitude of 53.3 km and 13 Ma to explore the jet characteristics as well as the performance in heat and drag reductions of the opposing jet in hypersonic nonequilibrium flows. The time-accurate, nonequilibrium N-S equations coupled with the five-species Park chemical kinetic model and vibrational energy excitation were applied, and an open source solver Hy2FOAM based on the OpenFOAM platform was adopted. Three opposing jets with different jet radii (R7 jet, R14 jet, and R21 jet) were investigated. The results show that with the increasing jet flow rate, the jet mode of the opposing jet with a small jet radius varies from the overflow mode to the long penetration mode (LPM) and finally to the short penetration mode (SPM), while that with a large jet radius directly changes from the overflow mode to the SPM. The state of the jet in the overflow mode is stable, whereas in SPM and LPM, it is unstable. The investigation of the heat and drag reductions for the R7, R14, and R21 jets shows that except for the jet in LPM, the jet in SPM and overflow mode can provide effective thermal protection, and the thermal protection is enhanced with the increasing jet flow rate. Moreover, the jet in both LPM and SPM can effectively reduce the aerodynamic drag, but the jet in overflow mode cannot provide effective drag reduction. Moreover, the jet with a large radius and in the overflow mode has a better thermal protection effect, and a small jet radius contributes to the drag reduction.

On the accuracy of two-temperature models for hypersonic nonequilibrium flow

On the accuracy of two-temperature models for hypersonic nonequilibrium flow

Sensitivity Analysis of the Catalysis Recombination Mechanism on Nanoscale Silica Surfaces.

A deep understanding of surface catalysis recombination characteristics is significant for accurately predicting the aeroheating between hypersonic non-equilibrium flow and thermal protection materials, while a de-coupling sensitivity analysis of various influential factors is still lacking. A gas–solid interface (GSI) model with a hyperthermal flux boundary was established to investigate the surface catalysis recombination mechanisms on nanoscale silica surfaces. Using the reactive molecular dynamics (RMD) simulation method, the effects of solid surface temperature, gas incident angle, and translational energy on the silica surface catalysis recombination were qualified under hyperthermal atomic oxygen (AO), atomic nitrogen (AN), and various AN/AO gas mixtures’ influence. It can be found that, though the Eley–Rideal (E–R) recombination mechanism plays a dominant role over the Langmuir–Hinshelwood (L–H) mechanism for all the sensitivity analyses, a non-linear increasing pattern of AO recombination coefficient γO2 with the increase in incident angle θin and translational energy Ek is observed. Compared with the surface catalysis under hyperthermal AO impact, the AN surface adsorption fraction shows an inverse trend with the increase in surface temperature, which suggests the potential inadequacy of the traditional proportional relationship assumptions between the surface adsorption concentration and the surface catalysis recombination coefficient for other species’ impact instead of AOs. For the incoming bi-component AO/AN gas mixtures, the corresponding surface catalysis coefficient is not the simple superposition of the effects of individual gases but is affected by both the intramolecular bond energies (e.g., O2, N2) and intermolecular energies (e.g., Si/N, Si/O).

Modeling of Thermochemical Nonequilibrium Flows Using Open-Source Direct Simulation Monte Carlo Kernel SPARTA

Chemical reactions are usually coupled with transfer of internal energies in high-temperature gas and have been an ongoing challenge for the direct simulation Monte Carlo (DSMC) method. In this paper, three typical reaction models are compared quantitatively, and the impact of vibrational favoring effects as well as three-body recombination are analyzed. The recently developed open-source DSMC kernel SPARTA is employed and modified in the present study. The verification results indicate that the SPARTA code produces a satisfactory description of the nonequilibrium reacting flow. A further application is made to the hypersonic nonequilibrium boundary-layer flows past an obstacle. It is found that SPARTA is in excellent agreement with continuum-based method for the low-altitude condition (); however, considerable differences arise at high altitudes () due to locally rarefied gas effects.

Influence of catalytic wall on the effective radius of a blunt body geometry in a nonequilibrium hypersonic flow

The effect of the surface catalycity on the effective radius of a blunt body geometry in hypersonic flow is numerically investigated. The blunt body geometry is defined in terms of a body radius with variation in both nose radius and the corner radius. Five different types of blunt body configurations are considered, that range from a flat-faced to a complete hemisphere geometry. The chosen blunt body configurations are investigated for four flow conditions with different levels of flow enthalpy. The effective radius is obtained by comparing the stagnation heat transfer of the blunt body geometry to that of the spherical geometry. To compute the stagnation heat transfer in the given blunt body configuration, a two-dimensional computational fluid dynamics (CFD) solver with thermochemical non-equilibrium is utilized. Both non-catalytic and fully-catalytic wall boundary conditions are considered in the computation. The obtained effective radius is additionally compared with the original data provided in the literature. The results show that surface catalycity influences the effective radius for the given blunt body configuration.

Evaluation of Fay and Riddell formula under hypersonic flight conditions

PurposeThe Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.Design/methodology/approachThe stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.FindingsThe comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.Originality/valueThe results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

Influence of Vibration–Dissociation Coupling and Number of Reactions in Hypersonic Nonequilibrium Flows

Abstract During the atmospheric cruising of a hypersonic vehicle, the thermal and chemical nonequilibrium effects characterize the flow field within the shock layer. Therefore an understanding of nonequilibrium flow is essential for the efficient design of a hypersonic vehicle. The present numerical study uses various canonical configurations to study the thermochemical nonequilibrium effects in hypersonic flows. The present study investigates the influence of the vibration–dissociation (V–D) coupling method and the number of reactions on shock standoff distance (SSD), vibrational relaxation process, and surface properties. A finite volume method-based solver using the open-source platform openfoam has been developed to analyze the thermochemical nonequilibrium effects in the hypersonic flow field. The current results show that thermal and chemical nonequilibrium flow assumptions significantly affect SSD, and hence these assumptions are necessary to study the cases with a higher degree of nonequilibrium. The number of reactions influences the vibrational relaxation of diatomic gases in the air. At the same time, the V–D coupling method used to calculate reaction rate constants has a negligible impact on the vibrational relaxation process. Moreover, the V–D coupling method and the number of reactions marginally affect surface pressure. However, in the case of surface heat flux, the 11 reaction model predicts higher peak values than the 17 reaction model.

A universal method of redistributing relaxation energies in inelastic molecular collisions

The Larsen–Borgnakke (L–B) model is most widely used to redistribute relaxation energies in direct simulation Monte Carlo (DSMC) method; the relaxation energies in an inelastic collision are determined beforehand and redistributed by sampling from the equilibrium distributions (not locally equilibrium distributions) of these energies that are appropriate to this collision. The present concern focuses on how to redistribute the selected energies when they have been determined to require relaxation. When certain energies are determined to require relaxation and redistribution in an inelastic collision, the hierarchical method and the serial or sequential method are used to complete the L–B procedure. Although the hierarchical method is theoretically accurate, it needs to complete the integration of the joint energy distribution function, so it is not applicable when the energy distribution function has a complex form or contains more than one discontinuous energy. Hence, researchers turn to the serial or sequential method, but the rationality proof of this method implies an assumption of locally thermal equilibrium, so it is obviously not appropriate in the DSMC method usually applied to hypersonic nonequilibrium flows. Then, a new method of redistributing relaxation energies to complete the L–B procedure is proposed, which does not include any integration process; the original form of the energy distribution function is used directly, so it can be expected to have excellent adaptability, especially for complex cases such as energy redistribution of reaction products. The effectiveness, efficiency, and extensive applicability of the method are proved by multiple examples.

Localized time accurate sampling of nonequilibrium and unsteady hypersonic flows: methods and horizons

Modern “non-intrusive” optical methods are providing revolutionary capabilities for diagnostics of hypersonic flow fields. They generate accurate information on the performance of ground test facilities and provide local time accurate measurements of near-wall and off-body flow fields surrounding hypersonic test articles. They can follow the true molecular motion of the flow and detect nonequilibrium states and gas mixtures. They can be used to capture a wide range of turbulent scales and can produce highly accurate velocity, temperature and density measurements as well as time-frozen images that provide intuitive understanding of flow phenomena. Recent review articles address many of these methods and their applications. The methods highlighted in this review are those that have been enabled or greatly improved by new, versatile laser systems, particularly including kHz rate femtosecond lasers and MHz rate pulse burst lasers. Although these methods can be applied to combusting environments, the focus of this review is on external high Mach number flows surrounding test articles and wind tunnel core flow properties. The high repetition rates enable rapid time evolving flows to be analyzed and enable the collection of large data sets necessary for statistical analysis. Future capabilities based on the use of atomic vapor filters and on frequency tunable, injection locked MHz rate lasers are promising.

Heat and drag reduction of single and combined opposing jets in hypersonic nonequilibrium flows

To establish a method of achieving effective thermal protection and drag reduction in hypersonic flows with an opposing jet under a low flow rate, this study compared three single and two combined jets. For a single jet, nozzles of different sizes (nozzles 1, 2, and 3) were investigated. The influence of the effective area of the annulus jet was studied for the combined jet, consisting of a circular jet and an annulus jet. A 2.6%-scale Apollo capsule was investigated with these jets in hypersonic flows at Mach 19 and an altitude of 60 km using a transient numerical method. Considering nonequilibrium effects (vibrational excitation and chemical reactions), the heat and drag reduction mechanisms of these single and combined jets in hypersonic flows were explored using a nonequilibrium Navier–Stokes–Fourier numerical approach. The results indicated that nonequilibrium effects exist in the shock wave and wake regions. The size of the nozzle in the single jet and the effective area of the annulus jet in the combined jet influence the heat and drag reduction. A single jet with an excessively small nozzle size considerably decreases the effects of heat and drag reduction. Compared with a single jet, the combined jet cannot reduce the aerodynamic drag at a low flow rate owing to the dispersion of the jet. However, a combined jet with a larger area of the annulus jet can effectively reduce the aerodynamic heat to 68%, whereas three single jets can considerably enhance the surface heat flux.

Heat Transfer and Ionization in Non-Equilibrium Hypersonic Flow Past a Blunt Plate

Heat Transfer and Ionization in Non-Equilibrium Hypersonic Flow Past a Blunt Plate

Thermochemical non-equilibrium effects on aerothermodynamic prediction of laminar double-cone flow

Hypersonic non-equilibrium air flows over a laminar double-cone configuration are numerically investigated. In this paper, the effects of thermochemical non-equilibrium gas, chemical non-equilibrium gas, and thermally perfect gas models on the prediction of the wall-surface heat transfer and pressure are investigated. Comparing to the high-enthalpy experimental data, the results of simulations indicate that all models have a similar tendency, and underpredict the length of the separation region, while the heat transfer peaks are overpredicted. The experimental data for surface pressure and heat transfer is insensitive to the choice of the thermally perfect gas model and non-equilibrium thermochemistry models. Quantitatively, the thermochemical non-equilibrium gas and thermally perfect gas models predict the same separation and reattachment locations within the uncertainty in the simulation, but the chemical non-equilibrium gas model predicts a smaller separation region.

Modified Nonlinear Coupled Constitutive Relations Model for Hypersonic Nonequilibrium Flows

To obtain accurate physical description of nonequilibrium flows, Eu proposed a set of generalized hydrodynamic equations (GHEs) using a nonequilibrium ensemble method. However, Eu’s equations are very difficult to solve by employing the well-established numerical schemes for hyperbolic partial differential equations. Recently, a simplified nonlinear model based on Eu’s equations has been proposed by Myong for GHEs in conjunction with hyperbolic conservation laws, which is called the nonlinear coupled constitutive relations (NCCR) model. However, in the NCCR model, two specific terms in the evolution equation of heat flux are omitted for providing simplification, which reduces the accuracy of GHEs to some degree especially for hypersonic flows. To address this deficiency in NCCR, a modified NCCR+ model is proposed in this paper, which includes the two omitted terms in the NCCR model. NCCR+ model is applied to compute the hypersonic flow past an Apollo capsule at different altitudes and in expansion corners in a tube with various expansion angles. It is found that the computed NCCR+ solutions are almost identical to the Navier–Stokes (NS) solutions at low Knudsen numbers, but as the Knudsen number increases, the difference between the NCCR+ model solutions and the NS results increases rapidly and the NCCR+ solutions become closer in agreement with the direct simulation Monte Carlo data. By adding the two omitted terms in the NCCR model, the NCCR+ model also improves the overall accuracy of the original NCCR model. The results presented in this paper demonstrate the potential of the NCCR+ model in simulation of nonequilibrium hypersonic flows in both compression and expansion regions at moderate Knudsen numbers.

Multiple temperature model of nonlinear coupled constitutive relations for hypersonic diatomic gas flows

The rotational energy of diatomic gases would be activated by the process of intermolecular collisions in high-temperature hypersonic flows. In this paper, a multi-temperature nonlinear coupled constitutive model has been proposed for simulating the transfer of energy between translational and rotational motions in hypersonic non-equilibrium flows. In this model, the nonlinear coupled constitutive equations are modified by introducing a rotational energy relaxation model and a changeable viscosity ratio related to local temperature. To confirm its accuracy, the new model is applied to investigate steady shock wave structures and high-speed gas flows around a cylinder and across a flat plate. The computational results are compared with the multi-temperature Navier–Stokes (NS) equations, the direct simulation Monte Carlo (DSMC) solutions, and the experiment data. The final results show the new model would reproduce the NS results at low Knudsen numbers but behave quite differently from the NS results as the non-equilibrium degree is enhanced. The new model is in better agreement with the DSMC solutions and the experimental data than the NS solutions in the far-from-equilibrium regions, which demonstrates the potential of the new relaxation model in the simulation of hypersonic non-equilibrium flows.

Development of a stagnation streamline model for thermochemical nonequilibrium flow

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.