Vibrational Nonequilibrium Effects Research Articles

Numerical investigations on flow and heat transfer characteristics of a high-enthalpy double-cone in thermal and chemical non-equilibrium for hypersonic propulsion

There are strong interests in hypersonic propulsion communities in predicting the flow and heat transfer characteristics over a hypersonic vehicle. However, this is quite challenging due to the emergence of thermal and chemical out-of-equilibrium effects as prominent in a high-temperature flow. In this work, we conduct 2D numerical investigations on the hypersonic double cone flow in a surrounding of the stagnation enthalpy of 15.23 MJ/kg by solving the laminar Navier–Stokes equation systems with the vibrational non-equilibrium processes and seven species air reactions. We then conduct the sensitivities analyses on the flow and heat transfer features, as different transport models and different thermochemical models are applied. It is shown that the aerodynamic heat is more sensitive to the transport models than the flow, and the transport coefficients computed by the Gupta-Yos model are more suitable for predicting the double cone flow at the high enthalpy. On the other hand, the flow field of the high enthalpy double cone is more sensitive to the thermochemical models than the heat transfer on the wall excluding the peak position. Behind the detached shock, chemical reactions are found to enhance thermal or vibrational out-of-equilibrium effects. However, vibrational non-equilibrium effects are revealed to weaken the degree of molecule dissociation reactions. Two flow separations occur in the flow field computed by using the thermal non-equilibrium gas models, but the flows of thermal equilibrium gas models separate only once. The maximum values of wall parameters without chemical reactions are found to deviate greatly from the experimental measurements. The thermochemical out-of-equilibrium gas model can predict the separation region size closer to the experiment than the two reported numerical results. The wall static pressure and heat flux are also shown to well match the experimental results. The present work should shed lights on better understanding thermochemical non-equilibrium effects of complex flow phenomenon like the shock wave/boundary layer interaction in hypersonic propulsion with high enthalpy surroundings.

Effects of high-temperature and entropy layer of Mach 12 oblique shock wave

In the current study, we numerically investigate the high-temperature inviscid flows over the 15-degree wedges with the sharp and blunt leading-edges. Firstly, the vibrational non-equilibrium effects in sharp wedge flow with different deflection angles are analyzed. Then, the influence of the vibrational non-equilibrium effects on the flow parameters behind the oblique shock wave is provided. Lastly, we discuss the high-temperature non-equilibrium flow over the 15-degree wedge with the entropy layer.

High temperature non-equilibrium flow characteristics of impinging shock/flat-plate turbulent boundary layer interaction at Mach 8.42

There are fewer reports on the impinging shock/boundary layer interaction in the high Mach number and high-temperature flow than that in the supersonic flow. High-temperature flow characteristics of the impinging shock/flat-plate turbulent boundary layer interaction (IS/FTBLI) at Mach 8.42 are numerically investigated by solving two-dimensional Reynolds averaged Navier–Stokes equations coupling with the thermal–chemical non-equilibrium model. An impinging shock is formed by the wedge with a 10° deflection angle. The inviscid flow parameters ahead of the cowl of a Mach 12 inlet are selected as the free-stream condition of this study. The primary emphasis of this study lies in understanding the thermal–chemical non-equilibrium effects in the IS/FTBLI. Moreover, the chemical non-equilibrium effects similar to previous reports from others are utilized for the comparative analysis. Our findings reveal that the vibrational or thermal non-equilibrium effects exhibit maximum prominence subsequent to the intersection of the impinging shock with separation shock, as well as in the convergence area of compression waves during the flow reattachment. On the other hand, the chemical non-equilibrium effects predominantly result from oxygen dissociation and atomic nitrogen production within the boundary layer; the chemical reactions are most intense within the separation zone. By comparing with a thermally perfect gas, a reduction in the flow separation is observed in the chemical non-equilibrium effects, but the flow separation is enhanced in the thermal–chemical non-equilibrium effects. The insights gained from our research are expected to contribute to the development of flow control technology in hypersonic IS/FTBLI scenarios and aid in configuring wave structures in the inner compression section of high Mach number scramjet inlets.

Hypersonic flow over spherically blunted cone capsules for atmospheric entry. Part 2. Vibrational non-equilibrium effects

Atmospheric entry capsules shaped as spherically blunted, large apex-angle cones are widely used in space missions. In Part 1 of this study (Hornung, Martinez Schramm & Hannemann, J. Fluid Mech., vol. 871, 2019, pp. 1097–1116) we explored flows over the two elements of the capsule shape, the sphere and the sharp cone with detached shock, theoretically and computationally. Using a large number of inviscid, perfect-gas computations, analytical functions of two independent variables, the normal-shock density ratio $\varepsilon$ and a cone-angle parameter $\eta$ (which is a function of $\varepsilon$ and the cone half-angle $\theta$ ) were found for the dimensionless shock wave stand-off distance and the drag coefficient of a sharp cone. An analytical description was found for the shock stand-off distance in the transition from the 90 $^\circ$ cone (flat-faced cylinder) to the sphere. In Part 1, it was speculated that the perfect-gas results have relevance to non-equilibrium situations if the normal-shock density ratio is replaced by the density ratio based on the average density along the stagnation streamline. In Part 2, the investigation is extended to blunted-cone capsule shapes. High-precision force measurements and schlieren image analysis are performed in the High-Enthalpy Shock Tunnel Göttingen (HEG) of the German Aerospace Centre using air as the test gas, at conditions where vibrational non-equilibrium effects are significant. Accordingly, results are compared with viscous numerical predictions using different physico-chemical models. A theoretical model is constructed for the density profile along the stagnation streamline that is determined by the free stream conditions and gives the average density. Comparisons of the experimental and numerical results for the dimensionless shock stand-off distance and the drag coefficient, with the extension of the analytical functions of Part 1 to vibrationally relaxing flow, exhibit very good agreement in all of a range of geometries.

Computational analysis of experiments on shock detachment in hypersonic flow of nitrogen and carbon dioxide over a wedge

One of the most dramatic effects of vibrational and chemical non-equilibrium in hypersonic flows occurs in the bow-shock detachment process in flow over a wedge. This was shown theoretically and in reflected shock tunnel experiments by Hornung & Smith (J. Fluid Mech., vol. 93, 1979, pp. 225–239). In the present work, the effect is first demonstrated by computation of two-dimensional non-equilibrium flows. The effect of the finite transverse extent of the wedge is then studied by three-dimensional computations of non-relaxing flows. An analytical formula is obtained that gives the shock detachment distance of a finite wedge for ideal-gas and equilibrium flows. In the experiment, the finite transverse extent of the wedge competes with the non-equilibrium effects, as each introduces a new length scale. The carbon dioxide and nitrogen flows of the experiment are therefore computed in three dimensions and with two-temperature chemistry accounting for vibrational and chemical non-equilibrium. In the case of nitrogen flow, the agreement between experiment and computation is not good, the experimental detachment distance being larger. A number of possible reasons are quantitatively examined. A conclusive resolution of the discrepancy is considered to require a repeat of the experiment with more accurately characterized conditions. In the case of the carbon dioxide experiments, the computed results agree remarkably well with experiment. This is partially due to the fact that the condition is very close to equilibrium, where the sensitivity of the detachment process to relaxation effects is small. The analytical expression for the dimensionless detachment distance agrees very well with all the three-dimensional computations of non-relaxing flows.

Effect of losses on hydrogen–oxygen–argon detonation cell sizes

This work revisits the effect of losses on detonation characteristic length scales. Low-pressure experiments of the very regular hydrogen–oxygen–argon detonations in the straight narrow channel and along the exponentially diverging ramp were reported, demonstrating the significant role of losses in increasing detonation velocity deficits and cell sizes. Both the theoretically established and experimentally obtained relationships show the exponential sensitivity of detonation cell sizes to losses in terms of flow divergence, which is controlled by the global activation energy. The presence of losses modulates the lengthening of the characteristic detonation reaction zones and thus results in larger cell sizes, as indicated by the linear correlation characterizing the amplification of cell sizes and induction length. Moreover, the present work proposed an effective method for calibrating the ideal Chapman–Jouguet (CJ) detonation cell size from experiments, by adopting a revised formulism of Mirels' laminar-boundary-layer theory and also the generalized Zeldovich–von Neumann–Doering (ZND) model in the presence of flow divergence. Comparisons of the ZND-model calibrated ideal CJ detonation cell sizes from experiments with those from detailed numerical simulations show that, while differences still exist for the relatively high pressure cases, accounting for wall losses could excellently reconcile the discrepancy for the lower pressure cases, which appears to suggest no evident influence of the vibrational non-equilibrium effects for the hydrogen–oxygen–argon reactive system.

Specific features of the gas-dynamic structure of supersonic axisymmetric microjets of a nonequilibrium SF6 gas

The effect of vibrational nonequilibrium of SF${}_{6}$ molecules on the gas dynamic structure of microjets is revealed, manifesting in a decrease in the longitudinal cell size of the wave structure and weakening of variations in flow parameters along the axis of the microjet compared to the equilibrium flow. The physical justification is found for the diameter of the nozzle, which is the boundary value between the macro- and microjets of vibrationally relaxing gases.

Simulations of Unsteady Three-Dimensional Hypersonic Double-Wedge Flow Experiments

Hypersonic flow over a three-dimensional 30–55 deg double wedge is investigated for three different conditions of varying enthalpy and Reynolds number with nitrogen as the test gas. Streamwise and spanwise wall heat flux are compared to the experimental data that were obtained at the University of Illinois at Urbana–Champaign and the California Institute of Technology. In previous studies, there were concerns that portions of the flowfield were rarefied; however, after an in-depth analysis, we find the flowfield to be firmly in the continuum regime. Comparisons of heat flux at an instant of time in the simulations show good agreement with the experiments. However, averaged heat flux over a long period of time relative to the experimental test time are underpredicted and develop low-frequency periodic motion. To better understand the unsteadiness and three-dimensionality of the flowfield, we analyze the mass flux through a spanwise plane, and we perform sparsity-promoting dynamic mode decomposition for the wall heat flux and midplane pressure. Finally, we analyze the effect of vibrational nonequilibrium on the flowfield. It is found that the flowfield dynamics vary with increasing enthalpy and Reynolds number. Furthermore, the flowfield is found to be three dimensional, unsteady, and asymmetric for all cases.

Modelling of vibrational nonequilibrium effects on the H2–air mixture ignition under shock wave conditions in the state-to-state and mode approximations

Kinetics of physicochemical processes occurring during combustion of a hydrogen–air mixture initiated by a shock wave was studied using state-to-state and mode models that take into account nonequilibrium vibrational excitation of N2, O2, H2, and OH molecules. The effect of vibrational–translational relaxation on the induction time was considered: it was shown that the delay in establishing thermodynamic equilibrium between vibrational and translational degrees of freedom slows down the initiation of combustion, while the intensity of this effect depends on the temperature and pressure of the gas behind the shock front. An analysis of the peculiarities of vibrational distributions showed that populations of the lower vibrational levels of molecules in the course of chain reactions of combustion behind the shock wave are close to the Boltzmann ones. Therefore, it is sufficient to use the mode approximation. Calculations of the induction time using models of mode approximation showed a significant dependence of the results on the choice of the nonequilibrium factor model. If the nonequilibrium factors are calculated based on the summation of level rate constants of physicochemical processes, the accuracy of the mode model is not inferior to the accuracy of the state-to-state approximation.

Analogy Between Vibrational and Chemical Nonequilibrium Effects on Stagnation Flows

The vibrational excitation and chemical reaction of diatomic molecules are two typical real gas effects that can significantly influence the flow and aeroheating characteristics of hypersonic vehicles, and the qualitative similarity between them has been observed long before. In this paper, based on the theoretical modeling method, a specific analogy of their effects on nonequilibrium stagnation flow is proposed. Therefore, the physical models and mathematical techniques employed in our previous studies on the chemical nonequilibrium flows can be extended to study the vibrational nonequilibrium effects that are dominant in the relatively lower-temperature flows. This analogy study introduces several nonequilibrium flow criteria and a formula that can be used to assess the vibrational nonequilibrium effects on stagnation point heat transfer to wall surfaces with an incomplete accommodation of the vibrational energy. The direct simulation Monte Carlo method is employed to validate the analytical results. This study could enrich the understanding of the nonequilibrium flow physics and similarity of the real gas flows.

Ensemble-Based Molecular Simulation of Chemical Reactions under Vibrational Nonequilibrium.

We present an approach to incorporate the effect of vibrational nonequilibrium in molecular dynamics (MD) simulations. A perturbed canonical ensemble, in which selected modes are excited to higher temperature while all others remain equilibrated at low temperature, is simulated by applying a specifically tailored bias potential. Our method can be readily applied to any (classical or quantum mechanical) MD setup at virtually no additional computational cost and allows the study of reactions of vibrationally excited molecules in nonequilibrium environments such as plasmas. In combination with enhanced sampling methods, the vibrational efficacy and mode selectivity of vibrationally stimulated reactions can then be quantified in terms of chemically relevant observables, such as reaction rates and apparent free energy barriers. We first validate our method for the prototypical hydrogen exchange reaction and then show how it can capture the effect of vibrational excitation on a symmetric SN2 reaction and radical addition on CO2.

Impact of Vibrational Nonequilibrium on the Supersonic Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic boundary layers has recently been shown to achieve a larger peak growth rate than the traditional second mode in particular circumstances relevant to free flight. In this environment, high levels of aerodynamic heating are encountered such that incorporation of chemical and vibrational nonequilibrium effects can become critical. The impact of thermal nonequilibrium (TNE) on the supersonic mode in particular has not been thoroughly and systematically investigated. This work uses thermochemical nonequilibrium (TCNE) direct numerical simulation (DNS) and TCNE linear stability theory (LST) to obtain a more complete investigation of the supersonic mode using both nonequilibrium and frozen gas models. The simulation is Mach 5 flow over a 1-mm-nose-radius axisymmetric cone 1 m in length, representative of experimental conditions in ground test facilities. Both LST and DNS results indicate that TNE effects are destabilizing compared with frozen flow and can lead to an -factor difference of approximately at the end of the cone. LST results also indicate that TNE effects are stabilizing to the second and supersonic modes in comparison with thermal equilibrium. The supersonic mode appeared to be slightly more affected by TNE than the second mode. Collectively, the findings in this work suggest that even in ground test facilities where TCNE effects are relatively small compared with free flight, incorporating nonequilibrium models in both the mean flow and stability solvers can have a practical effect on hypersonic boundary-layer transition prediction analyses.

Numerical study of a nonequilibrium [formula omitted] rocket nozzle flow

A numerical investigation is conducted to study an H2−O2 rocket nozzle flow in chemical and vibrational nonequilibrium. Therefore, a 9 reactions kinetic model was implemented in our two-temperature house code. The vibrational relaxation times taken from Skrebkov's theoretical model and utilized in our simulations are found to be better suited for the H2−O2 mixture than those evaluated using Millikan & White semi-empiric formula. The utilized 9 reactions kinetic model demonstrates a good modeling of the chemical nonequilibrium. The results show the presence of three regions in propulsive nozzles: an equilibrium region, a nonequilibrium region followed by a return to equilibrium region. Vibrational nonequilibrium effects on flowfield parameters and nozzle performances in fuel-rich flows of H2−O2 rocket are investigated, by comparing this baseline simulation to vibrational equilibrium simulation. Vibrational nonequilibrium effects on flowfield parameters and on nozzle performances are computed and shown to be minor. A reduction of 90% of computation time is observed when using the vibrational equilibrium configuration instead of the vibrational nonequilibrium configuration.

Effects of vibrational nonequilibrium on hypersonic shock-wave/laminar boundary-layer interactions

Recent numerical simulations of hypersonic double-cone and hollow-cylinder flare experiments have incorrectly predicted the sizes of separation regions, even at total enthalpies as low as 5.44 and 5.07 MJ/kg. This study investigates the effects of vibrational nonequilibrium to explain these discrepancies. According to an assessment of various flow models under post-shock conditions in comparison with state-specific simulations, the predictions obtained by treating the vibrational modes of molecular nitrogen and oxygen as a single mode, a strategy adopted routinely by the aerospace computational fluid dynamics community, are in close agreement with the state-specific results in terms of post-shock temperature and density profiles, whereas separation of the vibrational modes and assumption of calorically perfect gases would lead to evident errors. The double-cone flow is found to be sensitive to different flow models. In contrast, their effects on hollow-cylinder flare flow are insignificant. Given that the most representative flow model still underestimates the sizes of the separation regions for double cone flow and overestimates those for hollow-cylinder flare flow, it is concluded that inaccurate modeling of vibrational nonequilibrium may not be responsible for the discrepancies observed at the lowest total enthalpies. Suggestions for further study are also presented.

Effect of Vibrational Nonequilibrium on Isolator Shock Structure

Analyses of dual-model scramjet engines often rely on the assumption of thermally perfect gas, for which the internal modes of molecular motion are assumed to be in thermal equilibrium. With an increase in enthalpy and in the presence of shocks and expansion waves, the equilibrium assumption does not hold within a scramjet inlet-isolator section. For the flight Mach numbers considered here, the molecular vibrational modes are affected, leading to not only a change in the gas properties but a redistribution of the total energy. In this work, a multitemperature model is used to describe thermal nonequilibrium of flow through a square duct with an inlet Mach number of 1.9. The highly resolved simulations show that the pseudoshock structure is altered due to nonequilibrium, with the leading edge of the shock structure moving upstream. Moreover, the length of the pseudoshock is considerably increased. Both of these effects are shown to be caused by slow relaxation of the molecules. Furthermore, even at the isolator’s exit, equilibrium is not established, which is manifested as a pressure defect. If and when the fluid reaches thermal equilibrium, inside the downstream combustor, there is a potential for a sudden surge in local pressure that could endanger scramjet operation.

Effect of thermal nonequilibrium on reactions in hydrogen combustion

The presence of shocks in scramjet internal flows introduces nonequilibrium of internal energy modes of the molecules. Here, the effect of vibrational nonequilibrium on key reactions of hydrogen–air combustion is studied. A quasi-classical trajectory (QCT) approach is used to derive reaction probability for nonequilibrium conditions using ab initio-derived potential energy surfaces. The reaction rates under nonequilibrium are studied using a two-temperature description, where the vibrational modes are assumed to be distributed according to a Boltzmann distribution at a characteristic vibrational temperature, in addition to a translational temperature describing the translational and rotational population distribution. At scramjet-relevant conditions, it is found that the nonequilibrium reaction rate depends not only on the level of vibrational excitation, but also on the reactants involved. Conventional two-temperature models for reaction rates, often derived using empirical means, were found to be inaccurate under these conditions, and modified parameters are proposed based on the QCT calculations. It is also found that models that include details of the reaction process through dissociation energy, for instance, provide a better description of nonequilibrium effects.

Vibrational Nonequilibrium Effects in the Conductance of Single Molecules with Multiple Electronic States

Vibrational nonequilibrium effects in charge transport through single-molecule junctions are investigated. Focusing on molecular bridges with multiple electronic states, it is shown that electronic-vibrational coupling triggers a variety of vibronic emission and absorption processes, which influence the conductance properties and mechanical stability of single-molecule junctions profoundly. Employing a master equation and a nonequilibrium Green's function approach, these processes are analyzed in detail for a generic model of a molecular junction and for benzenedibutanethiolate bound to gold electrodes.

Multimode vibrational effects in single-molecule conductance: A nonequilibrium Green’s function approach

The role of multimode vibrational dynamics in electron transport through single molecule junctions is investigated. The study is based on a generic model, which describes charge transport through a single molecule that is attached to metal leads. To address vibrationally-coupled electron transport, we employ a nonequilibrium Green's function approach that extends a method recently proposed by Galperin et al. [Phys. Rev. B 73, 045314 (2006)] to multiple vibrational modes. The methodology is applied to two systems: a generic model with two vibrational degrees of freedom and benzenedibutanethiolate covalently bound to gold electrodes. The results show that the coupling to multiple vibrational modes can have a significant effect on the conductance of a molecular junction. In particular, we demonstrate the effect of electronically induced coupling between different vibrational modes and study nonequilibrium vibrational effects by calculating the current-induced excitation of vibrational modes.

Optimum Performance of Electron Beam Driven Magnetohydrodynamic Generators for Scramjet Inlet Control

This paper is devoted to the analysis and optimization of magnetohydrodynamic control of forebody flow compression and shock incidence in scramjet-powered vehicles that would fly at Mach 5-8. The short (about 30 cm long) magnetohydrodynamic region is created by placing a magnetic coil with B-field strength of several Tesla inside the forebody and ionizing the cold air flow by high-energy electron beams propagating along the magnetic field lines. The Faraday current flowing in the spanwise direction is presumed to be collected with electrodes that are mounted on sidewalls. The purpose of the magnetohydrodynamic device is to restore a shock-on-lip condition at Mach 8 for a vehicle geometry designed for Mach 5, while operating in self-powered mode (the magnetohydrodynamic generated electricity is enough to power the ionizing beams). Location and spatial dimensions of the magnetohydrodynamic region, beam-generated ionization profiles, magnetic field strength, and the magnet size are varied to maximize performance and reduce the magnet size. Two-dimensional inviscid steady-state flow equations are solved jointly with equations describing electron beam-induced ionization profiles, plasma kinetics, vibrational relaxation, and magnetohydrodynamic effects. The model predicts an interesting phenomenon of electric current reversal due to the nonuniformity of velocity, magnetic field, and conductivity in the magnetohydrodynamic region. Vibrational nonequilibrium effects are found to be substantial. Overall, the modeling shows that a considerable reduction in magnet size is possible with the optimum choice of parameters.

Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments

Effect of Vibrational Nonequilibrium on Hypersonic Double-Cone Experiments