Search

In this paper, we present a combined experimental and theoretical study that explored the initial sticking of water on cooled surfaces. Specifically, these ultra-high vacuum gas–surface scattering experiments utilized supersonic molecular beam techniques in conjunction with a cryogenically cooled highly oriented pyrolytic graphite crystal, giving control over incident kinematic conditions. The D2O translational energy spanning 300–750 meV, the relative D2O flux, and the incident angle could all be varied independently. Three different experimental measurements were made. One involved measuring the total amount of D2O scattering as a function of surface temperature to determine the onset of sticking under non-equilibrium gas–surface collision conditions. Another measurement used He specular scattering to assess structural and coverage information for the interface during D2O adsorption. Finally, we used time-of-flight (TOF) measurements of the scattered D2O to determine how energy is exchanged with the graphite surface at surface temperatures above and near the conditions needed for gaseous condensation. For comparison and elaboration of the roles that internal degrees of freedom play in this process, we also did similar TOF measurements using another mass 20 incident particle, atomic neon. Enriching this study are precise molecular dynamics simulations that elaborate on gas–surface energy transfer and the roles of molecular degrees of freedom in gas–surface collisional energy exchange processes. This study furthers our fundamental understanding of energy exchange and the onset of sticking and ultimately gaseous condensation for gas–surface encounters occurring under high-velocity flows. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The safe and stable operation of a hydrogen Knudsen compressor is essential for transporting hydrogen in microfluidic systems. This study uses proper orthogonal decomposition to identify the coherent structures within the hydrogen flow field during non-equilibrium evolution. A long short-term memory neural network is then used to create a multi-fidelity reduced-order model, connecting two-dimensional and three-dimensional data to uncover transient flow mechanisms and enable rapid flow field prediction. The results show that the coherent structures of hydrogen flow, representing the most energetic modes, retain 99% of the flow energy and significantly influence the evolution of Poiseuille and thermal transpiration flows during non-equilibrium processes. The multi-fidelity reduced-order model effectively captures hydrogen transient flow and instabilities at various stages, achieving a 99.4% reduction in computational time while maintaining a maximum relative error of 0.53%. This approach facilitates the rapid prediction and control of flow states during hydrogen transport. [Display omitted] • The coherent structures of hydrogen flow within microchannels are revealed. • The gradient distribution of coherent structures dominate hydrogen flow. • The coherent structures are consistent across different temperature rises. • A multi-fidelity reduced-order model for the Knudsen compressor is developed. • The prediction time for hydrogen flow within microchannels is reduced by 99.4%. [ABSTRACT FROM AUTHOR]

The present paper gives an overview of the recent modelling activities under NATO-STO AVT-349, focussed on the understanding and modelling of boundary layers for incompressible, high-Reynolds-number flows subject to non-equilibrium conditions such as strong pressure gradients, three-dimensionality, and surface roughness and heterogeneity. For this, we consider simpler cases where the above flow conditions are present separately or in a reduced number of combinations. First, we focus on the effect of roughness on the outer flow and the problems associated to its characterisation and prediction, with a particular emphasis on the conditions necessary for outer-layer similarity to hold. We then focus on how the presence of adverse and favourable pressure gradients affects the effect of roughness, and to what extent the figures used to quantify it are still useful under such conditions. We also consider the effect of surface heterogeneity, the shortcomings when modelling it and how these can be addressed. We then focus on the effect on the outer layer of pressure gradients and non-equilibrium conditions, to what extent similarity holds in those conditions, and how RANS models perform for such flows, identifying routes for their improvement to handle pressure gradients and non-equilibrium. We also discuss the use of data-driven and machine-aided methods in closure models. [ABSTRACT FROM AUTHOR]

NATO AVT-RTG-349 was dedicated to the validation of computational fluid dynamics (CFD) methods based on the Reynolds-Averaged Navier-Stokes (RANS) equations and statistical turbulence models for non-equilibrium turbulent-boundary-layer flows at high Reynolds numbers. This paper describes and discusses the errors and uncertainties arising in the comparison of RANS simulation results with experimental data from wind-tunnel experiments. These errors and uncertainties are associated with the CFD grid and the discretization, the physical modelling, the measurement accuracy, and the differences in the flow conditions between the experimental facility and the computational set-up. The results show the need for a grid-convergence study using systematically-refined families of CFD grids. The two major sources of errors are the RANS turbulence model and the uncertainty originating from the differences between the computational set-up and the wind-tunnel. Then two possible paths for future research are described: future CFD mesh generation, and future validation experiments at high Reynolds numbers. [ABSTRACT FROM AUTHOR]

Carbon Dioxide (CO2) is often released in the process of natural gases and is one of greenhouse gases that are being treated as the most troublesome environmental issues. One of the promising ways to economically remove CO2 in natural gas processes is to use the technology of supersonic separation that makes use of non-equilibrium condensation in supersonic swirling flows in convergent-divergent nozzle using wet outlet. In the present study, the mixture of Methane (CH4) and CO2 was considered as natural gas. Two-dimensional convergent–divergent nozzle was employed to produce supersonic swirling flow with non-equilibrium condensation. The Peng–Robinson real gas model was used for the mixture gas. A nucleation equation and a droplet growth equation were incorporated into the governing equations of the compressible Navier–Stokes with the k-ω turbulence closure. The predicted results were verified and validated with existing experimental data. The convergent–divergent nozzle was varied to investigate its effect on the non-equilibrium condensation of CO2 in the mixture flow. The Technique for Order of Preference by Similarity to Ideal Solution method was applied to achieve the optimum case with amounts of wetness (the mass fraction of liquid CO2 to the summation of the mass fraction of liquid and vapor CO2 at the outlet of the nozzle) and kinetic energy. Three locations of wet outlets for the optimum case were analyzed. The results show that an increase in the divergent angle of the nozzle, swirling intensity, and inlet supply pressure results in more nucleation of CO2. However, the enhancement of mole fractions of CO2 decreases the nucleation rate and wetness. The exit wetness from wet outlets was increased with increasing distance from the throat. [ABSTRACT FROM AUTHOR]

Thermochemical nonequilibrium phenomena are key factors affecting the numerical simulation results of flow fields of Mars rover. In order to make clear the flow field properties of the Mars Pathfinder, a multi-physics numerical model including the Navier–Stokes equations, 11 species and 59 chemical reactions of CO2 plasma, and a four-temperature thermodynamic nonequilibrium model is established in this study. Numerical simulations on the thermal-chemical nonequilibrium flow fields of the Mars Pathfinder spacecraft are performed. The distributions of flow-field parameters such as temperature, pressure, Mach number, molar fractions of CO and CO2 around the Mars Pathfinder at different altitudes are obtained. It is found that there is a subsonic backflow at the rear of the Mars Pathfinder, resulting in slightly higher temperatures than other areas; after the shoulder, the pressure decreases rapidly; as the altitude decreases, the intensity of chemical reactions decreases, and the thermal-chemical nonequilibrium effects gradually weaken. Based on the chemical kinetic model of CO2 we proposed, the numerical simulation of the nonequilibrium flow field of the Mars Pathfinder spacecraft showed good predictive accuracy and application potential, providing reference value for subsequent studies on the thermal-chemical nonequilibrium effects of the Mars Pathfinder spacecraft. [ABSTRACT FROM AUTHOR]

This work studies the exhaustive rovibrational state-specific collision-induced dissociation properties of the N2+N system by QCT (quasi-classical trajectory) combined with a neural network method based on the ab initio PES recently published by Varga et al. [Phys. Chem. Chem. Phys. 23, 26273 (2021)]. The QCT combined with a neural network for state-specific dissociation (QCT–NN–SSD) model is developed and used to predict the dissociation cross sections and their energy dependence on the thermal range from a sparsely sampled noisy dataset. It is conservatively estimated that using this method can reduce the cost of the calculation by 96.5%. The rate coefficient of thermal non-equilibrium between different energy modes is obtained by combining the QCT–NN–SSD model with the multi-temperature model. The results show that, for the equilibrium state, dissociation mainly occurs at high vibrational and moderately low rotational levels. When the system is in non-equilibrium, there is no obvious vibrational level preference and highly rotationally excited molecules play a major role in promoting the dissociation by compensating for the lack of vibrational energy. The use of neural network training to generate complete datasets based on limited and discrete data provides an economical and reliable way to obtain a complete kinetic database needed to accurately simulate non-equilibrium flows. [ABSTRACT FROM AUTHOR]

Procedures of the Direct Simulation Monte Carlo method for weakly ionized flows around reentry vehicles are presented. For ionization and recombination reactions, expressions for the model dependence of the reaction probability on velocities and energies of reagents are derived. An algorithm of dissociative recombination is presented, whose computational efficiency is reached by bypassing the modeling of the interaction of electrons and heavy particles. An approach to the construction of a weighting scheme for elastic collisions and chemical reactions is described, which significantly increases the computational efficiency of the algorithm. An example of using these numerical models and procedures for studying a weakly ionized flow around a reentry capsule under typical reentry co-nditions is given. The computation results are compared to plasma parameters measured in flight experiments. [ABSTRACT FROM AUTHOR]

Nonequilibrium flows of air components behind reflected shock waves are systematically studied on the basis of several theoretical models for the rate coefficients of fully coupled vibrational energy exchanges and chemical reactions. Numerical simulations are performed in the frame of the state-to-state approach under initial conditions corresponding to recent shock-tube experiments in mixtures O 2 /Ar, NO/Ar, NO/N 2 /Ar. The model takes into account partial vibrational relaxation between the incident and reflected shock waves, state-resolved dissociation, recombination, exchange reactions with formation of NO in the vibrationally excited states, as well as vibrational–vibrational and vibrational–translational energy transitions. It is shown that for oxygen, relaxation between the incident and reflected shocks is not frozen, and taking it into account in the most test cases considerably improves the agreement of calculated and experimentally measured pressure. For NO-containing mixtures, the effect of intermediate relaxation is weaker. Average deviation of the number density of molecular species with respect to the experimental one is analyzed for several hundreds of numerical simulations; on the basis of these estimates, recommendations are given for the best choice of model parameters. These recommendations can be used for modeling high-temperature flows, in particular, under reentry conditions. • Recent shock-tube experiments in air species are simulated numerically. • State-to-state models of vibrational–chemical coupling are validated. • Good agreement with experimental data is shown. • Recommendations are given for the best choice of model parameters. [ABSTRACT FROM AUTHOR]

In this study, an air-water vapor ionization reaction model is developed within the quantum-kinetic (Q–K) model of the direct simulation Monte Carlo method to investigate the detailed mechanism of how water vapor reduces electrons. The zero-dimensional simulations of a typical non-equilibrium flow field downstream of a normal shock are designed, where the electron number density decreases by two orders of magnitude due to water vapor. We conclude that the introduction of water vapor reduces the mole fractions of oxygen atoms and nitrogen atoms through five pairs of reactions and enhances the reverse nitric oxide associative ionization reaction, leading to electron consumption. The phenomena and corresponding mechanisms under varying mole fractions of water vapor, air temperatures, and water vapor temperatures are investigated. Based on the mechanisms, we propose that the addition of hydrogen ions could improve the water's mitigation effect, which is then proven to be able to reduce the electron number density by another two orders of magnitude, not only at high air temperatures but also at lower air temperatures or lower mass injection rates. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

High Reynolds number turbulent flow of hypersonic vehicles exhibits multi-scale flow structures and non-equilibrium high-frequency characteristics, presenting a significant challenge for accurate prediction. A deep neural network integrated with attention mechanism as a reduced order model for hypersonic turbulent flow is proposed, which is capable of capturing spatiotemporal characteristics from high-dimensional numerical turbulent data directly. The network model leverages encoder–decoder architecture where the encoder captures high-level semantic information of input flow field, Convolutional Long Short-Term Memory network learns low-dimensional characteristic evolution, and the decoder generates pixel-level multi-channel flow field information. Additionally, skip connection structure is introduced at the decoding stage to enhance feature fusion while incorporating Dual-Attention-Block that automatically adjusts weights to capture spatial imbalances in turbulence distribution. Through evaluating the time generalization ability, the neural network effectively learns the evolution of multi-scale high-frequency turbulence characteristics. It enables rapid prediction of high Reynolds number turbulence evolution over time with reasonable accuracy while maintaining excellent computational efficiency. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Understanding the dynamic response of soil moisture to rainfall is crucial for describing hydrological processes at the hillslope scale. However, because of sparse monitoring coupled with the complexity of water movement and steep topography, the findings of rainfall‐related soil moisture dynamics have not always been consistent, indicating a need for systematic investigations of soil moisture dynamics and infiltration patterns following rainfall inputs at multiple topographic positions along a hillslope. This study aimed to examine the nature of these responses by characterizing and quantifying the response amplitude, rate and time for 37 large rainfall events at 25 combinations of topographic positions and soil depths along a steep forested hillslope. Our results showed that soil moisture responses under different rainfall patterns could be attributed to one or the other rainfall characteristics, such as rainfall intensity and amount. However, soil moisture dynamics at different hillslope positions after rainfall varied widely due to the controls of soil properties, topography, and non‐equilibrium flow. Preferential flow was more evident under dry initial soil conditions than under wet initial soil conditions. Findings of this study reveal that the dynamic response patterns of soil moisture to rainfall do not always follow topographic controls, which can improve our understanding of water cycling related to the infiltration process at the hillslope scale, and support water resources management in subtropical mountain ecosystems. [ABSTRACT FROM AUTHOR]

Composition of deuterium (heavy) water in light water was drastically reduced to one-half by one stage of a newly invented device that can create a nonequilibrium vapor state driven by a dynamic system. Vapor density of heavy and light water is arbitrarily controlled. This system works at 20–60°C, even under atmospheric pressure. The mechanism should equally work even for tritium water, as tritium-contaminated water is a problem in the treatment of nuclear reactors as well as fusion reactors. [ABSTRACT FROM AUTHOR]

Copyright of Materials & Technologies / Materiali in Tehnologije is the property of Institute of Metals & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Data-driven discovery of governing equations is of great significance for helping us understand intrinsic mechanisms and build physical models. Recently, numerous highly innovative algorithms have emerged, aimed at inversely discovering the underlying governing equations from data, such as sparse regression-based methods and symbolic regression-based methods. Along this direction, a novel dimensional homogeneity constrained gene expression programming (DHC-GEP) method is proposed in this work. The DHC-GEP simultaneously discovers the forms and coefficients of functions using basic mathematical operators and physical variables, without requiring preassumed candidate functions. The constraint of dimensional homogeneity is capable of filtering out the overfitting equations effectively. The key advantages of DHC-GEP compared with the original gene expression programming, including being more robust to hyperparameters, the noise level and the size of datasets, are demonstrated on two benchmark studies. Furthermore, DHC-GEP is employed to discover the unknown constitutive relations of two representative non-equilibrium flows. Galilean invariance and the second law of thermodynamics are imposed as constraints to enhance the reliability of the discovered constitutive relations. Comparisons, both quantitative and qualitative, indicate that the derived constitutive relations are more accurate than the conventional Burnett equations in a wide range of Knudsen numbers and Mach numbers, and are also applicable to the cases beyond the parameter space of the training data. [ABSTRACT FROM AUTHOR]

Numerical analysis of a steady monatomic gas flow about the point of the regular reflection of a strong oblique shock wave from the symmetry plane is conducted with the Navier–Stokes–Fourier (NSF) equations, the regularized Grad 13-moment (R13) equations and the direct simulation Monte Carlo (DSMC) method. In contrast to the inviscid solution to this problem completely defined by the Rankine–Hugoniot (RH) relations, all three models predict a complicated flow structure with strong thermal non-equilibrium and a long wake with flow parameters not predicted by the RH relations. The temperature $T_y$ related to thermal motion of molecules in the direction normal to the symmetry plane has a maximum inside the reflection zone while in a planar shock wave the maximum is observed for the $T_x$ temperature. The R13 equations predict these features much better than the NSF equations and are in good agreement with the benchmark DSMC results. An analysis of the flow with the conservation equations was conducted in order to evaluate the effects of various processes on a fluid element moving along the symmetry plane. In contrast to the shock wave where effects of viscosity and heat conduction are one-dimensional with zeroth net contribution to the fluid-element energy across the shock, the flow across the zone of the shock reflection is dominated by two-dimensional effects with positive net contribution of viscosity and negative contribution of heat conduction to the fluid-element energy. These effects are believed to be the main source of the wake with parameters deviating from the RH values. [ABSTRACT FROM AUTHOR]

Over the last decade, substantial progress has been made in understanding the topology of quasi-two-dimensional (2-D) non-equilibrium fluid flows driven by ATP-powered microtubules and microorganisms. By contrast, the topology of three-dimensional (3-D) active fluid flows still poses interesting open questions. Here, we study the topology of a spherically confined active flow using 3-D direct numerical simulations of generalized Navier-Stokes (GNS) equations at the scale of typical microfluidic experiments. Consistent with earlier results for unbounded periodic domains, our simulations confirm the formation of Beltrami-like bulk flows with spontaneously broken chiral symmetry in this model. Furthermore, by leveraging fast methods to compute linking numbers, we explicitly connect this chiral symmetry breaking to the entanglement statistics of vortex lines. We observe that the mean of linking number distribution converges to the global helicity, consistent with the asymptotic result by Arnold [In Vladimir I. Arnold - Collected Works (ed. A.B. Givental, B.A. Khesin, A.N. Varchenko, V.A. Vassiliev & O.Y. Viro), pp. 357-375. Springer]. Additionally, we characterize the rate of convergence of this measure with respect to the number and length of observed vortex lines, and examine higher moments of the distribution. We find that the full distribution is well described by a k-Gamma distribution, in agreement with an entropic argument. Beyond active suspensions, the tools for the topological characterization of 3-D vector fields developed here are applicable to any solenoidal field whose curl is tangent to or cancels at the boundaries of a simply connected domain. [ABSTRACT FROM AUTHOR]

For precise application of Bhatnagar–Gross–Krook (BGK) methods, assessing its accuracy in non-equilibrium flows is necessary. Generally, this assessment relies on macroscopic parameters, which are moments of the velocity distribution function (VDF). However, in non-equilibrium flows, the significance of each moment diminishes as the VDF deviates from the Maxwellian VDF. This study investigates the VDF in non-equilibrium flows. Two Prandtl-corrected BGK methods, the ellipsoidal statistical BGK and Shakhov BGK (SBGK), are compared with the direct simulation Monte Carlo method. To observe the VDF while excluding the effects of convection, the homogeneous relaxation of the initial non-equilibrium state is analyzed. The VDF in Couette flow and normal shock waves, where collision and convection coexist, is then examined. When comparing the accuracy of the BGK methods using higher-order moments, inconsistencies are observed. However, when comparing the VDFs, the SBGK method reproduces the non-equilibrium VDF more accurately. The results demonstrate the importance of the VDF in the evaluation of non-equilibrium flows. [ABSTRACT FROM AUTHOR]

Flow-induced phenomena in entangled solutions of linear, monodisperse C 1000 H 2002 polyethylene dissolved in benzene were simulated under steady-state and startup uniaxial elongational flow via nonequilibrium molecular dynamics at a concentration of 13.5 c ∗ of the coil-overlap concentration, c ∗ . The simulations revealed that the solution exhibited a chemical phase separation of the polymer and solvent components when subjected to uniaxial extensional flow at extension rates faster than the inverse Rouse time of the solution, followed by flow-induced crystallization of the polymer-rich phase into fibrillar structures of roughly 50 Å in diameter. The polymer phase was generated by the migration of the polymer chains into locally concentrated domains due to the favorable energetics of the stretched polymer chains, which simultaneously resulted in the expulsion of the less energetically favorable solvent molecules, thus producing a configurationally-based flow-induced demixing effect of polymer and solvent. [ABSTRACT FROM AUTHOR]

A machine-learned model for predicting product state distributions from specific initial states (state-to-distribution or STD) for reactive atom–diatom collisions is presented and quantitatively tested for the N(4S) + O2( X 3 Σ g − ) → NO(X2Π) + O(3P) reaction. The reference dataset for training the neural network consists of final state distributions determined from quasi-classical trajectory (QCT) simulations for ∼ 2000 initial conditions. Overall, the prediction accuracy as quantified by the root-mean-squared difference (∼0.003) and the R2 (∼0.99) between the reference QCT and predictions of the STD model is high for the test set, for off-grid state-specific initial conditions, and for initial conditions drawn from reactant state distributions characterized by translational, rotational, and vibrational temperatures. Compared with a more coarse grained distribution-to-distribution (DTD) model evaluated on the same initial state distributions, the STD model shows comparable performance with the additional benefit of the state resolution in the reactant preparation. Starting from specific initial states also leads to a more diverse range of final state distributions, which requires a more expressive neural network compared with DTD. A direct comparison between QCT simulations, the STD model, and the widely used Larsen–Borgnakke (LB) model shows that the STD model is quantitative, whereas the LB model is qualitative at best for rotational distributions P(j′) and fails for vibrational distributions P(v′). As such, the STD model can be well-suited for simulating nonequilibrium high-speed flows, e.g., using the direct simulation Monte Carlo method. [ABSTRACT FROM AUTHOR]

A model to locate hydrogen refueling stations (HRSs) for hydrogen fuel cells vehicles (HFCVs) or hydrogen internal combustion engines vehicles (HICEVs) is proposed in this paper. The model integrated the flow-capturing location allocation (FCLA) model and stochastic user-equilibrium (SUE) status of network flow. An equilibrium algorithm obviating cannibalization was also presented. We compared the effectiveness between node location and link location determined by FCLA between SUE status and non-equilibrium status of the transportation network taking the city of Anaheim in California in America as an example. The results showed that the capture ratios of node-serving and link-serving are different. For the non-equilibrium case, equilibrium case, and hybrid case, the capture ratios of node-serving are 77.72%, 69.51%, and 60.25%, respectively, while the capture ratios of link-serving are 54.37%, 46.34%, and 31.49%, respectively. This means Node-serving performs better than link-serving in terms of capturing flow, either in equilibrium status or non-equilibrium status. The node locations or link locations obtained by the FCLA method in SUE status should be used for locating HRSs because they are consistent with peoples' route choice behavior and thus can fully capture the expected flow in reality. Practically speaking, link locations are preferable to node locations in locating HRSs because the construction and operation of HRSs on nodes are relatively difficult to implement. • A model of FCLA in SUE status to locate hydrogen refueling stations. • Node-serving and link-serving determined by non-equilibrium flow. • Node-serving and link-serving determined by SUE flow. • Compare the effectiveness between node-serving and link-serving in both cases. [ABSTRACT FROM AUTHOR]

Flows of a rarefied polyatomic gas confined in a nozzle with simple geometry are numerically studied based on the rational extended thermodynamics theory with six independent fields (RET 6 ). Using the theory, we can focus on, in particular, the effect of the dynamic pressure (nonequilibrium part of the pressure) on nozzle gas-flows. Development of a nonequilibrium state of a gas along the flow is studied by comparing the flow profiles to the ones predicted by the Euler theory of perfect fluids. Under some conditions, we find flow profiles that are qualitatively different from those by the Euler theory. Choking phenomena are also observed on the basis of RET 6 . From these findings we confirm that the RET 6 theory is useful also for the analysis of nozzle gas-flows. [ABSTRACT FROM AUTHOR]

One of the challenges in using Manning’s equation lies in accurately determining Manning’s roughness coefficient, especially due to sediment transport. The condition of sediment transport within a specific section of a river can be in equilibrium, meaning that the amount of sediment entering and exiting the segment is balanced or it can be in non-equilibrium, where there is an imbalance between the sediment entering and leaving the segment. Experiments were carried out in the laboratory to simulate both transport conditions, one involving sediment feeding (equilibrium condition) and the other without sediment feeding (non-equilibrium condition). A total of 180 mean velocity profiles were measured using an acoustic doppler velocimeter (ADV) in fixed and movable bed flows. The present experiment was combined with theoretical approaches to evaluate Manning’s coefficient in open channels under sediment transport-flow conditions and reach conclusive results. The shape of the velocity profile, u/U, for flows over a movable bed with sediment feeding is “slender” compared to those without sediment feeding. The presence of sediment transport affects the shape of the velocity profile, especially in the inner region, influencing Manning's roughness coefficient. This coefficient can be determined from two-point velocity measurements at z/H = 0.1 and 0.2 for fixed and movable bed flows with and without sediment feeding, respectively. On average, sediment feeding increases the coefficient by 19% compared to the non-sediment feeding case. [ABSTRACT FROM AUTHOR]

Shock/shock interactions (SSIs) often lead to high thermal loads. To understand the influences of thermochemical non-equilibrium effects on the Type III SSI, four gas models based on the assumption of thermal perfect gas (TPG), thermal equilibrium chemical non-equilibrium gas (TECNG), thermal non-equilibrium chemical frozen gas (TNCFG), and thermochemical non-equilibrium gas (TCNEG) are employed to simulate the Type III SSI at Mach 10. The intersection of incident shock and bow shock is determined by dimensionless intercept of 0.05 and 0.1. It is found that the chemical non-equilibrium effects significantly lift up the impingement position of shear layer by reducing the standoff distance of bow shock. As a result, the peaks of wall pressure and heat flux calculated by TECNG and TCNEG model are higher than TPG and TNCFG model, respectively. Type IIIa SSI occur in the flows calculated by the TECNG and TCNEG model for the case with a dimensionless intercept of 0.1. The peaks of wall pressure and heat flux calculated by TECNG model are both over four times higher than those of TPG model. The thermal non-equilibrium effects slightly increase the standoff distance of bow shock and lower the impingement position of shear layer. In addition, the thermal non-equilibrium reduces the angle to the horizontal direction of shear layer by increasing the specific heat ratio. • Type III shock/shock interaction at Mach 10 are simulated by four gas models. • The influences of non-equilibrium effects on flow fields are analyzed. • The chemical non-equilibrium effects significantly increase the peak values of heat flux and pressure. • The mechanisms of non-equilibrium effects on peak heat flux and pressure are revealed. [ABSTRACT FROM AUTHOR]

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited the extent of numerical validation studies to simple, often two-dimensional, flow problems. Recent algorithmic advancements for the Boltzmann–Bhatnagar–Gross–Krook equation introduced by the authors [Dzanic et al., J. Comput. Phys. 486, 112146 (2023)], consisting of a highly efficient high-order spatial discretization augmented with a discretely conservative velocity model, have made it feasible to accurately simulate unsteady three-dimensional flow problems across both the rarefied and continuum regimes. This work presents a comprehensive evaluation and validation of wall boundary conditions across a variety of flow regimes, primarily for the purpose of exploring their effects on momentum transfer in the low Mach limit. Results are presented for a range of steady and unsteady wall-bounded flow problems across both the rarefied and continuum regimes, from canonical two-dimensional laminar flows to unsteady three-dimensional transitional and turbulent flows, the latter of which are the first instances of wall-bounded turbulent flows computed by directly solving the Boltzmann equation. We show that approximations of the molecular gas dynamics equations can accurately predict both non-equilibrium phenomena and complex hydrodynamic flow instabilities and show how spatial and velocity domain resolution affect the accuracy. The results indicate that an accurate approximation of particle transport (i.e., high spatial resolution) is significantly more important than particle collision (i.e., high velocity domain resolution) for predicting flow instabilities and momentum transfer consistent with that predicted by the hydrodynamic equations and that these effects can be computed accurately even with very few degrees of freedom in the velocity domain. These findings suggest that highly accurate spatial schemes (e.g., high-order schemes) are a promising approach for solving molecular gas dynamics for complex flows and that the direct solution of the Boltzmann equation can be performed at a reasonable cost when compared to hydrodynamic simulations at the same level of resolution. [ABSTRACT FROM AUTHOR]

The hypersonic high enthalpy nitrogen flows over spheres are investigated by high-fidelity state-to-state (StS) modeling. The objective of the study is to understand the nonequilibrium behaviors in the shock layer, including the stagnation line features, surface heat transfer rate, and near-wall properties inside the thermal boundary layer. Two cases with the freestream total enthalpies of 16.5 and 15.5 MJ/kg are considered, and the numerical results are compared with the experimental data. The StS model yields an accurate prediction of the shock stand-off distance with the experiment rather than an underestimation by the traditional two-temperature model. Both the StS and two-temperature models provide general agreement of the stagnation point heat flux with the experiment. In comparison, the heat flux obtained by the StS model is lower than the two-temperature model. Note that our work finds distinctive behaviors of near-wall properties. The vibrational energy is not accommodated with the sphere surface and is in thermal nonequilibrium with the translational energy, with evidence showing that the vibrational temperature is much higher than the wall temperature and the translational temperature. The values of vibrational temperature in the immediate vicinity of the stagnation point are 9.3 and 10.0 times the wall temperature for the cases with total enthalpies of 16.5 and 15.5 MJ/kg, respectively. Moreover, the vibration temperature demonstrates a nonmonotonic variation trend with a local minimum, which can be explained by the nonequilibrium distributions of vibrational energy states due to vibrational-translational energy transfer and molecular recombination. [ABSTRACT FROM AUTHOR]

Precise process-based modeling of nonequilibrium water flow and solute transport continues to pose a significant challenge in vadose zone hydrogeology. Nonequilibrium water flow and solute transport in the vadose zone bring about various complexities associated with heterogeneity, variability, unsaturated flow processes, hysteresis effects, and time and scale dependencies. These challenges necessitate the utilization of advanced measurement techniques, robust modeling approaches, and a comprehensive understanding of the physical and chemical processes that take place in the vadose zone. This study focuses on the experimental and process-based modeling of nitrate transport that considers equilibrium and nonequilibrium (physical nonequilibrium) transport processes. This study was carried out by performing a laboratory-scale experimental study followed by a numerical simulation modeling study. The experimental study was conducted using a tank setup 60 cm long, 30 cm wide, and 60 cm deep, which was filled with sandy soil. The nitrate concentration was measured at different soil depths after a constant water flux, which contained 300 mg/L nitrate, was applied to the tank top surface. A numerical simulation modeling study was performed using HYDRUS-1D. Simulation runs were carried out by considering equilibrium (single porosity) and physical nonequilibrium (dual-porosity model) conditions. Various simulations used dual-porosity models, which consider different proportions of sorption sites that interact with the mobile water content and varying mass transfer coefficients. The simulation with a 75% mobile zone with a 10 day−1 mass transfer coefficient agreed well with the experimental data. [ABSTRACT FROM AUTHOR]

The strong coupling interactions of non-equilibrium flow, microscopic particle collisions and radiative transitions within the shock layer of hypersonic atmospheric re-entry vehicles makes accurate prediction of the aerothermodynamics challenging. Therefore, in this study a self-consistent non-equilibrium flow, collisional--radiative reactions and radiative transfer fully coupled model are established to study the non-equilibrium characteristics of the flow field and radiation of vehicle atmospheric re-entry. The comparison of the present calculation results with flight data of FIRE II and previous results in the literature shows a reasonable agreement. The thermal, chemical and excited energy level non-equilibrium phenomena are obtained and analysed for the different FIRE II trajectory points, which form the critical basis for studying the heat transfer and radiation. The non-equilibrium distribution of excited energy levels significantly exists in the post-shock and near-wall regions due to the rapid vibrational dissociation and electronic under-excitation, as well as the wall catalytic reactions. The analysis of stagnation-point heating of FIRE II illustrates that the translational--rotational convection and the dissociation component diffusion play key roles in the aerodynamic heating of the wall region. The spectrally resolved radiative intensity in the entire flow field indicates that the vacuum ultraviolet radiation caused by the high-energy nitrogen atomic spectral lines makes the main contribution to the radiative transfer. Finally, it is found that the non-equilibrium flow--radiation coupling effect can exacerbate the excited energy level non-equilibrium, and further affect the gas radiative properties and radiative transfer. This fully coupled study provides an effective method for reasonable prediction of atmospheric re-entry flow and radiation fields. [ABSTRACT FROM AUTHOR]

We formulate a regularized problem to describe the flow of a molecular gas in a hypersonic macrokinetic nonequilibrium thin viscous shock layer (kinetic TVSL) near a sharp edge. It is shown that the solution to the regularized problem of a kinetic TVSL on a sharp edge in terms of friction and heat transfer coincides with the solution of a similar TVSL problem in the Navier–Stokes formulation. It is shown that near the sharp edge the friction stress and normal wall heat flow in the kinetic TVSL are identical to the corresponding TVSL values for the Navier–Stokes model. We point out the similarity of flows near a sharp edge in the kinetic TVSL and Navier–Stokes formulations. We suggest a method for constructing a solution to the kinetic TVSL problem near a sharp edge based on the TVSL solution within the Navier–Stokes model. A formula is obtained for calculating the surface pressure in a kinetic TVSL flow near a sharp edge from the components of the (wall) solution of the TVSL problem obtained for the Navier–Stokes model. [ABSTRACT FROM AUTHOR]

A nitrogen jet expanding during its exhaustion from a nozzle into a vacuum chamber is numerically simulated by a hybrid approach. The flow parameters in the nozzle and in the near field of the jet are determined by solving the Navier–Stokes equations by using the ANSYS Fluent software. The gas flow at large distances from the nozzle exit is modeled by the Direct Simulation Monte Carlo method by using the SMILE software system. Such an approach makes it possible to perform sufficiently accurate simulations in the near field of the jet; moreover, the temperature nonequilibrium of the expanding gas jet and other effects of rarefaction in the far field of the jet are taken into account. The approach is verified by using various approximate analytical models of gas exhaustion into vacuum. A comparison of the numerical results with available experimental data shows that they are in good agreement. [ABSTRACT FROM AUTHOR]

In this study, shock stand-off distances for thermally and chemically non-equilibrium flows of nitrogen over wedges are computationally investigated via a hypersonic computational fluid dynamics solver, hyperReactingFoam by spanning a parameter space that consists of ranges of Mach number, 4–10, specific heat ratio, 1.40–1.61 and wedge angles, 60 ∘ –90 ∘ . Then, the space is reduced into the parameters of inverse density ratio across the shock and dimensionless wedge angle which will be used as variables for quadratic functions that represent shock stand-off distances. Besides the functions of shock stand-off distances, detached shock profiles of computationally modeled flows are represented by parabolic equations. The flows are observed to be chemically frozen for Mach number ranges of 4–5 regardless of the specific heat ratio value of the nitrogen mixture. Our results show that the shock stand-off distance decreases as Mach number is increased from 4 to 7, if the wedge angle and free-stream specific heat ratio are kept the same. On the other hand, if Mach number is increased beyond 7, the shock stand-off distance starts to extend due to the dissociation of nitrogen molecules behind the shock wave. At Mach 10, nitrogen completely dissociates over 90 ∘ wedge for all specific heat ratios considered in the present study. Increased leading edge angle of the wedge or specific heat ratio of free-stream yields longer shock stand-off distance. [ABSTRACT FROM AUTHOR]

This research aims at analyzing thermo-chemical properties of the hypersonic high-enthalpy flow in the L2K wind tunnel, situated in Köln at the German Aerospace Center (DLR). In the L2K wind tunnel, Martian atmosphere can be created, and the facility can simulate heat load conditions encountered during atmospheric entry of Martian missions. The focus of this project is the analysis of the non-intrusive experimental technique "Tunable Diode Laser Absorption Spectroscopy" (TDLAS), based on line of sight absorption spectroscopy, and applied to hypersonic flow. A simplified Martian atmosphere (97% CO 2 and 3% N 2) was used. A new interpretation for CO-TDLAS experimental technique applied to hypersonic wind tunnel flow analysis was developed. Numerical simulations with the DLR-TAU non-equilibrium flow solver were used as support of this analysis, and match between simulations and experiments was observed. Flow speed and absorption line's width were measured, and the knowledge of L2K's flow structure was extended. [Display omitted] • TDLAS experimental technique in L2K wind tunnel was comprehensively analyzed. • Recirculation process of the flow's outer layers was confirmed and analyzed. • Match between simulations of spectroscopic data and experiments was observed. [ABSTRACT FROM AUTHOR]

This study covers a simulation on conjugate free convective in a porous enclosure containing a side wall thickness and partially heated and cooled from sides under the considerations of local thermal nonequilibrium (LTNE) and non‐Darcy flow. Interest has been focused on how the side wall thickness and the locations of cooled and heated parts affect the effectiveness of the Nusselt number (Nu). Three different cases of localized heating and cooling locations have been implemented for the following ranges: scaled heat transfer coefficient (0.1≤H≤100 $0.1\le H\le 100$), wall to fluid thermal conductivity ratio (0.1≤Rk≤100 $0.1{\le R}_{k}\le 100$), modified Rayleigh number (200≤Ra*≤1000 $200\le {Ra}* \le 1000$), wall width (0.1≤Zˆ≤0.5 $0.1\le \hat{Z}\le 0.5$), inertial parameter (10−4≤Fs/Pr*≤10−2 ${10}^{-4}{\le F}_{s}/{P}_{r}^{* }\le {10}^{-2}$), and thermal conductivity ratio (0.1≤Kr≤100 $0.1\le {K}_{r}\le 100$). Outcomes show that Zˆ $\hat{Z}$ and the locations of cooled and heated parts have remarkable impacts on all the Nusselt numbers. The intensity of LTNE region considerably relies on Ra* ${Ra}{* }$, Kr ${K}_{r}$ and H $H$. The total average NuT is highly dependent on Rk ${R}_{k}$, Ra* ${Ra}{* }$, Zˆ $\hat{Z}$, Fs/Pr* ${F}_{s}/{P}_{r}^{* }$, and Kr ${K}_{r}$ as compared to H. The increase in Zˆ $\hat{Z}$ leads to change of the convective mechanism to conductive mode. The rise in Rk ${R}_{k}$ guides to increase Nu, where Rk ${R}_{k}$ can control the flow strength. The actions of Fs/Pr* ${F}_{s}/{P}_{r}^{* }$ on Nuf is more evident than Nus. For low H and Kr, the size of LTNE zone is considerably affected by H as compared to Kr although Kr has a high influence on Nu. For high Kr and H, the LTNE zone has closely vanished. Findings display that the Case 2 provided the highest Nu for all tested parameters except the case of Kr=0.1 ${K}_{r}=0.1$. Finally, it is evident that for the problems that employed solid conduction wall with localized heating and cooling sections, Case 2 is recommended for future use in the applications that implement a porous medium and depend on free convection. [ABSTRACT FROM AUTHOR]

A one-dimensional problem of heat transfer in a bounded domain (microchannel) filled with rarefied gas is considered. Two molecular beams enter the domain from the left boundary, the velocities of the particles are equal in the each beam. The diffuse reflection condition is set on the right boundary. It is shown using the Shakhov kinetic model that by varying the ratio of velocities in the molecular beams it is possible to obtain a heat flux of various magnitudes and signs such that the te-mperatures on the left and right boundaries are equal or the temperature gradient in the boundary layer has the same sign as the heat flux. This problem is related to the problem of constructing lattice Boltzmann equations with four velocities, which can reproduce the first Maxwell half-moments. It is shown that in this case the optimal ratio of discrete velocities is 1 : 4. [ABSTRACT FROM AUTHOR]

This paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and Fourier laws are violated (and, accordingly, the Chapman–Enskog method is inapplicable). For a reliable validation of anomalous transport effects, we use computational methods of different nature: the direct solution of the Boltzmann equation and direct simulation Monte Carlo. Nonclassical anomalous transport is manifested on scales of 5–10 mean free paths, which confirms the fact that a highly nonequilibrium flow is a prerequisite for the detection of the effects. Two-dimensional flow problems are considered, namely, the supersonic flow over a flat plate in the transient regime and the supersonic flow through membranes (lattices), where the flow behind the lattice corresponds to the spatially nonuniform relaxation problem. In this region, nonequilibrium distributions demonstrating anomalous transport are formed. The relationship of the effect with the second law of thermodynamics is discussed, the possibilities of experimental verification are considered, and the prospects of creating new microdevices on this basis are outlined. [ABSTRACT FROM AUTHOR]

This paper reports a systematic computational investigation that elucidates the fundamental thermochemical non-equilibrium physics that occurs when air at Mach number of 11 encounters a rectangular cavity of aspect ratio L/D = 2.0 embedded on a 25° compression ramp. The mechanistic details of this highly complex flow phenomenon are obtained by solving the compressible form of the Navier–Stokes equations in two dimensions using a finite-volume open-source library. Chemical and thermal non-equilibrium processes are treated using a five-species, 12-reaction chemical kinetics, and a two-temperature model, respectively. Following a detailed validation and grid sensitivity study, two simulations are conducted, one with isothermal boundary conditions and the other with conjugate heat transfer (CHT) to identify the effect of energy transmission to the material on surface heat flux. Fast Fourier transforms and near-wall velocity profiles inside and in the neighborhood of the cavity are used to identify primary oscillatory modes and shear layer dynamics. Two new descriptive states defined as "states I and II," representative of the minimum and maximum deflection of the shear layer, are used to discuss the dynamical behaviors in the cavity, including the separation region before the cavity, trailing edge effects, frequency analysis of probe data collected at several key locations, and the effect of CHT on surface heat flux. It is found that the flow features at the cavity's center strongly influence the separation upstream of the cavity, and the transrotational temperature near the cavity's trailing edge is strongly correlated with the oscillations of the shear layer. [ABSTRACT FROM AUTHOR]

This work proposes a new machine learning (ML)-based paradigm aiming to enhance the computational efficiency of non-equilibrium reacting flow simulations while ensuring compliance with the underlying physics. The framework combines dimensionality reduction and neural operators through a hierarchical and adaptive deep learning strategy to learn the solution of multi-scale coarse-grained governing equations for chemical kinetics. The proposed surrogate's architecture is structured as a tree, with leaf nodes representing separate neural operator blocks where physics is embedded in the form of multiple soft and hard constraints. The hierarchical attribute has two advantages: (i) It allows the simplification of the training phase via transfer learning, starting from the slowest temporal scales; (ii) It accelerates the prediction step by enabling adaptivity as the surrogate's evaluation is limited to the necessary leaf nodes based on the local degree of non-equilibrium of the gas. The model is applied to the study of chemical kinetics relevant for application to hypersonic flight, and it is tested here on pure oxygen gas mixtures. In 0- D scenarios, the proposed ML framework can adaptively predict the dynamics of almost thirty species with a maximum relative error of 4.5% for a wide range of initial conditions. Furthermore, when employed in 1- D shock simulations, the approach shows accuracy ranging from 1% to 4.5% and a speedup of one order of magnitude compared to conventional implicit schemes employed in an operator-splitting integration framework. Given the results presented in the paper, this work lays the foundation for constructing an efficient ML-based surrogate coupled with reactive Navier-Stokes solvers for accurately characterizing non-equilibrium phenomena in multi-dimensional computational fluid dynamics simulations. [ABSTRACT FROM AUTHOR]

The recent Lagrangian relaxation towards equilibrium (LaRTE) approach (Fowler et al. , J. Fluid Mech. , vol. 934, 2022, A44) is a wall model for large-eddy simulations (LES) that isolates quasi-equilibrium wall-stress dynamics from non-equilibrium responses to time-varying LES inputs. Non-equilibrium physics can then be modelled separately, such as the laminar Stokes layers that form in the viscous region and generate rapid wall-stress responses to fast changes in the pressure gradient. To capture additional wall-stress contributions due to near-wall turbulent eddies, a model term motivated by the attached eddy hypothesis is proposed. The total modelled wall stress thus includes contributions from various processes operating at different time scales (i.e. the LaRTE quasi-equilibrium plus laminar and turbulent non-equilibrium wall stresses) and is called the multi-time-scale (MTS) wall model. It is applied in LES of turbulent channel flow subject to a wide range of unsteady conditions from quasi-equilibrium to non-equilibrium. Flows considered include pulsating and linearly accelerating channel flow for several forcing frequencies and acceleration rates, respectively. We also revisit the sudden spanwise pressure gradient flow (considered in Fowler et al. , J. Fluid Mech. , vol. 934, 2022, A44) to review how the newly introduced model features affect this flow. Results obtained with the MTS wall model show good agreement with direct numerical simulation data over a vast range of conditions in these various non-equilibrium channel flows. To further understand the MTS model, we also describe and test the instantaneous-equilibrium limit of the MTS wall model. In this limit, good wall-stress predictions are obtained with reduced model complexity but providing less complete information about the wall-stress physics. [ABSTRACT FROM AUTHOR]

The present study reports the numerical analyses of lateral jet interaction around a Terminal High Altitude Area Defense-type (THAAD-type) model in hypersonic rarefied flows, with the real gas effect incorporated. The computation approach employed is the recently developed thermochemical non-equilibrium nonlinear coupled constitutive relations (NCCR) model. Regarding the simulation conditions, the flight velocity and height are set to 20 Ma and 80 km, respectively. To disclose the flow mechanism of lateral jet interaction, the complex flowfield characteristics and surface pressure distributions are discussed at length. Additionally, the research explores the impact of two key factors, namely, the jet pressure ratio and the jet Mach number, on the control performance of an in-flight vehicle's reaction control system (RCS). The results demonstrate that the complicated flowfield structures in lateral jet interaction are successfully reproduced by the NCCR model. With an increase in either the jet pressure ratio or the jet Mach number, the force and moment amplification factors decrease, while the absolute value of the normal force coefficient increases. Notably, it is found that the rarefied gas effect captured by the NCCR model against the Navier–Stokes–Fourier solution affects the lateral jet interaction flowfield, e.g., weakening the compressibility of the barrel shock and the expansibility of the Prandtl–Meyer expansion fan, as well as strengthening the jet wraparound effect. Importantly, the rarefied gas effect also exerts a prominent influence on the performance of RCS, with the degree of influence diminishing as the jet Mach number or the jet pressure ratio increases. [ABSTRACT FROM AUTHOR]