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Aerothermodynamic analysis was performed for blunt-body configurations with spikes mounted to determine drag reduction effectiveness. In-house perfect gas and chemical nonequilibrium solver...

Stability features of two-stream coaxial plasma jet simulations are investigated using numerical solutions to the spatio-temporal one-dimensional linear stability theory problem. The base states obtained from magneto-hydrodynamic simulations consider the flow as a mixture of gases in local thermodynamic equilibrium (LTE) while stability computations are performed assuming both a calorically perfect gas (CPG) model and LTE. Comparisons with solutions considering a simple CPG model show the non-negligible impact of the LTE on the stability attributes of the plasma jet. For all cases studied, a large region of absolute instability is found for the axisymmetric mode, starting at the jet inlet. The streamwise evolution of the absolute growth rate is found to depend both on the baroclinic torque and the displacement of the maximum shear toward low velocity regions of the jet, combining effects described in the literature. The jet is controlled by means of electric power and static pressure at constant mass flow. The former affects mainly the absolute growth rate through changes of the core-to-bypass stream velocity ratio, while the latter influences mostly the absolute frequency. Finally, the full impulse response reveals a competition mechanism between the absolute mixed modes dominating at low group velocities, and convective shear layer modes at higher group velocities, restricted to the first half of the chamber.

In this work, natural convection and temperature distribution of supercritical water in a side-wall heated cavity are studied by numerical simulation. Different from ordinary single-vortex flow of perfect gas, supercritical water shows a thinner boundary layer with much higher velocity and finally forms a double-vortex natural convection pattern in the cavity. Moreover, for supercritical water, the temperature near the top wall of the cavity will exceed that of the heating wall, which is called overheating. Temperature, pressure, temperature difference between wall and fluid and aspect ratio will all affect velocity and temperature in the cavity. The mechanism analysis shows that the unique physical properties of supercritical water are vital reasons affecting the buoyancy driven flow boundary layer. The strong flow boundary layer will further lead to double-vortex flow pattern and overheating phenomenon, which will also affect natural convection pattern and temperature distribution.

International audience; The purpose of this paper is to develop a high-order shock-capturing scheme capable of predicting flows where shock waves with high-temperature jumps interact with multi-component real gas mixtures, assuming a local thermodynamic equilibrium. We first propose a generalization of the Roe solver for distinct species with non-ideal thermodynamic properties that relies on the original method proposed by Vinokur & Montagné [1]. This method uses an approximation of compressibility factors to estimate a coherent value of the speed of sound at the Roe averaged state.This Roe averaged state is introduced in the One-Step Monotonicity-Preserving (OSMP) scheme, originally developed by Daru and Tenaud [2], to obtain an extension to the high-order with Lax-Wendroff procedure adequate for dealing with non-ideal gas flows. To avoid thermodynamic inconsistencies in the evolution of the Roe average state over a large stencil, we propose to reformulate the discrete total energy flux of the initial solver. This new formulation uses a combination of Riemann invariants related to the species mass fractions and avoids the influence of the independent values of the compressibility factors in the total energy flux computation. An additional M-P constraint on this new combination allows dealing with discontinuities. Based on the averaged speed of sound estimated by our proposed extension of the Vinokur & Montagné method, we demonstrate that this new formulation is equivalent to selecting a new combination of compressibility factors that completely fulfill the jump relationships of the Riemann problem.To properly capture discontinuities while optimizing the number of numerical cells, the new high-order OSMP scheme is combined with an Adaptive Multiresolution [3] procedure to automatically refine grid in regions where steep gradients occur and coarsen grid elsewhere. The order of the numerical method is evaluated on the convection of density and mass fraction waves. Its capability of capturing discontinuities is validated on a 1-D shock tube problem with a mixture of Nitrogen, Oxygen and dense refrigerant R22 gases. We show that smooth solutions, as well as discontinuities, are recovered with high accuracy. The 2-D interaction between a shock wave in Air with a cylindrical bubble initially filled with dense refrigerant R22 gas is also considered. Present results compare very well with both a recent fully resolved numerical solution of ideal gases and experimental results obtained with real gases. Compared to ideal gas solutions corresponding to calorically perfect gas, drastic changes are recorded on the predicted temperature and the bubble flow patterns that fully justify the use of relevant thermodynamics and the proposed numerical method to account for real gas properties.

Analytical equation of state for pure alkali metals (lithium, sodium, potassium, rubidium and cesium) in equilibrium gas phase is proposed. This equation has a simple form, generalizes the equation of state for a perfect gas and is universal for all alkali elements. It correctly reproduces the experimental data for the equilibrium gas phase over a wide range of pressures (up to $\sim 10^5$~Pa) and temperatures (up to $\sim 3 \cdot 10^3$~K). On the basis of this equation of state, expressions for thermal and caloric coefficients as well as for \textit{other physical characteristics} are obtained. The results of this study confirm feasibility of the principle of corresponding states in relation to the group of alkali elements., Comment: 18 pages, 2 figures, 1 table

A generic solver in a structured Cartesian adaptive mesh refinement framework is extended to simulate unsteady shock-induced combustion problems on a structured curvilinear mesh. A second-order accurate finite volume method is used with a grid-aligned Riemann solver for inviscid thermally perfect gas mixtures. To solve these reactive problems, detailed chemical kinetic mechanisms are employed with a splitting approach. The prolongation and restriction operators are modified to implement the adaptive mesh refinement algorithm on a mapped mesh. The developed solver is verified with several benchmark tests and is then used to simulate unsteady shock-induced combustion. The results show that the computed stand-off distance of waves and oscillation frequencies of mass fraction of products observed at the stagnation point are in good agreement with the results from experiments.

Equivalence transformations play one of the important roles in continuum mechanics. These transformations reduce the original equations to simpler forms. One of the classes of nonlocal equivalence transformations is the class of reciprocal transformations. Despite the long history of applications of such transformations in continuum mechanics, there has been no general method of obtaining them. Recently such a method was proposed. The method uses group analysis approach and consists of similar steps as for finding an equivalence group of transformations. The new method provides a systematic tool for finding classes of reciprocal transformations (group of reciprocal transformations). The present paper provides an application of this method to the one-dimensional magnetogasdynamics equations of an ideal perfect gas with infinite electrical conductivity. Equivalence groups, groups of reciprocal transformations are presented in the paper.

Usually, the temperature dependence of specific heats is neglected or the specific heats are frozen in interface computations for compressible two-material flows. In this paper, we present a practical interface treatment to faithfully capture the effect of high temperature on interface evolutions. A general technique for solving the Riemann problem equipped with a wide variety of equations of state (EOS) is established. In a unified framework for computing the interfacial states, it provides a convenient way to deal with the thermally perfect gas (PG) that considers the effect of temperature on specific heats. The algorithm of the complete and exact solution to Riemann problem with thermally PG is also designed in detail. Based on this technique, the modified ghost fluid method with an approximate Riemann solver is further extended to handle the interface of two-material flows involving thermally PG with chemical reactions. Several typical problems are selected to validate and test the present algorithm for the interaction between the thermally PG and other gases or liquids. The results indicate that the present algorithm enables an effective implementation for simulating various two-material multi-species flows with different types of EOS. As temperature increases, the behavior of the interfacial flows under the assumption of thermally PG EOS gradually differs from that under the assumption of calorically PG EOS.

Large wave drag and high surface heating are common problems encountered at hypersonic speeds and these should be properly dealt for the effective and safe flights. Many studies have been carried out to mitigate these problems by employing various active and passive techniques but most of these computational or experimental studies account lower stagnation enthalpy flows or perfect gas assumption. Hence the current study examines the effect of higher freestream stagnation enthalpy on flow field alteration for counter - jet drag reduction technique for a hemispherical object. Results also includes the real gas effects on flow field, wave drag and wall heat flux. Further the effect of various flow parameters is observed on surface pressure distribution, surface heat flux and drag force for the hypersonic flow over the hemisphere, using the in house developed perfect gas and non - equilibrium N - S flow solvers. Results reveal that the perfect gas assumption overestimates surface properties and wave drag value. Drag coefficient reduces with freestream total enthalpy ( H o ) in the presence of real gas effects. Around 30% drag reduction is observed at H o =1 MJ/kg for Mach number 5 as compared to no - jet case and this reduction increases at higher freestream total enthalpy for same injection pressure ratio. Higher pressure ratio of the jet results in lower surface pressure and Stanton number on the object which gives lower wave drag.

Nearly all illuminating classic hypersonic flow theories address aerodynamic phenomena as a perfect gas in the high-speed range and at the upper limit of continuum gas domain. The hypersonic flow is quantitatively defined by the Mach number independent principle, which is derived from the asymptotes of the Rankine-Hugoniot relationship. However, most hypersonic flows encounter strong shock-wave compressions resulting in a high enthalpy gas environment that always associates with nonequilibrium thermodynamic and quantum chemical-physics phenomena. Under this circumstance, the theoretic linkage between the microscopic particle dynamics and macroscopic thermodynamics properties of gas is lost. When the air mixture is ionized to become an electrically conducting medium, the governing physics now ventures into the regimes of quantum physics and electromagnetics. Therefore, the hypersonic flows are no longer a pure aerodynamics subject but a multidisciplinary science. In order to better understand the realistic hypersonic flows, all pertaining disciplines such as the nonequilibrium chemical kinetics, quantum physics, radiative heat transfer, and electromagnetics need to bring forth.

For the propagation of a shock (blast) in a self-gravitating perfect gas in case of spherical and cylindrical symmetry, an approximate analytical solution is investigated. The shock wave is considered to be a strong one, with the ratio $$ \left( {\frac{C}{{V_{S} }}} \right)^{2} $$ to be a small quantity, where $$ c $$ is the sound speed in an undisturbed medium and $$ V_{S} $$ is the shock wave velocity. The initial density in the undisturbed medium is taken to be varying according to a power law. To obtain the approximate closed-form similarity solution, the flow variables are expanded in a power series of $$ \left( {\frac{C}{{V_{S} }}} \right)^{2} $$ . The first- and second-order approximations are discussed with the help of power series expansion. The analytical solutions are constructed for the first-order approximation. The distribution of the flow variables for first-order approximation in the flow field region behind the shock wave is shown in graphs for both the cylindrical and spherical geometries. The effect of flow parameters, namely, ambient density variation index $$ \alpha $$ , adiabatic exponent $$ \gamma $$ and gravitational parameter $$ G_{0} $$ , are studied on the flow variables and on the total energy of disturbance in the case of the first approximation to the solutions. It is shown that the total energy of the disturbance in the flow field region behind the shock wave decreases with an increase in initial density variation index or adiabatic exponent, i.e. shock strength increases with increase in the value of adiabatic exponent or initial density variation index. A comparison is also made between the solutions obtained for non-gravitating and self-gravitating gases.

This article presents correlations for indirect measurement of skin friction inside a laminar separation bubble induced by hypersonic shock-boundary layer interaction (SBLI) on a flat plate. The correlations, based on parameters that are known to influence the SBLI region, were developed using exhaustive numerical and analytical studies. Experiments were conducted in a hypersonic shock tunnel at Mach 8.6 (±0.22) to measure surface heat-flux and pressure in the zone of SBLI on a flat plate, which were then used to supplement and validate the correlations. The data predicted by the correlations agreed reasonably well with that of exact solutions. The case studies contained non-reacting air, behaving as a perfect gas on a flat surface.

A study of dense-gas effects on the laminar, transitional and turbulent characteristics of boundary layer flows is conducted. The laminar similarity solution shows that temperature variations are small due to the high specific heats of dense gases, leading to velocity profiles close to the incompressible ones. Nevertheless, the complex thermodynamics of the base flow has a major impact on unstable modes, which bear similarities with those obtained for a strongly cooled wall. Numerical simulations of spatially developing boundary layers yield turbulent statistics for the dense gas flow that remain closer to the incompressible regime than perfect gas ones despite the presence of strongly compressible structures.

© 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. The effect of property modelling on the stability features of heated axisymmetric jets is investigated by comparing the results of unsteady simulations and spatio-temporal Linear Stability Theory (LST) analyses obtained with three different models of Thermodynamic and Transport Properties (TTP). Two of these models are commonly found in the literature and assume respectively constant properties and a Calorically Perfect Gas (CPG) assumption, while the third model is a novel approach for this kind of study as it considers a mixture of gases in Local Thermodynamic and chemical Equilibrium (LTE) accurate up to extreme temperatures. Each model is implemented in a DNS code already used in the literature for jet stability analyses, and the LST computations are carried out in the VKI Extensible Stability and Transition Analysis (VESTA) toolkit. The LST analysis is performed on the steady state obtained from DNS simulations using a Selective Frequency Damping (SFD) method. Results show that the choice of property model has a significant impact on the development of self-sustained oscillations through changes of the absolute region length. Variable properties introduced in the CPG and LTE model have a amplifying effect on absolute instabilities downstream of the inlet. However, the modification of temperature profiles in LTE is found to strongly damp absolute instabilities at high temperatures. Cases with a long enough absolute region are found to support global modes, which are investigated with a Fast Fourier Transform (FFT) method.

High-speed turbulent boundary layers of a dense gas (PP11) and a perfect gas (air) over flat plates are investigated by means of direct numerical simulations and large eddy simulations. The thermodynamic conditions of the incoming flow are chosen to highlight dense gas effects, and laminar-to-turbulent transition is triggered by suction and blowing. In the paper, the behavior of the fully developed turbulent flow region is investigated. Due to the low characteristic Eckert number of dense gas flows ( $$\hbox {Ec}=U_\infty ^2/c_{p,\infty }T_\infty$$ ), the mean velocity profiles are largely insensitive to the Mach number and very close to the incompressible case even at high speeds. Second-order velocity statistics are also weakly affected by the flow Mach number and the velocity spectra are characterized by a secondary peak in the outer region of the boundary layer because of the higher local friction Reynolds number. Despite the incompressible-like velocity and Reynolds-stress profiles, the strongly non-ideal thermodynamic and transport-property behavior of the dense gas results in unconventional distributions of the fluctuating thermo-physical quantities. Specifically, density and viscosity fluctuations reach a peak close to the wall, instead of vanishing as in perfect gas flows. Additionally, dense gas boundary layers exhibit higher values of the fluctuating Mach number and velocity divergence and a larger dilatational-to-solenoidal dissipation ratio in the near-wall region, which represents a major deviation from high-Mach-number perfect gas boundary layers. Other significant deviations are represented by the more symmetric probability distributions of fluctuating quantities such as the density and velocity divergence, due to the more balanced occurrence of strong expansion and compression events.

Propagation of cylindrical shock wave in a self-gravitating perfect gas under the influence of axial magnetic field using Lie group of transformation method is investigated. The flow is considered to be isothermal. Density and magnetic field are assumed to be varying in the undisturbed medium. Two different cases of solutions are brought out by the arbitrary constants appearing in the expressions of infinitesimals of local Lie group of transformations. One is with a power law shock path and the other one is with an exponential law shock path. Numerical solutions are obtained for both the cases of power law and exponential law shock paths. The effects of variation in Alfven-Mach number, gravitational parameter and ambient density variation index for power law shock path and effects of variation in Alfven-Mach number, gravitational parameter and ambient magnetic field variation index on the flow variables in the case of exponential law shock path are studied. Also the effects of increase in value of gravitational parameter and in the strength of ambient magnetic field on the shock strength are investigated. The increase in value of Alfven-Mach number leads to the increase in the density ratio which infers to the decrease in shock strength.

The development of two-dimensional subsonic disturbances in a supersonic boundary layer of a vibrationally excited gas on a flat plate was studied on the basis of the linear stability theory. A system of two-temperature gas dynamics including the Landau–Teller relaxation equation used as initial model. The unperturbed flow was described by a selfsimilar boundary layer solution for a perfect gas. In the linearized system of equations the temperature disturbances of the transport coefficients were taken into account. The neutral stability curves for the first and second most unstable modes are calculated. It is shown that for both modes the critical Reynolds numbers at maximum excitation exceed by approximately thirteen percentages the corresponding values for a perfect gas. For independently verification of the direct numerical solution neutral stability curves are also calculated on the basis of the asymptotic approach. It is shown that the thus-calculated neutral stability curves agree well with the results of the numerical solution of the original spectral problem.

This chapter will describe the extensions of the AUSM-family fluxes (specifically, SLAU2) to real fluids of multiphase flows, supercritical fluids, and magnetohydrodynamics (MHD), where the governing equations and/or their discretizations differ from those for the perfect gas. These fluids are of great importance to physics and industries, but call for special care due to the changes in the equations. Some readers may wonder why the author appears to have a preference for the AUSM family. Here is a list of primary reasons: 1. They are robust and accurate for resolving shock waves at high speeds. 2. All-speed variants (e.g., AUSM+-up, SLAU2) are available that are applicable to low speeds. 3. No differentiation of a flux function or its Eigenstructure is required, which allows its straightforward application to the complex equation-of-state (EoS) of multiphase flows, supercritical fluids, or MHD.

We investigate the time-asymptotically nonlinear stability of rarefaction waves to the Cauchy problem of an one-dimensional compressible Navier-Stokes type system for a viscous, compressible, radiative and reactive gas, where the constitutive relations for the pressure $p$, the specific internal energy $e$, the specific volume $v$, the absolute temperature $\theta$, and the specific entropy $s$ are given by $p=R\theta/v +a\theta^4/3$, $e=C_v\theta+av\theta^4$, and $s=C_v\ln \theta+ 4av\theta^3/3+R\ln v$ with $R>0$, $C_{v}>0$, and $a>0$ being the perfect gas constant, the specific heat and the radiation constant, respectively. For such a specific gas motion, a somewhat surprising fact is that, general speaking, the pressure $\widetilde{p}(v,s)$ is not a convex function of the specific volume $v$ and the specific entropy $s$. Even so, we show in this paper that the rarefaction waves are time-asymptotically stable for large initial perturbation provided that the radiation constant $a$ and the strength of the rarefaction waves are sufficiently small. The key point in our analysis is to deduce the positive lower and upper bounds on the specific volume and the absolute temperature, which are uniform with respect to the space and the time variables, but are independent of the radiation constant $a$., Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematics

We derive an exact, axially symmetric solution representing stationary accretion of the relativistic, collisionless Vlasov gas onto a moving Schwarzschild black hole. The gas is assumed to be in thermal equilibrium at infinity, where it obeys the Maxwell-J\"{u}ttner distribution. The Vlasov equation is solved analytically in terms of suitable action-angle variables. We provide explicit expressions for the particle current density and accretion rates. In the limit of infinite asymptotic temperature of the gas, we recover the qualitative picture known form the relativistic Bondi-Hoyle-Lyttleton accretion of the perfect gas with the ultra-hard equation of state, in which the mass accretion is proportional to the Lorentz factor associated with the black-hole velocity. For a finite asymptotic temperature, the mass accretion rate is not in general a monotonic function of the velocity of the black hole., Comment: 22 pages, 8 figures

International audience; During the last years, several thrust control systems of aerospace rocket engines have been developed. The fluidic thrust vectoring is one of them; it is simple in design and offers a substantial gain in weight and in performance. Most of the studies related to this device were carried out with cold gas. It is quite legitimate to expect that the thermophysical properties of the gases may affect considerably the flow behavior. Besides, the effects of reacting gases at high temperatures, under their effects all flow parameters like to vary. This study aims to develop a new methodology that allows studying and analyzing the fluidic thrust vectoring for a perfect gas, by taking into account the effects chemical reactions on the flow parameters, such as separation point, reattachment point downstream and pressure distribution upstream the injection port. In this study, the thrust vectorization implying frozen reacting hot gases was carried out by considering a chemical reaction mechanism. The thermodynamic parameters of the flow are calculated within the combustion chamber and different sections of the supersonic part of the nozzle. The results show a good agreement for cold gas, and as expected a slight difference for hot reacting gases. In parallel, in order to give more credibility to our work a study was carried out by numerical simulation for supersonic reactive and perfect flows in order to analyze the results of the method developed. In this work, the CFD performance of the fluidic thrust vectoring has been qualitatively and quantitatively analyzed. The Schlieren visualization and the wall pressure results are compared to analytical and experimental findings. Performance analysis is conducted, and basic conclusions are drawn in terms of thermodynamic gas properties effect on the fluidic thrust vector system. The primary effect was related to the gas molecular weight and its specific heat ratio. It is observed that for fixed injection conditions, the vectoring angle is different when the injected gas molecular weight and specific heat ratio are different. For a given mission of the launcher, it can be concluded that the mass of the embedded gas, used for the fluidic vectorization system, can be significantly reduced, depending on its molecular weight and specific heat ratio.

This article lists some tips for reducing gear case noise. With this aim, a static analysis was carried out in order to describe how stresses resulting from meshing gears affect the acoustic emissions. Different parameters were taken into account, such as the friction, material, and lubrication, in order to validate ideas from the literature and to make several comparisons. Furthermore, a coupled Eulerian&ndash, Lagrangian (CEL) analysis was performed, which was an innovative way of evaluating the sound pressure level of the aforementioned gears. Different parameters were considered again, such as the friction, lubrication, material, and rotational speed, in order to make different research comparisons. The analytical results agreed with those in the literature, both for the static analysis and CEL analysis&mdash, for example, it was shown that changing the material from steel to ductile iron improved the gear noise, while increasing the rotational speed or the friction increased the acoustic emissions. Regarding the CEL analysis, air was considered a perfect gas, but its viscosity or another state equation could have also been taken into account. Therefore, the above allowed us to state that research into these scientific fields will bring about reliable results.

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 inc...

The process of hollow jet formation during steam outflow through a thin nozzle was studied; the water steam was initially at high pressure and in the supercritical state. The numerical solution for this problem was obtained with the sonicFoam solver library from the open-source CFD software package OpenFOAM in 2D axisymmetric formula-tion. The reliability of results is estimated by comparing two approaches for simulation of the dynamics of unloading wave propagating in the high-pressure nozzle using the OpenFOAM package with Peng−Robinson equation of state and numerical solution of a similar problem by method of through computation in the case of 1D planar approximation for perfect gas equation of state.

An exact similarity solution for a magnetoradiative cylindrical shock wave in a self-gravitating rotating perfect gas is obtained. The density, azimuthal velocity, and magnetic field strength are assumed to vary in an undisturbed medium. It is shown that the flow variables, namely, the radial velocity, pressure, magnetic field strength, azimuthal velocity, mass, and the radiation flux, decrease from the highest values at the shock front to zero; however, the density tends to infinity as the symmetry axis is approached. The effects of variation in the magnetic field strength, gravitational parameter, rotational parameter, and in the adiabatic exponent on the flow variables and shock strength are discussed. The solutions obtained for self-gravitating and nongravitating media are compared. The total energy of the shock wave is shown to be not constant.

In this study, the nodal thermodynamic and dynamic analysis of an alpha type Stirling engine driven by Scotch-yoke mechanism is presented. The nodal thermodynamic section of the analysis is performed via 15 nodal volumes. The temperature variations in nodal volumes are calculated by means of the first law of the thermodynamics given for the open systems. The pressures in all of the nodal volumes are assumed to be equal and calculated via Schmidt relation. The momentary masses in nodal volumes are calculated via the perfect gas relation. The dynamic section of the analysis involves the motion equations of pistons and crankshaft. The motion equations are derived by means of the Newton method. In the derivation of the motion equations of pistons, the working fluid forces and friction forces are considered beside the inertia forces. In the derivation of motion equation of the crankshaft, moments of working fluid forces, moments of friction forces, the moment of external load and the moment of starter motor are considered as well as mass inertia moments. It is estimated that an engine having 1.8 L swept volume, 1000 K hot end temperature, 400 K cold end temperature, 3000 cm2 total inner heat transfer area, 5.1 bar charge pressure and 2000 W/m2 K inner heat transfer coefficient is capable of producing a shaft power above 2 kW. For these inputs and shaft power; the speed, speed fluctuation and torque are optimized as 138 rad/s, 16% and 14.9 N m respectively. The presented analysis is useful for engine development studies.

The aim of this work is to develop a new numerical calculation program to determine the effect of the stagnation temperature on the calculation of the supersonic flow around a pointed airfoils using the equations for oblique shock wave and the Prandtl Meyer expansion, under the model at high temperature, calorically imperfect and thermally perfect gas, lower than the dissociation threshold of the molecules. The specific heat at constant pressure does not remain constant and varies with the temperature. The new model allows making corrections to the perfect gas model designed for low stagnation temperature, low Mach number, low incidence angle and low airfoil thickness. The stagnation temperature is an important parameter in our model. The airfoil should be pointed at the leading edge to allow an attached shock solution to be seen. The airfoil is discretized into several panels on the extrados and the intrados, placed one adjacent to the other. The distribution of the flow on the panel in question gives a compression or an expansion according to the deviation of the flow with respect to the old adjacent panel. The program determines all the aerodynamic characteristics of the flow and in particular the aerodynamic coefficients. The calculation accuracy depends on the number of panels considered on the airfoil. The application is made for high values of stagnation temperature, Mach number and airfoil thickness. A comparison between our high temperature model and the perfect gas model is presented, in order to determine an application limit of the latter. The application is for air.

Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier–Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the $k-\varepsilon $ model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.

The Sjogreen and Yee [31] high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal magnetohydrodynamics (MHD). The basic idea is based on Tadmor's [40] original work for inviscid perfect gas flows. For the MHD four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov [14] non-conservative form, (c) the Janhunen [19] – MHD with magnetic field source terms, and (d) a MHD with source terms by Brackbill and Barnes [5] . Three forms of the high order entropy numerical fluxes for the MHD in the finite difference framework are constructed. They are based on the extension of the low order form of Chandrashekar and Klingenberg [9] , and two forms with modifications of the Winters and Gassner [49] numerical fluxes. For flows containing discontinuities and multiscale turbulence fluctuations the high order entropy conservative numerical fluxes as the new base scheme under the Yee and Sjogreen [31] and Kotov et al. [21] , [22] high order nonlinear filter approach is developed. The added nonlinear filter step on the high order centered entropy conservative spatial base scheme is only utilized at isolated computational regions, while maintaining high accuracy almost everywhere for long time integration of unsteady flows and DNS and LES of turbulence computations. Representative test cases for both smooth flows and problems containing discontinuities for the gas dynamics and the ideal MHD are included. The results illustrate the improved stability by using the high order entropy conservative numerical flux as the base scheme instead of the pure high order central scheme.

Hypersonic flow is a very complex regime due to high values of velocity that causes air dissociation and ionization. This paper explores the influence of air dissociation on aircraft aerodynamic properties. The approach is the creation of a block-structured mesh by means of ICEM CFD and further set-up of Fluent solver. Aircraft aerodynamics properties were calculated for cases of perfect gas and non-equilibrium flow. Based on the results of the calculation, a comparison was made between obtained drag pressure coefficients, skin friction coefficients, drag coefficients, lift coefficients, lift-to-drag ratios and pitching moment coefficients.

Steady states of inviscid, compressible and axisymmetric swirling flows of a single-phase, inert, thermodynamically supercritical fluid in a rotating, finite-length, straight, long circular pipe are studied. The fluid thermodynamic behaviour is modelled by the van der Waals equation of state. A nonlinear partial differential equation for the solution of the flow streamfunction is derived from the fluid equations of motion in terms of the inlet flow specific total enthalpy, specific entropy and circulation functions. This equation reflects the complicated, nonlinear thermo-physical interactions in the flows, specifically when the inlet state temperature and density profiles vary around the critical thermodynamic point, flow compressibility is significant and the inlet swirl ratio is high. Several types of solutions of the resulting nonlinear ordinary differential equation for the axially independent case describe the flow outlet state when the pipe is sufficiently long. The approach is applied to an inlet flow described by a solid-body rotation with uniform profiles of the axial velocity and temperature. The solutions are used to form the bifurcation diagrams of steady compressible flows of real fluids as the inlet swirl level and the centreline inlet density are increased at a fixed inlet Mach number and temperature. Focus is on heavy-molecule fluids with low values of $R/C_{v}$. Computed results provide theoretical predictions of the critical swirl levels for the exchange of stability of the columnar state and for the appearance of non-columnar states and of vortex breakdown states as a function of inlet centreline density. The difference in the dynamical behaviour between that of a calorically perfect gas and of a real gas is explored. The analysis sheds new fundamental light on the complex dynamics of high-Reynolds-number, compressible, subsonic swirling flows of real gases.

This article applies nonstandard analysis to study the generalized solutions of entropy and energy across one-dimensional shock waves in a compressible, inviscid, perfect gas. Nonstandard analysis is an area of modern mathematics that studies number systems that contain both infinitely large and infinitely small numbers. For an inviscid shock wave, it is assumed that the shock thickness occurs on an infinitesimal interval and that the jump functions for the field variables are smoothly defined on this interval. A weak converse to the existence of the entropy peak is derived and discussed. Generalized solutions of the Euler equations for entropy and energy are then derived for both theoretical and realistic normalized velocity profiles.

The high temperature gas occurs behind shock or near the wall surface of vehicle in the hypersonic flight. As the temperature exceeds 2 000K, 4 000K, respectively, O2 and N2 molecules are successively dissociated. Because of variable components at different temperatures and pressures, the dissociated air is no longer a perfect gas. In this paper, a new method is developed to calculate accurate thermal physical parameters with the dissociation degree providing the thermochemical equilibrium procedure. Based on the dissociation degree, it is concluded that few numbers of equations and the solutions are easily obtained. In addition, a set of formulas relating the parameter to the dissociation degree are set up. The thermodynamic properties of dissociated air containing four-species, O2 molecule and N2 molecule, O atom and N atom, are studied with the new method, and the results are consistent with those with the traditional equilibrium constant method. It is shown that this method is reliable for solving thermal physical parameters easily and directly.

Aerothermodynamic environment predictions play an important role in the heatshield design of Mars entry vehicle. This article investigates and presents the influences of geometric parameters of the heatshield on its aerothermodynamic performances. The three-dimensional coupled implicit compressible Reynolds Averaged Navier–Stokes (RANS) equations and perfect gas model with the specified effective specific heat ratio have been applied to numerically simulate the flow fields around the vehicle. Menter’s shear stress transport (SST) turbulence model with compressible correction is implemented to take account of the turbulent effect. The laminar and turbulent heating rates are demonstrated and analyzed in detail. Furthermore, a non-intrusive polynomial chaos (NIPC) method with Latin hypercube sampling (LHS) is utilized to establish the functional relationship between the aerothermodynamics and geometric parameters. In addition, Sobol indices as global sensitivity metrics have been introduced to investigate the relative contribution of each geometric parameter. The results show that for the maximum heat flux, the value of the cone angle (αc) with a high index is the top contributor to the both laminar and turbulent flow state, thus the geometric parameter αc should be considered firstly in the material design process of thermal protection system. Moreover, in the most region of MSL heatshield, cone angle (αc) also became the major influence factor. However, in a relatively small region, aerothermodynamics exhibits a great sensitivity to the change of nose radius (Rn). In all regions of heatshield, the parameter of shoulder radius (Rs) is always at a low level of Sobol index.

The aim of this work is to realize a new numerical program based on the development of a mathematical model allowing determining the parameters of the supersonic flow through a conical shock under hypothesis at high temperature, in the context of correcting the perfect gas model. In this case, the specific heat at constant pressure does not remain constant and varies with the increase of temperature. The stagnation temperature becomes an important parameter in the calculation. The mathematical model is presented by the numerical resolution of a system of first-order nonlinear differential equations with three coupled unknowns for initial conditions. The numerical resolution is made by adapting the higher order Runge Kutta method. The parameters through the conical shock can be determined by considering a new model of an oblique shock at high temperature. All isentropic parameters of after the shock flow depend on the deviation of the flow from the transverse direction. The comparison of the results is done with the perfect gas model for low stagnation temperatures, upstream Mach number and cone deviation angle. A calculation of the error is made between our high temperature model and the perfect gas model. The application is made for air. Keywords: Calorically imperfect gas, Conical shock, High temperature, Numerical integration, Oblique shock, Perfect gas model, Runge Kutta method, Supersonic flow

This study focuses on unstructured TVD, ENO and UNO schemes applied to solve the Euler equations in two- and three-dimensions. They are implemented on a finite volume context and cell centered data base. The algorithms of Yee, Warming and Harten 1982; Harten; Yee and Kutler; Yee Warming and Harten 1985; Yee; Yee and Harten; Harten and Osher; Yang 1990, Hughson and Beran; Yang 1991; and Yang and Hsu are implemented to solve such system of equations in two- and three-dimensions. All schemes are flux difference splitting and good resolution is expected. This study deals with calorically perfect gas model and in so on the cold gas formulation has been employed. Two problems are studied, namely: the transonic convergent-divergent symmetrical nozzle, and the supersonic ramp. A spatially variable time step is implemented to accelerate the convergence process. The results highlights the excellent performance of the Yang 1990 TVD scheme, yielding an excellent pressure distribution at the two-dimensional nozzle wall, whereas the Harten and Osher scheme yields accurate values to the angle of the oblique shock wave and the best wall pressure distributions in the two-dimensional ramp problem. On the other hand, the excellent performance of the Harten scheme in the three-dimensional nozzle problem, yielding an excellent pressure distribution at the nozzle wall, and the Yee and Harten scheme yielding an accurate value to the angle of the oblique shock wave and the best wall pressure distribution in the three-dimensional ramp problem are of good quality.

Ionic vacancy is, being produced as a byproduct in electrode reaction, a polarized free space of the order of 0.1 nm surrounded by oppositely charged ionic cloud. As a perfect gas in electrolyte solution, it does not interplay with other solution particles. On the other hand, magnetic field provides useful means to examine the natures of it. Using a special electrode operated in a magnetic field called cyclotron MHD electrode (CMHDE), we first determined the lifetime of vacancy in copper deposition as 1.2 sec, which is extraordinarily long in comparison with the collision interval of solution particles. Then, using kinetic theory of gas, we measured the collision radius of vacancy gas to be 0.70 nm, which was consistent with theoretical calculation 0.65 nm.

In this paper, we are concerned with the simple waves for the two dimensional (2D) compressible Euler equations in magnetohydrodynamics. By using the sufficient conditions for the existence of characteristic decompositions to the general quasilinear strictly hyperbolic systems, we establish that any wave adjacent to a constant state must be a simple wave to the two dimensional compressible magnetohydrodynamics system for a polytropic Van der Waals gas and a polytropic perfect gas.

We consider a gas-dynamic model of a one-dimensional flow of non-viscous perfect gas in the absence of heat conduction when a high-power localized heat source is switched on. Within the framework of this model, it is possible to thoroughly analyze the problem of the gas-flow regimes, which occur as a result of switch-on of such a source, in a wide range of values of the energy-deposition power and initial gas-dynamic characteristics of the flow. Eventually, we obtain a sufficiently general insight into the character of the resulting flows and the conditions of their realizations.

In order to obtain the standing conditions and stationary range of oblique detonation wave in methane-air combustible mixture, we use the Newton-Raphson iteration method to solve the perfect gas flow conservation equations of oblique detonation wave based on detonation theory. We investigate the variation laws of the oblique detonation stationary window and internal mechanism under different methane-air equivalence ratio, incoming flow velocity, initial pressure and initial temperature. The oblique detonation polar curve can be separated into three sections, each of which has different flow characteristics corresponding to different wave morphology. Among them, a stationary oblique detonation wave can be formed when the wedge angle is larger than the wedge angle of Chapman-Jouguet state oblique detonation wave, and smaller than the maximum wedge angle corresponding to the oblique detonation wave without detached. The wedge angle range is called the stationary window of the oblique detonation wave. We found that the oblique detonation is more easily formed when the methane-air mixture is under the oxygen-enriched condition, and the range of oblique detonation wave stationary window becomes larger as the incoming velocity increases. The changes of initial pressure and temperature have little influence on the stationary window. The change law of the stationary window of oblique detonation wave corresponds to the change law of Mach number behind CJ oblique detonation wave. In addition, the standing conditions are mainly related to the coupling of the incoming mixture kinetic energy and heat release.

Two issues related to the application of Chapman-Jouguet (C-J) theory have been investigated in this study. Firstly, the solution of the two-γ analytical model cannot agree with the exact solution calculated from the Chemical Equilibrium Compositions and Applications (CEA) code even all the required parameters are substituted with the exact ones. To root the source, the original derivation has been reviewed. It is believed that the perfect gas approximation induces the discrepancy, which will result in a huge discrepancy in the heat release at C-J state. Hence, a four-γ model for ideal gases has been derived, whose results are consistent with those from the CEA code though it requires more input parameters. Sensitive analysis implies that the accuracy of the four-γ model is greatly impacted by γ 2 ‾ and q C J . Besides, a parabola function that can describe the heat release and the lower heating value correlation has been proposed. Using this function, about ±5% relative error of estimated M S can be achieved when γ 2 ‾ is equal to 9/7 for most selected stoichiometric gas mixtures. Secondly, the energy distribution in a C-J detonation process is found quite different when attaching the reference frame to the ground or the detonation wave front. Hence, regarding the C-J state as the equivalent burned state at the exit of a detonation combustor is questionable. Accordingly, a four-step thermodynamic process for a closed system has been developed, which can quantitatively analyze the energy balance process of a C-J detonation. Discussion is made by comparing the process with a traditional steady thermodynamic process as well as constant-volume combustion.

In the present study, the shock-disturbances interaction in hypersonic inviscid flows with real gas effects is studied by applying a high-order accurate numerical method with the shock capturing technique. To consider real gas effects, the equilibrium air model is utilized here. The strong conservative form of the unsteady compressible Euler equations in the 2D generalized curvilinear coordinates is formulated and the resulting system of equations for the equilibrium air model is discretized by using the fifth-order finite-difference WENO scheme in space and the explicit third-order TVD Runge–Kutta scheme in time to provide a highly accurate and robust equilibrium airflow solver. The solution methodology adopted based on the high-order WENO scheme with the shock capturing technique can reasonably simulate the strong discontinuities in the solution domain without needing any numerical artifact and this feature makes the solution method suitable for the shock-disturbances interaction in hypersonic flows in which real gas effects are to be considered. To study the physical phenomenon of the shock-disturbances interaction problem in high-speed inviscid equilibrium airflows, two test cases are simulated by applying the solution methodology adopted. In the first test case, the interaction between the incoming fast acoustic wave with the bow shock formed around a cylinder with the nose radius of R N = 0 . 0381 m at M ∞ = 8 . 03 and T ∞ = 182 . 333 K is simulated. In the second test case, the cylinder radius is taken R N = 2 . 54 × 1 0 − 2 m and the upstream velocity and temperature are u ∞ = 5590 m/s and T ∞ = 1833 K, respectively, and all kinds of free stream disturbances, including the entropy wave and the fast and slow acoustic waves, for different wave numbers are considered. The computations are carried out for both the perfect gas and equilibrium air models and the effects of real gas on both the mean and disturbances fields are also studied. The present study introduces the first-known numerical investigation of the shock-disturbances interaction in hypersonic flow over blunt noses with real gas effects in which the numerical results obtained are thoroughly validated by the analytical/theoretical ones and good agreement is found.

In order to research the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider, thermochemical non-equilibrium flow and perfect gas model are employed to study the aerodynamics of an osculating-cone waverider under different angles of attack. The obtained results show that the slope of the oblique shock wave has little difference when considering the thermochemical non-equilibrium effect under the condition of zero angle of attack. However, under the condition of other attack angles, the slope of the oblique shock wave diminishes when considering the thermochemical non-equilibrium effect. Furthermore, the non-equilibrium effect moves the pressure center of the osculating-cone waverider forward by as much as 1.53% of the whole craft's length, which must be taken into consideration in the balance design of aircraft.

By using the model of an ideal inviscid perfect gas, the aerodynamic characteristics of a cylinder immersed in a stationary three-dimensional supersonic flow in the case of strong axisymmetrical blowing of air from the lateral surface into the shock layer (“fluid flare”) are investigated. The aim of the present work is to compare the dependences of the aerodynamic characteristics of the cylinder with a “fluid flare” on the angle of attack on increase of the latter from zero to 10o(straight motion) and on its further decrease from 10° to zero (backward motion).

Three continuum models extending the conventional Navier–Stokes–Fourier approach for modeling the shock wave structure in carbon dioxide are developed using the generalized Chapman–Enskog method. Multi-temperature models are based on splitting multiple vibrational relaxation mechanisms into fast and slow processes and introducing vibrational temperatures of various CO2 modes. The one-temperature model takes into account relaxation processes through bulk viscosity and internal thermal conductivity. All developed models are free of limitations introduced by the assumptions of a calorically perfect gas and constant Prandtl number; thermodynamic properties and all transport coefficients are calculated rigorously in each cell of the grid. Simulations are carried out for Mach numbers 3–7; the results are compared with solutions obtained in the frame of other approaches: multi-temperature Euler equations, model kinetic equations, and models with constant Prandtl numbers. The influence of bulk viscosity and Prandtl number on the fluid-dynamic variables, viscous stress, heat flux, and total enthalpy is studied. Bulk viscosity plays an important role in sufficiently rarefied gases under weak deviations from equilibrium; in multi-temperature models, non-equilibrium effects are associated with slow relaxation processes rather than with bulk viscosity. Using a constant Prandtl number yields over-predicted values of the heat flux. Contributions of various energy modes to the total heat flux are evaluated, with emphasis on the compensation of translational–rotational and vibrational energy fluxes.