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Flowfields of various gasodynamic parameters at high supersonic flows about the air intakes of flying vehicles are analyzed. Mathematical model of high supersonic flows is set and verified. Numerical simulation of perfect gas flow in non-profiled ducts of air intakes is provided. Various methods of multicomponent mixture simulation are used. Influence of flow multi-componence of shock waves near the head of flying vehicle is considered.

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.

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.

The interference of an impinging plane oblique shock wave with the viscous shock layer on a cylinder has been studied numerically for rarefied-gas flow regimes at the Reynolds numbers 15.5 ≤ ReR,0 ≤ 124 and Knudsen numbers 0.1 ≥ KnR,∞ ≥ 0.012. The calculations have been performed within the framework of the direct simulation Monte-Carlo technique [1] and the Navier-Stokes equations for a perfect gas using the shock capturing method [2]. The principal properties of flow parameters have been studied for five different types of interference at low Reynolds numbers. The differences with respect to the previously investigated interference regimes for high Reynolds numbers have been examined. The comparison analysis of numerical results and experimental data has been provided. It has been found that the local pressure and heat transfer coefficients on the surface of a cylinder may considerably (by a factor of 3.5) exceed the values on the edge stagnation line observed in the absence of interference. The type IV interference pattern observed in continuum flows has not been found in this study.

A numerical implementation of characteristic boundary conditions for Euler and Navier-Stokes equations is presented. The method combines the specified boundary conditions and the outgoing characteristic variables according to the wave propagation directions. In the general case, the proposed boundary conditions update the primitive variables by solving a small system of linear equations (4×4 in 2D, 5×5 in 3D) at each boundary point/cell. The method can be used for both preconditioned and non-preconditioned equations. For a perfect gas without preconditioning, a closed analytical solution is provided. Two possible methods of extrapolating the outgoing characteristic variables are discussed. Finally, the numerical approach is validated for the 2D internal flow in a channel with a bump.

International audience; The propagation of multidimensional gaseous detonations at elevated pressures was investigated numerically. Initial conditions at which deviations from ideal gas are expected (i.e., p0 > 2 MPa) were used to assess whether real gas effects influence their multi-cellular structure. The simplest equation of state that accounts for real gas effects was selected, Noble–Abel, and compared with the results obtained using perfect gas. Approximate and exact relationships are provided for the von-Neumann and Chapman–Jouguet states, as well as sound speeds, for both equations of state. Results show that real gas effects alter the multi-cellular structure of gaseous detonations at elevated pressures. Moreover, neglecting these effects renders a more irregular structure than that obtained when real gas effects are reinstated. The source of the perceived instabilities was identified as a Mach bifurcation due to jetting and their growth was related to a shear layer triple point interaction, giving birth to new triple points. The more unstable structure seems to arise from an effective change in the isentropic coefficient that is not included in the perfect gas formulation.

The transition from laminar to turbulent flow is a complex phenomenon and difficult to predict. There have been significant contributions over the years, enhancing the understanding of mechanisms that cause transition. The effect of chemical reactions on boundary-layer instability becomes significant for high-temperature flow. The existence of the secondary instability before the transition in a low-disturbance environment has been proved in earlier studies, although none of these studies considered high-temperature effects. The real gas (identified as a gas undergoing high-temperature phenomena) effects on the secondary subharmonic instability for a two-dimensional hypersonic boundary layer over a flat plate are studied using the Floquet model. The real gas is assumed to be in thermochemical equilibrium, where air is considered as a mixture of perfect gases in local thermal and chemical equilibrium. A five-species air model is used to compute the air mixture's thermal and transport properties. The stability of the primary disturbance is analyzed using linear stability theory, whereas a mean flow superposed with a second mode primary disturbance has been considered for the secondary instability analysis. The local and global methods have been used to solve the eigenvalue problem based on the finite difference method. The real gas effect on the secondary instability is destabilizing since the maximum secondary amplification rate is higher and appears at a lower Reynolds number for the real gas than that of the perfect gas. The increase in the primary wave amplitude increases the secondary amplification rate significantly. Furthermore, secondary disturbances decay faster into the freestream compared to primary disturbances. The eN method is employed to compute the amplification factor for the secondary amplification rate for the real and perfect gas. Based on the growth rate and N-factor for the secondary disturbances, it is found that the real gas flow is more unstable and susceptible to transitioning earlier than the perfect gas.

The effect of thermodynamic and transport properties on the convective-to-absolute transition in heated round jets is investigated with the spatio-temporal linear stability theory, by considering three sets of properties with increasing complexity. Present models include (i) a constant property model often used in the literature, (ii) a simplified model with variable properties, and (iii) a more accurate equilibrium air mixture model, accounting for dissociation reactions in the flow. A family of arbitrary single-stream and dual-stream jet profiles, representative of typical configurations studied in the literature, is investigated and adapted to each model. Our results show that considering a variable viscosity and thermal conductivity has a destabilizing effect on absolute instabilities in the viscous regime. Furthermore, this destabilization is stronger for the outer mode in dual-stream jets than for the inner mode or the jet-column mode in single-stream jets. With sufficient heating (S < 0.3), results obtained with the equilibrium model strongly depart from those of calorically perfect gas models and display absolute domains deformed by the chemical activity. For absolute instabilities triggered by the baroclinic torque such as jet-column and inner modes, the convective-to-absolute transition is shifted toward thinner and hotter configurations, while the opposite is observed for the outer mode. Finally, we observe a dependence of the equilibrium model stability properties on the static pressure.

We revisit and derive the shock change equations relating the dynamics of a shock wave with the partial derivatives describing the motion of a reactive fluid with the general equation of state in a stream-tube with arbitrary area variation. We specialize these to a perfect gas in which we obtain all shock change equations in closed form. These are further simplified for strong shocks. We discuss the general usefulness of these equations in problems of reactive compressible flow and in the development of intrinsic evolution equations for the shock, such as the approximations made by Whitham and Sharma.

While the compressible flow theory has relied on the perfect gas model as its workhorse for the past century, compressible dynamics in dense gases, solids, and liquids have relied on many complex equations of state, yielding limited insight into the hydrodynamic aspect of the problems solved. Recently, Le Metayer and Saurel studied a simple yet promising equation of state owing to its ability to model both the thermal and compressibility aspects of the medium. It is a hybrid of the Noble–Abel equation of state and the stiffened gas model, labeled the Noble–Able Stiffened Gas (NASG) equation of state. In the present work, we derive the closed form analytical framework for modeling compressible flow in a medium approximated by the NASG equations of state. We derive the expressions for the isentrope, sound speed, isentropic exponent, Riemann variables in the characteristic description, and jump conditions for shocks, deflagrations, and detonations. We also illustrate the usefulness by addressing the Riemann problem. The closed form solutions generalize in a transparent way the well-established models for a perfect gas, highlighting the role of the medium’s compressibility.

The combined effects of leading-edge bluntness and high enthalpy are examined for hypersonic flat plate flow. Experimental pressure and heat transfer data are presented for both sharp and blunt leading-edge flat plates. For the sharp leading-edge flows, the data are in agreement with perfect gas theory. For the blunt leading-edge flows, the low and high enthalpy pressure data approach the perfect gas blast wave theory as the flow proceeds downstream, consistent with earlier studies at low enthalpy. Toward the front of the plate, the heat transfer data lie above the corresponding values obtained with the sharp leading-edge configuration. The difference between sharp and blunt leading-edge heat transfer levels appears to be smaller at high enthalpy. This seems to be due to dissociation which occurs in the nose region, thus reducing the shock stand-off distance and increasing the chemical potential enthalpy of the flow. When the presence of dissociated species in the flow is accounted for, the data close to the leading-edge are seen to compare well with perfect gas bluntness–viscous similitudes. Farther downstream, the measured heat transfer values are greater than the perfect gas theoretical predictions for blunt leading-edge flow, and closer to both the corresponding predictions at chemical equilibrium, and sharp leading-edge theory for perfect gas flow.

Direct numerical simulations (DNS) of high–temperature supersonic turbulent channel flow of equilibrium air are conducted at constant dimensional wall temperature 1733.2 K. The Mach number based on the bulk velocity and the speed of sound at the isothermal wall is 3.0, and the Reynolds number based on the bulk density, bulk velocity, channel half–width, and viscosity at the isothermal wall is 4880. Bidirectional coupling (BC) and unidirectional influence (UI) conditions are investigated, conditions which take account, respectively, of the influence of turbulence on chemistry and the influence of chemistry on turbulence, and just the influence of turbulence on chemistry. The reliability of the DNS data for the UI condition is verified by comparison with the results of Coleman et al. [J. Fluid Mech. 305, 159–183 (1995)]. The results of present research show that the many turbulent statistics and instantaneous structures which hold for calorically perfect gas also hold for equilibrium air, even for the BC condition. The coupling condition has no significant influence on the van Driest transformed mean velocity and turbulent kinetic energy budget. The magnitudes of the mean and fluctuating specific heat and enthalpy for the BC condition are larger than those for the UI condition. An inverted trend is observed for the temperature and dissociation degree. Compared with the UI condition, the near–wall streaks for the BC condition are arranged in a more spanwise manner, owing mainly to the increase in anisotropy ratios. The large–scale structures become small, sharp, and chaotic for the BC condition.

We present direct numerical simulations of Boussinesq and non-Boussinesq Rayleigh–Benard convection in a rigid box containing a perfect gas. For small stratifications, which includes Boussinesq fluids, the first instability after steady rolls was an oscillatory instability (a Hopf bifurcation). The resulting convection was characterized by two hot and two cold blobs circulating each convective roll. The same sign thermal perturbations (blobs) are at diametrically opposite points on the circular rolls, i.e., they are symmetric about the roll center. The time for a hot (or cold) blob to circulate a roll was between two and three roll turnover times. When the stratification was of sufficient strength, there was a dramatic change in the nature of the bifurcation. The sign of the thermal perturbations became antisymmetric with respect to the roll center, i.e., a hot blob was diametrically opposite a cold blob. In this case, a hot or cold blob circulated around each roll in about one turnover time. In a stratified layer, the Rayleigh number varies with height. We found that at the Hopf bifurcation, the Rayleigh number at the base was closest to the Boussinesq value. The change in instability appeared to be related to an increase in the speed (or Mach number) of the circulating rolls. It did not seem to be affected by the transport property variation with temperature. If the along roll aspect ratio was less than 2 or the walls perpendicular to the roll axis periodic, then only the symmetric instability could be found. We describe how our results might be reproduced in a laboratory experiment of convection in cryogenic helium gas.

We extend the spiral vortex solution of Lundgren [Phys. Fluids 25, 2193 (1982)] to compressible turbulent flows with a perfect gas. This model links the dynamical and the spectral properties of incompressible flows, providing a k−5/3 Kolmogorov energy spectrum. In so doing, a compressible spatiotemporal transformation is derived, reducing the dynamics of three-dimensional vortices, stretched by an axisymmetric incompressible strain, into a two-dimensional compressible vortex dynamics. It enables us to write the three-dimensional spectra of the incompressible and compressible square velocities in terms of, respectively, the two-dimensional spectra of the enstrophy and of the square velocity divergence, by the use of a temporal integration. Numerical results are presented from decaying direct simulations performed with 5122 grid points; initially, the rms Mach number is 0.23, with local values up to 0.9, the Reynolds number is 700, and the ratio between compressible and incompressible square velocities is 0...

We consider a body immersed in a perfect gas, moving under the action of a constant force E along the x axis . We assume the gas to be described by the mean-field approximation and interacting elastically with the body, we study the friction exerted by the gas on the body fixed at constant velocities. The dynamic in this setting was studied in previous papers for object with simple shape, showing new features in the dynamic but not in the friction term. The case of more general shape of the body was left out for further difficulties, we believe indeed that there are actually non trivial issues to be faced for these more general cases. To show this and in the in the spirit of getting a more realistic perspective in the study of friction problems, in this paper we focused our attention on the friction term itself, studying its behavior on a body with a more general kind of concavity and fixed at constant velocities. We derive the expression of the friction term for constant velocities, we show how it is time dependent and we give its exact estimate in time. Finally we use this result to show the absence of a stationary velocity in the actual dynamic of such a body., 13 pages, 1 figure. arXiv admin note: text overlap with arXiv:1401.5942

Real gas and heat transfer effects are included in the solution of the blast wave resulting from a point or line explosion. Due to the extremely high temperatures, particularly at the beginning of shock propagation, the assumption of perfect gas is not valid. The equation of state takes into account the high temperature effects of vibration, dissociation, electronic excitation, and ionization, as well as the intermolecular forces at high pressures. The computation of the flow problem is carried out using the method of characteristics which has been modified to the effects of radiative and conductive heat transfer. The results show considerable deviation in the initial stages of the explosion from the perfect gas solution, in particular the temperature profiles and the thermodynamic state immediately behind the front.

Numerical solutions for steady inviscid flows in conventional converging–diverging nozzles are obtained. The fluids considered are Bethe–Zel’dovich–Thompson fluids, i.e., those having specific heats so large that the fundamental derivative of gas dynamics is negative over a finite range of pressures and temperatures. Three general classes of flow are delineated which include two nonclassical types in addition to the usual classical flows; the latter are qualitatively similar to those of perfect gases. The nonclassical flows are characterized by isentropes containing as many as three sonic points. Numerical solutions depicting finite‐strength expansion shocks, steady flows with shock waves standing upstream of the nozzle throat, and steady flows containing as many as three shock waves are presented. Flows having arbitrarily large‐exit Mach numbers are found to be possible only if a sonic expansion shock is formed in the nozzle. This observation contrasts with prediction based on the perfect gas theory which states that the occurrence of shock waves always results in a subsonic exit flow.

The flow resulting from a strong explosion at the center of an ideal gas sphere, whose density drops with the distance r from the origin as r−ω, is assumed to approach asymptotically the self‐similar solutions by Sedov and Taylor. It is shown that the Sedov–Taylor (ST) solutions that exist only for ω≤5 and are probably the most familiar example for self‐similar solutions of the first type fail to describe the asymptotic flow obtained for 3≤ω≤5. New second‐type self‐similar solutions that describe the asymptotic flow for 3≤ω≤5, as well as for ω≥5, are presented and analyzed. The shock waves described by these solutions are accelerating while the shock waves described by the ST solutions for ω≤3 are decelerating. The new solutions are related to a new singular point in Guderley’s map. They exist only for ω values smaller than some ωc that depends upon the adiabatic index of the gas. The asymptotic flow obtained for ω≥ωc is discussed in a subsequent paper.

Complex reaction systems that are subject to the partial‐equilibrium approximation are analyzed. In order to take proper account of equilibrium and finite rate reactions, a distinction is made between linearly independent and dependent species and reactions, respectively. The assumption of partial equilibrium removes short time scales from the problem and leads to a reduction in the number of independent thermodynamic variables. Making use of a fundamental property of equilibrium reactions, a general formulation for partial chemical equilibrium in complex reaction systems is obtained. Furthermore, a partially frozen sound speed is defined and an analytical expression for this sound speed is given. The concept of partial chemical equilibrium is applied to high‐speed reacting flows. A characteristic formulation of the conservation and rate equations is presented. Finally, a high‐enthalpy flow, namely the expansion of high‐temperature air through the axisymmetric nozzle of a shock tunnel, is calculated using the method of lines.

High‐temperature effects alter the physical and transport properties of a gas, air in particular, due to vibrational excitation and gas dissociation, and thus the chemical reactions have to be considered in order to compute the flow field. Linear stability of high‐temperature boundary layers is investigated under the assumption of chemical equilibrium and this gas model is labeled here as ‘‘real gas model.’’ In this model, the system of stability equations remains of the same order as for the perfect gas and the effect of chemical reactions is introduced only through mean flow and gas property variations. Calculations are performed for Mach 10 and 15 boundary layers and the results indicate that real gas effects cause the first mode instability to stabilize while the second mode is made more unstable. It is also found that the second mode instability shifts to lower frequencies. There is a slight destabilizing influence of real gas on the Goertler instability as compared to the perfect gas results.

A one‐dimensional model for bulk motion induced by a transient volumetric heat source in a confined gas at zero gravity is considered. Rational approximation methods are used to derive a quantitative theory for the gas response to a spatially distributed, time‐dependent internal power deposition. The resulting low Mach number compressible flow equations are solved by using perturbation methods. Solutions are given for a conduction‐free core and thin conductive boundary layers adjacent to the end walls. It is found that any spatially nonuniform power deposition will cause fluid motion. Net mass transport in the closed container will occur for certain spatially distributed heating. The model mimics the thermal effects of an exothermic gas phase reaction in vapor transport experiments conducted in space. The solutions demonstrate that thermally induced mass transport can be as large as diffusive mass transport in a typical experiment.

The response of a confined compressible perfect gas to an uneven time‐dependent volumetric heat source is studied. The low Mach number compressible Navier–Stokes equations are solved numerically by means of the pressure implicit with splitting of operators (P.I.S.O.) algorithm in the case where the characteristic time of the thermal perturbation is small compared to the diffusion time and large compared to the acoustic time. A comparison is made with first‐order asymptotic results previously obtained. The asymptotic analysis is then carried out up to the second order in the bulk. It is shown that: (a) a flow is generated from one side of the cavity to the other, confirming the asymptotic results previously obtained; (b) a flow towards the walls is found in thermal boundary layers because of a sink effect due to the lower temperature in these regions; (c) comparison with analytical results in the bulk is quite satisfactory except for the velocity where some differences are shown; (d) the second‐order asymptotic analysis shows that this approximation in the bulk is a mechanical perturbation caused by the contraction of the fluid layers near the boundaries; (e) the matching between analytical results and numerical results is improved by more than 50% when considering a second‐order solution; (f) this analysis validates both numerical code and scaling laws.

A comprehensive analytical/numerical treatment of triple points is based on over 5 × 103 parametric solutions. The approach is applicable to triple points in steady or unsteady, three-dimensional flow with a variable freestream. The analysis is for a perfect gas with three different ratios of specific heat values and an upstream Mach number that ranges from an onset value to 10. The structure and morphology of the solution manifold is extensively discussed. This includes solution type, solution overlap, double, triple, and split solutions, shock wave and slipstream angular orientations, the strength of the shocks, etc. Both the reflected and Mach stem shocks can be normal shocks. The occurrence, conditions, and parametric results for these normal shocks are provided.

We consider the compressible flow analogue of the solution known colloquially as the Hart-McClure profile. This potential motion is used to describe the mean flow in the original energy-based combustion instability framework. In this study, we employ the axisymmetric compressible form of the potential equation for steady, inviscid, irrotational flow assuming uniform injection of a calorically perfect gas in a porous, right-cylindrical chamber. This equation is expanded to order Mw4 using a Rayleigh-Janzen sequence in powers of Mw2, where Mw is the wall Mach number. At leading order, we readily recover the original Hart-McClure profile and, at Mw2, a closed-form representation of the compressible correction. By way of confirmation, the same solution is re-constructed using a novel application of the vorticity-streamfunction technique. In view of the favorable convergence properties of the Rayleigh-Janzen expansion, the resulting approximation can be relied upon from the headwall down to the sonic point and...

In this paper, we present a generalization of the gas lens technique developed by Dimotakis and Samtaney [“Planar shock cylindrical focusing by a perfect-gas lens,” Phys. Fluids 18, 031705 (2006)]. This technique is devoted to converting a planar shock wave into a cylindrical one through a shaped interface between two gases. We revisit this theory and demonstrate that the shape of the lens is either an ellipse or a hyperbola. A simple formula for its eccentricity is analytically obtained: e=Wt/Wi, where Wt and Wi are the transmitted and incident shock wave velocities, respectively. Furthermore, our theory is valid for fast-slow and slow-fast configurations. It also allows the generation of spherical converging shock waves. We present numerical simulations that successfully validate our lens design. Finally, we use the gas lens technique in order to design shock tube experiments: shock wave and hydrodynamic instabilities are studied and discussed in convergent geometry.

The generic problem of ignition of a particle undergoing an expansion given by a power law rate of decay behind a decaying shock is addressed in the present study. It is demonstrated, using a one-step Arrhenius irreversible reaction, that a sufficiently strong expansion wave can quench the reaction. The critical conditions for extinction are obtained in closed form in terms of the time scale for the expansion process and the thermochemical properties of the gas, yielding a critical Damkohler number, i.e., the ratio of the expansion time scale to the homogeneous ignition time scale, given by (γ−1)(Ea/RT)−1/n, where n is the power law exponent of the self-similar expansion. The critical ignition criteria, which are valid in the asymptotic limit n(γ−1)(Ea/RT)=O(1), were found in excellent agreement with numerical results. The applicability of the results obtained are discussed for ignition in rapidly expanding flows which occur behind decaying shock waves, as encountered in problems of detonation initiation ...

The bifurcation and global nonlinear stability of near-critical states of a compressible and axisymmetric swirling flow of a perfect gas in a finite-length straight, circular pipe is studied. This work extends the bifurcation and stability analyses of Wang and Rusak [Phys. Fluids 8, 1007 (1996); Wang and Rusak Phys. Fluids8, 1017 (1996)] to include the influence of Mach number on the flow dynamics. The first- and second-order equations of motion for the evolution of small axially symmetric perturbations on a base columnar state are developed. These equations are reduced to an eigenvalue problem for the perturbation shape function and critical swirl ratio and a model ordinary differential equation for the nonlinear evolution of the perturbations’ amplitude as function of swirl level and Mach number. It is found that noncolumnar equilibrium states bifurcate from the branch of the base columnar equilibrium states at the critical swirl ratio of a compressible vortex flow in the form of a transcritical bifurca...

This paper deals with the derivations of the extended forms of the continuum conservation equations for ideal gas flows with heat and mass transfer, from upscaled molecular transport considerations. It is shown that for strong local temperature and/or density gradients, diffusive transport of momentum, heat, and mass over subcontinuum length scales gives rise to additional terms in the corresponding continuum level constitutive relationships. An exact analogy with kinematically hypothesized extended rheological forms is established by casting the expression for momentum flux in an equivalent linear form, with the postulation of a gradient-based hypothesis. Possible considerations of extending the theory to more general flow conditions are also discussed.

The homogeneity condition in compressible flows requires that mean velocity gradient and mean thermodynamic variables must be spatially invariant. This has restricted the use of rapid distortion theory (RDT) for compressible flows to a small set of mean-velocity gradients. By introducing an appropriate body force, we show that the homogeneity condition can be satisfied for a large class of compressible turbulence. We proceed to derive RDT spectral covariance equations of all relevant moments and recover the limiting behavior at vanishing and infinite (pressure-release) Mach numbers for homogeneous shear, plain-strain, axisymmetric expansion, and contraction cases.

The derivation of the multicomponent diffusion law is revisited. Following Furry [Am. J. Phys. 16, 63 (1948)], Williams [Am. J. Phys. 26, 467 (1958); Combustion Theory, 2nd ed. (Benjamin/Cummings , Menlo Park, CA,1985)] heuristically rederived the classical kinetic theory results using macroscopic equations, and pointed out that the dynamics of the mixture fluid had been assumed inviscid. This paper generalizes the derivation, shows that the inviscid assumption can easily be relaxed to add a new term to the classical diffusion law, and the thermal diffusion term can also be easily recovered. The nonuniqueness of the multicomponent diffusion coefficient matrix is emphasized and discussed.

A recent formulation [J. Griffond, Phys. Fluids17, 086101 (2005)] of the linear interaction analysis (LIA) for mixtures of two perfect gases is applied to a field including a sinusoidal diffuse interface between two perfect gases. It offers an original way to investigate the initial phase of the Richtmyer-Meshkov instability. The approach is valid only in the limit of gases with close molar mass and specific heat (low Atwood numbers), but it applies to interfaces of arbitrary corrugation amplitude and diffusion thickness without Mach number limitation on the shock wave. The vorticity field deduced from LIA compares favorably with two-dimensional numerical simulations. In their limit of common validity, the LIA and the formulas of Wouchuk [Phys. Rev. E63, 056303 (2001); Phys. Fluids 8, 2890 (2001)] predict close asymptotic growth rates, contrary to impulsive models. The correction for initial diffusion of the interface proposed by Brouillette and Sturtevant [J. Fluid Mech.263, 271 (1994)] shows only weak d...

A theoretical model for the linear and nonlinear evolution of acoustic perturbations in nonuniform one-dimensional isentropic flows is developed. On the assumption that the length scale of the mean flow greatly exceeds that of the imposed disturbances, it is shown that the propagation of linear waves can be described in a closed form that is consistent with the conservation of acoustic power. This permits the application of a “nonlinearization” procedure (Landau [J. Phys. USSR 9, 496 (1945)],Whitham [Proc. R. Soc. London, Ser. A 201, 89 (1950)]), wherein the linear functional forms are assumed to hold for weakly nonlinear simple-wave disturbances, and the effects of amplitude on the wave speed are included to leading order. When nonlinear steepening results in the formation of shocks, they are fitted into the solution using the Rankine-Hugoniot relations. The method is applicable to arbitrary waveforms and, in the present study, the evolution of hump-like and periodic disturbances through nonuniform flows...

We document a gas lensing technique that generates a converging shock wave in a two-dimensional wedge geometry. A successful design must satisfy three criteria at the contact point between the gas lens and the wedge leading edge to minimize nonlinear reflected and other wave effects. The result is a single-point solution in a multidimensional parameter space. The gas lens shape is computed using shock-polar analysis for regular refraction of the incident shock at the gas lens interface. For the range of parameters investigated, the required gas-lens interface is closely matched by an ellipse or hyperbola. Nonlinear Euler simulations confirm the analysis and that the transmitted shock is circular. As the converging transmitted shock propagates down the wedge, its shape remains nearly uniform with less than 0.1% peak departures from a perfect circular cylinder segment. Departure from the design criteria leads to converging shocks that depart from the required shape. The sensitivity to incident shock Mach number, as well as the qualitative effects of the presence of boundary layers are also discussed.

The linear interaction analysis is applied to mixtures of two perfect gases. Differences of molar mass and constant volume specific heat between both gases are taken into account as two new wave families. Transfer functions across the shock wave from these waves to acoustic, shear or entropy waves are given. The approach is validated against numerical simulations of the interaction of concentration spots with a shock wave. The case of turbulence creation by a shock wave traveling in an inhomogeneous mixture is considered.

This Brief Communication gives a new exact solution of the nonlinear adiabatic equations of fluid flow for a perfect gas in infinite three‐dimensional domain that is not the trivial constant flow. The temperature of the gas is an arbitrary function of the radius. The velocity of the gas can be described by considering concentric spheres, one for each value of the radius, which rotate about the same fixed axis through the common center of the spheres, the angular velocity of each sphere being dependent upon the temperature at the radius. The velocity of the gas at a point is then that of the sphere at that point. The nature of this flow suggests that it be named an ‘‘onion vortex.’’ It is shown that onion vortices for the same temperature distribution have an additive property, which is surprising in the context of nonlinear equations.

The Van Hove scattering function, S(Q,ω), has been measured for xenon gas at five state conditions along the 30 C isotherm using the time‐of‐flight correlation spectrometer at Oak Ridge National Laboratory (ORNL). The data are normalized by division of S(Q,ω) by the static structure factor so that at each Q value the normalized function has unit area: these curves are bell‐shaped and are compared to two kinetic calculations by Dufty and Lindenfeld (unpublished). At the lowest density (0.185×1022 atom/cm3) the experimental data are consistent with the perfect gas and the two models. But at the highest density (0.458×1022 atom/cm3) the data probably differ significantly from these models.

At time t=0 a unit sphere containing a perfect gas at uniformly high pressure is allowed to expand suddenly into a homogeneous atmosphere. Solutions for short times later are sought by analytic (i.e., not numerical) methods. Viscosity and heat conduction are neglected. The particle velocity, sound speed, and entropy are developed in powers of y, which is proportional to the time (more precisely, the distance moved by the head of the rarefaction wave in time t), with coefficients depending on a slope coordinate q=(1/2N)[(2N−1) +(1−x)/y], where x is the radial coordinate, N=(½)(γ+1)/(γ−1), and γ is the ratio of specific heats. The zero‐order coefficients are the plane shock‐tube solution. First‐order corrections are derived for the various regions. Boundary conditions are approximated for small y at the surfaces of discontinuity, and the method for matching the solutions in the different regions is outlined. This matching process is carried out for the expansion of a diatomic gas into diatomic air.

The properties of water vapor are used to illustrate the point, previously found true for ethyl alcohol, that the modified Berthelot equation of state may not give a satisfactory evaluation of the deviation of thermodynamic properties from those of the hypothetical perfect gas. The entropy deviation for benzene, however, is accurate enough for most purposes, and the heat capacity is not too far out of line.On limited information, it appears that the Berthelot equation may be satisfactory for the vapors of ``normal'' liquids up to limited pressures. It is recommended, however, that some attempt be made to check the properties by means of vapor densities, obtained directly or by the Clapeyron equation, before results based upon the Berthelot equation are accepted.

The adsorption of methane on fused silica beads has been studied by gas chromatography from 5 to 120 atm for − 91.9 to 31.4°C. Only a few investigations of adsorption at high pressure have been reported due to the severe experimental difficulties. The “Hypothetical Perfect Gas” perturbation technique has been revised for application at high pressure to obtain the free gas volume. Two modifications in analysis are required: one for the steric effect of the perturbation gas and the second for the adsorption of the perturbation gas on the adsorbed phase. A second method of calculation based on solubility theory has been developed to correct for the solution of the perturbation gas in the adsorbed phase at high pressures. In addition to the usually measured differential or Gibbs adsorption, the gas chromatographic technique yields the absolute or total adsorption. This distinction is not observable at low pressures. A region of constant absolute adsorption in isotherms with increasing pressure was observed above the critical temperature of methane corresponding to a practically constant gas‐phase fugacity. Application of limiting conditions to the measurements of Gibbs adsorption at high pressure gave the same value for the constant region of absolute adsorption isotherm, as well as the same value for the adsorbed phase density, which was evaluated from the dependence of the gas‐phase volume upon the amount of absolute adsorption. This agreement substantiates the calculation method developed here.

Upper‐atmosphere air densities and temperatures have been calculated from the measured trajectory data of a falling sphere. Densities were calculated from the equation for the drag force on the falling sphere, and temperatures were then obtained by using the hydrostatic equation and the equation of state of a perfect gas. The aerodynamic background and instrumentation are described; the method of calculation and the errors are discussed. The results of four rocket flights which carried the experiment are given. Comparison with the average of other rocket measurements indicates agreement with these results.

The following relates to moving objects immersed in a perfect gas otherwise at rest. The momentum of the resulting gas flow is defined. It is shown that it ultimately approaches a definite magnitude as the object assumes a steady motion, said magnitude being independent of the history of the previous motion.This result is applied to the two‐dimensional flows of airship theory, and thus the airship theory is extended to include compressibility effects to a limited extent.

In this paper experiments with weak shocks in carbon dioxide are described. The incident shocks were arranged to reflect off the sloping surfaces of rigid ramps of various corner angles. Regular and Mach reflectionlike phenomena were observed, but because the incident shocks were so weak, all the waves in the reflecting systems showed evidence of either partial or complete dispersion. Consequently, the wave systems were different from the classical perfect gas theory systems described by the von Neumann theory. These wave systems were named ‘‘dispersed irregular reflections.’’

Formal features of Einstein–Maxwell equations for spherically symmetric distributions of a charged perfect fluid in equilibrium are discussed. An exact solution of the system of equations for a specified choice of matter density and fluid pressure, representing a charged perfect gas is presented.

An analytic solution of the relativistic field equations is obtained for a static, spherically symmetric distribution of charged fluid. The arbitrary constants are determined by matching it with the Reissner–Nordstrom solution over the boundary. The distribution behaves like a charged perfect gas. As a particular case a solution for a spherical distribution of charged incoherent matter is deduced where the charge density and the mass density are equal in magnitude. In the absence of the charge, the solution reduces to Tolman’s solution VI with B=0.

In addition to the symmetries that are known to apply to arbitrary flow, the self‐similar equations may present other symmetries of their own. We present here such a symmetry of the self‐similar unidimensional flow of an adiabatic inviscid fluid, with arbitrary polytropic index and arbitrary power‐law entropy distribution. The new symmetry can be extended to the non‐self‐similar case if the flow is assumed isentropic. A connection with the theory of Riemann invariants is also discussed.

The steepening of one‐dimensional finite‐amplitude waves in inviscid Van der Waals gases is described. The undisturbed medium is taken to be unbounded, at rest and uniform. The specific heat is taken to be large enough to generate an embedded region of negative nonlinearity in the general neighborhood of the saturated vapor line and thermodynamic critical point. Under these conditions the shock formation process may differ significantly from that predicted by the perfect gas theory. The present study illustrates these differences for both isolated pulses and periodic wave trains. It is further shown that as many as three shocks, two compression and one expansion, may be formed in a single pulse or, in the case of wave trains, repeated element. It is also shown that the convected sound speed may become identical to the thermodynamic sound speed of the undisturbed medium at three distinct values of the density; the first of these corresponds to the density of the undisturbed medium while the other two are related to an integral of the fundamental derivative along an isentrope. The results obtained are expected to hold for any fluid which possesses such an embedded region of negative nonlinearity.

The equations for general steady motion of a perfect gas are expressed in terms of a reduced number of basic dependent variables. Neither constant entropy nor constant flow energy is assumed throughout the flow, but only along individual streamlines. The basic dependent variables used are the ``reduced velocity'' vector w≡v/(2γγ−1pρ+v2)12 and the logarithm of the pressure, lnp. The resulting form of the dynamic equation is (w·grad)w+γ−12γ(1−w2) grad lnp=0, and that of the continuity equation is div[(1−w2)1/γ−1w]=0, representing four equations in four unknowns. The fundamental characteristic and shock relations are also expressed in terms of these reduced variables.

In this paper it is shown that the value of the similarity exponent α derived analytically by Fujimoto and Mishkin [J. Fluid Mech. 89, 61 (1978); Phys. Fluids 21, 1933 (1978)] is exactly the same as that found by Stanyukovich [Unsteady Motion of Continuous Media, (Academic, New York, 1960)]. Since the result found by Stanyukovich is an approximation to α, Fujimoto and Mishkin’s claim to have an exact expression of α is false. The two methods are outlined and Stanyukovich’s result is simplified to show its equivalence to the work of Fujimoto and Mishkin.

Exact solutions to the steady Navier–Stokes equations are given for laminar convective motion in open vertical slots immersed in a perfect gas. The solutions are for large temperature differences using Sutherland law transport properties and an arbitrary external temperature. The solutions are valid in the fully developed region where the opposite hot and cold vertical wall boundary layers are fully merged. It is found that the temperature, velocity, mass flow rate, and vertical heat flux are very sensitive to property variations, even though the horizontal heat flux is not. Furthermore, it is found that if only one end of the slot is open, the velocity and vertical heat flux are independent of the external temperature. Comparisons with constant transport property solutions and the well‐known Boussinesq limiting solution for small temperature differences are given for examples using air or hydrogen; these show that important but significantly different effects exist as a result of density and transport property variations.