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Shock tubes are used to investigate the chemical kinetics and radiative properties of gasses. Analyses of the flow conditions produced in shock tubes typically assume a single, constant shock speed...

A two dimensional fully nonlinear numerical wave flume is extended with a pneumatic model to compute the free surface flow inside the chamber of land-based Oscillating Water Column (OWC) devices. Potential theory and the Mixed Eulerian-Lagrangian method are employed to compute the fluid flow using the direct Boundary Element Method (BEM) enhanced by a non-uniform rational B-Spline function. Meanwhile, a pneumatic model is manipulated to obtain the instantaneous air pressure on the chamber's free surface. Spring-like behavior of a perfect gas through an adiabatic process and a linear power take-off mechanism are used in the pneumatic model that makes time derivative of the air pressure turns to a function of reciprocating air and fluid flows in the chamber. Therefore, temporary air pressure is taken into account on the fully nonlinear free surface boundary conditions implicitly along with the time marching algorithm. The hydrodynamic efficiency of an OWC interacting with second-order Stokes waves is compared with former studies to verify the present model. To assess the present model for simulating the air compressibility in a large-scale case study, the present solution is compared with experimental and mathematical results under an irregular wave. Afterwards, an OWC device is exposed to fifth-order Stokes waves in the flume to examine the numerical stability of computing the free surface flow outside and inside of the chamber.

Although receptivity plays a key role in the transition of hypersonic flows, most prior computational receptivity studies have neglected to study broadband frequency disturbance spectra. This work ...

The entropy split method is based on the physical entropies of the thermally perfect gas Euler equations. The Euler flux derivatives are approximated as a sum of a conservative portion and a non-conservative portion in conjunction with summation-by-parts (SBP) difference boundary closure of (Gerritsen and Olsson in J Comput Phys 129: 245–262, 1996; Olsson and Oliger in RIACS Tech Rep 94.01, 1994; Yee et al. in J Comp Phys 162: 33–81, 2000). Sjogreen and Yee (J Sci Comput https://doi.org/10.1007/s10915-019-01013-1) recently proved that the entropy split method is entropy conservative and stable. Standard high-order spatial central differencing as well as high order central spatial dispersion relation preserving (DRP) spatial differencing is part of the entropy stable split methodology framework. The current work is our first attempt to derive a high order conservative numerical flux for the non-conservative portion of the entropy splitting of the Euler flux derivatives. Due to the construction, this conservative numerical flux requires higher operations count and is less stable than the original semi-conservative split method. However, the Tadmor entropy conservative (EC) method (Tadmor in Acta Numerica 12: 451–512, 2003) of the same order requires more operations count than the new construction. Since the entropy split method is a semi-conservative skew-symmetric splitting of the Euler flux derivative, a modified nonlinear filter approach of (Yee et al. in J Comput Phys 150: 199–238, 1999, J Comp Phys 162: 3381, 2000; Yee and Sjogreen in J Comput Phys 225: 910934, 2007, High Order Filter Methods for Wide Range of Compressible flow Speeds. Proceedings of the ICOSAHOM09, June 22–26, Trondheim, Norway, 2009) is proposed in conjunction with the entropy split method as the base method for problems containing shock waves. Long-time integration of 2D and 3D test cases is included to show the comparison of these new approaches.

Shock tube experiments are a cornerstone of investigations into the hypersonic flight environment. However, the actual flow through the basic shock tube has not been well characterized in the literature, and nonuniformities arising in the test gases are not well understood. This work produces a quasi-one-dimensional analytical methodology for predicting the nonuniformities in the postshock test gas based exclusively on the experimentally measured history of shock speed down the tube. Wave effects extracted from shock speed variations are shown to provide all information necessary in order to reconstruct the test slug from any particular experiment. Accurate representation of flow dynamics is initially checked against argon test cases following accelerating and decelerating shock trajectories, each with a tube-end Mach number of 6.5 and a fill pressure of 66.66 Pa in a tube of 100 mm diameter. Agreement between the method and results from a viscous, axisymmetric Navier–Stokes solution is found to be within 1% in pressure and temperature.

The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

This wok focuses to develop a numerical computation program allowing to design new contours of a supersonic nozzle having several bells, adapted to several levels of different altitudes, going from sea level and progressively with the altitude up to space, giving a supersonic uniform and parallel flow to the exit section and a maximum possible thrust without loss, aiming to reduce considerably the side loads caused in the conventional and the dual bell nozzles when the ambient pressure decrease with the altitude. The first bell has a sonic, uniform and parallel inlet to the throat, and a sea level adaptation with a reduced supersonic Mach number, while the other bell have a supersonic, parallel and uniform inlet and an adaptation to a given altitude with a progressed increase of supersonic Mach number. The transition from one level of adaptation to another adjacent is done without mechanical activation. The purpose of this type of nozzle is to have the possibility of flying in several supersonic regimes adapted to several different altitudes with a reduced side loads. This type of nozzle is named by Several Bell Nozzle and has inflection points between bell and adjacent other. The design is done in the context of a calorically and thermally perfect gas. The problem is to design a typical bell having a uniform and parallel supersonic inlet and exit with two given Mach numbers. The design is made by the use of the Method of Characteristics. The resolution of the equations is done numerically by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the ratio of the critical sections, calculated numerically, to that given by the theory. In this case, all the design parameters converge automatically to the desired solution. The application is made for axisymmetric MLN having 3, 4, 5 and 10 bells.

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

Convection has been discussed in the field of accretion discs for several decades, both as a means of angular momentum transport and also because of its role in controlling discs' vertical structure via heat transport. If the gas is sufficiently ionized and threaded by a weak magnetic field, convection might interact in non-trivial ways with the magnetorotational instability (MRI). Recently, vertically stratified local simulations of the MRI have reported considerable variation in the angular momentum transport, as measured by the stress to thermal pressure ratio $\alpha$, when convection is thought to be present. Although MRI turbulence can act as a heat source for convection, it is not clear how the instabilities will interact dynamically. Here we aim to investigate the interplay between the two instabilities in controlled numerical experiments, and thus isolate the generic features of their interaction. We perform vertically stratified, 3D MHD shearing box simulations with a perfect gas equation of state with the conservative, finite-volume code PLUTO. We find two characteristic outcomes of the interaction between the two instabilities: straight MRI and MRI/convective cycles, with the latter exhibiting alternating phases of convection-dominated flow (during which the turbulent transport is weak) and MRI-dominated flow. During the latter phase we find that $\alpha$ is enhanced by nearly an order of magnitude, reaching peak values of $\sim 0.08$. In addition, we find that convection in the non-linear phase takes the form of large-scale and oscillatory convective cells. Convection can also help the MRI persist to lower Rm than it would otherwise do. Finally we discuss how our results help interpret simulations of Dwarf Novae., Comment: Accepted for publication in MNRAS (23 pages, 14 figures, 1 table)

In this paper, the approximate analytical solution for the propagation of a blast (shock) wave in a rotating perfect gas in the case of cylindrical geometry is studied. The axial and azimuthal components of fluid velocity are taken into consideration, and these flow variables in the undisturbed medium are assumed to be varying according to the power laws with distance from the symmetry axis. The shock wave is considered to be strong one for the ratio $${\left(C/{W}_{S}\right)}^{2}$$ to be a small quantity, where $$C$$ is the sound velocity in undisturbed fluid and $${W}_{S}$$ is the shock wave velocity. The initial density in the undisturbed medium is taken to be constant to obtain the similarity solution. To obtain the approximate analytical solution, the flow variables are expanded in power series in power of $${\left(C/{W}_{S}\right)}^{2}.$$ The first- and second-order approximations to solutions 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 the first-order approximation in the flow-field region behind the blast wave is shown in graphs. A comparison is also made between the solutions obtained for non-rotating and rotating medium. It is shown that the constant quantity $${J}_{0}$$ in the flow field region behind the shock front increases in rotating medium in comparison with its value in non-rotating medium; but an increase in adiabatic exponent causes a decrease in it. Further, it is concluded that shock strength increases with adiabatic exponent and decreases due to the consideration of the rotating medium.

The influence of thermal nonequilibrium on the laminar–turbulent transition is studied with the use of the $$\mathrm{e}^N$$ -method for two widespread flow regimes in a supersonic boundary layer at the Mach number $$\textrm{M}=4.5$$ . The set of the actual frequencies of spatial disturbances is determined on the basis of the neutral curves for temporal disturbances. Families of the curves of $$N$$ -factors are calculated for selected frequencies. Then, based on the envelopes of these curves, the transition Reynolds number $$\mbox{Re}_{\delta T}$$ for a given transition factor $$N_T$$ is determined. The calculations show that the transition region in the case with $$N_T=8$$ and vibrational excitation level below the dissociation limit is located 12–14% downstream as compared to the transition region in a perfect gas.

The present study aims to clarify the effect of the polytropic index (i.e., the ratio of specific heats in the context of a perfect gas) on the detonation structure. This is addressed by two-dimensional numerical simulations. To ease the clarification of the role of gasdynamics, a simple Arrhenius kinetic law is used for the chemical model. The activation energy, normalized by the shock temperature, is kept constant to obtain the same reaction rate sensitivity to temperature in all considered mixtures. This procedure dissociates the gasdynamic effects from the chemistry effects. The numerical results reveal that in mixtures with low polytropic indicies, the convective mixing is enhanced compared to mixtures with higher polytropic indicies. The mixing is evaluated using Lagrangian tracers. Moreover, mixtures with low polytropic indicies are found to have a shorter reaction length than mixtures with high polytropic indicies. Also, for the range of parameters considered in this study the results indicate that Mach stem bifurcation in detonations due to jetting is primarily a gasdynamic driven mechanism.

When gas flows at a high speed in a channel with a variable cross sectional area and high-intensity energy supply, it experiences complicated physical and chemical processes producing high-temperature gas effects. High-temperature gas effects are a key issue related to design and optimization of nozzles of plasmatron of alternating current. The finite volume method is applied to solve unsteady compressible Euler equations with high-temperature gas effects. Solutions of some benchmark test cases are reported, and comparison between computational results of chemically equilibrium and perfect air flowfields is performed. The results of numerical simulation of one-dimensional and two-dimensional under- and over-expanded nozzle flows with a moving region of energy supply are presented. Output nozzle parameters are calculated as functions of a number and time of burning of plasmatron arcs. The results obtained show a qualitative pattern of gas dynamics and thermal processes in the nozzle with unsteady energy supply demonstrating the displacement of the nozzle shock wave towards the nozzle outlet in the over-expanded nozzle flow in comparison to perfect gas flow.

Based on a critical analysis of the existing characteristics of an ideal gas and the theory of thermodynamic potentials, the article considers its new model, which includes the presence of an ideal gas in addition to kinetic energy of potential (chemical) energy, in the framework of which the isothermal and adiabatic processes in it are studied both reversible and irreversible, in terms of changes in the entropy of the system in question, observed in case. In addition, a critical analysis was made of the process of introducing the concept of entropy by R. Clausius, as a result of which the main requirements for entropy were established, the changes of which are observed in isothermal and adiabatic quasistatic processes, in particular, it was revealed that if in isothermal processes involving one in a perfect gas, the entropy ST is uniquely characterized by the value , regardless of whether the process is reversible or not, then when the adiabatic processes occur, the only requirement made of them is the condition of mutual destruction adiabats in this Carnot cycle. As a result of this circumstance, in fact, in thermodynamics various “adiabatic” entropies are used, namely; const SA = const R ln V и C V ln T , and in addition, as established in this paper, CV, which leads, despite the mathematically perfect introduction of the concept of entropy for the Carnot cycle, to the impossibility of its unambiguous interpretation and, therefore, the determination of its physicochemical meaning even for perfect gas. A new concept is introduced in the work: “total” entropy of an ideal gas SS = R ln V + C V , satisfying the criteria of R. Clausius, on the basis of which it was established that this type of entropy multiplied by the absolute temperature characterizes a certain level of potential energy of the system, which can besuccessively converted to work in an isothermal reversible process, with the supply of an appropriate amount of heat, and in the adiabatic reversible process under consideration.

An exact solution of the problem on the propagation of a cylindrical shock wave in a rotating perfect gas with an axial magnetic field in the case of an isothermal flow is obtained. The initial density, magnetic field strength, and the initial angular velocity in the ambient medium are assumed to vary according to the power law. An exact similarity solution obtained by the McVittie method for an isothermal flow in a rotating gas is first reported. Similarity transformations are used to transform a system of partial differential equations into a system of ordinary differential equations, and then the product solution of McVittie is used to obtain the exact solution. The effects of the values of the gas specific heat ratio, rotational parameter, and of the strength of the initial magnetic field are discussed. It is shown that the shock velocity increases and the shock strength decreases with increase in the values of these parameters. The effect of variation in the value of the initial density index is also studied. The obtained solutions show that the radial fluid velocity, density, pressure, and the magnetic field strength tend to zero as the axis of symmetry is approached.

Similarity solution for the propagation of a spherical shock wave in a self-gravitating perfect gas with an azimuthal magnetic field in the case of isothermal flow is investigated. The density and azimuthal magnetic field strength in the ambient medium are assumed to vary and obey power laws. An exact similarity solution obtained using the McVittie method in the case of isothermal flow is reported for the first time. The obtained solutions show that the radial fluid velocity, density, pressure, magnetic field strength, and the mass tend to zero as the point of symmetry is approached. The effects of the changes in the values of the adiabatic exponent γ and the exponent w in the variation of an initial density are considered in detail. It is shown that the magnetic field strength and mass increase with γ, whereas an increase in w exerts the reverse effect on these flow variables.

Phasepy is a Python based package for fluid phase equilibria and interfacial properties calculation from equation of state (EoS). Phasepy uses several tools (i.e., NumPy, SciPy, Pandas, Matplotlib) allowing use Phasepy under Jupyter Notebooks. Phasepy models phase equilibria with the traditional ϕ-γ and ϕ-ϕ approaches, where ϕ (fugacity coefficient) can be modeled as a perfect gas, virial gas or EoS fluid, whereas γ (activity coefficient) can be described by conventional models (NRTL, Wilson, Redlich-Kister expansion, and the group contribution modified-UNIFAC). Interfacial properties are based on the square gradient theory couple to ϕ-ϕ approach. The available EoSs are the cubic EoS family extended to mixtures through the quadratic, modified-Huron-Vidal, and Wong-Sandler mixing rules. Phasepy allows to analyze phase stability, compute phase equilibria, interfacial properties, and optimize their parameters for vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria for multicomponent mixtures. Phasepy implementation, and robustness are illustrated for binary and ternary mixtures.

The spaceplane is perspective vehicle due to wide maneuverability in comparison with a space capsule. Its maneuverability is expressed by the larger flight range and also by a possibility to rotate orbital inclination in the atmosphere by the aerodynamic and thrust forces. Orbital plane atmospheric rotation maneuvers can significantly reduce fuel costs compared to rocket-dynamic non-coplanar maneuver. However, this maneuver occurs at Mach numbers about 25, and such velocities lead to non-equilibrium chemical reactions in the shock wave. Such reactions change a physicochemical air property, and it affects aerodynamic coefficients. This paper investigates the influence of non-equilibrium reactions on the aerothrust aeroassisted maneuver with orbital change. The approach is to solve an optimization problem using the differential evolution algorithm with a temperature limitation. The spaceplane aerodynamic coefficients are determined by the numerical solution of the Reynolds-averaged Navier-Stokes equations. The aerodynamic calculations are conducted for the cases of perfect and non-equilibrium gases. A comparison of optimal trajectories, control laws, and fuel costs is made between models of perfect and non-equilibrium gases. The effect of a chemically reacting gas on the finite parameters is also evaluated using control laws obtained for a perfect gas.

Mathematical model is proposed that describes the process of pumping gas into a porous medium initially filled with methane and water. Non-ideal gas and non-isothermal effects during its filtration are taken into account. The hydrate formation process is assumed to be equilibrium. Methodology for solving the system of equations of the mathematical model is constructed. The methodology was tested, in the one-dimensional axisymmetric case the calculation results were compared with a self-similar solution for a perfect gas, which showed a good qualitative and quantitative agreement.

Similarity solutions for the propagation of a spherical shock wave generated by a moving piston in a nonideal gas under the influence of a gravitational field and azimuthal magnetic field with monochromatic radiation are obtained. The gravitational field is due to a central mass at the origin, i.e., the Roche model is valid. The gravitational effect of the gas itself is neglected in comparison with the attraction of the central mass at the origin. We considered that the radiation flux moves through an electrically conducting nonideal gas with constant intensity and energy is absorbed only behind the shock which moves in the direction opposite to the radiation flux. The results are discussed and compared with ones for a perfect gas, as well as for the cases of the influence of the gravitational field and of the absence of this field. The effect of the variations of the Alfven–Mach number, gravitational parameter, adiabatic exponent, and of the parameter of gas nonidealness are discussed in details.

The modern practice of using vibratory machines involving small seeds of low weight faces such an undesirable phenomenon as the effect exerted on the kinematics of vibrational movement of particles of fractions of the seed mixture by the aerodynamic forces and momenta. The periodic movement of air relative to the working planes of a vibratory machine arises due to fluctuations in the packets of these planes, which form flat aerodynamic channels. Consequently, the issues of studying the processes of interaction between the working bodies of vibratory machines and the air environment, aimed to justify their structural improvements, appear relevant. Existing mathematical models, which assess the parameters of air movement relative to the working planes of vibratory machines, produce only a generalized pattern and are flat. This paper proposes a statement, as well as an estimated finite difference scheme, of solving a three-dimensional boundary value problem on calculating the field of velocities and pressures in the region of air, located between two parallel synchronously oscillating planes. The problem employs a system of differential equations to describe the flow of the perfect gas. The finite difference scheme has been solved by a sweep method. Using the sweep method to solve these kinds of problems makes it possible to ensure the convergence and stability of estimation schemes, regardless of the step and other parameters of the grid applied. A variant of the calculation has been given, which demonstrated the feasibility of the proposed method for the assigned boundary conditions and parameters of the vibrational mode of machine operation. It has been established that in the working space enclosed between two oscillating planes there are both vertical (transverse) and horizontal (longitudinal) components of air velocity, which change over time

In the framework of Tsallis statistics, we study the effect of medium nonextensivity on the Jeans gravitational instability criterion for a self-gravitating protoplanetary cloud, the substance of which consists of a mixture of perfect gas and blackbody radiation. Generalized Jeans instability criteria have been found from the corresponding dispersion relations obtained both for a uniform cloud with radiation and for a rotating protoplanetary cloud. An integral generalized Chandrasekhar stability criterion for a gravitating spherical cloud has also been obtained. The presented results are analyzed for various values of deformation parameters $$q,$$ dimensionality $$D$$ of the velocity space and coefficient $$\beta $$, characterizing the fraction of radiation in the total pressure of the system. It is shown that radiation stabilizes the substance of nonextensive protoplanetary clouds, and for rotating clouds, the Jeans instability criterion is modified by the Coriolis force only in the transverse modes of perturbation wave propagation.

International audience; Liquid rocket, Diesel or aircraft engines may operate in the transcritical regime. In such thermodynamic conditions, the classical phase change that occurs at subcritical pressure disappears and the mixing layer between the dense and cold jet and the outer gaseous stream is characterized by large variations of density and thermodynamic properties. Fluids show strong departure from a perfect gas behavior and a real-gas formulation is needed to model the fluid state. The extension of the unstructured AVBP solver, jointly developed by CERFACS and IFPEN, to handle high-pressure thermodynamics is presented in details. It is then validated on the experimental coaxial injectors studied with the Mascotte test rig from ONERA that operate in the transcritical range, namely the LOx/GH2 cases A60 and C60 and the LOx/GCH4 configuration G2. The flame pattern observed in experiments is properly recovered, hence validating the numerical strategy. Numerical results are then discussed focusing on the role of the momentum flux ratio on the development of transcritical flames.

A compressible supersonic turbulent jet of a perfect gas in a co-flow with the formulation of stochastic spectral inflow boundary conditions is numerically modeled. The base equations are the LES averaged Navier – Stokes equations closed by the Smagorinsky model, the solution of which is carried out by the ENO scheme of the third order of accuracy. The stochastic boundary conditions at the inlet are constructed on the basis of the spectral method of generating fluctuations of gas-dynamic variables to obtain an inhomogeneous anisotropic turbulent flow. The numerical results of turbulent characteristics are compared with experimental data for the shear layer problem. The thickness of the shear layer is obtained, in which the growth of the shear layer between the jet and the co-flow for three types of grid (coarse, medium and fine) is demonstrated. Coherent vortex structures appearing in the jet are constructed in dynamics, which made it possible to analyze in detail the growth and development of vortices over time.

In problems involving strong shock waves (the problem of a strong explosion, the motion of bodies with large supersonic speeds, and the problem of supersonic piston expansion), a significant increase in temperature occurs in the disturbed flow region. It is therefore necessary to take the real properties of the gas into account when determining the parameters of the gas flow behind the front of a strong shock wave. This significantly complicates the construction of approximate analytical solutions. However, studies show that the effect of the real properties of the gas on the gas-dynamic parameters of the flow can be taken into account by changing the adiabatic index, i.e., by introducing an effective adiabatic index. If the gas behind the shock wave is in a state of thermodynamic equilibrium, then the effective adiabatic index changes insignificantly in the entire flow zone. This allows us to simulate the flow behind the shock wave front using some perfect gas, whose adiabatic index is determined by the shock wave front depending on the Mach number and the thermodynamic state of the gas. To obtain more accurate solutions for problems with strong shock waves, the model must allow a discontinuity in the adiabatic index at the shock wave. An explicit expression for gas parameters behind the front of an intense shock wave is obtained in this study under the assumption that the adiabatic index undergoes discontinuity during the transition of gas particles through the shock wave surface. Plane and axisymmetric cases are considered.

The concept of renormalized dissipative measures-valued (rDMV) solutions to a complete Euler system for a perfect gas was introduced in [8] and further discussed in [9]. Moreover it was shown there that rDMV solutions satisfy the weak (measure-valued)-strong uniqueness principle that makes them a useful tool. In this paper we prove the existerrce of rDMV solutions. Namely, we formulate the complete Euler system in conservative variables usual for numerical analysis and recall the concept of rDMV solutions based on the total energy balance and renormalization of entropy inequality for the physical entropy presented in [8]. We then give two different ways how to generate rDMV solutions. First via vanishing viscosity limit using Navier-Stokes equations coupled with entropy transport and second via the vanishing dissipation limit of the two-velocity model proposed by H. Brenner. Finally, we recall the weak-strong uniqueness principle for rDMV solutions proved in [8] and [9].

An asymptotic theory of the neutral stability curve of a supersonic boundary layer in a vibrationally excited molecular gas on a flat plate is constructed. The equations of the two-temperature viscous heat-conducting gas dynamics are considered as the initial mathematical model of the flow. On the basis of their linearization about the self-similar boundary layer solution for a perfect gas, a spectral problem is derived for the eighth-order system of linear ordinary differential equations. An algebraic secular equation with a typical decoupling into inviscid and viscous parts is derived from the linear combination of the boundary values of its solutions decreasing outside the boundary layer which solved numerically. It is shown that the neutral stability curves calculated in this way confirm the effect of increasing flow stability against the background of the relaxation process and within 12–15% agree with the previously obtained results of the direct numerical solution of the full spectral problem. The solution of the simplified system of equations for calculating the critical Reynolds number gives a similar result.

This study investigates the influence of surface distribution of the basic flowfield on the shapes and performances of the osculating axisymmetric waveriders. First, the design method of osculating...