Supersonic Gas Dynamics Research Articles

Solution of super- and hypersonic gas dynamic problems with a model of high-temperature air

The study considers the solution of a number of problems of supersonic and hypersonic gas dynamics using a model that takes into account the dissociation and ionization of air. The results of verification and validation of the developed numerical method using various difference schemes (the Roe scheme, Rusanov scheme, AUSM scheme) for discretizing convective flows are presented. The formulation of the mathematical model for high-temperature air uses the presence of equilibrium chemical reactions of dissociation and ionization. For this purpose, at high incoming flow velocities, the Kraiko model is applied, which includes equilibrium chemical reactions in air at high temperatures. To discretize the basic equations, the finite volume method on an unstructured grid is applied. One of the features of the constructed mathematical model is the implementation of the transition between physical and conservative variables. Relationships are given, with the help of which the transition from conservative variables to physical ones and vice versa is carried out when using the high-temperature air model. To ensure the stability of numerical calculations, an entropy correction is introduced. The decrease in entropy in the solution of hyperbolic equations is excluded by introducing an artificial viscosity according to Neumann, as well as by using the Godunov method with an exact solution of the Riemann problem and methods based on the approximate solution of the problem of the decay of an arbitrary discontinuity. A number of problems of supersonic gas dynamics (supersonic flow in a channel with a straight step and supersonic flow around a sphere) are numerically solved taking into account high-temperature effects. The criteria for the accuracy of numerical calculations related to the location of shock-wave structures are discussed. The calculated shock-wave structure of the flow is compared with the data available in the literature, as well as with calculations using the perfect gas model. Some results of numerical calculations are compared with the available experimental data. The shock-wave flow patterns obtained in the framework of the inviscid model, which takes into account the effect of viscosity and its dependence on temperature, and the turbulent flow model are compared. On the basis of numerical simulation data, the influence of viscous effects on the flow characteristics in a channel with a straight step and hypersonic flow around a sphere is considered. The influence of various numerical factors on the shape of the bow shock and the presence of fluctuations in the solution behind the shock is emphasized. As part of the work, a computational module was prepared for the commercial package Ansys Fluent, implemented with the help of user programming tools. The prepared module expands the standard capabilities of commercial software focused on solving computational gas dynamics problems, and is available to Ansys Fluent users for solving hypersonic aerodynamics problems. The developed means of numerical simulation can be useful in the design and optimization of hypersonic aircraft.

A generalized solution of a modified Cauchy problem of class R 2 for a hyperbolic equation of the second kind

One of the main problems in the theory of partial differential equations is the study of equations of mixed type. the modified Cauchy problem for some values of α is stated and investigated. The equations of the mixed type began to be studied systematically, after FI Frankl indicated their applications to the problems of transonic and supersonic gas dynamics. In this regard, the purpose of this work was to find out whether it is possible to find a more convenient form of representation of the solution of the Cauchy problem for a differential equation, with the help of which it would be possible to solve boundary value problems for a mixed type equation of both parabolic-hyperbolic and elliptic-hyperbolic types. The modified Cauchy problem for some values of α is stated and investigated. A convenient representation of the generalized solution of the modified Cauchy problem is obtained.

The large clusters influence on the supersonic flows gas dynamics in a rarefied medium

The processes of Van der Waals clusters formation in supersonic gas flows expanding into a rarefied medium are discussed in this report. The necessary conditions for cluster formation, methods for measuring the average size and size distribution of clusters in a rarefied gas flow are considered. The problems associated with electron-beam ionization of clusters during mass spectrometry of clustered flows are analyzed. The process of intracluster energy exchange in mixtures, that leads to the possibility of inverse pumping of electronic levels of atoms, is illustrated. The problems arising during optical measurements of density in cluster flows are demonstrated. The effect of large clusters formation on the shape and structure of supersonic flows is shown.

Modeling of Two-Phase Flow and Heat Transfer in Low-Temperature Oxygen-Fuel Spray Process

The low-temperature oxygen-fuel (LTOF) spray is a modification of high velocity oxygen fuel spray. In this process, the high-temperature gas is accelerated to supersonic speed through a Laval nozzle followed by a straight barrel. By injecting room temperature gas into the mixing chamber, the temperature of the gas can be controlled in a range of about 1000-2500 K, so that some oxygen and temperature-sensitive materials, such as titanium and copper, can avoid oxidation or decomposition during the spraying process. The purpose of this paper is to establish a 2-D mathematical model to simulate the supersonic gas dynamics and particles behavior in LTOF process. The temperature and velocity of the flow fields, and the trajectory and heating of in-flight particles are predicted for different operating parameters. The model is validated by experimental data in the literature. Effects of the mixing gas flow rates, particle sizes, and injection conditions on this process were investigated as well.

A New Model for the Separation of Meteoroid Fragments in the Atmosphere

This work is devoted to modeling of the transverse scattering of meteoroid fragments in the atmosphere by adopting supersonic gas dynamics around a system of bodies. Artem’eva and Shuvalov (1996, Shock Waves, 367) and Zhdan et al. (2004, Dokl. Phys., 315–317) found that the transverse force decreases with the increase of the distance between fragments, that is, fragments do not separate in a transverse direction under the action of constant repulsion force. This work on the decreasing transverse force uses the values of the transverse force coefficient by Zhdan et al. (2004, Dokl. Phys., 315–317) obtained from numerical modeling for spheres in a supersonic flow to derive the analytical solution of the dynamic equation for a fragment. The new model of layer-by-layer scattering of meteoroid fragments moving as a system of bodies is constructed on the basis of the analytical solutions derived in this work and the numerical data by Zhdan et al. (2005, Dokl. Phys., 514–518).

Non-self-similar characteristics of weak Mach reflection: the von Neumann paradox

This paper deals with the von Neumann paradox, an as yet unsolved major problem in supersonic gas dynamics. We conduct a series of experiments using a conventional shock tube and focus attention on the flow-field around the triple point at various locations of the incident shock wave. By measuring the position of the triple point and the angle made by the incident and reflected shocks for propagating shock waves, we prove that the flow-field around the triple point is not self-similar. The von Neumann paradox is at least partly ascribed to non-self-similarity because classical theory assumes pseudo-steadiness that results from self-similarity for shock reflection over a wedge in a shock tube. The non-self-similarity revealed here clarifies the classical experiments by Smith (Photographic investigation of the reflection of plane Shocks in air. OSRD Report 6271, Washington, USA, 1945) and Bleakney and Taub (Rev. Mod. Phys. 21 (1949) 584). Specifically, since they implicitly assumed self-similarity, they only measured the wave angles at some particular location for each reflecting wedge angle, and their relations between angles of incidence and reflection were recovered by the present experiment.

Efficient parallel computations of flows of arbitrary fluids for all regimes of Reynolds, Mach and Grashof numbers

This paper presents a unified numerical method able to address a wide class of fluid flow problems of engineering interest. Arbitrary fluids are treated specifying totally arbitrary equations of state, either in analytical form or through look‐up tables. The most general system of the unsteady Navier–Stokes equations is integrated with a coupled implicit preconditioned method. The method can stand infinite CFL number and shows the efficiency of a quasi‐Newton method independent of the multi‐block partitioning on parallel machines. Computed test cases ranging from inviscid hydrodynamics, to natural convection loops of liquid metals, and to supersonic gasdynamics, show a solution efficiency independent of the class of fluid flow problem.

Physics of mass loaded plasmas

In space plasmas the phenomenon of mass loading is common. Comets are one of the most evident objects where mass loading controls to a large extent the structure and dynamics of its plasma environment. New charged material is implanted to the fast streaming solar wind by planets, moons, other solar system objects, and even by the interstellar neutral gas flowing through our solar system. In this review we summarize both the current observations and the relevant theoretical approaches. First we survey the MHD methods, starting with a discussion how mass loading affects subsonic and supersonic gasdynamics flows, continuing this with single and multi-fluid MHD approaches to describe the flow when mass, momentum and energy is added, and we finish this section by the description of mass loaded shocks. Next we consider the kinetic approach to the same problem, discussing wave excitations, pitch angle and energy scattering in linear and quasi-linear approximations. The different descriptions differ in assumptions and conclusions; we point out the differences, but it is beyond the scope of the paper to resolve all the conflicts. Applications of these techniques to comets, planets, artificial ion releases, and to the interplanetary neutrals are reviewed in the last section, where observations are also compared with models, including hybrid simulations as well. We conclude the paper with a summary of the most important open, yet unsolved questions.

Two‐Wave Interactions for Hyperbolic Signaling Problems and the Application to Supersonic Gas Dynamics

The signaling problem for a system of conservation laws in a single space variable is treated through the deployment of a perturbation analysis. Our method of approach involves the direct use of two nonlinear phase variables making possible the study of weakly nonlinear interacting waves arising from a boundary disturbance consisting of two wave modes. As a result of our analysis, the asymptotic solution is derived, and the class of admissible boundary disturbances is distinguished as well. An application is then made to gas dynamics in one space dimension to investigate the propagation and interaction of two sound waves for which the base state is taken to be a steady supersonic flow.

Theoretical study of a supersonic high-repetition-rate H2+F2-pumped HF laser

A numerical model for calculating the performance of a premixed pulsed supersonic HF chemical laser, pumped by the H2+F2 chain reaction, is presented. The laser kinetic equations, which are coupled to the supersonic gas dynamics and to the chemical equations, are integrated along the flow direction. The model which has been shown to accurately predict the measured gain coefficients, the lasing induction times, and the laser power output, has been used for parametric studies leading to a better understanding of the laser operation. Conditions for maximum gain and maximum laser energy for each of the input parameters were investigated. The lasing zone length in the flow direction was studied. A comparison between the experimental and calculated results shows that the model can be used to evaluate unknown chemical and energy transfer rates.

A high-order Godunov scheme for steady supersonic gas dynamics

A high-order extension of Godunov's method is developed for the equations of steady supersonic flow. Sample calculations show that the method resolves smooth flow accurately and represents strong shock waves with very little diffusion and no post-shock oscillation.

Numerical study of supersonic gasdynamics in a duct in the presence of nonequilibrium processes

Numerical study of supersonic gasdynamics in a duct in the presence of nonequilibrium processes

Design of supersonic asymmetric nozzles

Problems which are associated with the design of the optimum contours of asymmetric plane nozzles are considered. In [1], in the case of the “minimum possible” length of the lower wall, this problem was solved exactly by the controlled contour method. For greater lengths of the lower wall, this method is inapplicable and it is necessary to use the so-called general method of Lagrange factors [2, 3]. On the basis of this method, the necessary conditions of optimality of the configurations proposed (but not investigated) in [1] are obtained below, a solution which contains a section of the two-sided extremum is constructed, and configurations which do not contain this section are analyzed. The specifics of the problem considered lead to situations which are different from those encountered earlier in the variational problems of supersonic gasdynamics. The latter is associated both with the specail features of formulation of the combined problem for determining the Lagrange factors and with the disposition of the lines of discontinuity of these factors. In the concluding part of the paper, which is a continuation of [4], the effect of the intensity of the compression wave on the thrust of a “ shortened” asymmetric nozzle is investigated. It is shown that the substitution of the centered wave by a compression wave of very moderate intensity significantly reduces the thrust of the nozzle.

Regular reflection of a magnetohydrodynamic shock wave from a conducting wall

In two-dimensional supersonic gasdynamics, one of the classical steady-state problems, which include shock waves and other discontinuities, is the problem concerning the oblique reflection of a shock wave from a plane wall. It is well known [1–3] that two types of reflection are possible: regular and Mach. The problem concerning the regular reflection of a magnetohydrodynamic shock wave from an infinitely conducting plane wall is considered here within the scope of ideal magnetohydrodynamics [4]. It is supposed that the magnetic field, normal to the wall, is not equal to zero. The solution of the problem is constructed for incident waves of different types (fast and slow). It is found that, depending on the initial data, the solution can have a qualitatively different nature. In contrast from gasdynamics, the incident wave is reflected in the form of two waves, which can be centered rarefaction waves. A similar problem for the special case of the magnetic field parallel to the flow was considered earlier in [5, 6]. The normal component of the magnetic field at the wall was equated to zero, the solution was constructed only for the case of incidence of a fast shock wave, and the flow pattern is similar in form to that of gasdynamics. The solution of the problem concerning the reflection of a shock wave constructed in this paper is necessary for the interpretation of experiments in shock tubes [7–10].

Nonlinear effects in steady supersonic dissipative gasdynamics. Part 2. Three-dimensional axisymmetric flow

Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is divided into zones based on the presence or absence of nonlinearity and dissipation. Estimates and criteria which describe the extent of these zones are given.

Non-linear effects in steady supersonic dissipative gasdynamics Part 1. Two-dimensional flow

Steady supersonic two-dimensional flows governed by the Navier–Stokes equations are considered. For flows past a thin body, the Oseen theory is shown to fail at large distances. An investigation of the equations bridging the linear and non-linear zones is made. From this, it follows that the resulting equations are a system of Burgers and diffusion equations. The Whitham theory is shown to result under the inviscid limit of our analysis. Various other limits are also obtained.An explicit expression for flows past a thin airfoil is given, and the flow past a double wedge is exhibited in terms of known functions.

A variational problem of supersonic gasdynamics

A large number of studies have been published which define bodies of minimal drag and nozzles of maximal thrust. A study has been made of the region of existence of the various solutions in planar flow, and it has been shown that the optimal profile in the presence of a length limitation may have a blunt end, which is a segment of a boundary extremum. The results of these studies and also the required bibiliography are contained in [1–3].

A Research on Large Deflexion Supersonic Turbine Blade Rows

Though supersonic gas dynamics has already been introduced in the design of supersonic turbine blades, many problems are left unsolved, which were made clear by our preliminary experiment of conventional blades. The problems are summarized as follows. (1) The shock boundary layer interaction around the leading edges.(2) The introduction of the effect of boundary layer displacement in the blade design.(3) The behavior of the supersonic flow around the trailing edges of turbine blades. Special model tests concerning these problems are performed to obtain new design data, which are applicable to improve the design method. A new design method to realize given velocity triangles is proposed. Using this method a new blade is designed, manufactured and tested to confirm the superior performances.

On the solution of variational problems of supersonic gas dynamics

In solving variational problems of supersonic gas dynamics by the method of Guderly and Armitage [1], it is essential to have linear dependence of the coefficients of the flow parameters being varied on the closing characteristic. This permitted the solution of a number of variatlonal problems [1 to 4] without having to consider the relations between the indicated variations, which arise from the equations of the characteristics. Some problems, however cannot be solved in this manner. In general, therefore, it is also necessary to include the relations on the closing characteristics in the auxilary functional. This is illustrated by the example below, in constructing the rear part of a minimum drag body with restriction on the length, when the contour may contain an end wall. Two cases are studied. In the first, the pressure on the end wall does not depend on the shapes of the desired contour. Here the Lagrange multipliers, introducing the relations on the characteristics, turn out to be zero, and the solution agrees with that obtained earlier [3]' In the second case, the pressure on the end wall is determined by a condition of the type of Korst's condition [5] and consequently, it depends on the shapes of the desired contour. Here it is necessary to introduce the relations on the closing characteristic. This example is also interesting in that for its solution, questions are considered which are connected with varying the position of the junction of the end wall and the segment of the two-sided extremum. The latter are important for the solution of other problems, e.g. in the construction of the nose part of minimum drag bodies.

Linearized Hyperbolic Steady Magnetohydrodynamic Flow Past Nonconducting Walls

Linearized steady hyperbolic flows of an ideally-conducting fluid past infinite insulating walls are considered. Because of the interaction between the magnetic fields in the fluid and in the solid wall, the fluid is everywhere disturbed and there are no regions of uniform flow. The flow cannot be constructed from shocks and simple waves as in ordinary supersonic gas dynamics, but must be found together with the field in the solid. Essentially, the linearized problem consists of a wave equation in the upper half-plane, and a Laplace equation in the lower half-plane, with appropriate boundary conditions on the interface and at infinity. A general procedure which yields the unique solution is given. Several specific examples are calculated, including the flow past a wavy wall, and the flow past a wall with two corners. It is shown that the flow past a single corner is not a meaningful problem, since the perturbations become infinite far away from the corner.