Supersonic Flow Past Bodies Research Articles

Ideal magnetohydrodynamic equations on a sphere and elliptic-hyperbolic property

This work contains the derivation and type analysis of the conical ideal magnetohydrodynamic equations. The 3D ideal MHD equations with Powell source terms, subject to the assumption that the solution is conically invariant, are projected onto a unit sphere using tools from tensor calculus. Conical flows provide valuable insight into supersonic and hypersonic flow past bodies, but are simpler to analyze and solve numerically. Previously, work has been done on conical inviscid flows governed by the Euler equations with great success. It is known that some flight regimes involve flows of ionized gases, and thus there is motivation to extend the study of conical flows to the case where the gas is electrically conducting. To the authors’ knowledge, the conical magnetohydrodynamic equations have never been derived, and so this paper is the first investigation of that system. Among the results, we show that conical flows for this case do exist mathematically and that the governing system of partial differential equations is of mixed type. Throughout the domain it can be either hyperbolic or elliptic depending on the solution.

Oscillatory Flow Regimes Resulting from the Shock Layer–Particle Interaction

The paper is devoted to the numerical study of the shock layer–particle interaction in a supersonic flow past bodies. The shock wave associated with a moving particle and the flow in the particle wake is taken into consideration. Distinctive features of the numerical technique are the adaptive Cartesian sliding grids of high resolution, a ghost cells immersed boundary method for the realization of conditions on curvilinear boundaries, parallelization of computations on graphics processors. The results of computational experiment obtained allows to study the characteristic shock and vortex structures formed during the passage of a particle rebounding from the surface through the bow shock wave. The oscillations observed for a flow over the fla-tended cylinder are discussed.

Nonstationary Conjugate Problem of Heat Transfer in Supersonic Flow Past Bodies in a Wide Range of Reynolds Numbers

In one of our earlier papers, we considered supersonic, laminar boundary-layer flows past bodies made of different materials and examined the possibility of controlling the temperature regime of a body immersed in flow. In the present work, for the conditions corresponding to aerodynamic experiments and to long flight times, we analyzed such values of deceleration parameters when regions of laminar, transitional, and turbulent regimes of flow are realized simultaneously in a boundary layer. The possibility of decreasing the level of maximal temperatures depending on the determining criteria of the problem has been evaluated for bodies made of different materials. The expediency of using simplified approaches is shown, including those for nonstationary conditions based on stationary solutions and on well-studied limiting cases of isothermal and adiabatic surface temperatures and allowing the determination of the temperature regimes in the entire range of thermophysical characteristics.

A comparison of plasma and thermal effects upon supersonic flow past aerodynamic bodies

The task of controlled variation of parameters of supersonic flow past a semicylindrical aerodynamic body is considered. The action of gas-discharge plasma on the flow by means of discharge-induced increase in the degree of nonequilibrium in the oncoming gas has been experimentally studied. For the flow parameters used in the experiment, the numerical simulation has been conducted for the thermal action of plasma upon the shock layer of a homogeneously heated region with the gas temperature equal to the electron temperature determined in the experiment. Comparison of the experimental and calculated data leads to the conclusion that the new mechanism based on increase in the degree of gas nonequilibrium in the source of energy supply can be used for controlling supersonic flows past aerodynamic bodies.

Aerodynamic and Numerical Study on the Influence of Spike Shapes at Mach 1.5

Taking into account the issue of configuration or aerodynamic heating, most supersonic and hypersonic flight vehicles have to use the blunt-nosed body. However, in supersonic especially in hypersonic flow the strong bow shock ahead of the blunt nose introduces a rather high shock drag that affects the aerodynamic performance of the vehicles seriously. A spike mounted on a blunt body during its flight pushes the strong bow shock away from the body surface and forms recirculation flow with low pressure ahead of the body surface, and then decreases the drag. The drag reduction effects of spikes in high supersonic and hypersonic flow had been validated through experimental and numerical methods. In order to analyze the influence of the spike on aerodynamic characteristics at low supersonic (M=1.5) flow past blunt-nosed bodies, numerical studies were carried out which included the influence of the spike shape, the analysis of the fluid flow structures and the effect on the aerodynamic characteristics of a blunt body.

Optimization of supersonic flows past thin bodies by using external effects on the flow

Problems of optimization of flows past a thin body of revolution and a slender profile at a small angle of attack in the presence of local energy release zones and an external force acting on the flow near the surface are considered. Analysis is based on an analytic theory of supersonic flow past thin bodies presented in previous papers. The following problems are considered: drag reduction of a thin body of revolution, lift force enhancement of a profile with infinite aspect ratio, attenuation of acoustic noise generated by supersonic flows past bodies.

On peculiarities of the application of Lagrangian variables in problems of time-dependent supersonic flow past bodies

The paper considers particularities in applying Lagrangian variables in problems of hypersonic flow past bodies. It is pointed out that, in problems with intense shock waves, it is advisable to introduce Lagrangian variables as the values of parameters that characterize a particle not on surface t = t0 (t0 = const) but on surface t = σ, where σ is the time instant at which the particle meets the surface of discontinuity. Considering examples of two-dimensional flow past two-dimensional and axisymmetric bodies moving with high time-dependent velocity, we show that the passage to Lagrangian variables enables us to obtain a system of equations describing the gas flow behind the front of an intense shock wave, which is suitable for the application of the thin-shock-layer flow method. A solution is constructed in the form of series in powers of a small parameter which characterizes the ratio of the gas densities at the front of the leading shock wave. We remark that all nonlinear effects of the problem are concentrated in the equation to determine the law of motion of a particle in zero-order approximation. The cases in which this equation can be integrated are pointed out. For the remaining unknowns, the solution is taken in quadratures. We study the rearrangement of the gas flow in the shock layer when the motion of the body is changed. The flow rearrangement zone is distinguished. Also, a condition to determine the life time of that region (the time of establishment of the new flow regime) is obtained. In a specific case of passing from a steady motion of a wedge to a uniformly accelerated motion, the time of establishment of the uniformly accelerated motion is determined from a quadratic equation.

Numerical modeling of the effect of geometric asymmetry on the damping aerodynamic characteristics of supersonic sectional flight vehicles

A method for calculating the steady inviscid supersonic flow past equivalent bodies is applied to the analysis of the time-dependent aerodynamic characteristics of sectional flight vehicles with an asymmetric rear stabilizer. The stabilizer asymmetry can be caused by either its deflection or a change in its shape due to heat-shield coating removal, boundary layer displacement thickness, developed separation flow zones, local deformations, or other distortions in the baseline form. Amathematical apparatus for modeling asymmetric sectional configurations by means of ruled surfaces with arbitrary contours of the reference cross-sections is developed. The uniform perfect-gas M∞ = 6 flow past sectional vehicles performing plane oscillations about the zero angle of attack is calculated (the adiabatic exponent γ = 1.4). The calculated results demonstrate the effect of various asymmetries in the body shape on the aerodynamic coefficients.

Magnetohydrodynamic control of supersonic flow past bodies: Possibilities and undesirable effects

Basic problems of super-and hypersonic magnetohydrodynamics (MHD) associated with the determination of the integral characteristics of bodies and vehicles inside which there are systems generating a uniform magnetic field are considered. Three classes of flows, namely, flow in a hypersonic multimode fixed-geometry air-intake; internal and external flow in a model of a hypersonic vehicle containing an air-intake with an MHD generator, a combustion chamber, and a supersonic nozzle; and hypersonic flow past a blunt cone are studied using numerical simulation and theoretical analysis (on the basis of the complete averaged system of Navier-Stokes equations and the electrodynamic equations). Attention is concentrated on the presence of an additionalmagnetic force acting on the system generating themagnetic field and, consequently, on the body and initiating an additional drag (in the case of a vehicle-reducing its thrust). Attractive possibilities for MHD flow control, namely, an increase in the degree of flow compression in the air-intake, a reduction in the ignition length in the combustion chamber, and a decrease in the heat flux to the nose of the body, are noted, as well as negative effects associated with the action of the magnetic force on the bodies considered.

Processing of Gasdynamic Numerical Solutions in Similarity Parameters

The distinctive features of the application of similarity parameters (those of Tsien and Hayes, Sychev, Messiter, the linear theory, and hypersonic theory of the flow past slender bodies) are considered with reference to examples of the supersonic flow past sharp bodies of revolution, thin delta wings, and blunt bodies (ellipsoids of revolution and elliptical cylinders). Approaches to the construction of generalizing dependences on the basis of numerical solutions are discussed. These dependences can simplify the overview of numerous solutions and the search for optimal shapes in certain classes of bodies; they give preliminary design estimates and can also be used in complicated problems in which the gasdynamic results are only part of a more general, for example, dynamic problem.

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

Methods are studied for improving the existing perturbation theories of supersonic flow past bodies of revolution. Applicability of the theory at high Mach Numbers is emphasized. For axial flow, a second-order solution isfound which represents a considerable improvement over the first-order result. For inclined flow, a second-order solution is not feasible except for a cone. Comparison with the exact solutions for cones shows that the slender-body series expansion causes large inaccuracies in both axial and inclined flow. The conclusion that first-order theory predicts the flow no better than slender-body theory is shown to be erroneous. When first-order theory is properly used,making no unnecessaryapproximations, greatly improved agreement is found with exact solutions and with experiment. The order estimates used to justify the approximations are shown to be invalid in most practical cases. A hybrid theory, combining first-order cross flow and second-order axial flow, gives further improvement. A physical explanation is advanced for the marked superiority of first-order theory over the true linearized theory. Nonlinearity in lift is shown to result primarily from viscous separation of the cross flow along the after portions of a long body. The magnitude of the resulting normal force can be estimated with reasonable accuracy using two-dimensional viscous sweep-back theory.

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

First- and Second-Order Theory of Supersonic Flow Past Bodies of Revolution

Control of the Flow Past Bodies Using Localized Energy Addition to the Supersonic Oncoming Flow

A possibility of controlling the supersonic flow past bodies of different shape by adding a small amount of energy to the freestream is studied experimentally. In the numerical calculations the model of a spatially distributed energy source based on the Euler equations for a perfect gas is used. The gasdynamic features of the flow around energy sources are studied, some new effects are revealed, and analytical models for their description are developed. It is shown that by optimizing the energy source parameters it is possible to initiate irregular regimes of flow past bodies characterized by radical changes in the bow shock structure with the formation of return flow zones. In this case an appreciable drag reduction can be achieved with high efficiency of energy expenditure.

Three-dimensional supersonic turbulent flows past conical bodies

The results of the numerical simulation of supersonic three-dimensional flow past sharp-nosed cones with circular and elliptic cross-sections in the turbulent shock-layer flow regime are presented. The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model. The numerical solutions are obtained by means of an implicit constant-direction finite-difference scheme. The emphasis is placed on the investigation of the transverse flow separation and the flow features associated with the turbulent flow regime.

Numerical analysis of supersonic viscous gas flow past axisymmetric nonpointed bodies

Supersonic viscous homogeneous gas flow past axisymmetric smooth nonpointed bodies is analyzed numerically for widely varying Mach and Reynolds numbers and flow geometry. The initial equations of a viscous shock layer are solved by the stabilization method. The effect of the determining parameters on the flow character and the heat transfer distribution along the surface is analyzed. The accuracy and domain of applicability of several approximate approaches to the solution of the problem are estimated.

Nonlinear unsteady supersonic flow analysis for slender bodies of revolution: Theory

We construct analytical solutions for the problem of nonlinear supersonic flow past slender bodies of revolution due to small amplitude oscillations. The method employed is based on the splitting of the time dependent small perturbation equation to a nonlinear time independent partial differential equation (P.D.E.) concerning the steady flow, and a linear time dependent one, concerning the unsteady flow. Solutions in the form of three parameters family of surfaces for the first equation are constructed, while solutions including one arbitrary function for the second equation are extracted. As an application the evaluation of the small perturbation velocity resultants for a flow past a right circular cone is obtained making use of convenient boundary and initial conditions in accordance with the physical problem.

Supersonic viscous flow past two-dimensional blunt-nosed bodies

Supersonic viscous flow past two-dimensional blunt-nosed bodies

Investigation of supersonic radiative flow past bodies at low altitudes

The radiative heat transfer problem for bodies traveling through the earth's atmosphere, as formulated in [1, 3], is considered in the case of low altitudes, i.e., for high gas densities and optical thicknesses in the shock layer. These factors require the use of improved methods of calculation.

Model of the explosion of a meteor

tion of pressure p~(H), density p~(H), temperature T~(H) and gravitational acceleration g~(H). A meteoroid enters the atmopshere from space with high ~elocity at a certain angle = to the horizontal. At first its interaction with the atmosphere is nonexplosive. This stage corresponds to quasisteady flight at hypersonic speed. With a certain approximation it can be modeled on the basis of well-developed theories: the physical theory of meteors [3] and the theory of supersonic (hypersonic) gas flow past bodies [4-6]. We will assume that the explosive process begins at a certain height H 0 above the Earth. Immediately before this let the cosmic body have a mass m 0, velocity V 0 (kinetic energy K 0 = m0V~/2), density P0, and characteristic dimension (radius) R 0. How the transition to explosion takes place and, in fact, what causes this transition is not yet accurately known. It may be assumed that in a number of cases the material of the body is converted into gas at high pressure, which determines its further explosive expansion. Since in what follows we shall be concerned primarily not with the process of transition to explosion but with the actual development of the explosive flow, as a model of the transition to explosion we will take a simple model of instantaneous conversion of the entire volume of the body into high-pressure gas. Thus, our task.~wiil~be consider the following gas dynamic problem. At the initial instant of time t = 0 a spherical (for simplicity volume of gas of radius R 0 with a velocity V 0 directed at an angle = to the Earth's surface, density P0 and a pressure P0 corresponding to a certain explosion energy E 0 is located at a certain height H 0 above the Earth in a stationary, generally inhomogeneous atmosphere. Since the thermodynamic properties of the gas into which the meteoroid material is converted are not known, in this stage the gas may be assumed to be perfect with a certain ratio of specific heats =~0 (in the example given below ~0 is taken equal to 1.4). It is assumed that the gas volume is situated in a flow that corresponds to the flow past a solid body of radius R 0 traveling at the supersonic velocity V 0 . This flow is calculated beforehand. In this formulation the problem is three-dimensional and unsteady and a concrete solution is accordingly very difficult to obtain. However, the problem can be reduced to two-dimensional axisymmetric form if the dimension R 0 of the body before and during the explosion is much less than the characteristic dimension H, = 7--8 km on which the effect of the inhomogeneity of the atmosphere becomes significant and if we neglect the inhomogeneity of the atmosphere and gravity in planes perpendicular to the direction of flight, taking them into account only in the direction of the velocity V 0. The latter

Conical wing of maximum lift-drag ratio in a supersonic gas flow

The calculation of supersonic flow past three-dimensional bodies and wings presents an extremely complicated problem, whose solution is made still more difficult in the case of a search for optimum aerodynamic shapes. These difficulties made it necessary to simplify the variational problems and to use the simplest dependences, such as, for example, the Newton formula [1–3]. But even in such a formulation it is only possible to obtain an analytic solution if there are stringent constraints on the thickness of the body, and this reduces the three-dimensional problem for the shape of a wing to a two-dimensional problem for the shape of a longitudinal profile. The use of more complicated flow models requires the restriction of the class of considered configurations. In particular, paper [4] shows that at hypersonic flight velocities a wing whose windward surface is concave can have the maximum lift-drag ratio. The problem of a V-shaped wing of maximum lift-drag ratio is also of interest in the supersonic velocity range, where the results of the linear theory of [5] or the approximate dependences of the type of [6] can be used.