Calculation of viscous compressible gas flow past a corner

We consider the problem of calculating the parameters for supersonic viscous compressible gas flow past a corner (angle greater than ). The complete system of Navier-Stokes equations for the viscous compressible gas is solved in the small vicinity Q₁. (characteristic dimensionl~1/R) of the corner point. The conditions for smooth matching of the solution of the Navier-Stokes equations and the solution of the ideal gas or boundary layer equations are specified on the boundary of Q₁. All these solutions are a priori unknown, and the conditions for smooth matching reduce to certain differential equations on the boundary of Q₁. Here account is taken of the interaction of the flows near the wall surface and in the so-called outer region [1].We note that no a priori assumptions are made in Q₁ concerning the qualitative behavior of the solution, in contrast with other studies on viscous flow past a corner (for example, [2–4]).The Navier-Stokes system in Q₁ is solved numerically, using the difference scheme suggested in [5]. This scheme permits obtaining the steady-state solution by the asymptotic method for large Reynolds numbers R, and also has an approximation accuracy adequate to account for the effects of low viscosity and thermal conductivity.     

Perturbation solution of the compressible annular Poiseuille flow of a viscous fluid

The isothermal annular Poiseuille flow of a weakly compressible Newtonian liquid with constant shear and bulk viscosities is considered. A linear equation of state is assumed and a perturbation analysis in terms of the primary flow variables is performed up to the first order using the isothermal compressibility as the perturbation parameter. The effects of compressibility, the bulk viscosity, the radii ratio, the aspect ratio, and the Reynolds number on the velocity and pressure fields are studied.     

Asymptotic study of viscous compressible gas flow past a blunt body

Supersonic viscous gas flow past a blunt body is examined. A method is proposed which permits constructing the asymptotic expansion of any order in the small parameter , which characterizes the viscosity and thermal conductivity coefficients. The asymptotic solution is constructed, including terras of zero, first, and second orders of . Acomparison is made with results of other authors who have studied various particular aspects of the subject problem using the method of inner and outer expansions [1–3].     

Two-dimensional compressible viscous sink flows

A theoretical investigation of two-dimensional viscous compressible sink flow is presented. An analytic solution in parametric form is obtained for specific values of the ratio of specific heats. For the more general case, a number of asymptotic solutions were also obtained for different flow regimes including hypersonic, transonic, acoustic and low Reynolds number flow.     

粘性可压混合层时间稳定性对称紧致差分求解

基于可压扰动方程组的一阶改型 ,将高精度对称紧致格式引入边值法数值线性稳定性分析。对所获非线性离散特征值问题给出了一个通用形式二阶迭代局部算法 ,实现了时间模式和空间模式的统一求解 ,并将扰动特征值及其特征函数同时得到。据此分析了可压平面自由混合层时间稳定性 ,涉及二维 /三维扰动波、粘性 /无粘扰动波、第一 /第二模态、特征函数、伪特征值谱等。研究表明 ,压缩性效应和粘性效应对最不稳定扰动波数和增长率呈相似的减抑作用 ;在 Mc=1附近 ,从高波数段开始 ,粘性效应可强化二维不稳定扰动波由第一模态向第二模态的过渡     

Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Inhomogeneous plane waves in compressible viscous fluids

The propagation of inhomogeneous plane waves in a compressible viscous fluid is considered. The frequency and the slowness vector are both allowed to be complex. There are seen to be two types of solutions: (a) two transverse waves, which involve no density or pressure fluctuations, (b) a longitudinal wave, which involves no fluctuations in vorticity. For each type, a propagation condition is obtained giving the (complex) squared length of the slowness vector as a function of frequency. Each depends also on the viscosities. It is seen how to recover the incompressible case as the limit in which the inviscid acoustic wave speed tends to infinity. Each wave is shown to be linearly stable for real frequencies. These waves are attenuated in space and time but nevertheless it is possible to define constant weighted mean values (over a cycle of the propagating part of the wave) of the energy density, energy flux and dissipation. The energy-dissipation equation and the propagation conditions are used to derive relationships between these constant weighted means, some of which are generalizations to compressible fluids of previously known results for incompressible fluids. Explicit expressions in terms of frequency are given for the weighted means.     

Problems of hydroelasticity for compressible viscous fluids

The complete text of a paper at the International Conference on Applied Mechanics (Peking, August 21–25, 1989), with a brief content published in the conference proceedings.     

Lp-approach to steady flows of viscous compressible fluids in exterior domains

We investigate steady compressible flows in three-dimensional exterior domains for small data and for both zero and nonzero (but constant) velocity at infinity. We prove existence and uniqueness of solutions in L ^p -spaces, p>3, and study their regularity as well as their decay at infinity.     

Numerical solution of the system of one-dimensional unsteady Navier-Stokes equations for a compressible gas

In many problems encountered in modern gasdynamics, the boundary layer approximations are inadequate to account for the dissipative factors-viscosity and thermal conductivity of the gas-and the solution of the complete system of Navier-Stokes equations is required. This includes, for example, flows with large longitudinal pressure gradients, which in order of magnitude are comparable with or exceed the transverse gradients (temperature jumps, sharp flow rotations, compression shocks, etc.). In many cases, for example in flows with low density, the scale of action of the longitudinal gradients becomes significant, which leads to the need for considering the flow structure in the vicinity of the large gradients. The formulation of certain problems of this type leads to a system of one-dimensional Navier-Stokes equations.We present a difference scheme for the solution of the system of one-dimensional stationary and nonstationary Navier-Stokes equations and give examples of the calculation of the structure of the stationary shock wave front, unsteady gas flow under the influence of sudden heating of one of the boundaries, and unsteady gas flow in the vicinity of the decay of an initial discontinuity. The solution of the stationary problems is accomplished as a result of stabilization as t .The author wishes to thank V. Ya. Likhushin and V. S. Avduevskii for interest in the study and for their valuable counsel during the investigation.     

Multidomain collocation techniques for a viscous compressible flow

This paper presents a viscous compressible flow problem to which an equilibrium solution, in terms of density and velocity, can be given implicitly by elementary functions. The corresponding initial boundary value problem is solved by time discretization by the Crank-Nicolson method, Newton linearization and space discretization using multidomain Chebyshev collocation techniques. The physical interval is covered by subintervals of equal length. Each subinterval utilizes the same number of collocation points and each interface consists of one or two points. Six ways of patching are tested. All of them yield solutions with spectral accuracy for a few time steps, but only three are stable in the long run. Details of the density evolution are illustrated.     

Nonlinear waves in a viscous compressible fluid with relaxation

The propagation and stability of nonlinear waves in a viscous compressible fluid with relaxation that satisfies a Theological equation of state of Oldroyd type are investigated. An equation that describes the structure of the wave perturbations and its evolution is derived subject to the condition of balance of the nonlinear dissipative and relaxation effects, and its solutions of the solitary wave type are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 31–35, May–June, 1993.     

Study of nonstationary problems for a compressible viscous fluid

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 4, pp. 111–115, April, 1989.     

A finite element method for compressible viscous fluid flows

This work presents a mixed three‐dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a ‘stable’ numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf–sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady‐state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible. Copyright © 2010 John Wiley & Sons, Ltd.