Numerical investigation of hypersonic nozzle flows at high reynolds numbers

The direct problem of viscous gas flow in a hypersonic nozzle of given geometry is solved on the basis of simplified Navier-Stokes equations. At a stagnation pressure of the order of several thousands of atmospheres, a compressibility factor is introduced into the equation of state. The gasdynamic parameter profiles and the Mach number distribution along the nozzle axis are obtained. The results of earlier calculations of profiled nozzles are revised. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 161–164, January–February, 1999.     

Some two-dimensional flows at finite magnetic reynolds numbers

Flows at finite magnetic Reynolds numbers are characterized by a strong effect of the induced magnetic fields on the stream. In the present paper we determine the current distribution and estimate the influence of the Lorentz force component perpendicular to the stream in a two-dimensional channel with electrodes. We also estimate the influence of nonuniformities of the velocity in the stream path of an incompressible fluid when the characteristic magnetic Reynolds numbers     

Calculation of two-dimensional shear-driven cavity flows at high reynolds numbers

The time-dependent Navier–Stokes equations are numerically integrated for two-dimensional incompressible viscous flow in a shear-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At Re = 30000 the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.     

Statistics of velocity gradients in turbulence at moderate reynolds numbers

A direct numerical simulation of the Navier-Stokes equation is performed in order to investigate the small scale structure of turbulence at moderately large microscale Reynolds numbers 40–140, using the spectral method with 340³ modes starting from a high-symmetric flow. It is shown that the small scale motion is statistically isotropic. The probability density distribution of the velocity is Gaussian, while those of the velocity gradients and the vorticity are not Gaussian but have long exponential tails. The moments of the velocity gradients are expressed in terms of the gamma function, and the ratio of the moments of the velocity gradients of successive orders increases linearly with the order. A comparison is made with a laboratory experiment.     

Laminar flow in a pipe at low and moderate reynolds numbers

Summary The laminar flow of a homogeneous viscous liquid in the inlet of a pipe is investigated numerically for a range of small and moderate Reynolds numbers where the boundary layer approximation is inapplicable. Velocity profiles and other characteristics of the flow are calculated and the results compared with approximate results obtained by other methods. The limiting case of vanishingly small Reynolds number is also treated analytically.Part of this work was performed while the second author was a summer visitor in the Applied Mathematics Department, Brookhaven National Laboratory, Upton (L.I.), New York.     

Calculation of oseen flows past a circular cylinder at low reynolds numbers

The velocity, pressure, vorticity and streamfunction are computed in the Oseen hydrodynamic field of an unbounded fluid past a circular cylinder in the Reynolds Number range going from 0.4 to 12. The boundary condition is satisfied by means of the method of least squares that determines suitable coefficients for Faxén series. Particular investigation is made of the wake region in which calculations are made of flow patterns, velocity and vorticity distributions. It is shown that, attached vortices arise at the rear of the cylinder at Reynolds Number Re=3.025. Calculated drag coefficients are in good agreement with known results of the works of several authors up to a Reynolds Number of 20.     

Optimization of body shape at small reynolds numbers

The problem of the optimization of the shape of a body in a stream of viscous liquid or gas was treated in [1–5]. The necessary conditions for a body to offer minimum resistance to the flow of a viscous gas past it were derived in [1], The necessary optimality conditions when the motion of the fluid is described by the approximate Stokes equations were derived in [2], The shape of a body of minimum resistance was found numerically in [3] in the Stokes approximation. The optimality conditions when the motion of the fluid is described by the Navier—Stokes equations were derived in [4, 5], and in [4] these conditions were extended to the case of a fluid whose motion is described in the boundary-layer approximation. The necessary optimality conditions when the motion of the fluid is described by the approximate Oseen equations were derived in [5] and an asymptotic analysis of the behavior of the optimum shape near the critical points was performed for arbitrary Reynolds numbers.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp, 87–93, January–February, 1978.     

Optimal control of viscous flow at high reynolds numbers

The most promising and most highly developed method for reducing drag in aerodynamics remains control of the flow by blowing and suction. In practice the main control problems remain the reduction of separation and the protracting of the transition of the boundary layer. These problems are solved mainly by experimental methods [1]. Meanwhile the main theoretical question remains unanswered: what is the theoretical minimum drag attainable by control through blowing (or suction)? In the present study an answer is given to this question for the cage of laminar flow round a body by a viscous incompressible fluid at high Reynolds numbers.     

Hypersonic flow over blunt edges at low reynolds numbers

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 161–168, July–August, 1989.     

Steady rotational motions of fluid masses at low reynolds numbers

The problem of steady rotational motions of an incompressible viscous fluid at small Reynolds numbers (R<1) between surfaces of rotationspecified in parametric form (1.3) is considered. Solutions of the Navier-Stokes equation are sought using the method of expansion in terms of the small parameter R. It is shown that in the case of twice continuously differentiable surfaces the solution of the problem in the first approximation enables the friction force torque on a fixed solid surface (1.3) to be determined with accuracy to R². Some solutions of Eq. (1.2) and the corresponding families of surfaces of revolution (1.3) are studied.     

Massively separated flows due to transverse sonic jet in laminar hypersonic stream

A numerical simulation of flow interactions due to a transverse sonic jet ejected from a two-dimensional slot into a hypersonic stream is carried out to examine the capability of Navier–Stokes solutions in predicting a massively separated flow upstream of the jet exit. Grid sensitivity has been studied using gradually refined meshes to address the numerical accuracy of the discretised solution of the governing equations. Comparison has been made with published experimental data regarding the separation and reattachment points and the pressure distribution in the separated region. Flow field visualisation provides further insight into the interaction region and reveals a small clockwise vortex immediately ahead of the jet exit, which is found to be responsible for the second peak in the surface pressure distribution. Received 30 June 1998 / Accepted 27 September 1998     

Constructing solutions of the navier-stokes equations for a fluid layer between moving parallel plates at low and moderate reynolds numbers

In this paper, we study exact solutions of the Navier-Stokes equations for a layer between parallel plates, the distance between which varies according to an arbitrary power law and whose boundary has a no-slip condition, are under study. A solution in the form of a power series of the Reynolds number is obtained. Comparison with the exact solutions is performed, and high accuracy of expansions for Reynolds numbers Re = 1–10 is shown. An accurate estimate of the error of the Reynolds thin layer approximation is obtained.     

End effects in magnetohydrodynamic channels at finite magnetic reynolds numbers

The effects of the magnetic Reynolds number have been examined via the distribution of the magnetic fields induced by the motion of a medium in a rectangular channel with conducting walls in the presence of an inhomogeneous magnetic field; the effects of wall conductivity and geometry of the external field are also examined as regards the distribution of the induced currents, the Joule loss, and the electric and magnetic fields over the cross section. The problem has previously been considered for a channel with insulating walls [1].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 19–27, May–June, 1971.We are indebted to A. B. Vatazhin for his interest.     

A mixed explicit-implicit antidiffusive method of navier-stokes equations for supersonic and hypersonic separated flows

The supersonic and hypersonic.laminar and turbulent vi-scous separated flows over two and three-dimensional com-pression corners are solved by the antidissipative explicit-implicit difference scheme presented in this paper.The re-sults obtained show that a high accuracy has been achieved bythis method and the time needed for computation is greatlyreduced.