Supersonic flow past a blunt wedge

A study is made of the asymptotic solution of the problem of flow past a blunt wedge by a uniform supersonic stream of perfect gas. By separation of variables it is shown that at large distances the disturbance of the flow is damped exponentially. In the case of subsonic flow behind the shock wave the exponent of the leading correction term in the expansion of the shock front is calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–140, July–August, 1984.     

Flow past a thin wedge in a wind tunnel with partially perforated walls at high subsonic velocities

The problem of flow past a thin two-dimensional wedge at high subsonic velocity in a wind tunnel with partially perforated walls is considered for low suction flow rates. The solution of this model problem may be used in determining the optimal parameters of the suction system for which the aerodynamic characteristics in the tunnel are closest to those in an unbounded stream.In conclusion the author wishes to thank E. M. Kalinin for suggesting the study of this problem.     

Viscous instability of hypersonic flow past a wedge

Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 55–60, March–April, 1992.     

Flow of a viscous incompressible fluid of temperature dependent viscosity past a permeable wedge with uniform surface heat flux

 The effect of uniform suction on the steady two-dimensional laminar forced flow of a viscous incompressible fluid of temperature dependent viscosity past a wedge with uniform surface heat flux is considered. The governing equations for the flow are obtained by using suitable transformations and are solved by using an implicit finite difference method. Perturbation solutions are also obtained near the leading edge and in the downstream regime. The results are obtained in terms of the local skin friction coefficient and the rate of heat transfer for various values of the pertinent parameters, such as the Prandtl number, Pr, the velocity gradient parameter, m, the local suction parameter, ξ, and the viscosity variation parameter, ɛ. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The effect of ξ, m and ɛ on the dimensionless velocity profiles and viscosity distribution are also presented graphically for Pr = 0.7 and 7.0, which are the appropriate values for gases and water respectively. Received on 22 July 1999     

Effect of freestream nonequilibrium on flow past a wedge

We examine the effect of flow freezing in the nozzle of a hypersonic wind tunnel on the parameters of nonequilibrium flow past a wedge.Zhigulev's solution [1] for vibrational relaxation is extended to the nonequilibrium freestream case.It is shown that in this case the perturbations of the frozen-flow parameters behind the oblique shock wave can change sign if the flow in the working section deviates significantly from equilibrium.A method is proposed for converting experimental results obtained in tunnels with frozen flow to the case of equilibrium freestream flow past the body.The author wishes to thank O. Yu. Polyanskyi and V. P. Agavonov for their interest in this study.     

A scheme of developed cavitation flow past a wedge

A scheme is proposed for studying the symmetric steady flow with developed cavitation of an ideal incompressible and weightless fluid past a wedge in a channel. This scheme generalizes the existing schemes of cavitation flow past bodies and describes flow that is intermediate between the flow past obstacles in the Riabouchinsky and Efros schemes. Detailed calculations have been made for the drag coefficient and the cavity size in the case of a plate in an unbounded flow. The results of the calculations are tabulated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–170, January–February, 1983.I thank P. M. Ivanov, Kh. Kh. Kalazhokov, and T. Sokhov for assistance in the computer calculations.     

Symmetric cavitation flow past a wedge in the presence of a source on the wedge or in the flow

A solution is found to the problem of symmetric cavitation flow over a wedge by an ideal incompressible fluid (in accordance with Efros's scheme [1]) in the presence of a point source in the flow or on the wedge. Expressions are obtained for the forces exerted on the source and the wedge by the fluid, the conditions under which there is a negative resistance (thrust) are indicated, and the profiles of the free streamlines are constructed for different values of the flow parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 6, pp. 137–141, November–December, 1979.We thank L. I. Sedov for his interest in the work.     

MHD mixed convection for viscoelastic fluid past a porous wedge

A magnetic hydrodynamic (MHD) mixed convective heat transfer problem of a second-grade viscoelastic fluid past a wedge with porous suction or injection has been studied. Governing equations include continuity equation, momentum equation and energy equation of the fluid. It has been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. Solutions of wedge flow on the wedge surface have been obtained by a generalized Falkner-Skan flow derivation. Some important parameters have been discussed by this study, which include the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the magnetic parameter (M), the porous suction and injection parameter (C) and the wedge shape factor (β). Results indicated that elastic effect (E) in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a wedge. In addition, similar to the results from Newtonian fluid flow and conduction analysis of a wedge, better heat transfer is obtained with a larger G and Pr.     

Flow past a sphere in density-stratified fluid

Stratified flow past a three-dimensional obstacle such as a sphere has been a long-lasting subject of geophysical, environmental and engineering fluid dynamics. In order to investigate the effect of the stratification on the near wake, in particular, the unsteady vortex formation behind a sphere, numerical simulations of stratified flows past a sphere are conducted. The time-dependent Navier–Stokes equations are solved using a three-dimensional finite element method and a modified explicit time integration scheme. Laminar flow regime is considered, and linear stratification of density is assumed under Boussinesq approximation. The effects of stratification is implemented by density transport without diffusion. The computed results include the characteristics of the near wake as well as the effects of stratification on the separation angle. Under increased stratification, the separation on the sphere is suppressed and the wake structure behind the sphere becomes planar, resembling that behind a vertical cylinder. With further increase in stratification, the wake becomes unsteady, and consists of planar vortex shedding similar to von Karman vortex streets.     

Mixed convection boundary layer flow past a wedge with permeable walls

The effects of suction/injection on steady laminar mixed convection boundary layer flow over a permeable horizontal surface of a wedge in a viscous and incompressible fluid is considered in this paper. The similarity solutions of the governing boundary layer equations are obtained for some values of the suction/injection parameter f ₀, the constant exponent m of the wall temperature as well as the mixed convection parameter λ. The resulting system of nonlinear ordinary differential equations is solved numerically for both assisting and opposing flow regimes using an implicit finite-difference scheme known as the Keller-box method. Numerical results for the reduced skin friction coefficient, the local Nusselt number, and the velocity and temperature profiles are obtained for various values of parameters considered. Dual solutions are found to exist for the case of opposing flow.     

Influence of the hall effect on hypersonic flow past a wedge

This paper deals with the problem of the steady-state hypersonic flow of an inviscid compressible gas past a wedge. Inside the wedge a magnetic field is excited in a direction perpendicular to the generator. The flow in the region of perturbation is investigated on the basis of the ordinary equations of magnetohydrodynamics and Ohm's law, written for the case where the Hall effect is taken into account. The system of equations obtained has been solved numerically on a computer by the method of finite differences. The results show that for the given problem the Hall effect intensifies the magnetohydrodynamic action of the magnetic field on the flow. M. D. Ladyzhenskii [1] has also studied hypersonic flow past bodies from inside which a magnetic field is excited. He has investigated the influence of a strong magnetic field on the flow for the case where the Hall effect is neglected. The object of the present study is to determine the importance of the Hall effect.The author wishes to thank M. D. Ladyzhenskii for formulating the problem and discussing the progress of the work.     

Flow characteristics of slot jet impingement on a wedge

An experimental investigation is made to study the flow characteristics of slot jet impingement on a wedge whose included angle is 90 degrees. The aim of this investigation is to study the characteristics of the flow field near the wedge surface for various parameters. The different parameters like, jet velocity, slot width, distance of wedge vertex from the jet exit and the inclination of the wedge to jet axis are systematically varied to see their effect on the flow field. The flow field near the wedge vertex is similar to stagnation point flow. Far away from the vertex, the flow field is like that of wall jet. Near the vertex, very large variations of static pressure are observed in streamwise and transverse directions. This is due to large streamwise curvature and stagnation of flow. The transverse pressure gradient slowly decays in the streamwise direction, as a result, the velocity profiles are different from the similarity profiles of stagnation point flow and wall jet in the respective regions. Experiments are conducted for slot widths of 10 mm, 15 mm and 30 mm each for the distance between slot and wedge vertex of 80 mm, 120 mm and 240 mm. The static pressure and velocity profiles are measured by calibrated disk type static pressure probe and pitot tube respectively at various streamwise locations.Es wurde eine experimentelle Studie über die Strömmungscharakteristiken eines auf einem rechtwinkligen Keil auftretenden Spaltstrahls durchgeführt. Das Ziel dieser Untersuchungen ist die Studie des Strömungsverhaltens in Keilnähe, in Abhängigkeit verschiedener Parameter wie Strahlgeschwindigkeit, Spaltbreite, Entfernung der Keilspitze und Winkel zwischen Strahlachse und Keil. Diese Parameter werden systematisch variiert um deren Einfluß auf das Strömungsverhalten zu bestimmen. Die Strömung an der Keilspitze ist ähnlich der Staupunktströmung. Weit hinter der Spitze gleicht das Strömungsfeld dem eines auf einer Wand auftreffenden Strahls. In Nähe der Keilspitze sind die Änderungen des statischen Drucks in Strömungsrichtung und quer zur Strömung groß. Grund dafür sind die starke Krümmung der Strömung und die Stagnation der Strömung. Der Druckgradient in Querrichtung nimmt langsam in Strömungsrichtung ab, daher unterscheiden sich die Geschwindigkeitsprofile von den Ähnlichkeitsprofilen der Staupunktströmung und des Wandstrahls in den jeweiligen Bereichen. Die Versuche wurden für Spaltbreiten von 10, 15 und 30 mm und Keilentfernungen von 80, 120 und 240 mm durchgeführt. Der statische Druck und die Geschwindigkeitsprofile wurden mit kalibrierten scheibenförmigen Drucksonden bzw. einer Pitot-Sonde an verschiedenen Orten gemessen.     

Flow past a plate with a moving surface

On the basis of a numerical solution of the unsteady Navier-Stokes equations, the flow past a finite plate with an upstream-moving surface is investigated. For the Reynolds numbers Re =10²−10⁴, the flow past the plate is analyzed as a function of the relative plate surface velocity. On the basis of this analysis a limiting mathematical model of the flow as Re → ∞ is proposed.     

Boundary-layer flow of Reiner–Philippoff fluids past a stretching wedge

This paper presents a numerical analysis of the steady boundary-layer flow of a Reiner–Philippoff fluid induced by a 90° stretching wedge in a variable free stream. The governing partial differential equations are converted into a set of two ordinary differential equations by the use of a similarity transformation. The flow is therefore governed by a stretching velocity parameter λ and two non-Newtonian fluid parameters γ and μ₀. The variation of the skin friction, as well as other flow characteristics, as a function of the governing parameters is presented graphically and tabulated. A stability analysis has also been performed for this self-similar flow based on linear disturbances to the steady similarity solutions. The results presented in this paper reveal that there are no multiple (dual) solutions for the present problem and the unique solution is stable.     

Flow past a suddenly cooled horizontal plate

The problem of unsteady laminar, incompressible free convection above a horizontal semi-infinite flat plate is studied theoretically. It is assumed that for timet<0 the plate is hotter than its surroundings and at timet=0 the plate is suddenly cooled to the same temperature of its surroundings. Three solutions of the momentum and energy equations are obtained, namely

1. an analytical solution which is valid for small time,
2. an asymptotic analytical solution which is valid for large time, and
3. a numerical solution which matches these two limiting analytical solutions.

It is found that the numerical solution matches the small and large time solutions accurately. Finally, the variation of the velocity, temperature, skin friction and heat transfer on the plate with time are discussed.     

Flow of a simple non-newtonian fluid past a sphere

Summary Creeping flow past a sphere is solved for a limiting case of fluid behaviour: an abrupt change in viscosity.List of Symbols d _ij Component of rate-of-deformation tensor - F _d Drag force exerted on sphere by fluid - G ^(d) Coefficients in expression for _ij in terms of d _ij - G _YOJK ^(d) Coefficients in power series representing G ^(d) - R Radius of sphere - r Spherical coordinate - V Velocity of fluid very far from sphere - v _i Component of the velocity vector - x Dimensionless radial distance, r/R - x _i Rectangular Cartesian coordinate - Dimensionless quantity defined by (26) - ^(d) Potential defined by (7) - Value of x denoting border between Regions 1 and 2 as a function of - ₁, ₂ Lower and upper limiting viscosities defined by (10) - Spherical coordinate - * Value of for which =1 - Value of denoting border between regions 1 and 2 as a function of x - Newtonian viscosity - _ij Component of the stress tensor - Spherical coordinate - ₁, ₂ Stream functions defined by (12) and (14) - Second and third invariants of the stress tensor and of the rate-of-deformation tensor, defined by (3)