Three-dimensional separation in the neighborhood of roughness on the surface of an axisymmetric body

Steady-state viscous incompressible fluid flow past an axisymmetric slender body is considered at high Reynolds numbers in the regime with vanishing surface friction in a certain cross-section. In a small neighborhood of this cross-section interaction between the boundary layer flow and the external irrotational stream develops. In order to study the structure of the three-dimensional flow with local separation zones it is assumed that there is three-dimensional roughness on the surface of the body with the scale of the interaction zone. For this zone a numerical solution of the problem is obtained and its nonuniqueness is established. The surface friction line (limiting streamline) patterns with their inherent features are constructed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 67–79, May–June, 1995.Thus, on the basis of the asymptotic marginal separation theory it is possible to obtain fairly simple solutions describing flows with a complex surface friction line structure.     

Construction of a method for calculating a plane boundary layer in weak solutions of polymers with laminar,transitional, and turbulent flow zones

The investigation of the effect of small polymer additives on the characteristics of the flow of a viscous liquid is, at the present time, one of the most promising approaches to the lowering of the friction resistance. One interesting question in this connection is the study of the effect of small polymer additives on the characteristics of the transitional region of flow in a boundary layer, as well as on the value of the friction resistance with the presence of laminar, transitional, and turbulent sections in the boundary layer. The article sets forth a possible method for calculation of a plane boundary layer and the friction resistance for the case of the motion of a body in weak polymer solutions with a constant concentration, taking account of the change in the flow conditions in the layer and based on the use of integral relationships. Questions connected with the development of a boundary at a body, with the feeding of a polymer in it, as well as with the effect of degradation or destruction of the polymer in the solution, are not discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–48, May–June, 1977.     

Existence and nonuniqueness of local separation zones in viscous jets

The plane steady problem of the flow of a viscous wall jet past a smoothed break in the contour of a body is considered. For convenience, the flow in the neighborhood of the junction between two flat plates inclined at an angle to each other is chosen for study. As a result of the small extent of the region investigated the flow field is divided into two layers: the main part of the jet, which undergoes inviscid rotation, and a thin sublayer at the wall, which ensures the satisfaction of the no-slip condition. Particular interest attaches to the flow regime in which the solution in the sublayer satisfies the Prandtl boundary layer equations with a given pressure gradient. A similar problem was studied in [1–4]. The present case is distinguished by the structure of the free interaction region in a small neighborhood of the point of zero surface friction stress. By means of the method of matched asymptotic expansions, applied to the analysis of the Navier-Stokes equations, it is established that the interaction mechanism is that described in [5–7]. As a result, an integrodifferential equation describing the behavior of the surface friction stress function is obtained. A numerical solution of this equation is presented. The range of plate angles on which solutions of the equation obtained exist and, therefore, flows of this general type are realized is determined. The essential nonuniqueness of the possible solutions is established, and in particular attention is drawn to the possible existence of six permissible friction distributions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–45, January–February, 1986.The author wishes to thank V. V. Sychev and A. I. Ruban for their useful advice and discussion of the results.     

Three-dimensional turbulent boundary layer on a body of complex shape

Flow and heat transfer problems associated with three-dimensional compressible gas flow past a body of complex shape at a small angle of attack are investigated on the basis of a finite-difference calculation. The results of a numerical solution of the equations of the three-dimensional turbulent boundary layer are presented. The effect of the leading parameters on three-dimensional flow development and heat transfer is analyzed. The characteristic flow regions in the boundary layer are found: lines of divergence and convergence on the surface, separation zones and flow interfaces. The location of the maximum values of the heat flux and friction on the surface is determined, the behavior of the limiting streamlines on the body is described, and the intensity of the secondary flows in the boundary layer is estimated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 25–35, September–October, 1986.     

Aerodynamics of end-wall boundary layer in a vortex chamber

The need for the inclusion of end-wall boundary layers in the study of the aerodynamics of vortex chambers has been frequently mentioned in the literature. However, owing to limited experimental data [1–3] with reliable information on the wall layers, the existing computational methods for end-wall boundary layers are not well-founded. The question of which parameters determine the formation of end-wall flow remains debatable. In some studies [4, 5], the vortex chambers are conditionally divided into short and long chambers. However, there is no unique opinion on the role of end-wall flows in vortex chambers of different lengths. It has also not been established for what geometric and flow parameters the chamber could be considered long or short. In the present study, as in [1, 5–8], solution is obtained for the end-wall boundary-layer equations using integral methods, considering the boundary layer in the radial direction in the form of a submerged wall jet. Such an approach made it possible to use the laws for the development of wall jets [9], and obtain fairly simple relations for integral parameters, skin friction, mass flow in the boundary layer, and other characteristics. Results are compared with available experimental data and computations of others authors; turbulent flow is considered; results for laminar boundary layer are given in [10].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 117–126, September–October, 1986.     

Unsteady effects in weakly perturbed pulsatile channel flows

Pulsatile incompressible laminar flow in a plane channel with slight asymmetric deformation of the walls is considered on the basis of an asymptotic approach to the solution of the Navier-Stokes equations at large Reynolds numbers. It is shown that for extended deformations the change in the direction of the undisturbed flow in the wall regions is accompanied by a sharp increase in the amplitude of the perturbations; this is an essentially unsteady process. For flows with a small positive friction stress two classes of eigensolutions are obtained in the quasisteady approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 96–104, March–April, 1987.The author is grateful to V. V. Sychev and A. I. Ruban for a number of useful consultations in the course of the work.     

Computation of Gas–Dynamic Parameters and Heat Transfer in Supersonic Turbulent Separated Flows near Backward–Facing Steps

Computation results of plane turbulent flows in the vicinity of backward–facing steps with leeward–face angles = 8, 25, and 45° for Mach numbers M_infin = 3 and 4 are presented. The averaged Navier—Stokes equations supplemented by the Wilcox model of turbulence are used as a mathematical model. The boundary–layer equations were also used for the case of an attached flow ( = 8°). The computed and experimental distributions of surface pressure and skin friction, the velocity and pressure fields, and the heat–transfer coefficients are compared.     

The Falkner–Skan Wedge Flows of Power-Law Fluids Embedded in a Porous Medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.     

The motion of snow avalanches in the conditions of limiting friction

We investigate the equations of motion of large snow avalanches, and in contrast with [1–3] we take into account the fact that the dry friction can reach a critical value above which the snow in the avalanche or the underlaying material cannot sustain the friction. We find asymptotic solutions for long times after the beginning of motion. These solutions describe the avalanche motion in which a part of the snow moves in the conditions of limiting friction over a tilted plane with a uniform layer of snow. The equations which are used to find these asymptotic solutions have the property that for certain depths the flow velocity of small perturbations decreases with increasing depth. This is related to a number of unusual features (from the hydraulic point of view) of the solutions. In particular, on relatively gentle slopes two zones are formed in the avalanche: the forward part, with a large velocity and thickness of the moving layer, and the rear part, which is significantly slower and thinner. The two parts are separated by a narrow region characterized by a sharp decline in velocity and thickness of the moving layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 30–37, September–October, 1977.     

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.     

Roughness effects on turbulent plane wall jets in an open channel

This paper reports the effects of surface roughness on the mean flow characteristics for a turbulent plane wall jet created in an open channel. The velocity measurements were obtained using a laser Doppler anemometer over smooth and transitionally rough surfaces. The power law proposed by George et al. (2000) was used to determine the friction velocity. Both conventional scaling and the momentum–viscosity scaling proposed by Narasimha et al. (1973) were used to analyze the streamwise evolution of the flow. The results show that surface roughness increases the skin friction coefficient and the inner layer thickness, but the jet half-width is nearly independent of surface roughness.     

Boundary layer in the vicinity of the stagnation point of a body of axial symmetry in a turbulent stream

The flow in the boundary layer in the vicinity of the stagnation point of a flat plate is examined. The outer stream consists of turbulent flow of the jet type, directed normally to the plate. Assumptions concerning the connection between the pulsations in velocity and temperature in the boundary layer and the average parameters chosen on the basis of experimental data made it possible to obtain an isomorphic solution of the boundary layer equations. Equations are obtained for the friction and heat transfer at the wall in the region of gradient flow taking into account the effect of the turbulence of the impinging stream. It is shown that the friction at the wall is insensitive to the turbulence of the impinging stream, while the heat transfer is significantly increased with an increase in the pulsations of the outer flow. These properties are confirmed by the results of experimental studies [1–4].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 83–87, September–October, 1973.     

Two-phase couette flow

A study is made of plane laminar Couette flow, in which foreign particles are injected through the upper boundary. The effect of the particles on friction and heat transfer is analyzed on the basis of the equations of two-fluid theory. A two-phase boundary layer on a plate has been considered in [1, 2] with the effect of the particles on the gas flow field neglected. A solution has been obtained in [3] for a laminar boundary layer on a plate with allowance for the dynamic and thermal effects of the particles on the gas parameters. There are also solutions for the case of the impulsive motion of a plate in a two-phase medium [4–6], and local rotation of the particles is taken into account in [5, 6]. The simplest model accounting for the effect of the particles on friction and heat transfer for the general case, when the particles are not in equilibrium with the gas at the outer edge of the boundary layer, is Couette flow. This type of flow with particle injection and a fixed surface has been considered in [7] under the assumptions of constant gas viscosity and the simplest drag and heat-transfer law. A solution for an accelerated Couette flow without particle injection and with a wall has been obtained in [6]. In the present paper fairly general assumptions are used to obtain a numerical solution of the problem of two-phase Couette flow with particle injection, and simple formulas useful for estimating the effect of the particles on friction and heat transfer are also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 42–46, May–June, 1976.     

A computational investigation of unsteady turbulent wake–boundary-layer interaction

The relative motion of rotor and stator blade rows in a turbomachine generates periodically unsteady flow on the blades due to travelling wake perturbations. To better understand the attendant wake–boundary-layer interaction a calculation procedure was developed to model the behaviour of this complex unsteady flow. Due to nonlinear interactions with the boundary layer, the travelling discrete frequency wakes were found to decrease the velocity profile shape factor. For the range of reduced frequencies examined (=0.33–9.33) the skin-friction coefficient was found to be frequency dependent. The calculated results for both steady and unsteady velocity profiles, and for skin friction compared well with experimental data. Although the agreement between measured and calculated velocity phase shift was poor, in both experimental and model results the negative phase shift throughout the boundary layer due to the travelling-wave fluctuations has been captured.     

Calculation of accelerated motion of fluid in a tube

The results of calculation of accelerated flow of a fluid in a tube are compared with known experiments [1] in the laminar regime. The difference method was used to obtain a solution for unsteady axisymmetric flow that becomes steady over the length of the tube; this case was calculated earlier by Gromeka in the form of a series. An expression is derived for the coefficient of friction as a function of the Reynolds number Re and the acceleration of the fluid. The comparison reveals agreement between the results with an error not worse than 37%. However, the calculation gives a coefficient of friction proportional to Re to the power –1.5, whereas the experiment [1] reveals a weaker dependence proportional to Re to the power –1.15.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 158–160, September–October, 1981.     

Discontinuous solutions of an interacting three-dimensional hypersonic boundary layer

The paper is a mathematical study of the three-dimensional flow of viscous gas in a hypersonic boundary layer that develops along a flat wing whose leading edge has a step shape. The flow interacts with a flap on the wing set at a small angle. A linear solution to the problem is constructed under the assumption that the deflection angle of the flap is small and the difference between the length of the plates is of order unity. It is shown that an important part in the formation of the flow near and behind the flap may be played by the change in the pressure along the span of the wing due to the step shape of the leading edge. It is significant that although the pressure and displacement thickness are continuous functions of the transverse coordinate, the longitudinal and transverse components of the friction force have discontinuities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 19–26, March–April, 1991.I thank V. V. Sychev and A. I. Ruban for suggesting the problem, for valuable advice, and assistance.     

Adaptive computation of aeroacoustic sources for a rudimentary landing gear

We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case, the drag force on the rudimentary landing gear. Turbulent boundary layers are modeled using a simple wall‐layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we find good agreement in sound pressure levels, surface velocities, and flow separation. We also compare with detailed surface pressure experimental data where we find largely good agreement, apart from some local differences for which we discuss possible explanations. Copyright © 2013 John Wiley & Sons, Ltd.     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Holographic sensor for measurement of wall velocity gradients

Time-resolved measurements of skin friction and boundary layer turbulence are important to the design of more fuel efficient aircraft. In this paper we describe the design and testing of a holographic fan fringe sensor that can non-intrusively measure time-resolved velocity gradients near an aerodynamic surface. The holographic sensor produces a set of optical interference fringes inside the viscous sub-layer that form a fan rather than a linear array. Particles scattering light in the sub-layer produce a Doppler frequency that is a direct measurement of the velocity gradient and is proportional to aerodynamic shear stress and skin friction. The holographic recording condenses the optics necessary to form the fringes into a small 3–5 mm package, eliminates the need for optical access from behind the model, and produces a compact and robust sensor.     

Friction and heat transfer with simultaneous convection on a permeable surface

The velocity and heat transfer fields near a vertical permeable surface with simultaneous convection are investigated. A solution is found for the boundary layer equations with known laws of surface temperature and flow velocity change. The transformed boundary layer equations contain the parameter G/R², which determines the effect of free convection on friction and heat transfer for constrained motion. Calculations of friction and heat transfer as functions of draft (suction) with simultaneous convection are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 96–100, March–April, 1973.