Showing papers in "Fluid Dynamics in 1982"

Asymptotic theory of short separation regions on the leading edge of a slender airfoil

Abstract: The two-dimensional flow of a viscous incompressible fluid near the leading edge of a slender airfoil is considered. An asymptotic theory of this flow is constructed on the basis of an analysis of the Navier—Stokes equations at large Reynolds numbers by means of matched asymptotic expansions. A central feature of the theory is the region of interaction of the boundary layer and the exterior inviscid flow; such a region appears on the surface of the airfoil in a definite range of angles of attack. The boundary-value problem for this region is reduced to an integrodifferential equation for the distribution of the friction. This equation has been solved numerically. As a result, closed separation regions are constructed, and the angle of attack at which separation occurs is found.

Asymptotic theory of separation flows

Abstract: A review is given of the results of theoretical investigations of the separation of laminar and turbulent boundary layers in an incompressible fluid obtained on the basis of matched asymptotic expansions valid at large Reynolds numbers (Re). The global picture of the separation flow behind a body of finite size as Re → ∞ is investigated.

Singular solution of boundary layer equations which can be extended continuously through the point of zero surface friction

Abstract: It is shown that the Prandtl equations for an incompressible boundary layer admit a solution which can be extended continuously through the point of zero friction on the surface and is singular at this point. A solution of this type is realized, in particular, at the leading edge of a slender profile at an angle of attack to the oncoming flow.

Convective instability of a fluid in a vibration field under conditions of weightlessness

Abstract: The problem of the convection and convective instability of a fluid in a high-frequency vibration field under conditions of weightlessness was formulated in an earlier paper of the authors [1]. In the present paper, the conditions of equilibrium are discussed and the boundaries of vibration instability are determined for some equilibrium states: a plane layer of fluid with transverse temperature gradient and arbitrary direction of the vibration, a cylindrical layer with radial gradient and longitudinal direction of the vibration, and an infinite circular cylinder with transverse and mutually perpendicular directions of the temperature gradient and the vibration axis.

Study of internal waves in the case of rapid horizontal motion of cylinders and spheres

Abstract: A sphere and a cylinder are simulated by mass sources distributed over their surfaces, and expressions are obtained for the wave resistance of such sources moving horizontally in an exponentially stratified fluid. It is shown that then, in contrast to the case of simulation of such bodies by point dipoles, the paradox of an infinite wave resistance does not arise. Different variants of the method of equivalent sources are discussed.

Theoretical and experimental investigation into the structure of supersonic flow past bodies of star-shaped form and their aerodynamic characteristics

Abstract: The results are given of a theoretical and experimental investigation into supersonic flow over bodies with star-shaped transverse section and flat faces having an equivalent circular cone of elongation 1.3 as a function of the number of “petals” of the star-shaped body and the interior radius at its midsection. Data are given on the coefficient of wave drag of such bodies, and the total drag calculated using a semiempirical theory is compared with the results of weight measurements.

Stability of preseparation boundary layer on the leading edge of a thin airfoil

Abstract: Numerous experiments on subsonic flow of gas past thin wing profiles (see the reviews [1, 2]) have shown that the flow near the leading edge of an airfoil is separationless only at angles of attack less than a certain critical value, which depends on the shape of the airfoil. If the angle of attack reaches the critical value, a closed region of recirculation flow of small extension is formed on the upper surface of the airfoil. Under ordinary flow conditions, the boundary layer on the leading edge of the airfoil remains laminar in the entire preseparation range of angles of attack. However, the appearance of the closed separation region is, as a rule, accompanied by transition from a laminar to a turbulent flow regime. Moreover, generation of turbulence is observed precisely in the flow separation region. The present paper is devoted to a study of the stability of the boundary layer on the leading edge of a thin airfoil in a flow of incompressible fluid. The case when the angle of attack of the airfoil relative to the oncoming flow differs little from the critical value is considered.

Numerical investigation of separated flow in front of a spiked cylinder

Abstract: The problem of axisymmetric flow of a perfect heat conducting gas over a cylinder from the front of which a spike projects is solved at subsonic and supersonic velocities of the oncoming flow in the model of a viscous fluid. The formation and development of the flow separation due to the spike ahead of the front surface of the cylinder is investigated. The change in the gas-dynamic and geometrical parameters of the separated flow is studied as a function of the Mach and Reynolds numbers of the oncoming flow. The obtained results are compared with the available experimental data.

Influence of turbulence on the formation of high nonequilibrium concentrations of atoms and free radicals in diffusion flames

Abstract: In the description of chemical reactions between previously unmixed reacting substances, it is frequently assumed that the reaction rate is very large, so that thermodynamic equilibrium is realized at every point of the flow. This assumption makes it possible to reduce the solution of the problem to the description of the concentration field of the inert (not reacting) component. However, in a number of cases such an assumption is inadequate. A characteristic example is provided by the formation of the oxides of nitrogen. In this case, small deviations from equilibrium in the temperatures and concentrations of the main combustion products lead to a large change in the concentrations of the free atoms and radicals [l], with the consequence that the nitrogen oxidation rate changes strongly. Similar problems arise in the analysis of the ignition of fuel by a jet of combustion products. The list of such examples can be extended. Since reactions in a turbulent flow have the main interest, it is natural to consider how the characteristics of turbulence influence the deviations from thermodynamic equilibrium. The present paper is devoted to examination of this question.

Aerodynamic characteristics of star-shaped bodies at Mach numbers M = 3–5

Abstract: The results are given of an experimental investigation into the aerodynamic characteristics of star-shaped bodies with flat faces at Mach numbers M = 3–5 and angles of attack α = 0–12 ° for different numbers of points of the star and different inner radii at the midsection. It is established that the star-shaped bodies have a much lower total drag than bodies of revolution of equivalent length and midsection area.

Turbulent separation flows

Abstract: Turbulent separation flows arise when objects move in the oceans and in the atmosphere, and also when a liquid or gas flows past elements of the Earth's relief, technological and industrial plant, and constructional elements. Therefore, problems of turbulent separation flows cover the entire range of velocities of continuum motions and under such varied boundary conditions that the forms, properties, and manifestations of turbulent separation are inexhaustible. The aim of the present paper is to discuss the available results and the possibilities for further development of computational models of turbulent separation flows. The somewhat nominal classification of such models given in the paper reflects essentially the sequence of their historical development.

An approximate method of determining the vorticity in the separation region as the viscosity tends to zero

Abstract: In accordance with the Prandtl—Batchelor theorem, the vorticity in a separation region is constant in a laminar flow with vanishingly small viscosity. Batchelor proposed that the vorticity should be determined by matching the inviscid flow and the boundary layer at the edge of the separation region. An approximate method is constructed and, under a number of simplifying assumptions, used to consider a flow with a separation region in a rectangular trough.

On the part played by the local pressure gradient in forming the flow in a corner

Abstract: Special experiments were made in the subsonic low-turbulence wind tunnel T-324 of the Institute of Theoretical and Applied Mechanics of the Siberian Branch, USSR Academy of Sciences with the aim of making a more detailed study of the conditions of occurrence of transverse flows in the case of laminar flow along a corner. The velocity U∞ of the undisturbed flow was varied from 2.3 to 5.5 m/sec [Re1 = (1.5–3.5) · 105 m−1].

Some problems of axisymmetric cavitation flows

Abstract: The equations for the shape of a slender axisymmetric cavity [1–3] are used to consider problems relating to pulsations of the cavity shape, the drag of a slender cavity-forming body, and the influence of surface tension on the shape of a steady cavity.

Drag of a flat wedge in a two-phase flow

Abstract: The drag of a flat wedge in a subsonic two-phase flow is investigated. In contrast to earlier work of Balanin and Zlobin [1] particular attention is devoted to the influence of the particle size. Detailed investigations are made of the dependences of the forces and aerodynamic coefficients on the concentration of the solid phase, the opening angle of the wedge, and the particle size. It is established that the drag coefficients depend on the particle size only for particles with diameters less than 30 um.

Displacement of oil by a slug of an active additive forced by water through a stratum

Abstract: The paper gives a solution to the problem of the displacement of oil by a slug for different forms of the sorption isotherm and the distribution function of the additive between the phases and for different values of the initial flooding of the stratum. The process is considered under conditions of reversible sorption and also under conditions of partial retention of the additive by the skeleton of the porous medium. The behavior of slugs in the case of cyclic pumping of a solution of an active additive is investigated.

Influence of acoustics and the flow regime in the boundary layer on nozzle walls on the mixing layer of an immersed jet

Abstract: Experimental determinations were made of the width of the mixing layer and the level of turbulent pulsations in the initial section of a subsonic circular immersed jet for different parameters of the boundary layer on the nozzle walls and in the presence of acoustic excitation. It was established that the rate of expansion of the turbulent mixing layer depends on the flow regime in the boundary layer. For laminar initial boundary layer, external acoustic excitation can lead to a decrease in the expansion velocity of the mixing layer and of the intensity of the velocity pulsations on the jet axis within the initial section. If the frequency and amplitude of acoustic excitation at which a decrease in the rate of expansion of the mixing layer and of the pulsation intensity was observed remained unchanged, the influence of the acoustics disappeared when the boundary layer became turbulent. The acoustic vibrations influenced the subsonic jets by generating vortex perturbations when they interact with the edge of the nozzle.

Rotating cylinder in a flowing viscous incompressible fluid

Abstract: New results are obtained in the problem of flow of a viscous fluid past a rotating cylinder by numerical solution of the Navier—Stokes equations for Reynolds numbers 10 ⩽ Re ⩽ 100. The drag and lift have been calculated. The oscillatory flow regime in the wake behind a fixed cylinder is investigated for Re = 80. The Strouhal number for auto-oscillations is 0.16.

Electrode region of a weakly ionized plasma in chemical equilibrium

Abstract: The paper is devoted to an analysis of the wall (electrode) region of disturbance of the electric parameters of a weakly ionized plasma, i.e., the region in which the concentrations of the charged particles and the values of the electric field change from the distributions corresponding to the conditions in the undisturbed plasma to the values determined by the boundary conditions on the wall.

Numerical investigation of the expansion of a cloud of dispersed particles or drops under the influence of an explosion

Abstract: The results are given of a numerical investigation into the expansion of clouds of fine disperse particles or drops suspended in air under the influence of a blast wave. Two possible situations are simulated: an explosion in front of a cloud and an explosion in the region of a cloud (explosion with simultaneous formation of a drop region behind the shock front). The influence that the determining parameters have on the range and extension of the expansion zone is analyzed, and the results of the numerical experiments are generalized by means of empirical dependences.

A method for deriving hydrodynamic equations for complicated systems

Abstract: A general algorithm is proposed for constructing a uniformly valid asymptotic solution of the kinetic equations under conditions when the number of slowly varying macroscopic variables is greater than the number of integral invariants of the collision operator. The case of a chemically reacting gas mixture is considered, and a method for constructing the asymptotic solution for this case is described. The hydrodynamic equations for reacting and relaxing gas mixtures are described in general form and it is noted that consistent allowance for the disequilibrium of the reaction and relaxation processes leads to the appearance in the hydrodynamic equations of a number of additional terms, which describe the dependence of the rates of these processes on the spatial derivatives of the hydrodynamic variables.

Nonstationary waves in a film of viscous liquid

Abstract: A numerical investigation is made of the development of initial perturbations in a thin film of viscous liquid. It is shown that the resulting wave structure passes through complicated intermediate shapes such as solitons in which there are elevations and depressions of the surface, At large times, a wave regime is formed that is close to the optimal regime with respect to the wave number. The picture of the intermediate wave forms depends on the initial data, while the final result of the development depends weakly on the initial data.

Development of the boundary layer on a plate in a rotating system

Abstract: A numerical investigation in the approximation of boundary layer theory has been made of the development of the flow near the surface of a rotating plate in a two-dimensional flow with rectilinear streamlines perpendicular to the leading edge in a rotating coordinate system attached rigidly to the plate. In an earlier investigation [1] using the approximate method of integral relations, Kurosaka obtained and described quantitatively a transition from a Blasius boundary layer to an Eckmann boundary layer in the form of three-dimensional oscillations. The solution described in the present paper confirms the oscillatory nature of the development of the boundary layer, but the quantitative results differ strongly from Kurosaka's.