Spatial flow regimes around a curved surface

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 87–93, January–February, 1989.     

Calculation of flow of highly attenuated gas around a body,taking into account interactions with the surface

The results of Monte Carlo calculations are given for the aerodynamic characteristics of different bodies in free-molecular and near-free-molecular conditions. The calculations are made for different models of the interaction between the attenuated-gas flow and the surface of the body. Analysis and comparison of the results obtained with available experimental and natural data serves as the basis for a discussion of the applicability of individual parameters of these models in practical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 117–123, September–October, 1978.It remains to thank M. N. Kogan, V. A. Perepukhov, A. I. Erofeev, A. I. Bunimovich, L. L. Zvorykin, A. A. Pyarnpuu, and V. F. Kameko for discussions of the results and for valuable comments.     

Supersonic flow around a large body in an exponential atmosphere

The problem of axisymmetric supersonic flow around a large body is solved in the case when the body is moving at constant velocity in an exponential atmosphere. The nonsteady conditions in the incoming flow are characterized by the Strouhal number. From numerical solutions for different Strouhal numbers, the deviation of the flow from quasisteady conditions is investigated.Translated from Izvestiya Akdemii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 158–161, May–June, 1978.It remains to thnak G. I. Petrov for supervising the work and for discussing the results.     

On superposed small deformations on a large deformation of an elastic Cosserat surface

Within the scope of the theory of a Cosserat surface, this paper is concerned with small deformations superposed on a large deformation in elastic shells and plates together with some related aspects of the subject. Special attention is given to problems of stability and vibrations of initially stressed isotropic plates.

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Résumé Dans le cadre de la théorie d'une surface de Cosserat, le présent rapport étudic, pour des plaques et coques élastiques, de petites déformations superposées à une grande déformation, ainsi que certains aspects connexes du sujet. Une attention particulière est accordée aux problèmes de stabilité et de vibrations de plaques isotropiques initialement sous tension.

     

Calculation of the breakaway flow of a flat stream of a nonviscous liquid around bodies

The article gives relationships which, within the framework of the theory of an ideal liquid, permit calculating breakaway flow around bodies of arbitrary form. It gives examples of the calculation, by numerical methods using a digital computer, of the flow of a flat stream around a round cylinder and a flat plate. The results obtained are in agreement with the experimental data in the self-similar region.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 72–82, March–April, 1972.     

Calculation of supersonic flow around v-shaped wings by the fitting method

The problem of flow around a V-shaped wing with supersonic leading edges is solved. The method employed is that of fitting with respect to a space variable in which the system of equations of motion is hyperbolic, using the computing scheme of V. V. Rusanov, A comparison between the results of these calculations and experimental data in relation to the pressure distribution along the wing span reveals excellent agreement, except for a limited region, in which the compression jump incident on the plane of the wing interacts with the boundary layer. A comparison between the results obtained by means of the oblique-jump equations and by numerical calculations indicates that the method in question is reasonably accurate.Translated from Izvestiya Akademu Nauk SSSE, Mekhanika Zhidkosti i Gaza, No. 3, pp. 180–185, May–June, 1971.The author is grateful to A. L. Gonor and V. V. Rusanov for interest in this work.     

Simulation of three-dimensional unsteady viscous free surface flow around a ship model

We present here a numerical method for solving the free surface flow around a ship at forward speed in calm water. The fluid is assumed to be Newtonian and the Reynolds-averaged Navier-Stokes equations are solved by a finite difference method. Modelization of turbulence is achieved by the algebraic model proposed by Baldwin and Lomax. Fully non-linear free surface conditions are satisfied in the model and a method to avoid the incompatibility between free surface conditions and no-slip conditions at the waterline is proposed. Numerical results obtained for a Wigley hull are compared with experimental results.     

Calculation of separated flow around multi-element aerofoils using conformal mapping

A method is presented to calculate the low-speed incompressible separated flow around multi-element aerofoils. The geometries of multi-element aerofoils in the physical plane are completely arbitrary and are transformed into multiple circles in the computational plane by a conformal mapping technique. Jacob's model, which distributes sources on the separated surfaces of multi-element aerofoils to simulate the effects of separation, is adopted here. The position of the separated point and the pressure on the surfaces of multi-element aerofoils are calculated by iteratively coupling the potential flow and boundary layer. The effects of the boundary layer are simulated by modification of the boundary condition. All iterative procedures converge rapidly as a result of using the fast Fourier transform (FFT) technique.     

Small deformations superposed on large deformations of an elastic-plastic material

In the context of a purely mechanical rate-type theory of plasticity, and utilizing a strain space formulation, an infinitesimal theory is developed for motions superposed on any given motion of an elastic-plastic material. The given motion may involve all forms of elastic-plastic deformation, including both loading and unloading, and in addition, the loading conditions are allowed to change due to the superposed motion. The infinitesimal theory is properly invariant under arbitrary finite superposed rigid motions.     

Computation of high Reynolds number flow around a circular cylinder with surface roughness

Incompressible high-Reynolds-number flows around a circular cylinder are analyzed by direct integration of the Navier-Stokes equations using finite-difference method. A generalized coordinate system is used so that a sufficient number of grid points are distributed in the boundary layer and the wake. A numerical scheme which suppresses non-linear instability for calculations of high-Reynolds-number flows is developed. The computation of an impulsively started flow at Re = 1200 is compared with corresponding experimental observations, and excellent agreements are obtained.A series of computations are carried out on the flow around a circular cylinder with surface roughness. The height of the roughness in these computations is 0.5% of the diameter. The range of Reynolds numbers is from 10³ to 10⁵; no turbulence model is employed. Sharp reduction of drag coefficient is observed near Re = 2 × 10⁴, which indicates that the critical Reynolds number is captured in the present computation.     

Calculation of the flow around wings of arbitrary planform over a wide range of angles of attack

A numerical method is described for the calculation of the distributed and total aerodynamic characteristics of a thin wing of any planform. We use only the generally accepted hypotheses-smoothness of flow around the wing and the Chaplygin-Zhukovskii condition of finite velocity at the trailing edges. The medium is considered ideal and incompressible.The development of a nonlinear theory for the wing of small aspect ratio in a compressible medium is one of the most important and difficult problems of wing theory. It has long attracted the attention of the aerodynamiscists. Chaplygin touched on this question in his 1913 report On the vortex theory of the finite span wing, presented to the Moscow Mathematical Society. Several interesting ideas and schemes were proposed by Golubev (see, for example, [2]). The first adequately correct and effective attempt to determine theoretically the nonlinear variation of wing normal force with angle of attack was that of Bollay [3]. In this work he studied rectangular wings of very small aspect ratio. The circulation variation law along the span was taken to be constant, and along the chord it was taken the same as for a flat plate of infinite span. It was also assumed that the centerlines of the free vortices trailing from the wing tips are straight lines and form the same angle with the plane of the wing. The magnitude of this angle was calculated from the average value of the relative velocity. The boundary condition at the wing was satisfied at a single point.In several later studies [4–8] attempts have been made to extend this approach somewhat. In [7] the circulation variation law along the wing chord is calculated, and the boundary conditions are satisfied more exactly. However, attempts to convert to the study of wings of more complex planform, when the circulation can no longer be considered constant along the span, are hydrodynamically incorrect [5, 6, 8]. In these studies schemes are used in which with smooth flow around the wing the free vortices stand off from the wing surface. The angles which the vortex centerlines form with the wing surface are assumed or are calculated on the basis of very arbitrary hypotheses.In the present paper the vortex layer which simulates the wing surface, just as in the linear theory [9, 10], is replaced by a system of discrete vortices. The free vortices away from the wing then are discrete curvilinear vortex filaments. Each of them is replaced by a series of rectilinear vortex segments. The number of bound and free discrete vortices may be increased without limit. The position of the free vortex segments is determined in the computation process, which is carried out sequentially for a series of angles of attack , beginning with 0 when the linear theory scheme holds. We note that the question of accounting for the effect of the leading-edge free vortex sheet is not considered here, although the method described may also be used to obtain results for this problem.The proposed method turned out to be very general, flexible and convenient for the digital computer. It permits studying the practical convergence of the solution, and also permits obtaining not only the total and distributed characteristics of the wing of arbitrary planform, but also studying such delicate questions as the rollup of the vortex sheet behind the wing.The author wishes to thank O. N. Sokolov and T. M. Muzychenko for the example calculations.     

Circulation flow around airfoils by a steady plane-parallel flow of a heavy liquid of finite depth with a free surface

Steady problems of a circulation flow around bodies by a flow of a heavy liquid bounded by a free surface and a straight bottom are solved. The method of complex boundary elements is used, which is based on the integral Cauchy formula written for a complex-conjugate velocity. Results of numerical calculations of the flow around a circular contour and the Joukowski airfoil are presented. Shapes of the free surface and the most important hydrodynamic characteristics of the process (velocity circulation over the airfoil and the lifting force and its moment relative to the sharp edge of the airfoil) are given. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 101–110, May–June, 2000.     

On the influence of buoyancy on the surface tension driven flow around a bubble on a heated wall

The surface tension driven flow in the liquid vicinity of gas bubbles on a heated solid wall has been investigated both, in a reduced gravity environment aboard a sounding rocket, and in an earth-bound experiment. Both experiments deal with temperature gradients within the liquid surrounding of a bubble which cause variations of the surface tension. These, in turn, lead to a liquid flow around the bubble periphery termed thermocapillary or thermal Marangoni-convection. On Earth, this phenomenon is widely masked by buoyancy. We therefore carried out an experiment under reduced gravitational acceleration. In order to simultaneously observe and record the flow field and the temperature field liquid crystal tracers have been applied. These particles offer the feature of selectively reflecting certain wavelengths of incident white light depending on the crystals temperature. Although the bubble injection system did not perform nominally during the flight experiment, some interesting flow characteristics could be observed. Comparison of results obtained in microgravity to data measured on Earth reveal that due to the interaction of thermocapillarity and buoyancy a very compact vortex flow results on ground, while in microgravity the influence on the surface tension driven flow penetrates much deeper into the bulk. This result is of special interest regarding the production of materials in space. Dedicated to Professor Dr. Julius Siekmann on the occasion of his 70th birthday The work described herein was supported by the German space agency DARA (Deutsche Agentur für Raumfahrtangelegenheiten GmbH) through DARA Grant 50 WM 9434. The authors thank the European Space Agency (ESA) for the opportunity to conduct the TEXUS 33 sounding rocket experiment. The flight hardware has been partly built by Daimler-Benz-Aerospace which is gratefully acknowledged. Also, the authors are indebted to Mr. H.-H. Wolf for his careful evaluation of the particle images