Interaction of an elastic shell with two-dimensional flows of an ideal fluid

In [1, 2], Kiselev and Rapoport investigated the flow of a jet over an elastic plate and shell. In the present paper, the problem of two-sided flow past an elastic shell is investigated in the exact nonlinear formulation. At a sufficiently high rigidity and small curvature of the shell in undeformed state it is shown that the problem has a unique solution, and a method is proposed for finding it. Some results of calculations are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–143, September–October, 1981.     

Potential model of the coanda effect

Three schemes of potential flow around a convex contour are examined: free jet; in the presence of a jet-directing wall extending to the contour (without a gap); and in the presence of a jet-directing wall not extending to the contour (with a gap). It is assumed that the jet, not branching, flows around the contour and on one side. The existence and (with certain limitations) uniqueness of the solution of integral equations corresponding to the first two schemes are proved. Their analytic solutions are given for the case of a flow of a sufficiently thin jet around a circle. The first problem is calculated numerically in the entire region of the parameters. The scheme with a gap is examined for the case of flow around a half-plane. The problem of closure of the given potential models is dicsussed. In the case of the scheme without a gap the situation is typical for potential flow problems: The position of the separation point is a free parameter of the model. At the same time, in the presence of a gap (in particular, for the case of a free jet) the flow is determined completely by a system ofa priori assigned geometric parameters.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 10–22, July–August, 1978.The author is grateful to M. A. Gol'dshtik for attention to the work and discussion of the results.     

Jet flow around an elastic plate

An iteration method to solve a certain class of nonlinear plane jet problems of static hydroelasticity is proposed. The convergence of simple iterations is proved. The problem of the symmetric flow around an elastic plate is solved by the Kirchhoff scheme as an illustration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 35–42, July–August, 1976.The authors are grateful to G. Yu. Stepanov who supervised the present research.     

Solution to the problem of a swirling jet from an annular orifice

The problem of the propagation of a laminar immersed fan jet with swirling was considered in [1–3]. In [1], the jet source scheme was used to find a self-similar solution for a weakly swirling jet. An attempt to solve by an integral method the analogous problem for a jet emanating from a slit of finite size was made in [2]. In [3], the equations of motion for a jet with arbitrary swirling were reduced under a number of assumptions to the equations that describe the flow of a flat immersed jet. This paper gives the numerical solution to the problem of the propagation of a radial jet emanating with arbitrary swirling from a slit of finite size and an analytic solution for the main section of the jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 49–54, March–April, 1991.     

Formation of a region of interaction and of a wake with the instantaneous start of a plate in an incompressible liquid

The flow arising in an incompressible liquid if, at the initial moment of time, a plate of finite length starts to move with a constant velocity in its plane, is discussed. For the case of an infinite plate, there is a simple exact solution of the Navier—Stokes equations, obtained by Rayleigh. The case of the motion of a semiinfinite plate has also been discussed by a number of authors. Approximate solutions have been obtained in a number of statements; for the complete unsteadystate equations of the boundary layer the statement was investigated by Stewartson (for example, [1–3]); a numerical solution of the problem by an unsteady-state method is given in [4]. The main stress in the present work is laid on investigation of the region of the interaction between a nonviscous flow and the boundary layer near the end of a plate. In passing, a solution of the problem is obtained for a wake, and a new numerical solution is also given for the boundary layer at the plate.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 3–8, March–April, 1977.     

Coaxial turbulent jets with strong central blowing

The results of solving the problem of the initial section of isothermal coaxial jets with strong central blowing, when the transverse pressure gradient has only a slight effect and there is no circulation zone in the central jet are given. The problem is solved by the integral relation method with allowance for jet interference and the presence of a cocurrent flow. The results of an experimental investigation of these jets over a wide range of the geometric and regime parameters are also given. The results of the calculations made using the formulas obtained are compared with the experimental data.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 52–59, May–June, 1996.     

On the flow in underexpanded supersonic water jets

The problem of a supersonic water jet exhausting from a cylindrical nozzle in the underexpansion regime is solved. The calculations are made with allowance lor splitting. The distributions of the parameters over the jet are given. It is shown that the splitting region depends on the degree of underexpansion of the regime. The solution is found by the method of stabilization based on the difference scheme of Godunov, Zabrodin, and Prokopov [3] generalized to the case of flow with splitting.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 155–157, March–April, 1982.I thank G. A. Atanov for discussing the work.     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

Jet flow around a wedge-shaped stanchion intersecting a free space

A solution to the problem of a jet flow around a narrow wedge-shaped stanchion intersecting a free space is examined. The dimensions of the cavity formed behind the stanchion and the coefficient of resistance are determined. The results of the calculations are compared with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 140–143, July–August, 1976.     

On swirling jets

An exact solution to the Navier-Stokes equations is found for a jet emanating from the end of a vortex filament into a region filled with a fluid. Depending on the degree of swirling of the jet, a closed or open flow regime is realized. In the case of strong swirling, the solution is not unique. Approximate analytic solutions to problems as well as numerical solutions are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 26–35, January–February, 1979.I am grateful to M. Kh. Pravdin for the numerical calculations.     

A case of jet flow of a gravity fluid

The problem of plane steady ideal heavy fluid flow bounded by an impermeable polygonal section, a curvilinear arc section, and a finite section of free surface is investigated in an exact nonlinear formulation. Hydrodynamic singularities may exist in the stream. A large class of captation problems of jet theory reduces to studying this kind of flow. The unique solvability of the problem under investigation is proved for sufficiently large Froude numbers and small arc curvature. A method of solution is given and an example is computed. Such problems have been solved earlier by numerical methods [1–3]. Some problems about jet flows of a gravity fluid with polygonal solid boundaries have been investigated by an analogous method in [4, 5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–143, May–June, 1975.     

A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).     

Calculation of axisymmetric twisted and nontwisted turbulent jets

The article gives the results of calculations of non-self-similar flows in turbulent jets. Use is made of the approximation of a boundary layer [1-3]; in the case of a high degree of twisting, when a zone of reverse flow forms in the initial section, the consideration is begun in a cross section corresponding to the end of the above zone. With a numerical solution the flow parameters are determined consecutively in cross sections located downstream from the starting cross section, where they are given by the conditions of the problem. The article gives a generalized Prandtl formula for the turbulent viscosity for the cases of the flows under consideration. The results of calculations carried out using this formula are compared with experimental data. The corresponding experimental constants are determined. An integral theory is proposed describing twisted jet flows with a weak deformation of the profiles of the gas-dynamic parameters.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 71–80, May–June, 1972.     

Theoretical and experimental investigation of condensation in a centered rarefaction wave

The analysis of the process of spontaneous condensation in one-dimensional formulation is dealt with adequately in many papers. However, in reality supersonic flows are not one-dimensional. The most striking effect of two-dimensionality is manifested in two-phase flows, for example in nozzles, inclined sections of jet turbine grills and rarefaction waves. The investigation of these flows, both in the experimental and theoretical aspect, is a complex problem for which a solution has been found only recently. The results are given in this paper of a theoretical and experimental investigation of spontaneous condensation of water vapor in a centered rarefaction wave formed by flow around a protuberant angle by a hypersonic stream.Translated from Prikladnaya Mekhanika i Tekhnicheskii Fiziki, No. 5, pp. 117–122, September–October, 1971.     

Impact of a figure of revolution in a stream of incompressible fluid with separation of a jet

The impact interaction of bodies with a fluid in a flow with jet separation has been considered in [1–3], for example. This investigation was in the two-dimensional formulation. The present paper considers the three-dimensional problem of impact of a figure of revolution in a stream of an ideal incompressible fluid with separation of a jet in accordance with Kirchhoff's scheme. A boundary-value problem is formulated for the impact flow potential and solved by the Green's function method. A method for constructing the Green's function is described. Expressions are given for the coefficients of the apparent masses. The results are given of computer calculations of these coefficients in the case of a cone using the flow geometry of the corresponding two-dimensional problem.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 176–180, November–December, 1980.     

Thermal multipoles for a jet in ambient spathermal multipoles for a jet in ambient space

A general solution of the thermal problem for a non-self-similar axisymmetric jet is determined on the basis of the multiple approach developed for problems of non-self-similar jets in ambient space [1, 2], and several problems of convective heat-transfer in simply- or doubly-connected domains are solved. The advantage of expanding the solution of the convective heat conduction equation in eigenfunctions of the problem is demonstrated. As an illustration, the solutions for a thermal dipole and quadrupole and for a jet flow in a heated tube are presented. The corresponding solutions are also obtained for a turbulent jet in ambient space. The most favorable heat-exchange regime for a jet in a heated tube is predicted on the basis of the particular behavior of the eigenfunctions of the thermal problem.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 40–46, January–February, 1996.     

Numerical study of flows of a viscous compressible gas and of an equilibrium gas mixture in a flat nozzle in the presence of strong blowing

The problem of the interaction of a viscous supersonic stream in a flat nozzle with a transverse gas jet of the same composition blown through a slot in one wall of the nozzle is examined. The complete Navier-Stokes equations are used as the initial equations. The statement of the problem in the case of the absence of blowing coincides with [1]. The conditions at the blowing cut are obtained on the assumption that the flow of the blown jet up to the blowing cut is described by one-dimensional equations of ideal gasdynamics. The proposed model of the interaction is generalized to the case of flow of a multicomponent gas mixture in chemical equilibrium. The exact solutions found in [2] are used as the boundary conditions at the entrance to the section of the nozzle under consideration. The results of numerical calculations of the flows of a homogeneous nonreacting gas and of an equilibrium mixture of gases consisting of four components (H₂, H₂O, CO, CO₂) are given for different values of the parameters of the main stream and of the blown jet. In the latter case it is assumed that the effect of thermo- and barodiffusion can be neglected.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 55–63, July–August, 1974.     

Transverse flow of a rarefield gas around a plate

A method of characteristics is developed for the numerical solution of kinetic equations in the case of fully developed plane-parallel motions of a gas. A solution is given to the problem of flow around a plate arranged normal to an oncoming supersonic flow. The results of the calculations are in satisfactory agreement with existing experimental data.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 107–113, November–December, 1972.     

Effect of proximity of barrier on lifting force produced by vertical solid jets

The effect of proximity to the ground on the lifting force generated by a vertical solid jet is studied in connection with development of vertical takeoff and landing devices and of air cushion devices. Such a study was made in [1 ] for planar flow by an incompressible ideal fluid. There a generalization of the results obtained on a compressible fluid was made by the approximation method. In the present work the planar problem of streamline flow past a dihedral barrier of a gas jet emerging from a channel with parallel walls was solved by the Chaplygin-Fal'kovich method [2, 3], The results of [1, 4–9] follow as a particular case from the solution obtained. Calculations were carried out clarifying the effect of the proximity of a barrier and the lifting effect of a fluid on flow characteristics at subsonic speeds.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 123–131, September–October, 1971.     

Transonic flows around an airfoil in wind tunnels with porous walls

A study is made of two-dimensional transonic flows of gas around an airfoil in the working part of a wind tunnel with porous walls. The values of the flow parameters are determined by the numerical solution of a boundary-value problem for the equation of the velocity potential; this problem simulates the gas flow around the profile in the tunnel with porous walls. The obtained results are then used to construct an asymptotic theory of the influence of the wind-tunnel height and the Mach number M of the flow in it on the characteristics of the flow around the airfoil.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 99–107, September–October, 1980.