Supersonic flow deceleration in plane and axisymmetric channels

Supersonic perfect gas flow in plane and axisymmetric channels with the same duct contour is studied on the basis of a numerical solution of the two-dimensional Navier-Stokes and Euler equations. The calculations were carried out at an inlet Mach number M_∞=4 for various Reynolds numbers and “bell-mouth“ half-angles. The effect of these parameters, as well as that of the flow three-dimensionality, on the flow pattern is demonstrated. In particular, the existence of viscous flow regimes providing the most effective supersonic flow deceleration and a higher degree of total pressure recovery as compared with the inviscid flow is established. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–152, March–April, 1998. The study was carried out with the support of the Russian Foundation for Fundamental Research (project No. 95-01-01129a).     

Dependence of the drag of a conical axisymmetric cavitation body on the cone angle and the cavitation number

Numerical investigations of flow past axisymmetric conical captation bodies have shown that the drag coefficient of the cavitation body, calculated from the maximum cross-sectional area of the cavity (midsection), depends on the cavitation number and the cone angle.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 170–173, May–June, 1995.In conclusion, the author is grateful to G. Yu. Stepanov whose critical remarks were helpful in making this paper more conclusive and more illustrative.     

Investigation of the flows in axisymmetric and plane divergent channels with preseparation boundary layers on their walls

The method of matched asymptotic expansions is used to develop a procedure for constructing separationless plane and axisymmetric diffusers for incompressible high-Reynolds-number flows with a given pressure distribution over the diffuser surface and minimum friction losses. The problem for the region of interaction between the boundary layer and the inviscid outer flow is numerically solved and the effect of variation of the on-design flow parameters in the entry section on the diffuser flow parameters is studied.     

Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: An axisymmetric problem

The paper studies the interaction of a rigid spherical body and a cylindrical cavity filled with an ideal compressible fluid in which a plane acoustic wave of unit amplitude propagates. The solution is based on the possibility of transforming partial solutions of the Helmholtz equation between cylindrical and spherical coordinates. Satisfying the interface conditions between the cavity and the acoustic medium and the boundary conditions on the spherical surface yields an infinite system of algebraic equations with indefinite integrals of cylindrical functions as coefficients. This system of equations is solved by reduction. The behavior of the system is studied depending on the frequency of the plane wave     

Calculation of cavity flows in an axisymmetric channel

The results are presented of a calculation of cavity flow in an axisymmetric channel with an annular obstacle. The problem was suggested to the author by G. B. Tsvetnov.The problem is solved by the method published in [1, 2].     

Profiling of plane and axisymmetric supersonic channels that realize discontinuous parameters at the exit and equalization of the flow

Supersonic channels realizing given nonuniform isentropic parameters at the exit section have been profiled numerically by Kraiko, Kireev, et al. [1–3]. The problem of profiling model channels to ensure a continuous isentropic flow at the exit in the case of a constant entropyS ₁ at the entrance was formulated by Kraiko and Shelomovskii [1]. In the present paper, two classes of supersonic channel are constructed. One of them realizes at the exit given discontinuous distributions of the entropy and the pressure p or the angle of inclination of the velocity vector w to the x axis. The other transforms a flow with discontinuous distributions of the gasdynamic parameters into a flow uniform with respect to p and . Schemes are proposed for the profiling of these classes of channels, and the results are given of calculations made by the classical method of characteristics and its layerwise modifications.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 155–159, May–June, 1984.We are very grateful to A. N. Kraiko for valuable discussions in preparing the material of the paper.     

Self-similar thermal boundary layers on plane and axisymmetric bodies

This paper proposes an approximate solution procedure for the prediction of the forced convection heat transfer through self-similar laminar boundary layers. The differential equations governing the viscous and thermal boundary layers have been reduced to a pair of algebraic equations for the boundary layer shape factor and the boundary layer thickness ratio. The local Nusselt number predicted under various pressure gradients turns out to be in excellent agreement with that of the exact solution over a wide range of the Prandtl number.     

Quasihomogeneous model of cavitation flows in diffuser channels

Starting with the experiments carried out by Reynolds in 1894, the flow in Venturi tubes has traditionally been used to study and demonstrate various forms of cavitation. Numerous authors have carried out experimental research on the various flow regimes in diffuser channels [1–7] or have investigated theoretical models of such flows [6, 8]. The occurrence and development of cavitation is closely associated with the phenomenon of turbulent separation complicated by the presence of two-phase flow in the dissipation zone. For a long time these effects were considered separately, until Gogish and Stepanov [9] proposed a single model of cavitation and separation based on the theory of intense interaction of an incompressible potential flow and a turbulent cavitation layer of variable density and embracing the various stages of cavitation. The object of this study is to demonstrate the possibilities of this model with reference to the simple example of flows accompanied by cavitation and separation in plane and axisymmetric diffuser channels of the Venturi tube type with straight and curved walls. The dissipative flow near the walls is described by a quasihomogeneous model of turbulent two-phase flow, in which the presence of two phases is taken into account only by varying the mean density. The potential core of the flow is considered in the one-dimensional formulation. The displacement thickness serves as the flow interaction parameter. The conditions of ocurrence and development of circulatory flows are determined. Examples of symmetrical and nonsymmetrical flows are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 47–54, September–October, 1986.     

Visualisation and les simulation of cavitation cloud formation and collapse in an axisymmetric geometry

Visualisation and Large Eddy Simulations (LES) of cavitation inside the apparatus previously developed by Franc (2011) for surface erosion acceleration tests and material response monitoring are presented. The experimental flow configuration is a steady-state closed loop flow circuit where pressurised water, flowing through a cylindrical feed nozzle, is forced to turn 90° and then, move radially between two flat plates towards the exit of the device. High speed images show that cavitation is forming at the round exit of the feed nozzle. The cavitation cloud then grows in the radial direction until it reaches a maximum distance where it collapses. Due to the complexity of the flow field, direct observation of the flow structures was not possible, however vortex shedding is inferred from relevant simulations performed for the same conditions. Despite the axisymmetric geometry utilized, instantaneous pictures of cavitation indicate variations in the circumferential direction. Image post-processing has been used to characterize in more detail the phenomenon. In particular, the mean cavitation appearance and the cavity length have been estimated, showing good correlation with the erosion zone. This also coincides with the locations of the maximum values of the standard deviation of cavitation presence. The dominant frequency of the ‘large-scale’ cavitation clouds has been estimated through FFT. Cloud collapse frequencies vary almost linearly between 200 and 2000 Hz as function of the cavitation number and the downstream pressure. It seems that the increase of the Reynolds number leads to a reduction of the collapse frequency; it is believed that this effect is due to the agglomeration of vortex cavities, which causes a decrease of the apparent frequency. The results presented here can be utilized for validation of relevant cavitation erosion models which are currently under development.     

Free-molecular gas flow in plane channels and grids

The problem of the flow of a rarefied gas in plane channels and grids in the free-molecular regime is considered. The parameters of the grid (channel) cells and the over-all geometrical dimensions of the grid are considered smaller than the mean free path of the molecules. The grid profiles are considered thin, the profile material is a perfect heat conductor. For the case of diffuse reflection of the molecules from the surface of the grid (channel), a calculation is made of the probability of passage of a molecule and the aerodynamic characteristics of the grid are determined.     

Effect of finite cavity width on flow oscillation in a low-Mach-number cavity flow

The current study is focused on examining the effect of the cavity width and side walls on the self-sustained oscillation in a low Mach number cavity flow with a turbulent boundary layer at separation. An axisymmetric cavity geometry is employed in order to provide a reference condition that is free from any side-wall influence, which is not possible to obtain with a rectangular cavity. The cavity could then be partially filled to form finite-width geometry. The unsteady surface pressure is measured using microphone arrays that are deployed on the cavity floor along the streamwise direction and on the downstream wall along the azimuthal direction. In addition, velocity measurements using two-component Laser Doppler Anemometer are performed simultaneously with the array measurements in different azimuthal planes. The compiled data sets are used to investigate the evolution of the coherent structures generating the pressure oscillation in the cavity using linear stochastic estimation of the velocity field based on the wall-pressure signature on the cavity end wall. The results lead to the discovery of pronounced harmonic pressure oscillations near the cavity’s side walls. These oscillations, which are absent in the axisymmetric cavity, are linked to the establishment of a secondary mean streamwise circulating flow pattern near the side walls and the interaction of this secondary flow with the shear layer above the cavity.     

Flow profiles in rectangular channels with gradually varying width

Summary We examine here the steady flow with constant discharge in an open channel of uniform bottom slope and with rectangular cross-section of uniformly increasing or decreasing width.The discussion of the dynamic differential equation of the gradually varied flow, using the theory of the singular point, permits us to describe the characteristics of the various flow profiles and also of the corresponding energy lines.This work was presented at the IX Convegno di Idraulica e Costruzioni Idrauliche, Trieste, May 1965.     

Nonlinear wave motions of a liquid in a vibrating axisymmetric cavity

The problem of the nonlinear wave deformation of the free surface of a liquid due to the translational motions of the containing vessel is examined. Bogolyubov's averaging method is used to investigate the characteristics of the wave motions of the liquid in the resonance zones in the case of a cylindrical vessel. Relations are obtained characterizing the variation of the amplitude of the circular wave with the frequencies of the external perturbations in the steady-state wave process; the conditions of occurrence and stability of such processes are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 120–125, May–June, 1989.     

Flow in the neighborhood of the cusp of an axisymmetric cavity

The steady-state axisymmetric potential flow of an ideal incompressible fluid is considered. The structure of the singularity at the point where the free stream surface leaves the axis of symmetry is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–176, September–October, 1989.     

Flow of gas mixtures with vibrational energy relaxation in plane and axisymmetric nozzles

A method is described for the calculation of plane and axisymmetric flows of gas mixtures with vibrational energy relaxation in the subsonic, transonic, and supersonic regions of the nozzle. The method is based on numerical solution of the inverse problem of nozzle theory. Results are given for the flow of a C0₂-N₂-H₂O-He mixture with vibrational relaxation and compared with the results of one-dimensional calculations. It is found that vibrational-energy relaxation has a significant effect on the gasdynamic parameters of flow in nozzles with large, relative expansion and therefore in choosing a nozzle shape, especially in the supersonic region, it is necessary to calculate the nonequilibrium flow. It is shown that the geometry of the transonic and supersonic regions of the nozzle has a considerable effect on the distribution of the inverse population of the level and the amplification factor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 125–131, September–October, 1977.     

Comparative analysis of viscous flows in cavities and channels containing axisymmetric obstacles

The flow past axisymmetric bodies of various shapes in expanding cavities and cylindrical channels is studied on the basis of a numerical solution of the Navier-Stokes equations. For each body shape velocity, pressure and shear stress distributions are obtained. These data are then used for the purposes of a comparative flow analysis in terms of body shape and Reynolds number. The properties characteristic of flows around bodies in channels and cavities with moving boundaries are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 60–66, May–June, 1988.     

On the shape of a slender axisymmetric cavity in a ponderable liquid

A solution is obtained to the equation for the shape of a slender axisymmetric cavity in a heavy liquid. The minimal cavitation numbers are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 133–136, November–December, 1979.I thank E. N. Kapankin, V. P. Karlikov, and Yu. L. Yakimov for interesting and helpful discussions of the work.