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 in the neighborhood of the stagnation point of an axisymmetric wake

The solutions of the equations of parabolic type describing the development of the flow in an axisymmetric wake under the Influence of viscosity and an adverse pressure gradient are considered. It is then shown that in the general case in the neighborhood of the stagnation point on the axis of the wake the solution is a singular one, the possibility of its continuation beyond the stagnation point being excluded. The following solutions are also obtained: a regular solution in the neighborhood of the stagnation point and a singular solution continuable downstream. This singular solution is the limit for the class of regular solutions having a miniumum in the velocity distribution on the axis as the minimum velocity tends to zero.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 53–59, March–April, 1986.The author is grateful to V. Ya. Neiland and Vik. V. Sychev for discussing the results and offering useful advice.     

Determining the shape of an axisymmetric body in a viscous incompressible flow on the basis of the pressure distribution on the body surface

A method is developed for determining the shape of an axisymmetric body on the basis of the pressure coefficient distribution specified along the meridional section of the body. Viscosity is taken into account within the framework of the boundary layer model. The method is based on an iterative process, which involves the solutions of the inverse problem in the plane case and of the direct problem for an axisymmetric body. A code implementing the iterative process is written, and examples of numerical results are given.     

Three-dimensional laminar boundary layer on a permeable surface in the neighborhood of a symmetry plane

Analytical and numerical methods are used to investigate a three-dimensional laminar boundary layer near symmetry planes of blunt bodies in supersonic gas flows. In the first approximation of an integral method of successive approximation an analytic solution to the problem is obtained that is valid for an impermeable surface, for small values of the blowing parameter, and arbitrary values of the suction parameter. An asymptotic solution is obtained for large values of the blowing or suction parameters in the case when the velocity vector of the blown gas makes an acute angle with the velocity vector of the external flow on the surface of the body. Some results are given of the numerical solution of the problem for bodies of different shapes and a wide range of angles of attack and blowing and suction parameters. The analytic and numerical solutions are compared and the region of applicability of the analytic expressions is estimated. On the basis of the solutions obtained in the present work and that of other authors, a formula is proposed for calculating the heat fluxes to a perfectly catalytic surface at a symmetry plane of blunt bodies in a supersonic flow of dissociated and ionized air at different angles of attack. Flow near symmetry planes on an impermeable surface or for weak blowing was considered earlier in the framework of the theory of a laminar boundary layer in [1–4]. An asymptotic solution to the equations of a three-dimensional boundary layer in the case of strong normal blowing or suction is given in [5, 6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–48, September–October, 1980.     

Hypersonic perfect-gas flow past an axisymmetric blunt body with a narrow groove in its frontal surface

The features of the flowfield and heat transfer on the surface of an axisymmetric body with a narrow groove in its nose immersed in a hypersonic perfect-gas stream (M_∞=6.1) are studied on the basis of a numerical analysis of the two-dimensional Navier-Stokes equations. The calculations are performed for both thermally insulated and isothermal surfaces having grooves of different width. The calculated results are compared with experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 117–124, January–February, 2000. The study was carried out with the support of the International Scientific and Technical Center (project No. 036).     

Control of vortex shedding in an axisymmetric bluff body wake

In the present experimental study the effect of a control disc mounted at the rear of an axisymmetric blunt-based body of revolution, first studied by Mair, is investigated in the Reynolds number range 3×10³≤Re_D≤5×10⁴ . As the distance of the control disc from the blunt base is increased, four vortex shedding regimes are identified: at small distances there is no effect, then a sharp increase of vortex shedding activity and total drag is observed, followed by an interval with reduced activity and drag and finally at large distances a regime where the flow around the main body and disc become essentially independent, i.e. where the drag forces of the two elements become additive. The near and far wake velocity fields corresponding to the different regimes are documented with time- and phase-averaged hot-wire and LDA measurements, with spectral analysis of the data and with flow visualizations of the near wake. The results are used to develop an improved understanding of the instability mechanism leading to high vortex shedding activity.     

Nonuniqueness of the solution of the problem of viscous interaction on an axisymmetric body

The article discusses solutions of the equations of the hypersonic boundary layer on an axisymmetric offset slender body (with a power exponent equal to 3/4), taking account of interactions with a nonviscous flow. It is shown that, in this case, the equations of the boundary layer have solutions differing from the self-similar solution corresponding to flow around a semi-infinite body. The solutions obtained are analogous to solutions for a strong interaction on a plate with slipping and triangular vanes [1–4], but are obtained over a wide range of values of the parameter of viscous interaction. An asymptotic solution is given to the problem with the approach to zero of the interaction parameter.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 41–47, September–October, 1973.The authors thank V. V. Mikhailova for discussion of the work and useful advice.     

Pressure effects on separation in axisymmetric stokes flows

Two Stokes flows which are known to lead to separation are reconsidered from a more dynamic perspective, and it is found that within the region of separated flow there is an extremum for the pressure. A simple argument is presented which indicates that this is true under reasonable conditions.     

Hydromagnetic boundary layer flow around an oscillating axisymmetric body

Boundary layer flow due to rotational oscillations of an axisymmetric body in the presence of a constant magnetic field is analysed by a process of successive approximations. The induced steady flow is confined only to the meridian place. The effect of the magnetic field is to decrease this steady flow.     

Shape of an axisymmetric liquid film on the surface of a rotating cylinder

The steady axisymmetric motion of a viscous film together with a cylinder is investigated. The shape of an axisymmetric film of constant mass depends not only on the physical properties of the liquid, the rate of rotation and the radius of the cylinder but also on the pressure difference between the liquid and the ambient medium. By calculation and by means of a qualitative investigation of the first integral of the basic equation it is shown that for different values of the parameters the free surface of the film may be cylindrical or wavy, intersect itself or consist of periodically distributed isolated annular layers. The calculation results correspond with the experimental data the more closely the thinner the film and the greater its transverse velocity. This is attributable to the absence of gravitational acceleration from the model of the steady axisymmetric motion.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 23–27, July–August, 1989.     

Three-dimensional axisymmetric flow in perfectly plastic metals

A method is presented for solving the three-dimensional axisymmetric field equations for a perfectly plastic material which obeys the von-Mises yield criterion and the Levy-Mises flow law. The method is used for the particular case in which a small axisymmetric perturbed flow is superposed on a uniform flow without flow reversal taking place. The method then leads to solving a fourth order differential equation for the velocity potential. The special case of a thick cylindrical shell under compressive flow is examined. The solution so obtained, being derived, from the three dimensional theory, includes a correct treatment of transverse shear distortion. A preferred mode of instability is identified having a wave-length in reasonable agreement with that obtained experimentally by other workers.     

Solution of plane axisymmetric problems for an ideal plastic body

Chelyabinsk Science Center, Urals Branch, Russian Academy of Sciences. Translated from Prikladnaya Mekhanika, Vol. 28, No. 9, pp. 29–35, September, 1992.     

Choice of optimal blunting radius of axisymmetric body with account for surface radiation

We consider the problem of determining the optimal blunting with respect to heat transfer of an axisymmetric body in supersonic gas flow at zero angle of attack with account for body surface radiation. Results are presented of a calculation of the optimal blunting radius of a cone with half-angle 10° for various values of the ratio of convective heat flux at the stagnation point to the radiative heat flux. It is shown that for small values of this ratio the small bluntings are optimal.     

Detonation combustion of hydrogen in an axisymmetric channel with a central body

The problem of initiation and stabilization of detonation combustion of a hydrogen–air mixture injected into an axisymmetric channel with a finite-length central body in a flow with a Mach number M₀ = 5–9 is solved. It is numerically demonstrated that the presence of the central body both in a convergent–divergent nozzle and in an expanding channel leads to stabilization of detonation combustion of a stoichiometric hydrogen–air mixture at free-stream Mach numbers M₀ > 7. Various channel configurations that ensure different values of thrust generated by detonation combustion of a stoichiometric hydrogen–air mixture are compared.