Some effects of strong blowing of gas into a supersonic flow

The intense evaporation of bodies moving in the atmospheres of planets at high supersonic velocities has been partly simulated both theoretically [1–5] (numerical calculations of strong blowing in the framework of the Navier-Stokes equations were also made at the Scientific-Research Institute of Mechanics at the Moscow State University by É. A. Gershbein and A. F. Kolesnikov [6]) as well as experimentally [7–9]. Below, the results are given of investigations of strong blowing of gas from the flat end of a cylinder into a supersonic flow at Reynolds numbers such that the mixing layer separating the blown and the oncoming gas is fairly thin. In this case, the mixing layer can be regarded as a contact surface, so that the problem of blowing can be solved in the framework of Euler's equations. The results of a numerical solution are compared with the results of experiments on the separation and profile of the shock wave, the thickness of the blowing layer on the axis, and also on the pressure distribution on the end of the cylinder. It was established experimentally, and then confirmed numerically that there is a downwash of the blown gas on the periphery of a porous end. It is shown that for the same blowing parameter K, which is equal to the ratio of the dynamic head of the blown gas to the dynamic head of the oncoming gas, and for a given distribution of K over the surface of the body the contact surface tends to a certain limiting position with increasing Mach number of the oncoming flow, i.e., the profile of the contact surface is stabilized. The influence of the adiabatic exponent on the thickness of the blowing layer is estimated. The present investigations continue earlier experimental studies, the main results of which have been presented in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 91–98, January–February, 1980.     

Calculation of the average phase velocity slip in turbulent multiphase channel flow

A closed system of equations of hydrodynamics and mass transfer of the inertial particle dispersed phase in turbulent channel flow is constructed on the basis of a statistical approach. Boundary conditions that take into account the nature of the interaction between the particles and the channel surface are obtained. The average velocity of the particles in circular pipes is calculated and the results of the calculations are compared with the available experimental data on the average phase velocity slip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 69–78, March–April, 1990.     

One-dimensional and two-dimensional analogs for three-dimensional viscous flows in the neighborhood of the plane of symmetry of a blunt body

An approximate method of determining the heat transfer and friction stress in three-dimensional flow problems using the two-dimensional and one-dimensional solutions is proposed. This method is applicable over a wide range of Reynolds numbers — from low to high. On the basis of a theoretical analysis of the approximate analytic solution of the equations of a three-dimensional viscous shock layer it is shown that the problem of determining the heat flux in the neighborhood of the plane of symmetry of bodies inclined to the flow at an angle of attack can be reduced, firstly, to the problem of determining that quantity for an axisymmetric body and, secondly, to the problem of determining the heat transfer to an axisymmetric stagnation point. On the basis of an analysis of the results of a numerical solution of the problem it is shown that corresponding analogs can also be used for the friction stress. The accuracy of the similarity relations established is estimated by solving the problem by a finite-difference method. A similarity relation of the same kind was previously obtained in [1] for a double-curvature stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 117–122, January–February, 1990.     

A class of solutions of the boundary layer equations

Exact solutions of the boundary layer equations can be obtained in closed form only in rare cases. These generally involve self-similar solutions for which the corresponding ordinary differential equation can be integrated exactly. In this paper solutions of more general form, containing additive functions of the longitudinal x coordinate in the expression's for the stream function and the self-similar variable, are considered in relation to two-dimensional steady boundary layers. This makes it possible to enlarge the class of problems whose solutions are analytic expressions and in a number of cases can be obtained in the form of expressions containing arbitrary functions of x, which makes possible various interpretations of the solution. In order to introduce arbitrary functions into the solutions of the equations of the axisymmetric boundary layer the problem is reduced to an overdetermined system of ordinary differential equations. This method is also capable of being applied more widely.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 45–51, March–April, 1990.     

Nonisothermal displacement of high-paraffin oils by water with allowance for solid-phase precipitation

A mathematical model of the nonisothermal displacement of oil by water with allowance for solid-phase precipitation is proposed. Self-similar solutions of the problem of nonisothermal displacement of oil from a homogeneous, thermally insulated formation are obtained. The inverse problems of determining the relative phase permeabilities and the temperature dependence of the paraffin saturation concentration from laboratory displacement data are solved. Exact solutions of the non-self-similar problems of the displacement of high-paraffin oil by a slug of hot water and of the thermal delay problem are obtained. The nonisothermal displacement of high-paraffin oils by water with allowance for heat transfer to the surrounding strata is subjected to qualitative analysis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 126–137, May–June, 1989.The authors are grateful to A. K. Kurbanov and Yu. V. Kapyrin for useful discussions and their interest in the work.     

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.     

Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵ are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.     

Coherent structures in unsteady swirling jet flow

An LDA technique and phase-averaging analysis were used to study unsteady precessing flow in a model vortex burner. Detailed measurements were made for Re=15,000 and S=1.01. On the basis of the analysis of phase-averaged data and vortex detection by the λ₂-technique of Joeng and Hussain (1995), three precessing spiral vortex structures were identified: primary vortex (PV), inner secondary vortex (ISV), and outer secondary vortex (OSV). The PV is the primary and most powerful structure as it includes primary vorticity generated by the swirler; the ISV and OSV are considered here as secondary vortical structures. The jet breakdown zone is the conjunction of a pair of co-rotating co-winding spiral vortices, PV and ISV. The interesting new feature described is that the secondary vortices form a three-dimensional vortex dipole with a helical geometry. The effect of coupling of secondary vortices was suggested as a mechanism of enhanced stability reflected in their increased axial extent.     

Integral formulation for a circular cylindrical cavity in infinite solid and a finite length coaxial cylindrical crack compressed axially

A method for solving problems of fracture of an infinite solid with a circular cylindrical cavity and a coaxial cylindrical crack near the surface under an uniform axial compression is proposed using a non-classical criterial approach associated with a mechanism of a local stability loss near the defect. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a system of linear algebraic equations with respect to the contraction parameter.     

Three-dimensional effects on line-of-sight visualization measurements of supersonic and hypersonic flow over cylinders

Flow visualization experiments were performed for supersonic and hypersonic nitrogen test gas flows over a cylinder. The results were used to quantify the influence of three-dimensional effects on optical line-of-sight visualization measurements. Images of cylindrical models of varying aspect ratios (length to diameter) were taken. Shock stand-off distance measurements for the models were compared with a two-dimensional approximation and numerical simulations. For aspect ratios of two and above, the two-dimensional approximation was acceptable within experimental uncertainty. The measured shock stand-off decreased by less than 5% from an asymptotic value for an infinite length cylinder. For smaller aspect ratios, a correction factor for the shock stand-off needs to be applied if comparisons between the two-dimensional approximation and experimental measurements are to be drawn. An estimate of this correction factor has been derived from an empirical fit to the available data.