Unsteady nonsimilar compressible laminar two-dimensional and axisymmetric boundary-layer flows

Summary Unsteady nonsimilar laminar compressibletwo-dimensional and axisymmetric boundarylayer flows have been studied when external velocity varies arbitrarily with time and the flow is nonhomentropic. The governing nonlinear partial differential equations with three independent variables have been solved using an implicit finite difference scheme with quasilinearization technique from the origin to the point of zero skin-friction. The results have been obtained for (i) an accelerating stream and (ii) a fluctuating stream. The skin friction responds to the fluctuations in the free stream more compared to the heat transfer. It is observed that Mach number and hot wall cause the point of zero skin friction to occur earlier whereas cold wall delays it.With 16 Figures     

Numerical study of laminar swirled flow in an annular channel

The effect of stream rotation on the velocity distribution in an annular channel is studied by the numerical method. The degrees of swirling corresponding to the initiation of stream separation are presented as functions of the Reynolds number for different values of the geometrical parameter of the channel.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 2, pp. 273–280, February, 1978.     

Heat transfer and drag in the laminar flow of a gas with variable properties through an annular channel

The drag and heat transfer problem has been solved numerically, in the boundary-layer approximation, for the laminar flow of a gas with variable properties through an annular channel.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 4, pp. 658–666, April, 1972.     

Axial laminar flow of a viscoplastic fluid in an annular tube

Approximate relations suitable for engineering calculations are derived for determining the boundary of the core when the pressure gradient is given, the boundary and width of the core when the volumetric flow rate is given, and the pressure losses.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 18, No. 6, pp. 1098–1106, June, 1970.     

Unsteady wave flows of a gas suspension with account for phase changes

A system of equations of unsteady motion of a gas suspension with account for heat and mass transfer is presented. As a result of the computational experiment, the effect of the gas vibrations at the channel inlet on the motion of the gas suspension and the rate of heat and mass transfer is studied. Specifically, it is shown that, in the considered parametric region, the gas vibrations enhance the interphase heat and mass transfer. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 3, pp. 487–492, May–June, 2000.     

Wall-bounded laminar sink flows

Summary The laminar flow near an infinite plane wall perpendicular to a line sink of constant strength is investigated in the limit of large Reynolds numbers. Self-similarity requires that fluid is issuing from the boundary layer. The inviscid flow outside the boundary layer is governed by the Euler equations. A one-parametric set of solutions to the Euler equations with appropriate boundary conditions is given. Uniqueness of the inviscid flow solution is obtained from matching with the boundary layer expansion. The solution of the boundary-layer equations is given both in closed form and numerically. It is found that at the edge of the boundary layer the vorticity decays algebraically.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday     

On laminar two-phase flows in magnetohydrodynamics

We consider the Hartmann flow of a conducting fluid in the channel between two horizontal insulating plates of infinite extent, there being a layer of non-conducting fluid between the conducting liquid and the upper channel wall. A suitable volumetric flow-rate factor is defined, and it is shown that significant increases can be obtained in the flow-rate of the conducting fluid for suitable ratios of the depths and viscosities of the two fluids.     

Unsteady laminar flow over a rough surface

A model is developed for the unsteady laminar flow of athin fluid film over a substrate with roughness of the same order as the film height. The limits of large and small surface resistance and small surface-roughness are investigated and it is shown that at leading order the classical parabolic form for the velocity profile is retrieved in all cases. Empirical expressions for the depth-averaged velocity and the ratio of the average to maximum velocities are investigated and shown to agree with the present theory under certain conditions. The method is verified by comparison with experiments for steady uni-directional flow over a surface of known roughness.     

Simulation of a subsonic isothermal turbulent submerged jet flowing from an annular nozzle

A simulation of the flow in a jet has been carried out with the use of the Reynolds-averaged, space-filtered Navier-Stokes equations closed by the k-ε model of turbulence and the subgrid RNG model of eddy viscosity. The results of calculations carried out on the basis of the k-ε model and the results of simulation of large vortices are in quantitative and qualitative agreement with the corresponding measurement data, which is evidence in favor of the main laws defining the decay of the gas-dynamic behavior of cold-gas submerged jets and the fluctuations of their parameters. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 312–320, March–April, 2008.     

Unsteady mixed flows with in-passage shocks

The problem of blade flutter in an infinite cascade of thin, sinusoidal blades is explored in the framework of a linearized theory. The model admits normal shocks in the blade-passages. Closed form analytical solutions are formed in the regions of both the supersonic and subsonic flows.     

Heat exchange in descending annular gas-liquid flows

Experimental data on heat exchange in turbulent descending liquid flows with an accompanying gas flow are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 2, pp. 218–222, February, 1986.     

Unsteady flows of a binary mixture of incompressible Newtonian fluids in an annulus

This paper is concerned with applying the mixture theory of two chemically inert incompressible Newtonian fluids to some simple unsteady flows in the annular region between two infinitely long coaxial cylinders. The equations governing the motion of the binary mixture under discussion are reduced to a system of coupled partial differential equations. With the help of finite Hankel transforms, the exact solutions of these equations are obtained in series form for the following three problems: (i) unsteady axial Couette flow in an annulus, (ii) unsteady Poiseuille flow in an annulus, (iii) unsteady circular Couette flow in an annulus.     

Calculation of a laminar axial flow of a nonlinear viscoplastic medium in an annular channel

We calculate the fundamental field and integral characteristics (velocity profiles, tangential stresses, outflow rate, pressure loss, boundaries of the quasirigid core) for a nonlinear viscoplastic Cesson medium in stationary stabilized flow in a coaxially cylindrical channel.Translated from Inzherno-Fizicheskii Zhurnal, Vol. 19, No. 4, pp. 689–697, October, 1970.     

Second-order effects in self-similar laminar compressible boundary-layer flows

Second-order effects associated with longitudinal curvature, transverse curvature, entropy gradients, stagnation enthalpy gradient, velocity slip, temperature jump and displacement speed in self-similar two-dimensional and axisymmetric flows of a compressible fluid are studied. The self-similar governing equations for second-order effects show that the four parameters, due to longitudinal curvature, transverse curvature, displacement and body shape are needed to describe the flow. Numerical solutions and several closed form solutions are obtained. The present study is found to contain all the previous studies in the self-similar domain as special cases.     

Unsteady two-dimensional and axisymmetric MHD boundary-layer flows

Summary Nonsimilar solution of the unsteady laminar incompressible magneto-hydrodynamic boundary layer flow and heat transfer for an electrically conducting fluid over two-dimensional and axisymmetric bodies in the presence of an applied magnetic field has been obtained. The effects of surface mass transfer, Joule heating and viscous dissipation are included in the analysis. Numerical computation have been carried out for the flow over a circular cylinder and a sphere using an implicit finite difference scheme in combination with a quasi-linearization technique. It is observed that magnetic field and suction cause the location of vanishing skin friction to move downstream while, the effect of injection is just the opposite. The effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer. On the other hand, the heat transfer is strongly affected by the viscous dissipation and the effect is more for larte times. However, heat transfer responds comparatively less to the fluctuations of the free stream than the skin friction.     

Generalized similarity of laminar nonisothermic flows of a viscous gas in thin pipes of variable cross section

The method of generalized similarity of the boundary-layer theory is applied to the problem of laminar flow of a viscous gas in thin circular pipe with cross section which varies along the length of the pipe.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 2, pp. 285–289, February, 1982.     

Second-order boundary-layer theory of laminar jet flows

Summary Laminar jet flows are investigated by asymptotic expansions in terms of large Reynolds numbers and large distances from an orifice in a wall. For two-dimensional flow, previously known results are modified and extended. For axisymmetric flow, the expansion breaks down as the distance from the orifice tends to infinity. An error analysis indicates that the range of applicability of classical boundary layer theory is severely limited.With 4 Figures     

Unsteady compressible boundary layer swirling flow in a nozzle and a diffuser

This paper presents the results of the study of unsteady swirling boundary-layer flow of compressible fluid in a nozzle and a diffuser when the free stream velocity, mass transfer and wall temperature vary arbitrarily with time. The set of coupled nonlinear partial differential equations governing the flow which involves three independent variables has been solved numerically using an implicit finite-difference scheme. Both the heat transfer and skin friction are strongly affected by the free stream velocity, variation of the density-viscosity product across the boundary layer, mass transfer and swirl parameter. However, the variation of the wall temperature with time strongly affects only the heat transfer. Also, separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction.     

Semianalytical solution of unsteady quasi-one-dimensional cavitating nozzle flows

Unsteady quasi-one-dimensional bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial-boundary value problem of the evolution equations is then formulated and a semianalytical solution is constructed. The solution for the mixture pressure, the mixture density, and the void fraction are then explicitly related to the solution of the evolution equations. In particular, a relation independent of flow dimensionality is established between the mixture pressure, the void fraction, and the flow dilation for unsteady bubbly cavitating flows in the model considered. The steady-state compressible and incompressible limits of the solution are also discussed. The solution algorithm is first validated against the numerical solution of Preston et al. [Phys Fluids 14:300–311, 2002] for an essentially quasi-one-dimensional nozzle. Results obtained for a two-dimensional nozzle seem to be in good agreement with the mean pressure measurements at the nozzle wall for attached cavitation sheets despite the observed two-dimensional cavitation structures.