Diffusion to a particle at large péclet numbers and small Reynolds and Hartmann numbers

A study is made of the influence of a homogeneous magnetic field on the mass transfer for a spherical solid particle and a liquid drop in a flow of a viscous electrically conducting fluid. The previously obtained [1] velocity field of the fluid is used to calculate the concentration distribution in the diffusion boundary layer, the density of the diffusion flux, and the Nusselt number, which characterizes the mass transfer between the particle and the surrounding medium.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 189–192, January–February, 1980.     

EHD flows at large electric Reynolds numbers

The motion of a medium consisting of neutral particles and charged particles of single sign is studied under the assumption that the electric Reynolds number (R_q=u/bE) is large. We calculate the freezingin integral and the Bernoulli and Cauchy-Lagrange integrals, study the fluid motion in a stream tube, and formulate the boundary layer problem.     

Spin-down of a fluid in a low cylinder at large Reynolds numbers

The problem of the axisymmetric motion of a fluid between infinite disks is solved by the method of matched asymptotic expansions without introducing model assumptions. For the strongly nonlinear stage of spin-down solutions are found that correspond to initial states different from rigid-body rotation, when the boundary layer is not a Kármán layer. The experimental results obtained are in qualitative and quantitative agreement with the theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 39–46, May–June, 1986.The authors wish to thank A. M. Obukhov and F. V. Dolzhanskii for formulating the problem and for constructive discussion.     

Slow motion of a conducting fluid between two rotating walls

Summary An investigation is presented of the flow of a viscous, conducting fluid between two plane walls, which rotate around a common axis towards each other. The flow is considered to be under the influence of a magnetic field, set up by a line-current along the axis of rotation.Under the assumption of low hydrodynamic and magnetic Reynolds-number, expressions are given for the velocity and the pressure gradient.At present at Brussels: Ecole Royale Militaire, Physique des Plasmas.     

Instability of steady shearing flows in a non-linear viscoelastic fluid

This paper proves the non-existence of global smooth solutions to an equation for a viscoelastic fluid shearing flow. The non-existence of smooth solutions is interpreted physically as the formation of a vortex sheet and an instability in the fluid motion.Dedicated to Clifford Truesdell on the occasion of his sixtieth birthday     

Magnetohydrodynamic flow past a drop at low Reynolds and Hartmann numbers

The flow of an electrically conductive liquid past a solid spherical particle at low Reynolds and Hartmann numbers in longitudinal and transverse magnetic fields was first investigated in [1,2]. The effect of a weak magnetic field on the strength of the resistance of a conductive drop in a dielectric medium was considered in [3]. In the present paper we consider the motion of a conductive liquid drop in an electrically conductive medium and calculate the strength of the resistance in the Stokes approximation for an arbitrary orientation of the uniform magnetic field and in the Oseen approximation for the case in which the direction of the magnetic field coincides with the direction of the oncoming stream. As in the previous studies, we do not consider the possibility of the formation of a double layer on the interface between the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 19–25, November–December, 1978.The authors are grateful to G. I. Petrov and the participants in the seminar they conducted for their comments on the work.     

Numerical calculations of steady viscous incompressible fluid flows

Most authors use the stream function for the calculation of two-dimensional viscous incompressible fluid flows. The velocity field is determined by numerical differentiation, which reduces the computation accuracy significantly. In the following we study steady viscous fluid flow fay a method which makes it possible to avoid this drawback; in this case the problem of the Navier-Stokes equations reduces to a different equivalent problem: an implicit finite-difference scheme constructed on the basis of the results of [1, 2] is proposed for the numerical solution of the resulting system of equations.     

Stability of Hartmann flows

The stability of Hartmann flows for arbitrary magnetic Reynolds numbers is investigated in the framework of linear theory. The initial three-dimensional problem reduces to the equivalent two-dimensional problem. Perturbation theory is used to find asymptotic expressions for the eigenvalues. Distinguishing two types of disturbances — magnetic and hydrodynamic — is shown to be advantageous in a number of cases. Simple features of the stability are considered for particular cases. The well-know Lundquist result is generalized. An energy approach is applied to the problem of stability. The results of simulations involving the solution of the linear stability problem are described. A distinctive picture of stability is developed. There are several types of instability and they can develop simultaneously. The hydrodynamic and magnetic phenomena interact with each other in a very complex fashion. The magnetic field can either enhance flow stability or reduce it.Novosibirsk. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 17–31, November–December, 1972.     

Slow steady rotation of an axially symmetric body in a micropolar fluid

This paper examines the Stokes' flow due to an axially symmetric body rotating about its axis of symmetry in a micropolar fluid which sustains anti-symmetric stress and couple stress. General solutions are obtained to the coupled differential equations governing such a flow and the special case of a sphere is deduced. Then, with the aid of a concentrated couple, a simple formula for the couple experienced by a body is derived in terms of the angular velocity of the flow field.     

LES of incompressible heat and fluid flows past a square cylinder at high Reynolds numbers

This paper presents large eddy simulation (LES) results of incompressible heat and fluid flows around a square cylinder (SC) at zero incident angle at high Reynolds numbers (Re) in the range from 1.25×10⁵ to 3.5×10⁵. LES results are obtained on the basis of swirling strength based sub-grid model, and a higher order upwind scheme developed with respect to the Taylor expansion. It was found that, for the zero incident SC wake flows at a Reynolds number in the range {Re₅ = Re/10⁵ ∈ [1.25, 3.5]}, the Strouhal number equals to 0.1079, completely independent of the Reynolds number; the coefficient of drag is around 1.835 with an uncertainty of about 1.9%, almost non-sensitive to the Re. When Re is beyond 3.0×10⁵, the time-averaged peak value of sub-grid viscosity is over 340, implying that the role of sub-grid model is crucial in some regions where vortex motion is active and vortex interaction is intense. The time–spanwise (t-z) averaged sub-grid viscosity ratio profiles and the profiles of fluctuations of the sub-grid viscosity ratio and velocity components at four locations downstream of the SC are presented. The fields of the t-z averaged sub-grid viscosity ratio, and the instantaneous fields of streamwise and spanwise vorticities are also reported and discussed. The predicted mean Nusselt number is compared with empirical correlations, revealing that swirling strength based LES has its potential in predicting natural and industrial flows.     

On Oseen flows for large Reynolds numbers

This investigation offers a detailed analysis of solutions to the two-dimensional Oseen problem in the exterior of an obstacle for large Reynolds numbers. It is motivated by mathematical results highlighting the important role played by the Oseen flows in characterizing the asymptotic structure of steady solutions to the Navier–Stokes problem at large distances from the obstacle. We compute solutions of the Oseen problem based on the series representation discovered by Tomotika and Aoi (Q J Mech Appl Math 3:140–161, 1950) where the expansion coefficients are determined numerically. Since the resulting algebraic problem suffers from very poor conditioning, the solution process involves the use of very high arithmetic precision. The effect of different numerical parameters on the accuracy of the computed solutions is studied in detail. While the corresponding inviscid problem admits many different solutions, we show that the inviscid flow proposed by Stewartson (Philos Mag 1:345–354, 1956) is the limit that the viscous Oseen flows converge to as Re → ∞. We also draw some comparisons with the steady Navier–Stokes flows for large Reynolds numbers.     

Motion of a cylinder below the free surface of a fluid at large froude numbers

A method of solving the problem of the motion of a cylinder of given shape below the free surface of an infinitely deep heavy fluid is perfected for large Froude numbers. The motion of a circular cylinder is investigated at small distances from the free surface. Solutions of the problem are given for cylinders with noncircular cross-sections. Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 34–45, July–August, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (projects Nos. 99-01-00169 and 99-01-00173).     

Three-dimensional steady flows of stratified fluid and internal waves

A study is made of three-dimensional steady flows of an ideal heavy incompressible fluid stratified in each layer over a flat or asymptotically flat base. Mixed Euler-Lagrange variables are chosen in which surfaces of constant density, including the layer division boundaries, become flat and parallel to the plane of the base. The original problem is reduced to a nonlinear boundary-value problem for a system of three quasilinear equations in a plane layer. This system of equations is used to construct an asymptotic theory of long waves in the three-dimensional case, which has particular solutions in the first approximation in the form of solitons and soliton systems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 127–132, May–June, 1985.     

Wave flows of a conducting viscous fluid film in a transverse magnetic field

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 96–100, May–June, 1990.     

Stabilization of the unstable steady states of a conducting fluid in an electromagnetic field

The linear disturbance spectrum is determined for the solution with the fluid at rest and its unstable region identified. It is shown that an electric field has a destabilizing effect, while a magnetic field and viscosity affect only the rate of damping of the disturbances and not the actual existence of instability. An example of a feedback regulator that stabilizes two unstable modes is constructed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 138–142, November–December, 1993.     

Deconvolution‐based nonlinear filtering for incompressible flows at moderately large Reynolds numbers

We consider a Leray model with a deconvolution‐based indicator function for the simulation of incompressible fluid flow at moderately large Reynolds number (in the range of a few thousands) with under‐resolved meshes. For the implementation of the model, we adopt a three‐step algorithm called evolve–filter–relax that requires (i) the solution of a Navier–Stokes problem, (ii) the solution of a Stokes‐like problem to filter the Navier–Stokes velocity field, and (iii) a final relaxation step. We take advantage of a reformulation of the evolve–filter–relax algorithm as an operator‐splitting method to analyze the impact of the filter on the final solution versus a direct simulation of the Navier–Stokes equations. In addition, we provide some direction for tuning the parameters involved in the model based on physical and numerical arguments. Our approach is validated against experimental data for fluid flow in an idealized medical device (consisting of a conical convergent, a narrow throat, and a sudden expansion, as recommended by the U.S. Food and Drug Administration). Numerical results are in good quantitative agreement with the measured axial components of the velocity and pressures for two different flow rates corresponding to turbulent regimes, even for meshes with a mesh size more than 40 times larger than the smallest turbulent scale. After several numerical experiments, we perform a preliminary sensitivity analysis of the computed solution to the parameters involved in the model. Copyright © 2015 John Wiley & Sons, Ltd.