Motion of a Rod in a Viscous Flow

The equations of the dynamics of a finitelength curved rod in a viscous flow are derived. The longitudinal stability of the rod against small deflections from a rectilinear form is studied for two types of flow (pure and simple shear). The minimum flexural rigidity of the rod that ensures rod stability for any orientation in the flow is found. The effective viscosity of a suspension filled with rectilinear discrete fibers is estimated.     

Pore-Scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element simulations of the Stokes equations for assemblies of 8–200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients.     

Dual-Family Viscous Shock Waves in n Conservation Laws with Application to Multi-Phase Flow in Porous Media

We consider shock waves satisfying the viscous profile criterion in general systems of n conservation laws. We study S _{i, j} dual-family shock waves, which are associated with a pair of characteristic families i and j. We explicitly introduce defining equations relating states and speeds of S _{i, j} shocks, which include the Rankine–Hugoniot conditions and additional equations resulting from the viscous profile requirement. We then develop a constructive method for finding the general local solution of the defining equations for such shocks and derive formulae for the sensitivity analysis of S _{i, j} shocks under change of problem parameters. All possible structures of solutions to the Riemann problems containing S _{i, j} shocks and classical waves are described. As a physical application, all types of S _{i, j} shocks with i>j are detected and studied in a family of models for multi-phase flow in porous media.     

The Development of the Asymptotic Viscous Dissipation Profile in a Vertical Free Convective Boundary Layer Flow in a Porous Medium

The effect of viscous dissipation on the development of the boundary layer flow from a cold vertical surface embedded in a Darcian porous medium is investigated. It is found that the flow evolves gradually from the classical Cheng–Minkowycz form to the recently discovered asymptotic dissipation profile which is a parallel flow.     

Stability of Flow with Viscous Dissipation in a Horizontal Porous Layer with an Open Boundary Having a Prescribed Temperature Gradient

A buoyancy-induced stationary flow with viscous dissipation in a horizontal porous layer is investigated. The lower boundary surface is impermeable and subject to a uniform heat flux. The upper open boundary has a prescribed, linearly varying, temperature distribution. The buoyancy-induced basic velocity profile is parallel and non-uniform. The linear stability of this basic solution is analysed numerically by solving the disturbance equations for oblique rolls arbitrarily oriented with respect to the basic velocity field. The onset conditions of thermal instability are governed by the Rayleigh number associated with the prescribed wall heat flux at the lower boundary, by the horizontal Rayleigh number associated with the imposed temperature gradient on the upper open boundary, and by the Gebhart number associated with the effect of viscous dissipation. The critical value of the Rayleigh number for the onset of the thermal instability is evaluated as a function of the horizontal Rayleigh number and of the Gebhart number. It is shown that the longitudinal rolls, having axis parallel to the basic velocity, are the most unstable in all the cases examined. Moreover, the imposed horizontal temperature gradient tends to stabilise the basic flow, while the viscous dissipation turns out to have a destabilising effect.     

Self-Similar Unsteady Viscous Flow

Four examples of self-similar flows of a viscous fluid are considered: separated flow over an expanding plate immersed in an unbounded unsteady viscous flow, the evolution of the velocity field induced by a vortex-source, the flow near an unsteadily moving permeable flat plate, and the flow near an unsteadily rotating disc. For the first example, a numerical solution is constructed. For the next two examples, an analytical solution is found, while the solution of the last problem is reduced to a system of ordinary differential equations.     

Study on Viscous Fluid Flow in Disordered-Deformable Porous Media Using Hydro-mechanically Coupled Pore-Network Modeling

Transport in Porous Media - We investigate viscous fluid flows and concurrent fluid-driven deformations in porous media. The hydro-mechanically (H-M) coupled pore-network model (PNM) is developed,...     

Spatial Motion of a Rod in a Viscous Fluid Flow

Equations of spatial motion of a curved finitelength rod in a viscous fluid flow are derived. Analytical solutions of problems on the motion of a straight rod under conditions of pure shear, simple shear, and uniaxial extension of the fluid are obtained. Longitudinal stability of the straight rod during its spatial motion is considered. Effective viscosity of a suspension filled by rigid straight rods is evaluated.     

Viscous Profiles for Shock Waves in Isothermal Magnetohydrodynamics

We prove existence of viscous profiles for slow and fast shock waves in isothermal magnetohydrodynamics with a general pressure law both using the Conley index and connection matrices.     

Viscous Flow Past a Periodic Array of Spheres

Viscous flow past an infinite periodic array of rigid spheres is considered. The hydrodynamic interaction of all the particles in the array is taken into account. An analytical solution of the problem is proposed. The forces exerted by the fluid on the array particles are calculated and an expression for the velocity of fluid filtration through the array is obtained. The results are compared with the previous theoretical and experimental results.     

空泡流粘性效应研究

我们用激光多普勒技术(LDV)对钝头圆柱体、带小槽1.5度卵形头回转体、带背阶半球头回转体的绕流进行了测量。试验在600×600mm~2水洞中进行,雷诺数从0.75×10~5到6×10~5。给出了平均速度和脉动速度均方根值的分布并做了脉动速度的功率谱。得出了与过去热线流速计测量结果略有不同的结论。并且通过小槽内流动的测量对空泡的产生进行了分析。此外,本文提出一种捡测流动转捩现象的方法,用此法的实验结果与前人一致。     

Asymptotic Investigation of the Thin Viscous Shock Layer Equations in the Neighborhood of the Stagnation Point for Low Reynolds Numbers

Hypersonic three-dimensional viscous rarefied gas flow past blunt bodies is investigated in the neighborhood of the stagnation point. The problem of applicability of the model of a thin viscous shock layer to the regime of transition from continuum to free-molecular flow is considered. In [1], it was shown that at low Reynolds numbers three hypersonic flow regimes can be distinguished and one of those regimes was investigated. In the present study an asymptotic solution of the thin viscous shock layer equations is obtained for another flow regime. With decrease in the Reynolds number the heat transfer coefficient determined by the solution obtained approaches its free-molecular value and the friction coefficient approaches its free-molecular limit, provided that the shock layer thickness is small. The analytical solution is compared with a numerical solution and the results of calculations based on direct Monte Carlo simulation.     

Modeling the Effect of Freestream Turbulence on Unsteady Boundary Layer Flow

We present a new version of the two-equation turbulence model, which makes it possible to calculate continuously the entire flow range from laminar to turbulent, including transition, in the case of a time-periodic, high-turbulence-level freestream. The influence of the parameters characterizing the harmonic fluctuations of the external velocity and the freestream turbulence intensity and scale on the parameters of the flat-plate flow are analyzed. A comparison of the numerical solutions with the experimental and theoretical data indicates the possibility of describing the wall flow properties on the basis of a quasi-stationary turbulence model, as the Reynolds number varies from low to high values.     

Long-Time Behavior of Scalar Viscous Shock Fronts in Two Dimensions

We prove nonlinear stability in L ¹ of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem.     

Propagation of Waves in an Elastic Half-Space Interacting with a Viscous Liquid Layer

International Applied Mechanics - The problem of the propagation of acoustic waves in a layer of a compressible viscous fluid that interacts with an elastic half-space is solved using the...     

Propagation of a Stationary Shock Layer in the Presence of a Boundary

We are interested in the large-time behavior of a stationary shock layer in the presence of a boundary effect. It is shown that the stationary shock propagates away from the boundary with speed inversely proportional to the time . Consequently, the location of the wave front is of order . We show therefore that the zero-viscosity and time-asymptotic limits do not commute. Our analysis involves detailed point-wise estimates, which allow us to trace the shock. (Accepted April 16, 1996)     

On Time-Periodic Flow of a Viscous Liquid past a Moving Cylinder

We show existence, uniqueness and spatial asymptotic behavior of a two-dimensional time-periodic flow around a cylinder that moves orthogonal to its axis, with a time-periodic velocity, v. The result is proved if the size of the data is sufficiently small, and the average of v over a period is not zero.     

Flow Structure in the Separation Zone in the Interaction between Shock Waves and the Boundary Layer on a Plate with Slip

A model which makes it possible to calculate the reverse-flow parameters in the separation zone is constructed on the basis of the results of an integrated experimental study of the characteristics of the separated flow developed in the transition from free to non-free interaction between plane shock waves and the boundary layer on a plate with slip. The effect of the Mach number of the reverse flow in the separation zone on the properties of inner boundary layer separation is analyzed. Features of the interference flow due to boundary layer transition are described. The present study is a continuation of investigations [1–3] devoted to the study of a new steady-state type of interaction between shock waves and the boundary layer on a plate with slip in which the separation line formed would propagate upstream beyond the sharp leading edge if no leading edge was present, i.e., so-called non-free interaction.     

Slow Viscous Flow Between Hexagonal Cylinders

The creeping flow between packed hexagonal cylinders is solved by eigenfunction expansions and point match methods. Both longitudinal flow and transverse flow are considered. It is found that the junction, which is the confluence of three channels, has considerable effect on the flow and resistance of the whole fluid network.