On a model of fluid motion near a solid surface

The possibility is examined of using the model of micropolar media [1] to describe the anomalous change in the mechanical properties and the associated appearance of the scale effect in the boundary layers of certain fluids.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 70–75, May–June, 1981.     

Kinetic model for the motion of compressible bubbles in a perfect fluid

Collective behavior of compressible gas bubbles moving in an inviscid incompressible fluid is studied. A kinetic approach is employed, based on an approximate calculation of the fluid flow potential and formulation of Hamilton's equations for generalized coordinates and momenta of bubbles. Kinetic equations governing the evolution of a distribution function of bubbles are derived. These equations are similar to Vlasov's equations. Conservation laws which are direct consequences of the kinetic system are found. It is shown that for a narrowly peaked distribution function they form a closed system of hydrodynamical equations for the mean flow parameters. The system yields the analogue of Rayleigh–Lamb's equation governing oscillations of bubbles. A variational principle for the hydrodynamical system is established and the linear stability analysis is performed.     

Drag force on a sphere in creeping motion throug a carreau model fluid

In the report of Chhabra and Uhlherr [1], a theoretical formulation for the drag force on a sphere in a fluid governed by the Carreau viscosity equation was presented. The formulation gave a good representation of the drag force when compared with experimental measurements, although the experiments were carried out on fluids exhibiting both shear-thinning and elastic behaviour. In the present work the ‘boundary element method’ has been used to obtain a fully numerical solution for comparison with the theoretical predictions. The two sets of results agree closely. We also present a simple empirical relation which gives a good first approximation to the drag force (～ 10%).     

Self motion of a body in a fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 111–118, March–April, 1990.     

Exact solution of electroosmotic flow in generalized Burgers fluid

An exact solution is developed for the time periodic electroosmotic flow of a non-Newtonian fluid between the micro-parallel plates. The constitutive equations of a generalized Burgers fluid are used in the mathematical formulation. The resulting problem is solved by a Fourier transform technique. Graphs are plotted and discussed for various emerging parameters of interest.     

Newtonian heating in stagnation point flow of Burgers fluid

The Newtonian heating effects in the stagnation point flow of a Burgers fluid are addressed in this paper. The boundary layer flow problems are stated in the spatial domain from zero to infinity. The solution expressions for the velocity and the temperature are obtained and examined for the influential variables. The tabulated values show comparison with the previous results. It is observed that the obtained results are in good agreement with the existing results in limiting sense.     

Plane surface suddenly set in motion in a viscoelastic fluid with fractional Maxwell model

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. The flow near a wall suddenly set in motion is studied for a non-Newtonian viscoelastic fluid with the fractional Maxwell model. Exact solutions of velocity and stress are obtained by using the discrete inverse Laplace transform of the sequential fractional derivatives. It is found that the effect of the fractional orders in the constitutive relationship on the flow field is significant. The results show that for small times there are appreciable viscoelastic effects on the shear stress at the plate, for large times the viscoelastic effects become weak. The project supported by the National Natural Science Foundation of China (10002003), Foundation for University Key Teacher by the Ministry of Education, Research Fund for the Doctoral Program of Higher Education     

A note on longitudinal oscillations of a generalized Burgers fluid in cylindrical domains

The starting solutions for the oscillating motion of a generalized Burgers fluid due to longitudinal oscillations of an infinite circular cylinder, as well as those corresponding to an oscillating pressure gradient, are established as Fourier–Bessel series in terms of some suitable eigenfunctions. These solutions, presented as sum of steady-state and transient solutions, describe the motion of the fluid for some time after its initiation. After that time, when the transients disappear, the motion of the fluid is described by the steady-state solutions which are periodic in time and independent of the initial conditions. These solutions are also presented in simpler but equivalent forms in terms of modified Bessel functions of first and second kind. In both forms, the steady-state solutions can be specialized to give the similar solutions for Burgers, Oldroyd-B, Maxwell, second grade and Newtonian fluids performing the same motions. Finally, the required time to reach the steady-state for cosine and sine oscillations of the boundary is obtained by graphical illustrations.     

The motion of microbubbles in a forced isotropic and homogeneous turbulence

We have studied the concentration distribution of microbubbles in forced isotropic turbulence. An initially uniform concentration field is shown to evolve to a highlyintermittent orspotty concentration distribution at long time due to the interactions of microbubbles with small-scale, intense, and coherent flow vortical structures. The maximum bubble concentration can be as large as 3,000 times the mean concentration and the local accumulations occur preferentially in the regions of high flow vorticity and low flow pressure. A quantitative measure of global nonuniformity in the concentration field is used to confirm that the preferential accumulation does follow Kolmogorov scaling, as opposed to the large-scale scaling commonly used for dispersion quantification.     

Peristaltic motion of a non-Newtonian fluid

Summary To understand theoretically the flow properties of physiological fluids, we have considered as a model the peristaltic motion of a power law fluid in a tube, with a sinusoidal wave of small amplitude travelling down its wall. The solution for the stream function is obtained as a power series in terms of the amplitude of the wave. The stream function and the velocity components are evaluated by solving numerically two point boundary value problems with a singular point at the origin. The influence of the applied pressure gradient along with non-Newtonian parameters on the streamlines and velocity profiles are discussed in detail.     

Large-scale turbulence in a thin layer of nonisothermal rotating fluid

The dynamics of large-scale nonisothermal turbulence in a thin rotating layer of fluid are investigated. An hierarchical model, obtained by averaging the initial Boussinesq equations with respect to the vertical coordinates and subsequently projecting the two-dimensional equations onto a basis consisting of a system of axisymmetric spiral vortices of progressively decreasing scale, is proposed. It is shown that the presence of horizontal temperature inhomogeneities leads to a considerable increase in the turbulence decay time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 48–55, July–August, 1988.     

Visualization of turbulence and internal waves in a stratified fluid

A method for visualizing the velocity field in stratified flow by means of tracer particles made from wooden sawdust is described. The wood particles absorb water and salinity and may match the local density of stratified salt water.     

Viscous fluid motion in a precessing cylinder

The solution of the linearized Navier-Stokes equations for determining the steady relative motion of a low-viscosity Oincompressible fluid partly filling a cylindrical vessel executing regular precession with a small angle of nutation is constructed. The shape of the free surface and the axial component of the moment of the forces exerted by the fluid on the lateral surface of the vessel are determined.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 134–137, November–December, 1993.     

Accelerating motion of a sphere in a maxwell fluid

The translatory accelerating motion of a sphere due to an arbitrarily applied force in an unlimited Maxwell fluid is considered. The exact solutions for the velocity of the sphere for three particular types of accelerating motion are presented. The first is for a falling sphere; the second is for the decelerating motion of a sphere after the force which maintains the sphere with a constant velocity is removed; the third is for the motion of the sphere subjected to an impulsive force. The exact solutions are expressed in terms of real, regular, definite integrals which can be evaluated by numerical technique. Also presented are the asymptotic solutions for the velocity of the sphere in all three cases which are valid for small values of time.     

Vorticity field in a cascade model of turbulence

We propose a model which interprets the behavior of the spontaneous singularity and the intermittent structure in fully developed turbulence simultaneously. The model is justified in the framework of a cascade model of turbulence.     

Analysis of low-pass filters for approximate deconvolution closure modelling in one-dimensional decaying Burgers turbulence

The idea of spatial filtering is central in approximate deconvolution large-eddy simulation (AD-LES) of turbulent flows. The need for low-pass filters naturally arises in the approximate deconvolution approach which is based solely on mathematical approximations by employing repeated filtering operators. Two families of low-pass spatial filters are studied in this paper: the Butterworth filters and the Padé filters. With a selection of various filtering parameters, variants of the AD-LES are systematically applied to the decaying Burgers turbulence problem, which is a standard prototype for more complex turbulent flows. Comparing with the direct numerical simulations, it is shown that all forms of the AD-LES approaches predict significantly better results than the under-resolved simulations at the same grid resolution. However, the results highly depend on the selection of the filtering procedure and the filter design. It is concluded that a complete attenuation for the smallest scales is crucial to prevent energy accumulation at the grid cut-off.     

Analytical model of motion of turbulent vortex rings in an incompressible fluid

An analytical model describing the motion of vortex rings in an incompressible fluid is constructed. The model is valid both for homogeneous and inhomogeneous vortices buoyant in the gravity field, as well as for combined vortices. The expansion angle of a buoyant vortex is found from the characteristic parameters that define the flow rather than specified on the basis of experiments. Significant differences in the expansion angles of homogeneous and buoyant vortex rings are explained. The calculation results for the proposed model are compared with the results of laboratory experiments and data on the rise of the cloud produced by an atomic explosion.     

Vortex motion in a rotating barotropic fluid layer

To study vortex motion and the mechanisms of geostrophic adjustment (i.e. the equilibrium between pressure gradient and Coriolis force, which leads to the weakening of inertio-gravity waves) in large scale geophysical flows, we simulate the dynamics of a shallow-water layer in uniform rotation, without any forcing other than the initial injection of energy and potential enstrophy. Such a flow generates inertio-gravity waves which interact with the rotational eddies. We found that both inertio-gravity waves and rotation reduce the non-linear interactions between vortices, namely the condensation of the vorticity field into isolated coherent vortices, corresponding to the inverse rotational energy cascade, and the associated production of vorticity filaments, due to the direct potential enstrophy cascade. Rotation also inhibits the direct inertio-gravitational energy cascade for scales larger than the Rossby deformation radius. Therefore, if inertio-gravity waves are initially excited at large enough scales, they will remain trapped there due to rotation and there will be no geostrophic adjustment. On the contrary, if inertio-gravity waves are only present at scales smaller than the Rossby deformation radius, which are insensitive to the effect of rotation, they will non-linearly interact and cascade towards the dissipative scales, leaving the flow in geostrophic equilibrium.     

Peristaltic motion of a third-order fluid in a planar channel

In order to determine the characteristics of the peristaltic transport of shear thinning non-Newtonian materials, the motion of a third-order fluid in a planar channel having walls that are transversely displaced by an infinite, harmonic traveling wave of large wavelength and negligibly small Reynolds number was analyzed using a perturbation expansion in terms of a variant of the Deborah number. Within the range of validity of this analysis, we found the pumping rate of a shear-thinning fluid is less than that for a Newtonian fluid having a shear viscosity the same as the lower-limiting viscosity of the nonNewtonian material. Also, the space of variables for which trapping of a bolus of fluid occurs is reduced for the shear-thinning fluid investigated here.