The flow of a non-Newtonian liquid near a stagnation point

Zusammenfassung Die Bewegungsgleichungen für die Strömung einer nicht-Newtonschen Flüssigkeit nahe einem Staupunkt sind integriert worden nach der Kármán-Pohlhausen-Methode. Es ist gefunden worden, dass der Effekt der Querviskosität von einem dimensionslosen ParameterK=_c a/u abhängt. Die Grenzschichtdicke nimmt ab vonK=0 zuK=0,15 und wächst dann mitK, Die Wand-Scherbeanspruchung nimmt ab mit zunehmendemK, während die Normalkraft an der Wand unabhängig ist von Viskosität und Querviskosität.     

Some problems for a non-Newtonian liquid and their application to the study of polycarbonate flow

Approximate solutions are obtained for problems of polymer flow in certain cylindrical channels. The polymer is regarded as an isotropic viscoelastic medium. Solutions are constructed by the method of perturbations from the corresponding solutions for a Newtonian liquid. The velocity distribution is calculated for a polycarbonate melt flowing in circular, elliptical and square channels.Mekhanika Polimerov, Vol. 2, No. 4, pp. 603–610, 1966     

Predominantly unidirectional rotation of a solid body and a viscous liquid

Under consideration are two problems of the time-periodic motion of a hydro-mechanical system consisting of a viscous liquid and solid bodies bordering it. A new hydro-mechanical effect is discovered.     

MHD non-Newtonian flow due to non-coaxial rotations of an accelerated disk and a fluid at infinity

The magnetohydrodynamic (MHD) flow due to non-coaxial rotations of a porous disk, moving with uniform acceleration in its own plane and a second grade fluid at infinity is examined. The fluid is electrically conducting in the presence of a uniform magnetic field. The effects of non-Newtonian fluid characteristics and uniform acceleration of the disk on the velocity field are presented both analytically and numerically. A very good accuracy has been seen.     

Analytic solution of natural convection flow of a non-Newtonian fluid between two vertical flat plates using homotopy analysis method

An analysis has been performed to study the natural convection of a non-Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non-Newtonian nature of fluid on the heat transfer are studied. The governing boundary layer and temperature equations for this problem are reduced to an ordinary form and are solved by homotopy analysis method (HAM), and numerical method. Velocity and temperature profiles are shown graphically. The obtained results are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and non-linear equations and so can be found widely applicable in engineering and sciences.     

Volume flowrate in a plane convergent forced flow of an incompressible non-Newtonian liquid

A study is made of the plane convergent forced flow of an incompressible liquid with anomalous viscosity, whose rheological properties obey a power law. A reduction in flow cross section leads to the development of a counterpressure whose existence produces near the inlet a counterflow in the region adjacent to the fixed wall. By analogy with the case of plane-parallel flow an equation is derived for the volume flowrate per unit width of a plane convergent flow.Mekhanika Polimerov, Vol. 2, No. 1, pp. 116–122, 1966     

The rotation class of a flow

Generalizing a construction of A. Weil, we introduce a topological invariant for flows on compact, connected, finite dimensional, Abelian, topological groups. We calculate this invariant for some examples.     

Improvement of H/V technique by rotation of the coordinate system

In this work we investigate the application of the rotation of the coordinate system before applying denoising techniques aimed at improving the H/V spectral ratio for seismic site effects estimation. By this rotation, one can detect the direction of maximum and minimum matching between any couple of orthogonal H/V ratios. The direction of minimum matching should represent the direction of maximum anisotropy of the surface layer or a directional noise. To further improve the method, singular spectrum analysis and WASEE techniques are then applied.     

The evolution strategy applied to drag minimization on a body of revolution

A new optimization method, the evolution strategy, has been applied to a problem in hydrodynamics. This procedure was developed to describe biological change but has application in many areas. The approach is to make small random changes in parameters describing the problem. In this illustration of the use of the method, a minimum drag shape for an axisymmetric body placed in a uniform flow parallel to its axis is sought. Small random changes in the parameters which describe the body shape are made. A performance parameter, the drag coefficient, is evaluated for each set of changes. A significant decrease in drag coefficient was found as a result of applying the evolution strategy.     

Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

A spectral element—Fourier method (SEM) for Direct Numerical Simulation (DNS) of the turbulent flow of non-Newtonian fluids is described and the particular requirements for non-Newtonian rheology are discussed. The method is implemented in parallel using the MPI message passing kernel, and execution times scale somewhat less than linearly with the number of CPUs, however this is more than compensated by the improved simulation turn around times. The method is applied to the case of turbulent pipe flow, where simulation results for a shear-thinning (power law) fluid are compared to those of a yield stress (Herschel–Bulkley) fluid at the same generalised Reynolds number. It is seen that the yield stress significantly dampens turbulence intensities in the core of the flow where the quasi-laminar flow region there co-exists with a transitional wall zone. An additional simulation of the flow of blood in a channel is undertaken using a Carreau–Yasuda rheology model, and results compared to those of the one-equation Spalart-Allmaras RANS (Reynolds-Averaged Navier–Stokes) model. Agreement between the mean flow velocity profile predictions is seen to be good. Use of a DNS technique to study turbulence in non-Newtonian fluids shows great promise in understanding transition and turbulence in shear thinning, non-Newtonian flows.     

On the flow of a non-Newtonian fluid between rotating,coaxial discs

In recent times, workers in numerical methods for non-Newtonian flows have been concerned with the high Weissenberg number problem. This problem which may be caused by a number of different things, manifests itself in the failure of numerical methods at some finite and often small Weissenberg number.This paper is concerned with the torsional flow of an Oldroyd-B fluid. The kinematics is restricted to that commonly referred to as Von Kármán kinematics. These restrictions allow the reduction of the problem to a set of ordinary differential equations. The problem is then solved with finite differences using well-known branch following and jumping techniques.The solution of this set of equations is discussed, and it is found that the solutions either lose stability at subcritical bifurcation points, or fold back on themselves at limit points. Either of these will cause a high Weissenberg number problem.Comparisons are also made with the known solutions to the Newtonian problem by considering small values of the Weissenberg number.     

The flow due to a rough rotating disk

Von Kármáns problem of a rotating disk in an infinite viscous fluid is extended to the case where the disk surface admits partial slip. The nonlinear similarity equations are integrated accurately for the full range of slip coefficients. The effects of slip are discussed. An existence proof is also given.     

Stabilization of horizontal symmetric flow of a liquid film by a heat flux controller

Linearized equations of motion are used to analyze the stability of flow of a liquid film on the walls of a plane-parallel horizontal channel which melt in a stream of hot viscous gas. For materials with a high specific heat of fusion, this flow is shown to be unstable relative to small-amplitude long-wave perturbations.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 60, pp. 74–78, 1986.     

The flow due to a rough rotating disk

Von Kármáns problem of a rotating disk in an infinite viscous fluid is extended to the case where the disk surface admits partial slip. The nonlinear similarity equations are integrated accurately for the full range of slip coefficients. The effects of slip are discussed. An existence proof is also given.     

Stability of symmetric inclined flow of a liquid film in the presence of phase transition

A simplified system of differential equations is applied to analyze the stability under small long-wave perturbations of the inclined flow of a thin layer of a heavy incompressible viscous liquid produced by melting of channel walls in a stream of a hot viscous gas. The flow of the liquid film is shown to be unstable under such perturbations.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 53–58, 1987.     

Distortion of liquid metal flow in a square duct due to the influence of a magnetic point dipole

We consider liquid metal flow in a square duct with electrically insulating walls under the influence of a magnetic point dipole using three-dimensional direct numerical simulations with a finite-difference method. The dipole acts as a magnetic obstacle. The Lorentz force on the magnet is sensitive to the velocity distribution that is influenced by the magnetic field. The flow transformation by an inhomogeneous local magnetic field is essential for obtaining velocity information from the measured forces. In this paper we present a numerical simulation of a spatially developing flow in a duct with laminar inflow and periodic boundary conditions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global weak solution to the flow of liquid crystals system

In this paper, we study a simplified system for the flow of nematic liquid crystals in a bounded domain in the three‐dimensional space. We derive the basic energy law which enables us to prove the global existence of the weak solutions under the condition that the initial density belongs to L^γ(Ω) for any $\gamma >\frac{3}{2}$. Especially, we also obtain that the weak solutions satisfy the energy inequality in integral or differential form. Copyright © 2009 John Wiley & Sons, Ltd.     

An algorithm for the electromagnetic scattering due to an axially symmetric body with an impedance boundary condition

Let B be a body in R³ and let S denote the boundary of B. The surface S is described by $\text{S = {(x, y, z): (x}{}^2\text{+ y}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= f(z), ?1 ? z ? 1}}$, where f is an analytic function that is real and positive on (?1, 1) and f(±1) = 0. An algorithm is described for computing the scattered field due to a plane wave incident field, under Leontovich boundary conditions. The Galerkin method of solution used here leads to a block diagonal matrix involving 2M + 1 blocks, each block being of order 2(2N + 1). If, e.g., N = O(M²), the computed scattered field is accurate to within an error bounded by $\text{Ce}{}^{\mathrm{<mtext>?cN</mtext><mtext>1</mtext><mtext>2</mtext>}}$, where C and c are positive constants depending only on f.     

The stability of the rotation of a heavy body with a viscous filling

The stability of the permanent rotation of a symmetrical heavy body with a viscous filling is investigated. A finite-dimensional phenomenological model of the “internal friction” with which the filling acts on the wall of the cavity is constructed based on the Helmholtz equations for a vortex. The boundaries of the stability limit are constructed and the interaction between the internal friction and the external damping is tracked. It is shown that the cases of a cavity that is oblate and prolate along the axis of rotation lead to the existence of different forms of stability regions.     

The stream function coordinate system for solution of one-dimensional unsteady compressible flow problems

A one-dimensional unsteady compressible isentropic flow problem is solved using a floating grid finite difference method. GENMIX, a computer program for solution of two-dimensional parabolic flow problems, has been adopted for this purpose. The advantages of utilizing the staggered floating grid method are demonstrated through solution of flow in a shocktube. The present method is able to precisely locate the discontinuities in temperature and density profiles.