Unsteady weakly perturbed motion of a body of revolution in a liquid with jet separation

The unsteady weakly perturbed motion of a body in a liquid with jet separation has been investigated on various occasions in the twodimensional formulation [1–3]. The present paper gives a generalization of the formulation of this two-dimensional problem to the threedimensional case of flow past a body of revolution in accordance with Kirchhoff's scheme. A method is proposed for solving the obtained boundary-value problem using a Green's function. This function is constructed in a special system of curvilinear coordinates. To obtain an effective solution, a Laplace transformation is used. Expressions are given for the Laplace transforms of the vectors of the force and torque acting on the body in the unsteady motion.     

Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

The aim of this note is to present the exact solutions corresponding to two types of unsteady flows of an Oldroyd-B fluid in a channel of rectangular cross-section. The solutions that have been obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For λ_r or λ→0 they tend toward similar solutions for a Maxwell or second-grade fluid. If both λ_r and λ→0, the solutions for Navier-Stokes fluids are recovered.     

Cycle-to-cycle variation effects on turbulent shear stress measurements in pulsatile flows

Accurate evaluation of turbulent velocity statistics in pulsatile flows is important in estimating potential damage to blood constituents from prosthetic heart valves. Variations in the mean flow from one cycle to the next can result in artificially high estimates. Here we demonstrate a procedure using a digital, low-pass filter to remove the cycle-to-cycle variation from turbulence statistics. The results show that cycle-to-cycle variations can significantly affect estimates of turbulent Reynolds stress and should be either eliminated or demonstrated to be small when reporting pulsatile flow results.List of symbols D inside diameter of aortic valve - R radius of model aorta - t time window - t time - T period of cycle - T duration of outflow pulse from ventricle - U instantaneous axial velocity - U _L low-pass axial velocity - U _p mean periodic axial velocity - U ensemble averaged axial velocity - uv ensemble-average turbulent velocity product - u root-mean-square of turbulent axial velocity - U _max maximum, ensemble-averaged axial velocity - V instantaneous radial velocity - y vertical distance from aorta centerline - z axial distance downstream of prosthetic heart valve This paper was presented at the Tenth Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986     

Unsteady flows in elastico-viscous liquids

Summary Consideration is given to two problems involving the unsteady motion of a sphere in aMaxwell liquid. In both problems the full solutions are obtained and compared in each case to the solution obtained using an approximation procedure. Good agreement is obtained for large values of the elastic parameter. The approximation reduces the mathematics considerably and thus allows experimentalists to determine the elastic parameter involved.With 2 figures     

Unsteady layered vortical fluid flows

An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived. The solution generalizes that describing the Couette flow. Two ways of preassigning the boundary conditions at the upper boundary of a fluid layer are considered. These are the time-dependent variation of the velocity value with the conservation of its direction and the variation of the angle at which the velocities parallel to the coordinate axes are directed. It is shown that at certain values of vorticity, viscosity, and the layer thickness the velocities within the layer can be severalfold greater than the given velocity at the boundary.     

Unsteady flows of inhomogeneous incompressible fluids

In this paper, we study the unsteady motion of inhomogeneous incompressible viscous fluids. We present the results corresponding to Stokes' second problem and for the flow between two parallel plates where one is oscillating.     

Unsteady interaction of uniformly vortex flows

The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows. An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998.     

Unsteady flows of a viscoplastic medium in channels

We numerically study the nonstationary Poiseuille problem for a Bingham-Il’yushin viscoplastic medium in ducts of various cross-sections. The medium acceleration and deceleration problems are solved by using the Duvaut-Lions variational setting and the finite-difference scheme proposed by the authors. The dependence of the stopping time on internal parameters such as density, viscosity, yield stress, and the cross-section geometry is studied. The obtained results are in good agreement with the well-known theoretical estimates of the stopping time. The numerical solution revealed a peculiar characteristic of the stagnant zone location, which is specific to unsteady flows. In the annulus, disk, and square, the stagnant zones arising shortly before the flow cessation surround the entire boundary contour; but for other domains, the stagnant zones go outside the critical curves surrounding the stagnant zones in the steady flow. The steady and unsteady flows are studied in some domains of complicated shape.     

Theory of slightly perturbed three-dimensional flows in nozzles

The theory of slightly perturbed flows in conical nozzles is used to determine the transverse force and moment generated in the presence of asymmetric perturbations. A system of ordinary differential equations is derived for finding the transverse force and moment. An approximate analytical solution of this system is constructed and its qualitative features are studied. A comparison is made with a numerical solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–154, January–February, 1977.     

Unsteady RANS simulation of oscillating mould flows

Mould flow oscillations are of major importance for the performance of the continuous casting process. They are suspected to promote entrainment of slag and other unwanted secondary phases into the melt pool. These oscillating turbulent flows are investigated by means of numerical simulations. The numerical model is based on the equation of continuity and the unsteady Reynolds averaged Navier–Stokes equations. The system of flow equations is closed by a Reynolds stress turbulence model in combination with non‐equilibrium wall functions. The unsteady simulation resolves low‐frequency oscillations of the flow field. These frequencies and numerically resolved mean values are in agreement with results of corresponding model experiments. The proposed model should be advantageous in order to investigate the mechanisms of the oscillations and the process of slag entrainment in more detail. Copyright © 2006 John Wiley & Sons, Ltd.     

Unsteady quasi-one-dimensional flows of relaxing nitrogen tetroxide

The decay of an arbitrary discontinuity and the reflection of a fan of rarefaction waves from a fixed wall in dissociating nitrogen tetroxide are considered. The system of the equations of gas dynamics and the equation of the conservation of the mass of component i have been integrated numerically by MacCormack's method. It is shown that the kinetics has a significant influence on the characteristics of a shock wave and a contact discontinuity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–164, July–August, 1981.     

Unsteady boundary layers with small cross flows

Despite the intensive development of computer technology and methods of solving the Navier-Stokes and Reynolds equations, the unsteady problems of the three-dimensional boundary layer are of significant interest in aerodynamics. So far these problems have been little studied as a result of objective difficulties related with the large dimensionality of the system of equations and the complexity of its investigation [{xc1}]. Therefore, analytic results in this field are important. In the present study the unsteady three-dimensional boundary layer equations are investigated in the case of small cross flows using the perturbation method. An intermediate system of equations, which includes the basic three-dimensional effects but is significantly simpler than the initial system is derived. The features of the formulation considered are studied in relation to the important practical problems of boundary layer flow past slender wings and weakly asymmetric bodies at small angles of attack.     

Unsteady flows of a third-order viscoelastic fluid

Summary Unsteady third-order viscoelastic flow is examined for the purpose of determining a method by which certain material constants in theRivlin-Ericksen theory can be measured. The concept of an intrinsic pressure hole error is used, and an expression for this error is derived for third-order flow. It is also shown that the velocity field for unsteady creeping motion of a third-order fluid is identical at any time to a corresponding steady third-order flow. The pressure field, however, depends upon the rate of change of the flow with time.

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Zusammenfassung Es wird die instationäre Strömung dritter Ordnung einer viskoelastischen Flüssigkeit untersucht zu dem Zweck, eine Methode anzugeben, mit deren Hilfe gewisse Stoffkonstanten in der Theorie vonRivlin undEricksen gemessen werden können. Dazu wird das Konzept des intrinsic pressure hole error verwendet, und es wird für diesen Fehler im Rahmen der Theorie dritter Ordnung ein Ausdruck abgeleitet. Weiter wird gezeigt, daß das Geschwindigkeitsfeld für die instationäre schleichende Strömung einer Flüssigkeit dritter Ordnung zu jeder Zeit mit der zugeordneten stationären Strömung dritter Ordnung identisch ist. Im Gegensatz dazu hängt das Druckfeld jedoch von der zeitlichen Änderung der Strömungsgeschwindigkeit ab.

     

Dynamics of pulsatile flows through microtubes from nonlocality

In this paper we introduce a new notion of complexified nonlocal-in-time-space material derivative operator and we discuss its implications in fluid mechanics. After deriving the complexified fluid equations, we investigate the problem of laminar flow of a particle fluid in a microtube. We demonstrate the occurrence of pulsatile flows through microtubes in agreement with recent findings.     

Singularly perturbed solution for weakly nonlinear equations with two parameters

A class of singularly perturbed boundary value problems of weakly non- linear equation for fourth order on the interval[a,b]with two parameters is considered. Under suitable conditions,firstly,the reduced solution and formal outer solution are con- structed using the expansion method of power series.Secondly,using the transformation of stretched variable,the first boundary layer corrective term near x=a is constructed which possesses exponential attenuation behavior.Then,using the stronger transfor- mation of stretched variable,the second boundary layer corrective term near x=a is constructed,which also possesses exponential attenuation behavior.The thickness of second boundary layer is smaller than the first one and forms a cover layer near x=a. Finally,using the theory of differential inequalities,the existence,uniform validity in the whole interval[a,b]and asymptotic behavior of solution for the original boundary value problem are proved.Satisfying results are obtained.