A variant of the low-Reynolds-number two-equation turbulence model applied to variable property mixed convection flows

Previous work has demonstrated that the low-Reynolds-number model of Launder and Sharma (1974) offers significant advantages over other two-equation turbulence models in the computation of highly non-universal buoyancy-influenced (or “mixed convection”) pipe flows. It is known, however, that the Launder and Sharma model does not possess high quantitative accuracy in regard to simpler forced convection flows. A variant of the low-Reynolds-number scheme is developed here by reference to data for constant property forced convection flows. The re-optimized model and the Launder and Sharma formulation are then examined against experimental measurements for mixed convection flows, including cases in which variable property effects are significant.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Small-scale measurements in a partially stirred reactor

This paper describes an experimental study of a partially stirred reactor (PaSR). The reactor is a cubic box in which air (either pure or mixed with a tracer) is continuously injected through 12 jets situated in two opposite planes and impinging through the center. The flow in the reactor interior is well approximated as stationary, globally homogeneous and isotropic. Global properties of turbulent flow and passive scalar mixing are studied, in terms of length scales, characteristic times, spectra, etc. Particular attention has been paid to a proper determination of the mean value of the passive scalar variance dissipation rate 〈ε _Z 〉, in the central quasi-homogeneous zone of the reactor.     

Ein interaktives Verfahren zur Auswertung von Kaustiken an Trennflächenrissen

Übersicht In diesem Beitrag wird eine auf der interaktiven numerisch/graphischen Bildverarbeitung beruhende Methode zur Ermittlung der Spannungsintensitätsfaktoren, für Trennflächenrisse in Verbundmaterialien vorgestellt. Eine Anzahl von detenpunkten entlang der experimentell aufgezeichneten Kaustik wird als Eingabe verwendet. Das Verfahren überprüft die Genauigkeit und Zuverlässigkeit der Ergebnisse selbst, indem die auf der Basis des Resultats numerisch generierte Kaustik mit der experimentellen verglichen wird.

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An interactive method for data processing from crack tip caustics at interfaces

Summary An interactive numerical-graphical image processing method for the evaluation of stress intensity factors at interface cracks in composites will be presented. Based on a set of experimental data points suitably chosen along the caustic the multipoint overdeterministic data reduction technique provides reliable and rapidly coverging results by cross-checking experimental caustics with numerically generated iterative caustics.

     

Non-Markovian diffusion process in polymers and stretched exponential relaxation

In this contribution, we model the long-time behaviour of the desorption from an LDPE sheet, using non-Markovian random walks. It is shown that the mass of penetrant in the final stage of desorption decays as t ^–m , where m is proportional to the exponent of the probability distribution (t) t ^–(1+u), 0 < v < 1. Furthermore, it is shown that this model may lead to the so-called mechanical stretched exponential relaxation, and that Wagner's memory function can be obtained as a special case.Presented at the second conference Recent Developments in Structured Continua, May 23–25, 1990, in Sherbrooke, Québec, Canada     

Electrohydrodynamic monodispersion of liquids

In electrostatic dispersion of a liquid from a meniscus at the end of a capillary through which the liquid is passed the emitted droplets are unstable with respect to their self-charge and break up, ejecting about 100 smaller (by two orders of magnitude) droplets. However, if the liquid is passed through the capillary under pressure, then, depending on the pressure, there exist ranges of values of voltages applied to the electrodes for which the emitted droplets are stable both with respect to their self-charge and with respect to the external electric field of the system of electrodes. In this paper, the sizes, charges, and specific charges of such droplets are calculated on the basis of the principle of least dissipation of the energy.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 32–40, March–April, 1991.     

Analytical investigation of Bénard-Marangoni convection heat transfer in a shallow cavity filled with two immiscible fluids

The mechanism of natural and Marangoni convection in a system with two stratified fluid layers without mass transfer at the interface is investigated. The basis of the analytical solution is an assumption of parallel flow over a large portion of the system. The two cases of heat fluxes through horizontal or vertical opposite walls are considered. It is demonstrated that four different patterns of convection can be observed in the present system. The zone of occurrence of these flow patterns are specified in terms of non-dimensional parameters. Velocity and temperature distributions, stream function and Nusselt number are presented over a wide range of the governing parameters. The results obtained are explained in terms of the basic physical mechanisms that govern these flows showing many interesting aspects of the complex interaction between the buoyant and surface tension mechanisms.     

Fluctuating fluid forces acting on a circular cylinder and interference with a plane wall

The flow around a circular cylinder placed close to a horizontal plane wall was investigated experimentally. Fluctuations of lift and drag of the cylinder and wall interference effects were studied in terms of the gap height between the cylinder and wall and the thickness of the turbulent wall boundary layer. The fluctuating fluid forces acting on the cylinder sharply increased, and the regular vortex shedding, i.e. Kárman vortex streets, started to form beyond a critical gap height. The formation of Kárman vortex streets was abruptly interrupted when the bottom of the cylinder came in contact with the outer layer of the boundary layer developed on the wall. This critical gap height correlated well with the thickness of the boundary layer.     

Homogeneous Cooling States¶are not always¶Good Approximations to Granular Flows

A widespread belief in the study of granular flow is the existence of “homogeneous cooling states”, i.e., self-similar solutions which would attract all solutions, faster than the equilibrium solution does. In most cases, the existence of these self-similar solutions is an open problem. Here we consider a one-dimensional model, which has been used for some years, and for which simple self-similar solutions do exist. However, we prove that the approximation is quite poor. Our proof makes use of the powerful and simple tools of mass transportation, and exploits the structure of the evolution equation, seen as a nonlinear transport equation.     

WAVE PROPAGATION IN A SYSTEM OF COAXIAL TUBES FILLED WITH INCOMPRESSIBLE MEDIA: A MODEL OF PULSE TRANSMISSION IN THE INTRACRANIAL ARTERIES

The propagation of harmonic waves through a system formed of coaxial tubes filled with incompressible continua is considered as a model of arterial pulse propagation in the craniospinal cavity. The inner tube represents a blood vessel and is modelled as a thin-walled membrane shell. The outer tube is assumed to be rigid to account for the constraint imposed on the vessels by the skull and the vertebrae. We consider two models: in the first model the annulus between the tubes is filled with fluid; in the second model the annulus is filled with a viscoelastic solid separated from the tubes by thin layers of fluid. In both models, the elastic tube is filled with fluid. The motion of the fluid is described by the linearized form of the Navier–Stokes equations, and the motion of the solid by classical elasticity theory. The results show that the wave speed in the system is lower than that for a fluid-filled elastic tube free of any constraint. This is due to the stresses generated to satisfy the condition that the volume in the system has to be conserved. However, the effect of the constraint weakens as the radius of the outer tube is increased, and it should be insignificant for the typical physiological parameter range.