The numerical computation of turbulent flows

Fundamental Principles Laminar Boundary Layer Flow Laminar Duct Flow External Natural Convection Internal Natural Convection Transition to Turbulence Turbulent Boundary Layer Flow Turbulent Duct Flow Free Turbulent Flows Convection with Change of Phase Mass Transfer Convection in Porous Media.

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Convection Heat Transfer

A theoretical framework is proposed for the analysis of adhesion between cells or of cells to surfaces when the adhesion is mediated by reversible bonds between specific molecules such as antigen and antibody, lectin and carbohydrate, or enzyme and substrate. From a knowledge of the reaction rates for reactants in solution and of their diffusion constants both in solution and on membranes, it is possible to estimate reaction rates for membrane-bound reactants. Two models are developed for predicting the rate of bond formation between cells and are compared with experiments. The force required to separate two cells is shown to be greater than the expected electrical forces between cells, and of the same order of magnitude as the forces required to pull gangliosides and perhaps some integral membrane proteins out of the cell membrane.

https://science.sciencemag.org/content/sci/200/4342/618.full.pdf

Models for the specific adhesion of cells to cells

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segree & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

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The lift on a small sphere in a slow shear flow

A comprehensive and critical review of closure approximations for two-equation turbulence models has been made. Particular attention has focused on the scale-determining equation in an attempt to find the optimum choice of dependent variable and closure approximations. Using a combination of singular perturbation methods and numerical computations, this paper demonstrates that: 1) conventional A:-e and A>w formulations generally are inaccurate for boundary layers in adverse pressure gradient; 2) using "wall functions'' tends to mask the shortcomings of such models; and 3) a more suitable choice of dependent variables exists that is much more accurate for adverse pressure gradient. Based on the analysis, a two-equation turbulence model is postulated that is shown to be quite accurate for attached boundary layers in adverse pressure gradient, compressible boundary layers, and free shear flows. With no viscous damping of the model's closure coefficients and without the aid of wall functions, the model equations can be integrated through the viscous sublayer. Surface boundary conditions are presented that permit accurate predictions for flow over rough surfaces and for flows with surface mass addition.

Reassessment of the scale-determining equation for advanced turbulence models

The equation governing four-wave interactions in a nonlinear dispersive system is studied. It is shown that a nonlinear steady-state plane wave can bifurcate into nonplanar steady-state solutions. In the case of an isotropic medium, the bifurcation is degenerate and the bifurcated solutions may preserve or break the symmetry. An example is given of a symmetry-breaking solution for deep-water gravity waves and its stability is discussed.

/pdf/bifurcation-and-symmetry-breaking-in-nonlinear-dispersive-12rn0uqpw8.pdf

Bifurcation and symmetry breaking in nonlinear dispersive waves

Vortex Induced Lift on Two Dimensional Low Speed Wings

This paper examines the existence and properties of steady finite-amplitude waves of cats-eye form superposed on a unidirectional inviscid, incompressible shear flow. The problem is formulated as the solution of nonlinear Poisson equations for the stream function with boundary conditions on the unknown edges of the cats-eyes. The dependence of vorticity on stream function is assumed outside the cats-eyes to be as in the undisturbed flow, and uniform unknown vorticity is assumed inside. It is argued on the basis of a finite difference discretization that the problem is determinate, and numerical solutions are obtained for Couette-Poiseuille channel flow. These are compared with the predictions of a weakly nonlinear theory based on the approach of Benney & Bergeron (1969) and Davis (1969). The phase speed of the waves is found to be linear in the wave amplitude.

Finite-Amplitude Waves in Inviscid Shear Flows

The shape and stability of twodimensional, uniform patches of vorticity in incompressible inviscid fluid are calculated. The object of the study is to investigate the effect of wind shear on traili...

Counter-rotating vortex patches in shear: a model of the effect of wind shear on aircraft trailing vortices

The necessary conditions are examined for a film in contact with its own vapor to flow without dissipation. When the local gas is in equilibrium with the vapor of a bulk reservoir, the equilibrium thickness of the flowing film is the same as that of the film at rest. For nonsteady flow, the predicted thickness depends on a nonequilibrium condition that cannot be deduced from thermodynamic arguments. A plausible form is proposed for the needed condition. It is shown that the film may be thinner than the rest value for times large compared with apparent relaxation times of the system. The results reconcile a number of experiments which had previously appeared contradictory. In addition, the theory is consistent with measurements of the convection speed of third sound and shows why previous efforts to explain the attenuation of third sound have failed.

Philip Geoffrey Saffman

Papers

Bifurcation and symmetry breaking in nonlinear dispersive waves

Vortex Induced Lift on Two Dimensional Low Speed Wings

Finite-Amplitude Waves in Inviscid Shear Flows

Counter-rotating vortex patches in shear: a model of the effect of wind shear on aircraft trailing vortices

The theory of nondissipative flow in the helium film