Bart J. Daly

Transport Equations in Turbulence

Turbulence transport equations, describing the dynamics of transient flow of an incompressible fluid in arbitrary geometry, have been derived in such a manner as to incorporate the principles of invariance (tensor and Galilean) and universality. The equations are described in detail and their applicability is demonstrated by comparison of solutions with experiments on turbulence distortion and on the turbulence in the flow between flat plates.

An Eulerian differencing method for unsteady compressible flow problems

Abstract An Eulerian finite difference method is presented which can be used with a high-speed computer to solve the time-dependent equations of motion for the compressible flow of a fluid. The difference equations are described in detail, and the nature of the truncation errors introduced by the numerical approximations is discussed, as are the stability properties of the equations. Three solutions involving time-dependent flow in two space dimensions are described and analyzed: the diffraction of a weak shock travelling through a z -shaped tunnel, the interaction of a supersonic blunt body with a plane shock wave, and the passage of a plane shock over a conical body. Good agreement with experimental data is obtained in all cases where comparisons are made.

NUMERICAL STUDY OF TWO FLUID RAYLEIGH--TAYLOR INSTABILITY.

A new computing technique for the time‐dependent calculation of the interaction of two incompressible fluids is used to study the linear and nonlinear phases of Rayleigh‐Taylor instability. The variation of the linear growth rate with Reynolds number is examined for Reynolds numbers < 200 at a ratio of fluid densities of 2 : 1. These findings support Chandrasekhars predictions of the magnitude of the growth rate and the Reynolds number for which maximum growth rate is attained. A series of inviscid flow calculations, at density ratios between 1.1 : 1 and 10 : 1, is used to explore the effect of density ratio on aspects of the nonlinear Rayleigh‐Taylor instability. It is found that such influences as form drag and Kelvin‐Helmholtz instability decrease rapidly in importance as the density ratio increases.

Numerical Study of the Effect of Surface Tension on Interface Instability

A new technique for including the effect of surface tension in time‐dependent, incompressible flow calculations is used to examine the linear and nonlinear phases of Rayleigh‐Taylor instability. The variation of the linear growth rate with the surface tension coefficient and (for a fixed coefficient) with the wavenumber of the perturbation is shown to be in good agreement with Chandrasekhars analytic prediction. In the nonlinear regime, it is shown how surface tension affects the growth of the Rayleigh‐Taylor spike and provides the mechanism for drop separation from the spike.

A technique for including surface tension effects in hydrodynamic calculations

Abstract A technique is described for including the effects of surface tension in time-dependent, hydrodynamics calculations. The fluid interface is initially marked with a sequence of interface particles, which thereafter move through the computation mesh at the local fluid velocity. At each calculation cycle these particles are joined by sections of cubics in order to determine the orientation of the fluid interface. From this orientation the surface tension contribution to the fluid acceleration is determined.

Numerical Study of Density‐Current Surges

The marker and cell technique for the calculation of time‐dependent incompressible flows is used to study density‐current surges at density ratios between 1.05 and 3.0. The study is performed using the full two‐fluid approach as well as a single‐fluid technique involving solute transport and a Boussinesq approximation to the Navier‐Stokes equation. A comparison of these results indicates that the Boussinesq approximation is reasonably accurate for density ratios less than 1.3. The results of free surface and confined flow calculations are compared and the effects of slope, viscosity, and surface tension on density current flows are examined. Complete descriptions are given for the first time of the techniques used for including solute transport and surface tension in marker and cell calculations, and an analysis of the calculational stability properties of the method is included. The numerical results, which are in good agreement with available experimental measurements, provide information about some previously univestigated aspects of density current flows. Of particular importance here is the variation of the front velocity and height with density ratio, for ratios in the range, 1.2‐3.0. New analytical treatments of the initial current surge, the steady flow, and the effects of viscosity are presented and compared with computed results.

A numerical study of pulsatile flow through stenosed canine femoral arteries

Abstract A numerical study is made of pulsatile flow through stenosed canine femoral arteries for lumen constrictions in the range 0–61%. Comparison of results with in vivo measurements indicates that the pressure drop across the stenosis and the time averaged peak wall shear may be sufficiently large when the areal restriction is 61% to result in the development of atheromatous lesions and endothelial damage proximal to the stenosis, but that these effects are unlikely when the restriction is 44% or less. Local flow reversal is observed in the wake of the stenosis during systole and during diastolic flow reversal, but the rate of development of the local reverse flow is very sensitive to stenosis height. For the more severe stenoses this local reverse flow results in a finite wall shear throughout the wake region, except at the point where the boundary of local reverse flow attaches at the stenosis. The amplitude and phase of the pressure gradient over the stenosis, relative to those in a normal section of artery, were found to be sensitive indicators of stenosis development.

A Model of Countercurrent Steam-Water Flow in Large Horizontal Pipes

AbstractA numerical study was performed to derive a model of countercurrent steam-water flow in large horizontal pipes, with application to the emergency core cooling (ECC) system of a pressurized water reactor. The purpose of the study was to provide data from which simple correlations could be obtained to describe mass, momentum, and energy exchange between the phases during hot leg ECC injection. It was assumed that steam, driven by a pressure drop from the upper plenum to the ECC injection port, flows counter to the subcooled ECC water. Several series of calculations were performed to determine the sensitivity of the ECC flow velocity at the entrance to the reactor vessel to the pressure drop, for several values of the mass and momentum exchange coefficients used in the numerical method. The results were consistent with those obtained from solution of the mixture equation, which did not involve interfacial drag or condensation.

Inclusion of turbulence effects in numerical fluid dynamics

To show this distinction, consider the flow of water past a circular cylinder. For very slow speeds, the flow development is uniquely determined by the magnitude of the Reynolds number, Re E ud/9, in which u is the input flow speed, d is the diameter of the cylinder, and 9 is the kinematic viscosity of the water. Since these are macroscopic parameters, this flow is called laminar. As the speed increases, a double vortex develops behind the cylinder, and when the Reynolds number exceeds about 40, the double vortex begins to oscillate. Except for an arbitrary phase, however, the oscillations are uniquely determined by the macroscopic parameters, u, d, and ~, and the flow is still completely laminar. As the Reynolds number continues to increase, the changing pattern maintains its laminar property until a stage is reached in which noticeable effeots are observed that do not depend upon the macroscopic parameters. These spurious features are the result of microscopic perturbations, which for lower Reynolds numbers could never amplify to significance. They depend upon the details of cylinder roughness , slight mechanical vibrations and minor fluctuations of input water speed, and signify the onset of turbulence.