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Showing papers on "Volume of fluid method published in 1970"


Journal ArticleDOI
TL;DR: In this article, a theory for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat was developed.
Abstract: An effort is made to understand turbulence in fluid systems like the oceans and atmosphere in which the Richardson number is generally large. Toward this end, a theory is developed for turbulent flow over a flat plate which is moved and cooled in such a way as to produce constant vertical fluxes of momentum and heat. The theory indicates that in a co-ordinate system fixed in the plate the mean velocity increases linearly with height z above a turbulent boundary layer and the mean density decreases as z3, so that the Richardson number is large far from the plate. Near the plate, the results reduce to those of Monin & Obukhov.The curvature of the density profile is essential in the formulation of the theory. When the curvature is negative, a volume of fluid, thoroughly mixed by turbulence, will tend to flatten out at a new level well above the original centre of mass, thereby transporting heat downward. When the curvature is positive a mixed volume of fluid will tend to fall a similar distance, again transporting heat downward. A well-mixed volume of fluid will also tend to rise when the density profile is linear, but this rise is negligible on the basis of the Boussinesq approximation. The interchange of fluid of different, mean horizontal speeds in the formation of the turbulent patch transfers momentum. As the mixing in the patch destroys the mean velocity shear locally, kinetic energy is transferred from mean motion to disturbed motion. The turbulence can arise in spite of the high Richardson number because the precise variations of mean density and mean velocity mentioned above permit wave energy to propagate from the turbulent boundary layer to the whole region above the plate. At the levels of reflexion, where the amplitudes become large, wave-breaking and turbulence will tend to develop.The relationship between the curvature of the density profile and the transfer of heat suggests that the density gradient near the level of a point of inflexion of the density curve (in general cases of stratified, shearing flow) will increase locally as time goes on. There will also be a tendency to increase the shear through the action of local wave stresses. If this results in a progressive reduction in Richardson number, an ultimate outbreak of Kelvin–Helmholtz instability will occur. The resulting sporadic turbulence will transfer heat (and momentum) through the level of the inflexion point. This mechanism for the appearance of regions of low Richardson number is offered as a possible explanation for the formation of the surfaces of strong density and velocity differences observed in the oceans and atmosphere, and for the turbulence that appears on these surfaces.

27 citations


Patent
Jack R Hulme1
16 Jul 1970
TL;DR: In this paper, the volume of fluid leakage in a conduit exceeds a predetermined percentage of the total fluid flow by measuring the leakage volume from the conduit and comparing the volume with a predetermined proportion of the volume in total flow.
Abstract: Method and apparatus for determining when the volume of fluid leakage in a conduit exceeds a predetermined percentage of the volume of total fluid flow by measuring the volume of fluid leakage from the conduit, comparing the volume of fluid leakage with a predetermined percentage of the volume of total fluid flow and generating a distinctive signal based on the comparison.

24 citations


Patent
28 Sep 1970
TL;DR: In this paper, a method and apparatus for determining the weight of a moisture-free, compressible material in a given volume of fluid suspension is described, where the material in the confined suspension is compressed with a movable porous surface at a predetermined pressure to form a mat of the material.
Abstract: A method and apparatus are described for determining the weight of a moisture-free, compressible material in a given volume of fluid suspension. The given volume of the suspension is confined and the material in the confined suspension is compressed with a movable porous surface at a predetermined pressure to form a mat of the material. The thickness of the mat thus formed is measured and the weight of the material is determined therefrom from a known relationship. The apparatus may be flushed out by movement of a lower non-porous piston which retracts to open an outlet from the chamber.

4 citations


Journal ArticleDOI
TL;DR: In this paper, the initial release problem of a finite volume of dense fluid underlying a deeper layer of less dense fluid is studied, where the flow is modelled by the shallow-water equations in three spatial dimensions which are expressed as a system of nonlinear hyperbolic conservation laws.
Abstract: The steady-state propagation of cold domes of dense fluid lying beneath a layer of less dense fluid and overlying a sloping bottom have been studied previously by Nof [I]. Such research is important in improving the understanding of heat and mass transport in the oceans, and much of the presentday understanding relies on the assumption that the flow is in geostrophic balance. Such an assumption is not valid either when inertial effects in the flow dominate, or when the flow is near the equator. The research presented concerns the initial release problem of a finite volume of dense fluid underlying a deeper layer of less dense fluid. The flow is modelled by the shallow-water equations in three spatial dimensions which are expressed as a system of nonlinear hyperbolic conservation laws. Numerical solutions are achieved through the use of a finite-difference relaxation method developed previously by Jin and Xin [2], and modified for use in this specific situation by Montgomery [3]. Results are presented showing the resulting time-dependent flow for the initial release problem of a cylinder of dense fluid, with varying rotation rates and bottom slope to help investigate the times required for the inertial spreading to become primarily geostrophic.

1 citations


DOI
01 Jan 1970
TL;DR: The numerical stability of a VOF-based code is maintained during the simulation of five wave periods which are generated by a weakly reflective boundary condition (WRIB) as mentioned in this paper.
Abstract: The volume of fluid method (VOF) of Hirt and Nichols' is applied in the simulation of transient waves at coastal structures where the fluid free surface gets mostly distorted at impact zone and important wave interactions with external boundaries take placed The numerical stability of a VOF based code is maintained during the simulation of five wave periods which are generated by a weakly reflective boundary condition (WRIB). In this paper, the VOF method is not fully introduced but numerical techniques for solving the Poisson equations at arbitrary boundaries are discussed with cases of wave flows in a 35. m long and 1.5m deep pool with a slope are shown.