Showing papers on "Volume of fluid method published in 1990"

Turbulent fountains in an open chamber

Abstract: The flow and density distribution produced by injecting dense fluid upwards at the bottom of a homogeneous fluid have been investigated experimentally and theoretically. Both axisymmetric and line sources have been studied using small-scale laboratory experiments in which salt water is injected into a tank of fresh water. The turbulent fountain formed in this way rises to a maximum height which can be related to the Froude number of the inflow, and then falls back and spreads out along the floor. Continuing the inflow builds up a stable stratification in a similar manner to that discussed earlier for the ‘plume filling box model’ of Baines & Turner (1969) which is complementary to the present work. The fountain flows considered here have the important new feature that the volume of the inflow is significant, so the total volume of fluid in the ‘open’ container increases with time. The evolution is determined by the rate of entrainment into the fountain from its surroundings, which is found directly by experiment. Re-entrainment of fluid into the fountain continually changes the density profile in the mixed fluid collecting at the bottom of the chamber below the level of the fountain top, and controls the rate of rise of a ‘front’ of marked fluid. The top of the fountain rises linearly in time, at a rate which, for axisymmetric fountains, has been shown both experimentally and theoretically to be close to half the rate of rise of the free surface due to the inflow. Thus at a certain time the front rises above the top of the fountain. Once the mixed fluid at the bottom of the chamber has risen above the fountain its density profile remains unchanged. The front velocity, the fountain height and the density profile have all been obtained as functions of time using a theory which is in good agreement with the experimental results for a large range of input Froude numbers. For line fountains the results are less precise owing to an instability which causes the flow to switch irregularly from a symmetrical state to one in which the downflow occurs on one side only, and with a smaller maximum height. In concluding we discuss the applications which motivated the work, particularly the development of a stratified hybrid layer in magma chambers replenished from below, and the dynamically identical, but inverted problem of heating large buildings through ducts located near the roof.

Buoyancy-driven fluid fracture : similarity solutions for the horizontal and vertical propagation of fluid-filled cracks

Abstract: Buoyancy-driven flows resulting from the introduction of fluid of one density into a crack embedded in an elastic solid of different density are analysed. Scaling arguments are used to determine the regimes in which different combinations of the buoyancy force, elastic stress, viscous pressure drop and material toughness provide the dominant pressure balance in the flow. The nonlinear equations governing the shape and rate of spread of the propagating crack are formulated for the cases of vertical propagation of buoyant fluid released into a solid of greater density and of lateral propagation of fluid released at an interface between an upper layer of lesser density and a lower layer of greater density. Similarity solutions of these equations are derived under the assumption that the volume of fluid is given by Qtα, where Q and α are constants. Both laminar and turbulent flows are considered.Fluid fracture is an important mechanism for the transport of molten rock from the region of production in the Earth's mantle to surface eruptions or near-surface emplacement. The theoretical solutions provide simple models which describe the relation between the elastic and fluid-mechanical phenomena involved in the vertical transport of melt through the Earth's lithosphere and in the lateral intrusion of melt at a neutral-buoyancy level close to the Earth's surface.

Velocity measurement system

Abstract: A sonic-type fluid flow measuring system wherein reflections or echoes of an ultrasonic acoustic emitter (10) are sensed (14) typically comprise a number of frequencies representative of a number of discrete velocities of flow in a volume of fluid. As a sample, they simply appear as a voltage plot as a function of time and wherein the time width of a given signal excursion relates to the frequency of a given signal. Thereafter, this time domain signal sample (38) is converted to a frequency domain sample whereby the presence and magnitude of each frequency component, or velocity component, is isolated, this being typically done by what is known as a Fast Fourier Transform (42). The highest frequency, velocity signal from each of a rapid succession of samples is then obtained and stored in a memory (54). The highest and lowest of these are then discarded (56), and the remaining are averaged (58) to obtain more likely representations of velocity. As the goal is to determine an average fluid velocity for a whole cross section of fluid flow, the measured peak velocity is a detected reference from which a lesser velocity, for example, 0.9, of it is chosen (60, 62). To achieve a value for volume of flow, the average velocity is then multiplied by the cross-sectional area of the containment (8) through which flow occurs.

Method of evaluating fluid loss in subsurface fracturing operations

Abstract: An implementation of the present invention will typically be performed through use of two test fracturing or "mini-frac" operations to determine formation parameters. A first mini-frac operation will be performed to determine the fluid efficiency of the formation, and a second mini-frac operation will be performed to determine a late time fluid leak-off coefficient. The data thus obtained will be functionally related to simultaneously solve integral expressions to determine the total volume of fluid lost during pumping and the total volume of fluid lost during shut-in in response to an assumed spurt time. The fluid loss values will then be functionally related to the established fluid efficiency to estimate an early time fluid leak-off coefficient. The early time fluid leak-off coefficient thus determined will then be applied in a balance equation to verify the accuracy of such value in response to the assumed spurt time. The assumed spurt time may then be varied and the above fluid loss values iteratively reevaluated until the balance equation is satisfied within an acceptable range of tolerance.

Method and apparatus for regulating fluid flow

Abstract: Method and apparatus for regulating the passage of fluid through a chamber or other type of conduit. Fluid passage is terminated when the volume of fluid which has swept through a chamber equals a selected multiple of the chamber's internal volume, which multiple is known as swept chamber volumes.

A method of mixing and a mixing unit therefor

Abstract: A method of mixing first and second fluids, which are at different pressures, provides for the flow of said fluids along respective first and second flow paths which converge in a mixing zone A mixing unit for carrying out the above method includes a housing 1 to which are attached valves (13, 14) which control the flow of said first and second fluids through first and second flow paths 24, 23 respectively A nozzle 22 reduces the cross sectional area of the second flow path 23 through which the second flow passes to create in a mixing zone a jet or thrust of the second fluid which draws from the first flow path 24 a greater volume of fluid to improve throughput of the first flow and the mixing characteristics of the fluids

Liquid Argon Maximm Convective Heat Flux vs. Liquid Depth

Abstract: In order to help answer questions about the magnitude of heat flux to the liquid argon in a liquid argon calorimeter which could cause boiling (bubbles), calculations estimating the heat flux which can be removed by free convection were made in February, 1988. These calculations are intended to be an estimate of the heat flux above which boiling would occur. No formal writeup was made of these calculations, although the graph dated 3 Feb 88 and revised (adding low-velocity forced convection lines) 19 Feb 88 was presented in several meetings and widely distributed. With this description of the calculations, copies of the original graph and calculations are being added to the D0 Engineering Note files. The liquid argon surface is in equilibrium with argon vapor at a pressure of 1.3 bar, so the surface is at 89.70 K. The liquid is entirely at this surface temperature throughout the bulk of the volume, except locally where it is warmed by a solid surface at a higher temperature than the bulk liquid. This surface temperature is taken to be the boiling temperature of argon at the pressure corresponding to 1.3 bar plus the liquid head; hence it is a function of depth below the surface. The free and forced convection correlations used are 'from Kreith, 'Heat Transfer', for heated flat plates in a large (i.e., no other objects nearby enough to disturb the flow) uniform volume of fluid. Heat flux is a function of plate size, really length along the flow path (since a boundary layer increases in thickness starting from the leading edge of the plate), and orientation (i.e., vertical or horizontal). The maximum heat flux which can be carried away by free convection (i.e., the heat flux above which boiling occurs) is .001 W/sq.cm. at 4 inches below the surface and 0.1 to 0.2 W/sq.cm. 15 feet below the surface. Forced convection over a 1 cm plate with a fluid velocity of 1 cm/sec, or a 10 cm plate at 10 cm/sec, is about like free convection. The line for much higher heat flux is 10 cm/sec flow over a 1 cm plate.

An approach to the free surface flow analysis by FEM using the VOF method.

Abstract: A numerical analysis technique for free surface flow problems by FEM is presented. The VOF (Volume of Fluid) method is employed in order to represent the free surface by Eularian mesh. FEM with the VOF method mentioned here is convenient to simulate the large deformation of the free surface without re-meshing. The convective equation of VOF is solved by a fully implicit scheme, thus simulating shapes and locations of the free surfaces accurately. Numerical calculations were carried out for the breakdown flow of a dam and the mold filling simulation in die casting and these results were examined in comparison with experimental results and calculation results in the references.

Modelling of Cavitation within Highly Transient Flows with the Volume of Fluid method

Abstract: Cavitation is the sudden vaporization of liquids due to rapid pressure drops within high-speed liquid flows. The presence of cavitation can cause tremendous pressure oscillations and result in significant mechanical damage. In civil hydraulics, failure to account for the potential of cavitation within dam structures can result in potentially catastrophic damage [1]. Likewise, cavitation within casting dies during high pressure die casting can result in die damage and increased maintenance and resulting part failure. Clearly, modelling cavitation and designing systems to minimize its effects are important in many industries. This work showcases modelling of cavitation and associated phase changes within highly transient, threedimensional free surface multiphase flows. Benchmark studies with experimental data are shown, along with examples of cavitation with real-world simulations in the fields of hydraulics and high pressure die casting. Benchmark examples presented show good agreement with regards to location and time evolution of cavitation behaviour. Forces on adjacent solid structures are also predicted. All simulations are performed using the soon-to-be released Version 11.1 of the computational fluid dynamics (CFD) software package FLOW-3D ® .