Jump conditions and entropy sources in two-phase systems. Local instant formulation

Publisher Summary This chapter reviews recently published research dealing with gas-liquid two-phase flow in microchannels. Only microchannels with hydraulic diameters of the order of 0.1 to 1 mm and with long length-to-hydraulic diameter ratios are considered here. The hydrodynamic phenomena reviewed includes the two-phase flow regimes, void fraction, and frictional pressure drop in narrow rectangular and annular passages, a micro-rod bundle, and microchannels under conditions where surface tension and inertial forces are both significant. In these systems the channel characteristic dimension is of the same order of magnitude, or smaller than, the neutral interfacial wavelengths predicted by the Taylor stability analysis. The review is also restricted to situations where the fluid inertia is significant in comparison with surface tension. Such microchannels and flow conditions are encountered in miniature heat exchangers, research nuclear reactors, biotechnology systems, the cooling of high-power electronic systems, the cooling of the plasma-facing components in fusion reactors, and the heat rejection systems of spacecraft, to name a few. The flow through cracks and slits when such cracks develop in vessels and piping systems containing high-pressure liquids is another application of two-phase flow in microchannels of interest here.

Two-phase flow in microchannels

A nonequilibrium two-phase flow model is described for the analysis of critical flows in variable diameter tubes. Modeling of the two-phase flow mixture in the tube is accomplished by utilizing a one-dimensional form of conservation and balance equations of two-phase flow which account for the relative velocity and temperature differences between the phases. Closure of the governing equations was performed with the constitutive equations which account for different flow regimes, and the solution of the nonlinear set of six differential equations was accomplished by a variable step numerical procedure. Computations were carried out for a steam--water mixture with varying degrees of liquid subcooling and stagnation pressures in the vessel upstream of the tube and for different tube lengths. The numerical resuls are compared with the experimental data involving critical flows with variable liquid subcoolings, stagnation pressures, and tube lengths, and it is shown that the nonequilibrium model predicts well the critical flow rate, pressure distribution along the tube, and the tube exit pressure.

Nonequilibrium Modeling of Two-Phase Critical Flows in Tubes

Two-Phase Flow, Boiling, and Condensation by S. Mostafa Ghiaasiaan

Highlights of two-phase critical flow: On the links between maximum flow rates, sonic velocities, propagation and transfer phenomena in single and two-phase flows

From international symposium on two-phase systems; Haifa, Israel (29 Aug 1971). See CONF-710836-. For describing two-phase one-component annular flows with thermodynamic equilibrium in constant cross-section pipes, a system of four differential equations must be solved by a stepby-step procedure. It is shown that this system must include one continuity equation, two momentum equations, and one energy equation. The critical flow condition is given by the vanishing condition of a fourth-order determinant. At given pressure and quality, this condition can be presented as a relation between critical mass-velocity and slip- ratio. An entropy balance equation is deduced from the other balance equations by means of the second principle of thermodynamics and it is shown that it can be used to derive the same critical flow condition. This variable slip model exhibits the increase of critical flow-rates with decreasing slip ratios occurring experimentally when decreasing the L/D parameter. The hypothesis of thermal equilibrium may be avoided in order to include jet flows which occur in short pipes. This requires an additional heat-balance equation. The critical flow conditions are also determined for two-component flows with separated phases with or without thermal equilibrium. (auth)

Arthur Fritte

Papers

Two-phase two- and one- component critical flows with the variable slip model