Two-phase critical flow

In this paper, the modelling of pure fluid steady-state adiabatic flashing flow through a pipe involving an abrupt enlargement is presented. The thermal non-equilibrium two-phase flow model DEM has been adjusted for subcooled inlet conditions close to saturation and/or for inlet two-phase mixture state. The multichoking flow phenomenon occurs when two basic criteria are simultaneously fulfilled. A general procedure taking into account this possible occurrence is developed on the basis of two iterative algorithms. The first algorithm is applied to the mass flow rate upstream from the enlargement and the second algorithm is based on the length of the pipe downstream from the enlargement. The proposed methodology involves the improved physical one-dimensional two-phase flow model DEM and the global non-equilibrium model through the abrupt enlargement. (C) 1999 Elsevier Science Ltd. All rights reserved.

Steady-state critical two-phase flashing flow with possible multiple choking phenomenon: Part 1: Physical modelling and numerical procedure

Experimental study of the critical flashing flow through a relief line: evidence of the double-choked flow phenomenon

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)

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

The numerical results from the proposed methodology given in part 1 are presented. The sensitivity of the wall roughness of the pipe is analysed for both cases: subcooled liquid or two-phase mixture at the entrance of the pipe. A systematic comparison between models HEM and DEM and the experimental results shows that the metastability effects of the liquid phase must be taken into account even for long pipes. The predictions of the DEM are compared favourably with the experimental data of the mass flow rate as well as of the pressure profile obtained for simple-choked and double-choked steam-water flashing flows. (C) 1999 Elsevier Science Ltd. All rights reserved.

Steady-state critical two-phase flashing how with possible multiple choking phenomenon - Part 2: comparison with experimental results and physical interpretations

A Theoretical Approach to Two-Phase Critical Flow : (4th Report, Experiments on Saturated Water Discharging through Long Tubes)

Saturated water discharging through orifices is theoretically and experimentally studied and the following results are obtained. (1) Saturated critical flow through frictionless channel can be easily treated by combining critical condition with such upstream parameters as static pressure and steam quality, and this method can be applied to predicting of discharging rate of saturated water through orifice except the cases where thermodynamical metastability is established. (2) Ratio between back pressure and upstream pressure is not invariable, but this seems to form one of flow conditions. (3) The magnitudes of orifice diameter and upstream pressure which can be treated by traditional orifice constant of around 0.6 are in a considerably wide range. (4) In the case when orifice flow rate is calculated as homogeneous flow, orifice constant seems to converge around 0.4 as for large orifice size and high upstream pressure. (5) The flow rate through orifice varies with a decreasing back pressure until the critical condition is reached.

A Theoretical Approach to Two-Phase Critical Flow : (5th Report, Several Problems on Discharging of Saturated Water through Orifices)

By means of"eigen-value method"(which defines critical condition as the divergent point of flow equations), critical flow rates of two-phase fluid are predicted with"energy model", and are compared with the results obtained by existing methods (which define critical velocity as sonic velocity or derive it from dW/dp=0* relation by the use of"entropy model"). And the following results are concluded ; (*W : flow rate, p : pressure) (1) By the use of"eigen-value method", both"energy model"and"entropy model"can be treated easily by the existing method. (2)"Energy model"is not generally equal to"entropy model"and this difference comes from different transfer velocities of kinetic energy between the phases. (3) As for"energy model", the derivative of slip ratio (ds) can be neglected in evaluating critical flow rate, where an analytical expression of it is derived. These predicted values are satisfactorily compared with the existing empirical data.

A Theoretical Prediction of Two-Phase Critical Flow

"Eigenvalue method", already proposed by the author for two-phase critical flow, is developed for the axial steady flow equations system where separate momentum conservation can be strictly postulated. Besides the comparisons of physical meanings in two-phase critical flow between energy and entropy, conservation equations are also investigated. The conclusions for steam water mixtures are as follows. (1) "Eigenvalue method"defines the criticality as the discontinuous condition of steady flow differential equations system and can treat easily such a complicated system composed of separate momentum between two phases, energy, and mass conservation equations. (2) The solutions given by the above theory can well explain the former empirical data except for critical slip ratio which has not well been investigated experimentally. (3) Critical condition with energy conservation gives a more accurate solution than one with entropy conservation. But the latter is still good approximation.

Hideo Ogasawara

Papers

A Theoretical Approach to Two-Phase Critical Flow : (4th Report, Experiments on Saturated Water Discharging through Long Tubes)

A Theoretical Approach to Two-Phase Critical Flow : (5th Report, Several Problems on Discharging of Saturated Water through Orifices)

A Theoretical Prediction of Two-Phase Critical Flow

A Theoretical Approach to Two-Phase Critical Flow : (3rd Report, The Critical Condition Including Interphasic Slip)