Replacing Complex Two-Fluid Models With A Simple Model 

Replacing Complex Two-Fluid Models With A Simple Model That Has No Adjustable Parameters and That is Agreeable With Experimental Data Including Both Non-Equilibrium and Equilibrium Flashing Flows

By: Hans K. Fauske, D. Sc., Regent Advisor, Fauske & Associates, LLC (FAI)

In contrast to the two-fluid models that require numerous assumptions and the corresponding closure equations, the Simple Model can be stated as:

(1)

where G (kg m^-2 s^-1) is the Non-Equilibrium or Equilibrium two-phase flow rate including the effects of subcooling (G_SC), Y is the dimensionless independent variable ranging from 0 to 1 and G₀ and G₁ are the corresponding asymptotic flow rate limits. For all specified stagnation conditions (subcooled liquid, saturated liquid and liquid-vapor mixtures) and flow geometries (nozzle, short and long), the easy to estimate G values in the region between the known asymptotic limits with no arbitrary adjustable parameters are in remarkable agreement with available experimental data. The nozzle constant area length L is the key parameter and values (Y) leading to non-equilibrium and equilibrium flashing flows is provided by (Fauske, 1985, 2017).

An example is illustrated below the agreement of the simple model is consistently good for all inlet quality (X_o) conditions, where G_c is the dimensionless mass flux, defined as G/√P_oρ_o, and quoting Sozzi and Sutherland (1975), stagnation quality (X_o) in the vessel upstream of the nozzle is based on the density in the vessel and the stagnation pressure (P_o):

(2)

when the liquid is subcooled, v_f >1/ρ and, consequently Eq. 2 results in X_o < 0 as a negative quality.

It should be noted that the short nozzle No. 2 (D = 12.7 mm and L/D = 1) non-equilibrium data by Sozzi and Sutherland (1975) have provided difficulties in predicting especially with two-fluid modelling which required empirical adjustment to fit the test results (Levy, 1993).

For more information or to discuss two-phase flow concerns, contact Kris Fauske at 630-887-5213, kfauske@fauske.com

References

Hans K. Fauske, 1983, "Flashing Flows Or: Some Practical Guidelines for Emergency Releases," Plant/Operations Progress, July, 1985.

Hans K. Fauske, 2017, "Further Clarification of Non-Equilibrium and Equilibrium Flashing Flows Through TOP Located Relief Valves (SRVs)," Process Safety News, Summer 2017, Volume 24, Number 3.

Solomon Levy, 1999, "Two-Phase Flow in Complex Systems," A Wiley Interscience Publication, 1999.

Sozzi, G. L. and Sutherland, W. A., 1975, "Critical Flow of Saturated and Subcooled Water at High Pressure," Report NEDO-13418, General Electric Company, San Jose, Ca (July).