---
title: Replacing Complex Two-Fluid Models With A Simple Model 
description: Replacing Complex Two-Fluid Models With Simple Model Agreeable With Experimental Data Including Both Non-Equilibrium and Equilibrium Flashing Flows
image: https://www.fauske.com/hubfs/https___cdn2.hubspot.net_hubfs_232514_Fall-2017-Process-Safety-News-1.jpg
---

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**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:

![Equation 1](https://www.fauske.com/hs-fs/hubfs/Untitled-1-10.jpg?width=203&name=Untitled-1-10.jpg "Equation 1")(1)

where G (kg m-2 s-1) is the Non-Equilibrium or Equilibrium two-phase flow rate including the effects of subcooling (GSC), 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).

![sozzi_sutherland_nozzle](https://www.fauske.com/hs-fs/hubfs/https___cdn2.hubspot.net_hubfs_232514_Fall-2017-Process-Safety-News-1.jpg?width=359&name=https___cdn2.hubspot.net_hubfs_232514_Fall-2017-Process-Safety-News-1.jpg "sozzi_sutherland_nozzle")

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

![Equation 2](https://www.fauske.com/hs-fs/hubfs/Untitled-2.jpg?width=129&name=Untitled-2.jpg "Equation 2")(2)

when the liquid is subcooled, vf >1/ρ and, consequently Eq. 2 results in Xo < 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](mailto: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).

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