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TECHNICAL BRIEFS

# Thermodynamics of Void Fraction in Saturated Flow Boiling

[+] Author and Article Information

Departamento Ingeniería Mecánica, CPS-B Universidad Zaragoza, Zaragoza, 50018, Spainfjk@unizar.es

Carlos Monné, Andrés Medrano

Departamento Ingeniería Mecánica, CPS-B Universidad Zaragoza, Zaragoza, 50018, Spain

Antonio Pascau, Daniel Fuster

Departamento Ciencia Material and Fluidos, CPS-B Universidad Zaragoza, Zaragoza, 50018, Spain

J. Heat Transfer 128(6), 611-615 (Oct 18, 2005) (5 pages) doi:10.1115/1.2190696 History: Received July 22, 2005; Revised October 18, 2005

## Abstract

Recently, Collado (Proc, IMECE 2001, Symposium on Fluid Physics and Heat Transfer for Macro- and Micro-Scale Gas-Liquid and Phase Change Flows) suggested calculating void fraction, an essential element in thermal-hydraulics, working with the “thermodynamic” quality instead of the usual “flow” quality. The “thermodynamic” quality is a state variable, which has a direct relation with the actual vapor volumetric fraction, or void fraction, through phase densities. This approach provides a procedure for predicting void fraction, if values of “thermodynamic” quality are available. However, the standard heat balance is usually stated as a function of the “flow” quality. Therefore, we should search for a new heat balance between the mixture enthalpy, based on “thermodynamic” quality, and the absorbed heat. This paper presents the results of such analysis based on the accurate measurements of the outlet void fraction measured during the Cambridge project by Knights (1960, “A Study of Two-Phase Pressure Drop and Density Determination in a High-Pressure Steam-Water Circuit,” Ph.D. thesis, Cambridge University Engineering Lab, Cambridge, UK) in the 1960s for saturated flow boiling. In the 286 tests analyzed, the pressure and mass fluxes range from 1.72 MPa to 14.48 MPa and from 561.4 to 1833.33 $kgm−2s−1$, respectively. As the main result, we find that the slip ratio would close this new thermodynamic heat balance. This has allowed the accurate calculation of void fraction from this balance, provided we can predict the slip ratio. Finally, the strong connection of this new thermodynamic heat balance with the standard one through the slip ratio is highlighted.

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## Figures

Figure 10

Void fraction prediction in vertical flow with Eq. 8

Figure 9

Void fraction prediction in horizontal flow with Eq. 8

Figure 8

Slope of the S correlation versus heat flux at different pressures for vertical flow

Figure 7

S correlation for vertical flow at 600psia(4.14MPa)

Figure 6

Point of crossing with the ordenate axis of the S correlation versus heat flux for horizontal flow

Figure 5

Slope of the S correlation versus pressure for horizontal flow

Figure 4

S correlation for horizontal flow at 600psia(4.14MPa)

Figure 3

New thermodynamic heat balance, which explicitly includes S, for saturated flow boiling

Figure 2

Thermodynamic heat balance discrepancy

Figure 1

Outlet void fraction versus outlet “flow” quality

## Errata

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