Local and Non-Local Correlations for Critical Heat Flux at Low and Medium Pressures
Authors: Jafri T. , Dougherty T. J. , Yang B. W. 
Published: July 2023

Abstract
The local and non-local correlations [1] developed based on more than 10,000 Critical Heat Flux (CHF) data points arc reviewed and the effects of the pressure and Peclet number are examined under low and medium pressure conditions (up to 110 bar).
Examination of CHF data from many sources covering a wide range of operating conditions, reveals that both local and non-local CHF data exist with different dependencies on operating conditions, and different correlations are required to represent these data. These two distinct types of correlations imply the existence of at least two distinct mechanisms for CHF. Instead of the equilibrium quality, X, the true mass fraction, Xt, based on a non-equilibrium, homogeneous model, was used in developing the CHF correlations. The true mass fraction was calculated from a simple kinetic model based on an extension of the Saha-Zuber (S-Z, 1974) correlation for the Onset of Significant Vaporization (OSV). In this model, Xt is a function of exit equilibrium quality, X; the quality at OSV, Xo, and the quality at which significant vaporization begins Xb; estimated from the Saha-Zuber (S-Z) correlation. This model contains no adjustable parameters. When Xi &lt; Xo (both negative), Xb = Xo and Xt is independent of Xi, and is a function of local variables only. When CHF is determined by local conditions (G, Xt, and P), the correlation is a local correlation. For Xi &gt; Xo, Xb = Xi, and Xt depends on Xi, a nonlocal variable, and, in this case, CHF, even when determined by local conditions (G, Xt, and P), obeys a nonlocal correlation. This model appears to be satisfactory for pressures less than 110 bar, where the S-Z correlation is known to be reliable. Above 110 bar the method of calculating Xo, and consequently Xt, appears to fail. This paper will focus on the low pressure range, pressures up to 35 bar or 500 psia, and medium pressure range, pressures from 35 (500 psia) to 110 bar (1500 psia).
In this study, two regimes of CHF are observed which will be referred to as the high CHF regime and the low CHF regime. In the high CHF regime, for pressures less than 110 bar, CHF (qc) is determined by local conditions and is accurately represented by qc = (1.2/D1/2)exp[-γ(GXt)1/2], where the parameter γ is an increasing function of pressure only. Most of the medium pressure CHF data, but not all, fall in this regime.
For the medium pressure range, 500 psia to 1500 psia, the pressure dependency is given by γ = 0.12 (P/Pc)1/2. Below 35 bar (500 psia), based on the limited amount of local CHF data, the pressure dependency of this local condition appears to be very weak and γ is approximately 0.05.
Below 35 bar, the bulk of the available data lies in the low CHF regime and appears to be nonlocal. For Peclet numbers less than 70,000, the two-parameter, nonlocal correlationqs/qc=d+A{1-exp[-B(Xo-Xi)]} correlates the low pressure data reasonably well. The parameters A and B are functions of pressure only. The variable qs = −λGXiD/4L is the heat flux to produce an exit quality of zero (saturation heat flux), and d is a dimensionless variable defined as D/4LS, where S is the value of the Stanton number at OSV, as predicted by the Saha-Zuber correlation, and is a function of Peclet number. The coefficient A increases with pressure and the coefficient B varies inversely with pressure. The best fit values of A and B are presented for each range of pressure up to 41 bar.