22-07-2014, 10:38 AM
The Applicability of Two Critical Flow Correlations for
Two-Phase Flow Through a Valve
The Applicability.pdf (Size: 334.47 KB / Downloads: 57)
ABSTRACT
This report investigates the limits of applicability of two critical flow correlations
throughout the range of qualities for two-phase steam flow. In order to accurately model
the blowdown of a pressure vessel, it is important to understand the applicability of
various critical flow correlations. The Henry-Fauske (HF) critical flow correlation
(Reference 1) and the Homogenous Equilibrium Model (HEM) (Reference 2) are
evaluated in this study to determine the applicability of each throughout the two-phase
region.
Investigating the applicability of these two critical flow correlations is an issue in the
area of thermal hydraulic safety analysis of Pressurized Water Reactors (PWRs).
Predicting the blowdown of the Reactor Coolant System (RCS) of a Pressurized Water
Reactor (PWR) via the Power Operated Relief Valve (PORV) on the pressurizer is
important for understanding the details of the Once Through Core Cooling (OTCC)
operational transient.
This report plots the HF and HEM critical flow correlations against data at four
different stagnation pressures (200 psia, 300 psia, 400 psia, and 500 psia). The results
show that on average for each of the stagnation pressures investigated the HF critical
flow correlation fits the data to within 11% while the HEM correlation shows an average
percent error as high as 36%. In the low quality region (i.e., less than 0.03) the HF
correlation consistently fits the data to within about 11% while the HEM correlation
under predicts the data by as much as 51%. The difference between these two
correlations in the low quality region is due to differences in the treatment of the quality
of the flow at the throat; the HEM model assumes equilibrium throughout the path, while
the HF model explicitly treats the non-equilibrium condition of the flow using the
experimental parameter N.
Introduction
This report investigates the limits of applicability of two critical flow correlations
throughout the range of qualities for two-phase steam flow. In order to accurately model
the blowdown of a pressure vessel, it is important to understand the applicability of
various critical flow correlations. Two of such critical flow correlations will be evaluated
in this study to determine the applicability of each given different conditions. The
condition that will be investigated for this evaluation is two-phase saturated steam / liquid
flow over the full range of qualities at various stagnation pressures.
Two critical flow correlations are considered in this report, the Henry Fauske (HF)
critical flow correlation (Reference 1) and the Homogenous Equilibrium Model (HEM)
critical flow correlation (Reference 2). These two critical flow correlations are compared
to data from References 3 and 4 (which are taken from plots presented in Reference 1,
see Section 2.3) to determine the applicability of each correlation to the range of
stagnation qualities. Each correlation is developed and plotted from the derivations
presented in References 1, 2 and 5.
The equations used to describe each correlation are developed for several different
stagnation pressures over the entire range of two-phase qualities and are compared to data
from References 3 and 4. Comparing the two different correlations to each other and to
the data highlights the differences between the HF and HEM critical flow models and
shows their ability to match the experimental data.
The HF correlation is typically considered to be applicable to subcooled or saturated
liquid flows; however, it may also be applicable to some portion of the two-phase
saturated steam / liquid flow range. The HEM correlation is typically considered to be
applicable to single phase saturated steam; however, this may also be applicable to some
portion of the upper end of the two-phase saturated steam / liquid flow range.
Two-phase critical flow calculations are used in thermal hydraulic analyses for a
variety of applications. Some of these applications include:
Background
As mentioned in the introduction, the applicability of different two-phase critical
flow correlations is reemerging as an issue in the area of thermal hydraulic safety analysis
of PWRs. In general, RCS blowdown characteristics have been an area of interest since
the meltdown of the Three Mile Island (TMI) PWR (see References 7, 12, and 13). The
TMI accident was initiated by a loss of all secondary-side cooling to both of the two
Steam Generators (SGs) and involved an RCS coolant leak through a PORV that failed to
reseat properly. As the accident progressed, a variety of operator errors lead to the
uncovering and eventual melting of fuel inside the reactor vessel. Many post-TMI
thermally hydraulic safety analyses have focused on developing operational guidance and
strategies for mitigating an accident similar to the TMI event (see Reference 12). Many
of these procedures are highly dependent on accurate predictions of RCS pressure
responses and RCS discharge flowrates.
Once Through Core Cooling (OTCC) is one of the strategies that was developed as a
result of the post-TMI thermal hydraulic analyses. This procedure is essential for
mitigating a loss of secondary-side cooling transient. The OTCC strategy instructs
operators to intentionally open the pressurizer PORVs and start the Safety Injection (SI)
system to make up the coolant lost through the opened valves (this is illustrated in
Figure 1). The success of this strategy is highly dependent on the amount of
depressurization provided by the PORVs and the rate at which RCS coolant is lost
through the valves. Thermodynamic fluid analyses used to analyze these situations use
critical flow correlations to determine the mass flowrate and resulting pressure drop
across the PORVs.
In order to und
Analysis
This section documents the development of the two critical flow correlations that are
analyzed in this report. The methodology used to solve these equations is also presented
in this section. The steam and liquid water thermodynamic properties that are used in
these calculations are taken from Reference 11.
Conclusions
Although the HF critical flow correlation is typically considered to only be
applicable to the low quality flow region, the results presented in this report show that the
HF critical flow correlation fits the data very well throughout the two-phase region for
the four stagnation pressures investigated here. On average the HF correlation fits the
data to within 11% both in the low quality region (less than 0.03) as well as at qualities
greater than 3%. The HEM model was shown to predict critical flow rates well below
what the data indicates. The HEM correlation fits the data with an average percent error
of about 36%, and in the low quality regions, this average percent error increases to
approximately 51%