9.1. How to set up models for the flashing of pressurized water?
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The flashing of the coolant water from a break is treated by means of pre-expansion using the sortam file in GASFLOW-MPI. The underlying theory of pre-expansion and the methodology for configuring a pre-expansion scenario are detailed in the user manual.
It is often desirable to pre-calculate the expansion process and then use this pre-expanded source as the source. Figure 8.1.1 illustrates various two-phase pre-expansion scenarios in a classical temperature-entropy diagram under the initial conditions stated in the sortam file, which are then expanded to a containment pressure:
Path A-B represents an isentropic expansion, where entropy remains constant.
Path A-C denotes an isenthalpic process, characterized by constant enthalpy.
Path A-D describes an isenergetic expansion, where the internal energy is conserved.
In general, we're interested in the production of the vapor component during the expansion or flashing process. Displaying the vapor production is shown in Figure 8.1.2 where we plot vapor mass fraction as a function of Temperature. The least amount of vapor is produced by the isentropic expansion, while the maximum amount is produced by the isenergetic process.
Steam table data has been introduced into the GASFLOW-MPI code to accurately predict the above-mentioned expansions from saturation conditions of up to 200 bars (639 K) down to 0.01 bars (280 K). The equation governing the expansion is
Eq. 8.1‑1
Eq. 8.1‑2
where the subscript i refers to the property associated with expansion A-B, A-C, or A-D. Solving for the quality yields
Eq. 8.1‑3
Eq. 8.1‑3 is used to generate the results shown in Figure 8.1-2.
The ingf and sortam files are available for download below.
The user can specify which expansion they want by using the tenth (10th) entry in the gasdef statement
gasdef(1:24,2) = 32, 35, 39, 42, 7, 8, 1, -1, -2, 1, 0., 1.e+99,
'n2', .0, 'o2', .0, 'h2', -306, 'h2o', -304, 'h2ol', -305, 'xenon', -307,
The meaning of 10th entry is defined by
gasdef(10,*)
Option flag for specification of gas composition: 1 for mass fraction, 2 for volume fraction, > 9 implies a time dependent function for the pressure and temperature will be specified. In addition, < 0 values imply pre-expansions:
-101 is an isentropic expansion with sortam data specified in terms of mass fractions;
-201 is an isenthalpic expansion with sortam data specified in terms of mass fractions;
-301 is an Isenergetic expansion with sortam data specified in terms of mass fractions;
-102 is an isentropic expansion with sortam data specified in terms of volume fractions;
-202 is an isenthalpic expansion with sortam data specified in terms of volume fractions;
-302 is an Isenergetic expansion with sortam data specified in terms of volume fractions;
When using the pre-expansion option, it is assumed that the expansion will occur from the pressure specified in the sortam file, column #2 in the above example, to a value characteristic of the containment pressure. As written in the new user manual, |gasdef(8,*)| > 1,000,000, then it is a packed i, j, k, iblk location for a reference pressure located in cell i, j, k, iblk.
In the following gasdef statement, we specify an isenergetic expansion from the data in the sortam file to the reference pressure located in cell i=36, j=43, k=08, and iblk=1.
gasdef(1:24,2) = 32, 35, 39, 42, 7, 8, 1, -36430801, -2, -301, 0., 1.e+99,
'n2', .0, 'o2', .0, 'h2', -306, 'h2o', -304, 'h2ol', -305, 'xenon', -307,
Since GASFLOW-MPI solves the internal energy equation as one of the primitive variable equations, it isn't too surprising to see that the results obtained with no pre-expansion (a natural expansion) and the isenergetic pre-expansion are nearly identical in the pressurization of the containment.
At the beginning of the accident, the source is almost liquid water with high-pressure and -temperature. The gasdef (1:24,2) in ingf file defines the pre-expention of such liquid water into the containment atmosphere with low pressure and temperature. The user can run the calculation using the ingf file together with the sortam file.
The calculation results can be plotted by opening the following files with pyscan.
where is the desired expansion property at condition A, is the saturated liquid value of the same property, is the difference between the saturated vapor and liquid values for the same property, and is quality or vapor mass fraction. Expanding now to the second state at the containment pressure, actually the saturation temperature for the containment pressure, gives
