12.137. The only practical way to model transient behavior such as that described above in a system consisting of connected components is to use subprograms for the individual component volumes and then join them together at the component interfaces. Improved accuracy is obtained by subdividing the component and piping volumes shown in Fig. 12.10 to a level balanced by the resulting increased computational cost. Thus, we have the primary coolant circuit divided into a number of control or nodal volumes connected by junctions at which the properties change, and fluid mass, momentum, and energy are transferred as a function of time. Within each volume, so-called field equations describe in a numerical finite-difference manner the conservation of mass, momentum, and energy. A typical system code is likely to have hundreds of nodal volumes, with time steps taken to model a LOCA of the order of milliseconds. Should longer transients be modeled, the number of volumes must be reduced to keep the computing time from becoming excessive.

12.138. In Fig. 12.11 is shown a practical level of volume subdivision for the analysis of the blowdown phase in a large cold leg break LOCA for a two-loop PWR. The model for this blowdown analysis consists of 45 volumes, 56 junctions, and 28 heat slabs. Three volumes are used to model the core. Also, within the reactor vessel, the downcomer, upper and lower plenums, and core bypass are represented by other volumes. Discharge into the containment (volume 40) flows through two imaginary “valves” used to model various break sizes [36].

12.139. In modeling the various stages of a LOCA, the picture is com­plicated by the need for a two-phase description which must also account for the transfer of the conserved quantities between phases in a given volume. The reflood stage is a particular challenge. Since the physics of two-phase flow is very complex, it is necessary to apply simplifying as­sumptions for practical modeling. In the most drastic simplification, the so-called one-dimensional homogeneous, no-slip, equilibrium model, the steam-water mixture is treated as one fluid at the saturated temperature moving in one dimension. In attempting to develop greater modeling so­phistication to account for nonequilibrium and nonhomogeneity, various

SIMULATED (FLUID VOLUME) PLANT

Fig. 12.10. Schematic representation of actual and fluid-volume models of a PWR coolant loop for LOCA calculations. (The intact loops are not shown but are included in the computations.)

averaging procedures have been developed to convert the local instanta­neous governing equations written for each phase to suitable averaged governing equations for the mixture. This lumped-parameter approach is generally used for licensing-type calculations.

12.140. Higher levels of sophistication are used in the best estimate codes. Here, one also starts with a two-fluid or two-phase model but retains the individual phase relations in the calculation with expressions for in­terfacial mass and energy exchange included. However, some simplification is still needed. This varies depending on the needs of the problem. In fact, the features of most codes in common use are being updated continually. The level of representation can vary among different subprograms describ­ing behavior in individual coolant system components. Details may be found in other sources [10] and in the current literature.

12.141. A feature of the various system codes is the need to incorporate within the various subprograms available engineering correlations to pre­dict such values as heat-transfer coefficients and vaporization rates as in­troduced in Chapter 9. Selection of the proper correlation for each region of application must be provided by the code system. Associated with the use of correlations is uncertainty analysis to determine the confidence level of the results. This may be done by estimating error bands for each cor­relation and determining the cumulative error through the computational process. Of course, modeling simplifications would contribute additional uncertainties. Therefore, experimental programs that simulate various types of LOCA behavior in individual components play an important role in system code development.