12.11. Input Description

Table 12.11.1 lists the input information that is needed in order to run the voiding model section of SAS4A/SASSYS‑1. This information is of two types: that used directly in the voiding calculation and that used by models which provide necessary input to the voiding model. This listing is a subset of the full input listing given in Section 12.16. To simplify the discussion of the information displayed in Table 12.11.1, the input variables will not be examined in the order presented in the table, but rather, they will be presented in groups of data by category, i.e., all variables pertaining to materials properties will be discussed together, all which give problem geometry information will be grouped together, etc. This discussion should be helpful to users trying to assemble input decks for running their own problems.

The variables which provide information on materials properties will be described first. Most materials-property information, other than that for sodium, is provided through input rather than being fixed within the code in order to allow greater flexibility in the use of SASSYS-1. In most cases, this information is input in the form of tables; however, in the case of the solid fuel density and fuel thermal conductivity, either tables or coefficients for functional relationships can be entered. The choice between these two options is made on a channel-by-channel basis and is flagged by the variable IRHOK; a positive value of IRHOK indicates that the functional form has been selected, and a non-positive value means that the tabular format has been chosen. The variable COEFDS contains the coefficients for the fuel density relationship as a function of temperature, while RHOTAB contains a table of fuel density as a function of temperature RHOTEM. Similarly, the coefficient for the thermal conductivity function can be read into COEFK, while a table of thermal conductivity values can be used in XKTAB together with a table of temperatures in XKTEM. In addition, the specific heat of the fuel is read into the table CPFTAB as a function of temperature CPFTEM.

Table 12.11.1 List of Input Variables Needed by the Voiding Model

Equation Variable	Reference Equation	Input Variable	Suggested Value	External Reference
-	-	NCHAN	-	-
-	-	IFUEL1	-	-
-	-	ICLAD1	-	-
-	-	IPLUP	-	-
-	-	ITKEL	-	-
-	-	IPOWER	-	-
-	-	IPOWOP	-	-
-	-	MAXSTP	-	-
-	-	IPO	-	-
-	-	IPOBOI	-	-
-	-	IBLPRT	-	-
-	-	NPREAT	-	-
-	-	NPRES	-	-
-	-	IFLOW	-	-
-	-	NT0TAB	-
-	-	DT0	-	-
-	-	DTMXB	-	-
-	-	TIMAX	-	-
-	-	DTFUEL	-	-
-	-	DTCLAD	-	-
-	-	DTMMXB	-	-
-	-	DPWMAX	-	-
	-	POW	-	-
	-	PREATB	-	-
	-	PREATM	-	-
	-	FRPR	-	-
	-	FRFLOW	-	-
\(\rho_{f}\)	-	COEFDS	\(11.08 \times 10^{3}\) \(2.04 \times 10^{-5}\) \(8.7 \times 10^{-9}\)	-
\(k_{f}\)	-	COEFK	\(2.1\), \(2.88 \times 10^{-3}\) \(2.52 \times 10^{-5}\) \(5.83 \times 10^{-10}\) \(5.75 \times 10^{-2}\) \(5.03 \times 10^{-4}\) \(2.91 \times 10^{-11}\)	-
\(k_{c}\)	-	EXKTB	-	-
-	-	EXKTM	-	-
\(\rho_{f}\)	-	RHOTAB	-	-
-	-	RHOTEM	-	-
-	-	TR	300	-
\(k_{f}\)	-	XKTAB	-	-
-	-	XKTEM	-	-
\(C_{f}\)	-	CPFTAB	-	-
-	-	CPFTEM	-	-
-	-	TFSOL	-	-
-	-	TFLIQ	-	-
-	-	UFMELT	-	-
-	-	TESOL	-	-
-	-	TELIQ	-	-
-	-	UEMELT	-	-
-	-	CPCTAB	-	-
-	-	CPCTEM	-	-
\(\left( \rho \right)_{e}\)	-	CROETB	-	-
-	-	CROETM	-	-
\(C_{e}\)	-	CE	690	-
\(\gamma\)	Eq. (12.7-21)	GAMGAS	1.3 - 1.6	-
\(P_{x}\)	-	PX	-	-
-	-	PDEC	-	-
-	-	PDEC1	-	-
-	-	PDEC2	-	-
-	-	PRETAB	-	-
-	-	PRETME	-	-
\(T_{O}\)	-	T0TAB	-	-
-	-	T0TME	-	-
-	-	ZPLENL	-	-
-	-	ZPLENU	-	-
\(\Delta Z_{bl}\)	Eq. (12.7-28)	DZBCGL	.1	-
\(\Delta Z_{bu}\)	-	DZBCGU	.25	-
-	-	IDBUGV	-	-
-	-	IERSTP	-	-
-	-	IRHOK	-	-
-	-	NPLN	-	-
-	-	NREFB	-	-
-	-	NREFT	-	-
-	-	NZNODE	-	-
-	-	NT	-	-
-	-	IFUELV	-	-
-	-	IFUELB	-	-
-	-	ICLADV	-	-
-	-	IHGAP	-	-
-	-	NPIN	-	-
-	-	NSUBAS	-	-
-	-	MZUB	-	-
-	-	MZLB	-	-
-	-	IHEX	-	-
-	-	ISSFUE	-	-
-	-	ILAG	-	-
-	-	ICLADB	-	-
-	-	MFAIL	-	-
-	-	IFAIL	-	-
-	-	JFAIL	-	-
-	-	IDBFLG	-	-
-	-	IDBSTP	-	-
-	-	IEQMAS	-	-
-	-	IBLPRN	-	-
-	-	IDBGBL	-	-
-	-	IDBLST	-	-
-	-	ISSFU2	-	-
-	-	IFILM	-	-
-	-	NZONF	-	-
-	-	IFUELI	-	-
-	-	NODSUM	-	-
-	-	IGASRL	0 or 1	-
-	-	IGRLTM	0 or 1	-
\(A_{c}\)	Eq. (12.2-1)	ACCZ	-	-
\(\Delta z\)	Eq. (12.2-4)	AXHI	-	-
\(D_{h}\)	Eq. (12.2-7)	DHZ	-	-
-	-	DSTIZ	-	-
-	-	DSTOZ	-	-
-	-	PLENL	-	-
-	-	RBR	-	-
-	-	RER	-	-
-	-	RBRPL	-	-
-	-	RERPL	-	-
-	-	RINFP	-	-
-	-	ROUTFP	-	-
-	-	ZONEL	-	-
-	-	SRFSTZ	-	-
-	-	AREAPC	-	-
-	-	DRFO	-	-
-	-	RBR0	-	-
-	-	RER0	-	-
\(p_{e}\)	Eq. (12.3-2)	SER	-	-
-	-	DRFI	-	-
-	-	VFC	-	-
\(\gamma_{s}\)	-	GAMSS	-	-
\(\gamma_{c}\)	-	GAMTNC	-	-
\(\gamma_{e}\)	-	GAMTNE	-	-
-	-	PSHAPE	-	-
-	-	PSHAPR	-	-
-	-	AHBPAR	-	-
-	-	BHBPAR	-	-
-	-	CHBPAR	-	-
-	-	HBMAX	-	-
-	-	HBMIN	-	-
-	-	HBPAR	-	-
\(k_{s}\)	-	XKSTIZ	-	-
\(k_{s}\)	-	XKSTOZ	-	-
-	-	DEL	-	-
-	-	P0GAS	-	-
\(k_{f}\)	-	XKRF	-	-
\(\rho_{c}\)	-	DENSS	-	-
\(\left( \rho c \right)_{s}\)	-	RHOCSI	-	-
\(\left( \rho c \right)_{s}\)	-	RHOCSO	-	-
\(\left( \rho c \right)_{r}\)	-	RHOCR	-	-
\(\left( \rho c \right)_{g}\)	-	RHOCG	-	-
\(R_{g}\)	-	RG	-	-
\(A_{fr}\)	Eq. (12.2-2)	AFR	0.1875	5-22
\(b_{fr}\)	Eq. (12.2-2)	BFR	-0.2	5-22
-	-	C1	-	5-22
-	-	C2	-	5-22
-	-	C3	-	5-22
-	-	DWMAX	0.2	-
\(w\)	-	W0	-	-
\(K_{or}\)	Eq. (12.2-9)	XKORI	-	5-23
\(\left( \Delta z_{i} / A \right)_{b}\)	Eq. (3.9-9)	DZIAB	\(\left(D_{h} / 2 A_{c} \right)\)	-
\(\left( \Delta z_{i} / A \right)_{t}\)	Eq. (3.9-9)	DZIAT	\(\left(D_{h} / 2 A_{c} \right)\)	-
\(\theta_1\)	Eq. (12.2-17)	THETA1	-	-
\(\theta_2\)	Eq. (12.2-17)	THETA2	-	-
-	-	DTLMAX	-15	-
-	-	DTVMAX	50	-
-	-	DZIMAX	0.1	-
\(h_{cond}\)	-	HCOND	-	-
-	-	SLMIN	0.02	-
-	-	TUPL	-	-
-	-	WFMIN	0.667 x	-
-	-	WFMINS	WFMIN	-
\(w_{fs}\)	Eq. (12.5-13)	WFS00	WF0	-
\(f_{m}\)	Eq. (12.7-1)	FRACP	-	-
-	-	FRUPT	-	-
\(w_{fe}\)	Eq. (12.5-9)	WF0	-	-
-	-	DTSI	3	-
-	-	DTS	10	-
\(A_{fr}\)	Eq. (12.6-9)	AFRV	0.316	5-22
\(b_{fr}\)	Eq. (12.6-9)	BFRV	-0.25	5-22
-	-	XMINL	0.05	-
-	-	DTCMIN	-	-
-	-	WFMIND	-	-
-	-	WFMNSD	-	-
\(f_{2\phi}\)	Eq. (12.6-10)	FVAPM	0	5-7
\(A_{fr}\)	-	AFRF	0.316	5-22
\(b_{fr}\)	-	BFRF	-0.25	5.7
-	-	TPDMIN	\(1.0 \times 10^{-5}\)	5-22
\(A^{*}\)	Eq. (12.7-1)	AGSRLS	-	-
\(K_{g}\)	Eq. (12.7-1)	GASKOR	1.5 - 2.0	-
		PGRMIN	-	-
\(M_{wg}\)	Eq. (12.7-31)	GASMW	100 - 130	-
		TMFAIL	-	-

Since the SAS4A/SASSYS‑1 calculation can accommodate up to eight different types of fuel material, the number of fuel types used in a given data deck must be specified. This is done through the variable IFUEL1. The fuel types must then each be designated as belonging to the core or the blankets. If, in a given channel, the blankets are of one homogeneous material and the core is of another, the quantity IFUELV specifies which of the IFUEL1 fuel types is assigned to the core, while IFUELB (Bloc 51, 16) indicates which is assigned to the radial blankets. If, on the other hand, the core and/or blankets each consist of radial bands of different types of fuel, the variable IFUEL1 is used to match up each radial zone with the appropriate fuel type in both the core and the blankets.

The cladding properties are used only in tabular form by the code. Although only one type of cladding material is used in any one channel, different types may be used in different channels. The total number of types (maximum of three) for a particular run is designated in ICLAD1, and the type assigned to each channel is specified in ICLADV. The cladding thermal conductivity values are input to EXKTB as a function of temperature EXKTM. The specific heats are entered in CPCTAB with the corresponding temperatures CPCTEM. The product of the cladding specific heat and the density is entered as a variable in CROETB as a function of temperature CROETM. In addition, the specific heat of the cladding at the solidus temperature is specified in CE. Finally, the density of the solid cladding at an input reference temperature is given for each channel in DENSS.

The material properties for the structure and reflector regions are also input in tabular form. In the case of the structure, the code allows different sets of properties to be used for the inner and outer structure nodes. However, the properties are constant for each node within a particular zone and are independent of temperature. The thermal conductivity for the inner structure node is stored in XKSTIZ, and that for the outer node is input to XKSTOZ. Similarly, the product of the density and the heat capacity for the inner node is read into RHOCSI, and for the outer node, this quantity is stored in RHOCSO. Of course, the structure properties can vary from channel to channel.

The materials properties for the reflectors are also considered to be constant within a given zone and independent of temperature. However, unlike the case of the structure, the reflector variables are not allowed to differ between the inner and outer segments. The thermal conductivity is given in XKRF, and the product of density and heat capacity is input to RHOCR. These, too, may be different in different channels.

A couple of properties are input for the gas plenum. The product of density and heat capacity for the plenum gas is found in RHOCG, and the thermal resistance of the gas is given in RG. These are both independent of temperature and variable form channel to channel.

As indicated earlier in the text, several fluid heat-transfer coefficients are required in order to model the heat transfer to the sodium. For the bond which exists between the fuel and the cladding, the heat-transfer coefficient is given by a correlation for which the coefficients are read into AHBPAR, BHBPAR, CHBPAR, and HBPAR. The limits on the bond heat-transfer coefficient are set in HBMAX and HBMIN. Also, the option exists for calculating the coefficient by the method used in the SAS3D code; this option is invoked by setting the variable IHGAP to zero. The convective heat-transfer coefficient of the sodium is given by the Dittus-Boettler correlation, for which the coefficients C1, C2, and C3 must be input. If condensation of sodium vapor onto the cladding or structure is occurring, the user-supplied condensation heat-transfer coefficient HCOND must be employed.

Much of the input to the voiding model is concerned with the geometry of the problem. Most of this information can be varied from channel to channel, but a few geometry-related features are consistent throughout the system. First, of course, the number of channels must be specified in NCHAN. The location of the gas plenum must also be set through the variable IPLUP; IPLUP=0 fixes the plenum above the core, while IPLUP=1 designates that it does below the core. The heights of the lower coolant plenum inlet and the upper coolant plenum outlet (ZPLENL and ZPLENU) must be input. Finally, because modeling exists in SASSYS-1 to allow material expansion with temperature, the temperature at which the input geometry information is measured must be known; this is specified in TR.

Much of the geometric information is initially assumed constant within each axial zone and therefore is read in zone by zone. This requires specification of the number of zones. The pin section always constitutes ne axial zone, and each reflector contains from one to five zones. The number of zones in the lower axial reflector is read into NREFB, while that for the upper reflector is given in NREFT. The data which are input on a zonal basis are the coolant flow area per fuel pin ACCZ, the hydraulic diameter DHZ, and the length of each zone ZONEL. The structure variables designating the thickness of the inner node (DSTIZ) and the outer node (DSTOZ) are read in by zone, as is the structure perimeter SRFSTZ. Finally, the thicknesses of the outer and inner reflector segments (DRFO and DRFI, respectively) and the reflector perimeter SER are all input by zone.

Some of the remaining geometric information is read in by axial mesh segment. The input information required about the axial mesh structure includes the number of mesh segments in the gas plenum NPLN, the number of segments in the upper and lower blankets (MZUB and MZLB, respectively), and the total number of segments in each axial zone (NZNODE). Quantities for which a value must be entered for each axial mesh segment in the pin region include AXHI, the length of each axial segment; RBR, the inner radius of the cladding; RER, the outer radius of the cladding; RINFP, the fuel inner radius; and ROUTFP, the fuel outer radius.

Some geometric variables define the radial composition of the problem. These include data such as the number of radial temperature segments in the fuel (NT), the number of concentric rings of different types of fuel in the core and blankets (NZONF), the radial mesh boundaries of the fuel rings (NODSUM), and a flag to specify whether the radial mesh is set up on an equal radius or equal mass basis (IEQMAS).

A few additional pieces of information on the problem geometry must be input. The cladding inner and outer radii in the gas plenum (RBRPL and RERPL) must be specified separately from the values in the pin region (RBR and RER, mentioned above), as must values for the nominal cladding inner and outer radii (RBR0 and RER0). The nominal radii simply represent average values in the pin region; usually the cladding radii in the pin are all equal at the beginning of a run, and the nominal radii are just set to these values. The length of the fission-gas plenum is given in PLENL, the area of the coolant channel plus the pin is set in AREAPC, and the volume fraction of the coolant in the channel is represented in VFC. The inertial terms below and above the subassembly are read into DZIAB and DZIAT, and the orifice coefficients at the entrance and exit of each axial zone are stored in XKORI. The number of pins per subassembly is given in NPIN, and the number of subassemblies represented by the channel is designated in NSUBAS.

Another category of input data is that of temperature initialization. The inlet temperature T0TAB must be specified as a function of time T0TME, with NT0TAB being the number of entries in the inlet temperature table. The temperature of any liquid sodium which reenters the subassembly from the top is fixed at TUPL. The solidus and liquidus temperatures of the fuel are given in TFSOL and TFLIQ, respectively, while those for the cladding are defined in TESOL and TELIQ. The flag which directs whether an Eulerian or a Lagrangian liquid temperature calculation is performed prior to flow reversal is set in ILAG, and the amount of superheat required before boiling can begin is fixed in DTS. The superheat required for formation of new bubbles after voiding has begun is given by DTSI.

Several pieces of information concerning reactor power must be input. The code contains an option for specifying either the power or the external reactivity as a function of time, and the flag IPOWER indicates which quantity is chosen. A total of NPREAT values of the power are read into the array PREATB, with the corresponding times read into array PREATM. The flag IPOWOP determines whether the total steady-state reactor power is computed form the power in the peak axial segment, or vice versa, and the power in the peak axial segment is entered in POW. The fraction of the total reactor power represented by all the SASSYS-1 channels must be given, since some possible channel configurations omit a few low power channels which must be given, since some possible channel configurations omit a few low channels which have a minimal impact on the calculation, and this number is input to FRPR.

The remaining power-related data must be inserted channel by channel. The fraction of the total power due to direct gamma heating must be specified for the structure (GAMSS), coolant (GAMTNC), and cladding (GAMTNE). In addition, the axial and radial shapes of the power distribution are read into PSHAPE and PSHAPR, respectively.

Several conditions concerning the coolant pressure must be designated through the input. The coolant exit pressure is held constant throughout the calculation and is read into variable PX. The magnitude of the coolant inlet pressure at steady state is computed by the code, but, if the PRIMAR-4 option is not invoked, the variation of the normalized inlet pressure with time is either read from a table or calculated from a simple equation. The flag NPRES determines whether the table or the equation will be used. If the equation is chosen, the coefficients PDEC, PDEC1, and PDEC2 must be entered. If the inlet pressure is to be determined from a table, the values are entered in PRETAB, with the corresponding times specified in PRETME. There is also an option to enter the coolant flow rather than the driving pressure in PRETAB. This option is indicated by the flag IFLOW. The user specified coolant flow vs. time is only available if the PRIMAR-1 option is used, IPRION ≠ 4. With this option, the coolant flow rate in channel IFLOW is specified as a function of time. The outlet plenum pressure is also specified as a function of time. The code back-calculates the inlet plenum pressure required to give the specified flow rate, and this inlet plenum pressure drives the coolant flow in all other channels. Currently, this option does not work after the onset of boiling in channel IFLOW. Finally, the initial gas pressure in the gas plenum at the reference temperature TR is input through P0GAS.

Two other areas for which input data are needed are the expressions for calculation of friction discussed earlier and the determination of sodium film thickness in voided regions. The coefficients \(A_{fr}\) and \(b_{fr}\) which are used in the friction expressions are user-input rather than fixed within the code to allow greater flexibility. These include coefficients for the liquid slugs (AFR and BFR), the sodium vapor (AFRV and BFRV), and the liquid sodium film (AFRF and BFRF). Also, the fraction of the two-phase friction factor to be used in voided regions is set in FVAPM. The calculation of film thickness requires information about the initial film thickness left on cladding and structure as the voiding front passes by; these numbers are stored in WF0 for the cladding and WFS00 for the structure. In addition, the SASSYS-1 model does not try to predict when the sodium films will evaporate completely (zero film thickness); rather, the films are considered to be evaporated when the calculated estimates them to be less than user-input values. In the early part of the calculation, these minimum values are WFMIN for the cladding and WFMINS for the structure, but after IFILM axial segments have experienced dryout, the values in WFMIND and WFMNSD are used instead.

A few additional pieces fo information are needed inorder to run the calculation. The steady-state coolant mass flow rate is input to W0 and the fraction of the total reactor flow which is actually represented by core channels is read into FRFLOW (again, to accommodate channel maps which do not include all the subassemblies in the reactor; see the discussion of FRPR given above). The heat of fusion for the fuel is given in UFMELT, and that for the cladding is read into UEMELT. Also, the product of the Stefan-Boltzmann constant and the emissivity is assigned to the variable DEL.

The options for gas release due to pin failure are determined by IGASRL and IGRLTM. If IGASRL=0, this option is not used. The method in which pin failure is determined is specified by IGRLTM. If IGRLTM=0, then DEFORM-5 triggers pin failure in pin group M when the cladding life fraction exceeds FRUPT(M). If IGRLTM=1, then gas release in pin group M occurs in node IFAIL at time TMFAIL(M). In addition, the gas release model requires input values for DZBCGL and DZBCGU for cutting off bubbles after they flow out the top of the subassembly. GAMGAS and GASMW provide properties of the gas. FRACP(M) specifies the fraction of the pins in each group. AGSRLS and GASKOR determine the gas flow rate through the cladding rip, and PGRMIN specifies when gas release will be shut off. The initial plenum gas pressure is determined by P0GAS if it is not calculated by DEFORM.

Time-step control involves specification of a number of input variables. The maximum number of main time steps is given in MAXSTP, and the maximum problem time is TIMAX. The initial main time-step size is DT0, and the maximum size after the initiation of voiding is DTMMXB. The maximum heat-transfer time-step length after boiling has begun is DTMXB. The minimum coolant time-step size before voiding is DTCMIN; after the onset of boiling, it is TPDMIN.

The different time-step sizes are limited by several input criteria. The main time step must be small enough so that the power does not make a fractional change greater than that specified in DPWMAX during the step. The heat-transfer time step must be limited so that, over its span, the fuel temperature does not change by more than DTFUEL, the cladding temperature by more than DTCLAD, and, prior to voiding, the coolant flow rate by DWMAX. The coolant time-step size must be small enough so that the liquid temperature does not change by more than DTLMAX, the vapor temperature by more than DTVMAX, and the position of any liquid-vapor interface by more than DZIMAX.

Printout of results is guided by several input variables. Normally, a standard printout pertaining just to the voiding model is output at the end of designated coolant time steps, and a general standard printout is given at the end of designated main time steps. Boiling printout occurs every IBLPRN coolant time steps. General printout is done every IPO main time steps up until main time step IBLPRT; after step IBLPRT, general printout is given every IPOBOI time steps. The temperatures in the general printout may be listed in units of degrees Kelvin or degrees centigrade at the discretion of the user through the variable ITKEL; however, the user is advised that the labels in the printout will state that temperatures are listed in degrees Kelvin regardless of which option is chosen.

If desired, more detailed output can be obtained through several of the input variables. This is intended primarily for the use of the code developers and outside users who wish to modify the code, but it may on occasion be helpful if problems are encountered in simply running the code. The simplest of this additional output is flagged by the variable IHEX. This number will activate a hexadecimal printout of the sum of the coolant temperatures in a channel. The hexadecimal print is an exact representation of the sum (without truncation) and is therefore useful when comparing two different runs of similar data decks to indicate at what point the two calculations began to diverge. A more extensive output is invoked by the variable IDBUGV. Many different printout options are incorporated into IDBUGV. The print selected will begin at step IERSTP. Prints specialized to the voiding model are also available. The variable IDBGBL will trigger the same extensive voiding-related output as the IDBUGV=4 option, but it will begin the output on coolant time step IDBLST rather than on main time step IERSTP. This allows the user to begin a lengthy printout much closer to the time at which the difficulty develops than is possible with IDBUGV. The array IDBFLG initiates more specialized voiding points. The coolant time step on which each of these prints starts is stored in array IDBSTP.

A few additional input variables remain to be discussed. The remaining quantities include THETA1 and THETA2, the coefficients which determine the degree of implicitness of the liquid slug calculation; SLMIN, the minimum length of a liquid slug in between two vapor bubbles (minimum slug length is required to stabilize the calculation); and XMINL, the bubble length above which the pressure gradient voiding model is used and below which the pressure gradient voiding model is used.