3.9. Solid Heat Structures
A time-dependent heat-conduction equation is solved for each solid structure, with an implicit scheme (backward Euler teta = 1.0) or a semi-implicit scheme (Crank Nicholson teta = 0.5). As an approximation, which greatly improves computational efficiency and speed, we assume that heat conduction is one-dimensional, i. e., heat conducts only in a direction perpendicular to the interface between the solid and fluid. (In other words, if three orthogonal faces of an obstacle are exposed to fluid, then the code solves a 1D heat-conduction equation for each of the directions independently.) Another simplification is that the solid properties (conductivity, density, and heat capacity) have negligible dependence on temperature changes.
For the purpose of heat-conduction calculations, we distinguish the solid surfaces where energy exchange with the fluid occurs into two types: wall heat structures and slab heat structures, depending on the depth of solid material behind the surfaces. In addition, we can include so-called distributed heat sinks, which are planar walls of a given volume thickness and material.
3.9.1. Wall/Slab Heat Structures
Definition: a wall heat structure is two-sided, with its temperature profile determined by the adjacent fluid cell temperatures on both sides and by its heat capacity and conductivity. There are two cases in which we have wall heat structures:
All impenetrable surfaces defined by walls in NAMELIST group xput will be considered wall heat structures, because by definition, these are infinitely thin surfaces between adjacent fluid cells.
For obstacle mesh cells (defined by mobs in NAMELIST group xput) surrounded by fluid cells on opposite sides, whether the heat structure type is a wall depends on the thickness between the two opposite sides which are exposed to fluid.
A solid surface belongs to a slab heat structure if the solid material is defined in mobs. In the default option, a slab is considered infinitely thick so that within the problem time scale, the heat or temperature wave due to exchange with the fluid never penetrates deep enough to affect the temperature profile near its back side. Therefore, if its backside is also exposed to fluid, then the backside surface will be treated as belonging to a separate slab heat structure, and the temperature distribution within each slab will only be affected by the temperature of the fluid in contact with its front side.
There are two cases where we have slab heat structures:
All boundaries of the computational domain not open to flow will be treated as slabs, if a material number is specified for the boundary material (matbdy >0). If matbdy is set to zero, the boundary of the computational domain is adiabatic.
For obstacles (defined by mobs and associated with a material number > 0), each surface exposed to fluid will be treated as an independent slab surface.
3.9.2. Heat Conduction in Wall Heat Structures
For surfaces defined by walls, the user will have to input an effective physical thickness, even though mathematical surfaces between adjacent fluid cells in the mesh have no thickness. Furthermore, the user must define the material in the wall.
Input array: these definitions are accomplished through the 8th element of the walls array in NAMELIST group xput and through the walldef array in NAMELIST group rheat:
walls(8,*) Integer to identify the type of wall through the walldef array that stores the material identification number and thickness for each wall type (see Section 3.5.1).
walldef(1,*) Material identification number.
Material numbers 7 to 12 and 13 to 18 in the property library denote identical structure materials. This was intentionally made to allow the user to assign identical material properties and give structures for 3D visualization different material numbers to selectively only display structures with selected material numbers (see parameter matdef and matpanel) .
walldef(2,*) Thickness of wall (cm).
walldef(3,*) Sets boundary condition for first fluid/wall surface (BC#1). It should be noted that the wall located at the positive face (+i east, +j north and +k top) of the fluid cell has the same index as this fluid cell. Therefore, BC#1 is the wall boundary surface attached on the positive face of the fluid cell.
walldef(3,*) = 0.0 implies a fluid-wall heat exchange (default);
walldef(3,*) > 0.0 implies a constant wall temperature boundary condition with T = walldef(3,*);
walldef(3,*) < 0.0 implies an adiabatic wall boundary condition.
walldef(4,*) Sets BC#2 for last fluid/wall surface. It should be noted that the wall located at the negative face (-i west, -j south and -k bottom) of the fluid cell has the same index as the negative adjacent fluid cell. Simply speaking, BC#2 is always located at the positive side of BC#1.
walldef(4,*) = 0.0 implies a fluid-wall heat exchange (default);
walldef(4,*) > 0.0 implies a constant wall temperature boundary condition with T = walldef(4,*);
walldef(4,*) < 0.0 implies an adiabatic wall boundary condition.
walldef(5,*) δx for the first node in the wall.
walldef(5,*) = 0.0 implies a uniform mesh spacing for heat-conduction nodes;
walldef(5,*) > 0.0 implies a variable mesh spacing for heat-conduction nodes with walldef(5,*) =δx of surface heat-conduction node on both sides of the wall.
walldef(6,*) Fraction of wall area from mesh surface that is used for heat transfer.
walldef(7,*) Flag for further specification of BC on negative side of wall:
walldef(7,*) = 0 no further modification;
walldef(7,*) > 0 gives table number from surftab that specifies time-dependent surface temperature, with the initial temperature at t=0 taken from walldef(3,*);
walldef(7,*) = –1 applies heat flux walldef(9,*) and/or heat transfer with coefficient walldef(10,*) and applies fluid temperature walldef(3,*) on negative side.
walldef(8,*) Flag for further specification of BC on positive side of wall:
walldef(8,*) = 0 no further modification;
walldef(8,*) > 0 gives table number from surftab that specifies time dependent surface temperature, with the initial temperature at t=0 taken from walldef(4,*);
walldef(8,*) = –1 applies heat flux from walldef(9,*) and/or heat transfer with coefficient walldef(10,*) and applies fluid temperature walldef(4,*) on positive side.
walldef(9,*) Heat flux [erg/cm2·s] applied as BC by walldef(7,*) or walldef(8,*). Positive flux means add heat to the wall (i.e., condensation), which is the same convention as in the fluid wall condensation/vaporization heat flux from GASFLOW-MPI.
walldef(10,*) Heat-transfer coefficient [erg/(cm2·s·K)] applied as BC by walldef(7,*) or walldef(8,*).
The GASFLOW-MPI code also allows the specification of additional heat-conducting materials, which can be defined explicitly in the input.
This table input allows the simulation of composite structures (i.e., a liner on top of a concrete structure) in which thermal conductivities and heat capacities can vary from node to node.
The extended options above walldef(6,*) require the specification of the following additional data in block rheat:
ntotmat Total number of structure materials. (ntotmat <=20, Default =6).
mpreset Materials from imat = 1 to mpreset in Table are automatically loaded into the property tables for each of the nhteslab, nhtewall, and nhtesink elements used in the 1D heat conduction simulation (Default =6).
nhteslab Number of 1D heat conduction elements in a slab heat structure (<100).
nhtewall Number of 1D heat conduction elements in a wall heat structure (<100).
nhtesink Number of 1D heat conduction elements in a sink heat structure (<100).
wltabslab(*,imat) Thermal conductivity table for material imat for each of the nhteslab elements of the slab structure. Tables for Materials 1 to mpreset are automatically filled with constant values from Table. Tables must be input nodewise only for material numbers from mpreset+1 to ntotmat.
wltabwall(*,imat) Thermal conductivity for material imat for each of the nhtewall elements of the wall structure. Tables for Materials 1 to mpreset are automatically filled with constant values from Table. Tables must be input nodewise only for material numbers from mpreset+1 to ntotmat.
wltabsink(*,imat) Thermal conductivity for material imat for each of the nhtesink elements of the sink structure. Tables for Materials 1 to mpreset are automatically filled with constant values from Table. Tables must be input nodewise only for material numbers from mpreset+1 to ntotmat.
surftab(2,j,i) Pair of time [s] and temperature [K] at time tj for temperature table i. 2 means the two variables, namely time and temperature. “j” is the number of time and temperature pair. “i” is the number referenced by walldef(7,*) or walldef(8,*) and by sinkdef(14,*) or sinkdef(15,*), respectively. In the current version, the maximum number of points per table is 50 and the maximum number of tables (i) is 30. (The problem time must never exceed the maximum of the table time.)
twall0 Initial wall surface temperature on the wall side for which walldef does not define the surface temperature (walldef(3,*) and/or walldef(4,*) = 0). If twall0 < 0, then the surface temperature from the adjacent fluid node is applied on the undefined sides of the wall.
Example 1
Wall of 10 cm thickness with 29 heat-conducting elements, fluid on both sides, and composite material. (All but the 15th structure element is made of concrete; the 15th structure element is made of steel.) Use backward Euler scheme (teta = 1.0 = default). Use of dynamic mesh expansion with a small surface node of 0.01 cm on both sides of the wall (example shown in Figure below for 10 elements only).
$xput
…
gasdef(1:14,1) = 1, 4, 1, 2, 1, 4, 1,1.0e6, 400.0, 2, 0.0, 0.0, 'air', 1.0,
walls(1:8,1) = 3, 3, 1, 2, 1, 2, 1, 1,
...
$end
$rheat
...
teta = 1.0,
ihtflag = 1,
ntotmat = 4,
nhteslab = 20,
nhtesink = 10,
nhtewall = 29,
twall0 = -1,
walldef(1:5,1) = 4, 10.0, 0.0, 300.0, 0.01,
wltabwall(1:29,4) = 14*_2.0e+5, 5.0e+6, 14*_2.0e+5,
wltabslab(1:20,4) = 10*_2.0e+5, 5.0e+6, 9*_2.0e+5,
wltabsink(1:10,4) = 5*_2.0e+5, 5.0e+6, 4*_2.0e+5,
rcptabwall(1:29,4) = 14*_6.25924e+7, 3.84964e+7, 14*_6.25924e+7,
rcptabslab(1:20,4) = 10*_6.25924e+7, 3.84964e+7, 9*_6.25924e+7,
rcptabsink(1:10,4) = 5*_6.25924e+7, 3.84964e+7, 4*_6.25924e+7,
…
$end
Concrete wall on top of an obstacle with specified heat flux of 10e+10 erg/cm2-s on the obstacle side of the wall and fluid conditions on the fluid side. Solve with Crank Nicholson scheme (teta = 0.5).
$xput
…
gasdef(1:14,1) = 1, 4, 1, 2, 1, 4, 1, 1.0e6, 400.0, 2, 0.0, 0.0, 'air', 1.,
mobs(1:8,1) = 2, 3, 1, 2, 2, 3, 1, 1,
walls(1:8,1) = 2, 2, 1, 2, 2, 3, 1, 1,
…
$end
$rheat
…
ihtflag = 1,
teta = 0.5,
nhtewall = 29,
twall0 = -1.0,
walldef(1:9,1) = 1, 10.0, 0.0, 1.0, 0.01, 1.0, 0, -1, 1.0e+10,
…
$end
3.9.3 Heat Conduction in Sink Heat Structures
In some practical problems where the computational mesh is not fine enough to represent the details of all internal structures, it is desirable to have the capability of modeling the heat-transfer effects of these “subgrid” structures. We accomplish this by defining a third type of heat structure, which we call distributed heat sinks.
Definition: Sinks are heat structures defined by the user which are assumed to be distributed within the fluid cells. Similar to the other heat structure types, 1D heat-conduction is calculated across the sink structure thickness. Both sides of a sink heat structure are exposed to the same fluid cell, and it is assumed that the structure temperature profile is symmetric about the centerline, so that only conduction in half the structure thickness needs to be calculated.
Input Array: Definition of sink heat structures is done with the input array sinkdef in NAMELIST group rheat:
sinkdef(1,*) Beginning i mesh index (cell face number).
sinkdef(2,*) Ending i mesh index (cell face number).
sinkdef(3,*) Beginning j mesh index (cell face number).
sinkdef(4,*) Ending j mesh index (cell face number).
sinkdef(5,*) Beginning k mesh index (cell face number).
sinkdef(6,*) Ending k mesh index (cell face number).
sinkdef(7,*) Block number (must be 1 for GASFLOW-MPI).
sinkdef(8,*) Material identification number (defaults Table 6-1).
sinkdef(9,*) Total material volume volsink (cm3).
sinkdef(10,*) Average material thickness avgthick (cm).
sinkdef(11,*) Sets BC for sink/fluid surface (BC#1).
sinkdef(11,*) = 0.0 implies that the BC#1 will be sink-fluid heat exchange (default).
sinkdef(11,*) > 0.0 implies a wall temperature boundary condition of T = sinkdef(11,*) on the fluid side.
sinkdef(12,*) Sets the sink centerline BC (BC#2).
sinkdef(12,*) = –1.0 implies an adiabatic BC(default) will be applied at the sink centerline.
sinkdef(12,*) > 0.0 implies a temperature boundary condition will be applied at the sink centerline of T = sinkdef(12,*).
sinkdef(13,*) δx for the first node in the sink.
sinkdef(13,*) = 0.0 implies uniform mesh spacing for heat-conduction nodes.
sinkdef(13,*) > 0.0 implies variable mesh spacing for heat-conduction nodes, with sinkdef(13,*) = dx of first heat-conduction node if internal BC is adiabatic and sinkdef(13,*) = dx on outer and inner sink surface nodes if internal BC is nonadiabatic.
sinkdef(14,*) Flag for further specification of BC on negative side:
= 0 no further modifications (default);
0 gives table number from surftab that specifies time-dependent surface temperature. The initial temperature at t=0 is taken from sinkdef(11,*).
sinkdef(15,*) Flag for further specification of BC on positive side (centerline) of slab:
= 0 no further modification (default);
>0 gives table number from surftab that specifies time-dependent surface temperature, with the initial temperature at t=0 taken from sinkdef(12,*);
= –1 applies heat flux from sinkdef(16,*) and/or heat transfer with coefficient sinkdef(17,*) and fluid temperature sinkdef(12,*) on positive side (positive heat flux means add energy to the sink).
sinkdef(16,*) Heat flux [erg/cm2·s] applied as BC by sinkdef(15,*).
sinkdef(17,*) Heat-transfer coefficient [erg/cm2·s·K] applied as BC by sinkdef(15,*).
Note that each sink definition can cover a fluid region (specified by the starting and ending i, j, and k mesh indices) consisting of multiple fluid cells. If such is the case, then the code will distribute the sink material to each fluid cell according to the cell volume, i. e., a fluid cell having twice the volume of another one will get twice as much sink material.
The following relation exists between the sink volume volsink, the input thickness avgthick, and the total surface to which the fluid is exposed:
thickness = avgthick/2
area= volsink / thickness
thickness denotes the actual thickness of the sink structure in the heat-conduction solution.
Example
Sink structure of steel with positive (central) BC defined by heat transfer from an outside fluid of 373 K. Apply 10 elements for heat conduction and a small surface node of 0.01 cm on both sides. Second sink applies surface temperature table 1 for temperature transient on the positive (central side).
$rheat
...
ihtflag = 1,
nhtesink = 10,
tsink0 = -1,
sinkdef(1:17,1) = 2, 4, 1, 2, 1, 2, 1, 2, 8000., 10., 0.0, 873., 0.01, 0, -1, 0., 10000.,
sinkdef(1:15,2) = 2, 3, 1, 2, 2, 3, 1, 2, 4000., 10., 0.0, 400., 0.01, 0, 5,
sinkdef(1:13,3) = 2, 4, 1, 2, 2, 3, 1, 2, 4000., 10., 0.0, -1.0, 0.01,
surftab(1:2,1:3,5) = 0.0, 500., 1., 800., 3.5, 1000.0,
...
$end
3.9.4. Other Heat Structure Input
The heat-conduction equations are solved by finite difference. The finite differences are applied to a one-dimensional mesh that is either planar or cylindrical depending upon the value of cyl. The user can specify the number of nodes used for each type of heat structure.
Note that all heat structures of the same type will have the same number of nodes. The input variables for this purpose are in NAMELIST group rheat and are explained below:
nhtesink Number of discretized elements to be used for calculating heat conduction in a sink heat structure. Default = 2. (Max < 100)
nhtewall Number of discretized elements to be used for calculating heat conduction in a wall heat structure. Default = 2. (Max < 100)
nhteslab Number of discretized elements to be used for calculating heat conduction in a slab heat structure. Default = 2. (Max < 100)
In GASFLOW-MPI, all solid heat structures can be defined to have a uniform temperature distribution in the beginning of a problem. These initial heat structure temperatures can be specified with the following input variables in NAMELIST group rheat:
tsink0 Initial temperature in sink heat structures (K). Default = 300.
twall0 Initial temperature in wall heat structures (K). Default = 300.
tslab0 Initial temperature in slab heat structures (K). Default = 300.
If any initial temperature is set negative, then the corresponding heat structures are assumed to be in thermal equilibrium with the contacting fluid cells. This default initialization of the structure temperatures can change when the boundary conditions specify different temperatures on both sides of the structures or when heat transfer from external fluid conditions or heat fluxes are specified on one side of the structure at the onset of the analysis.
3.9.5. Heat Conduction in Slab Heat Structures (Boundary Cells)
The slab temperature boundary conditions for all blocks and all boundary cells can either be input as a single number (see below) or as the slabdef array which allows a slab’s thickness, initial temperatures, boundary conditions, and material type to be dependent upon the block number and upon whether the boundary cell is on the east, west, north, south, top, or bottom boundary.
tslabbc Inner slab temperature boundary condition (default –9.123) for all blocks and boundaries (uniform). Can be overridden individually for each of the 6 slab planes using slabdef. tslabbc < 0 implies adiabatic BC. tslabbc > 0.0 implies fixed temperature BC on the inside of the slab, with T(bc) = tslabbc.
tslab0 Initial slab temperature (default 300 K) can be overridden using slabdef.
If tslab0 < 0, use temperature of the adjacent fluid node to define initial slab temperature.
If tslabbc > 0 and islablin = 1, a linear steady-state profile from the fluid surface to tslabbc at the inner surface of the slab is set up.
If tslabbc > 0 , islablin = 1, and hslablin > 0, a linear profile between the slab surface temperature on the fluid side and the inner slab temperature tslabbc is set up. The slab surface temperature on the fluid side is then calculated from steady-state fluid to slab heat transfer on the fluid side with tslab0 being the fluid temperature and hslablin the heat-transfer coefficient on the fluid side of the slab. tslabbc is the surface temperature on the inside (positive side) of the slab.
slabdef(25,*) Sets tslab0, tslabbc, and slabthk for specific boundaries and blocks. Conditions on the east boundary generally apply to the slabs on the west side of all obstacles. Correspondingly, the west side boundary conditions are applied to all slabs on the east side of obstacles, and so on similarly for the other four planes.
slabdef(1,n) Block number (must be 1 for GASFLOW-MPI).
slabdef(2,n) Thickness of slabs on east boundary.
slabdef(3,n) Thickness of slabs on west boundary.
slabdef(4,n) Thickness of slabs on north boundary.
slabdef(5,n) Thickness of slabs on south boundary.
slabdef(6,n) Thickness of slabs on top boundary.
slabdef(7,n) Thickness of slabs on bottom boundary.
slabdef(8,n) Initial temperature for slabs on east boundary (applied instead of tslab0).
slabdef(9,n) Initial temperature for slabs on west boundary(applied instead of tslab0).
slabdef(10,n) Initial temperature for slabs on north boundary(applied instead of tslab0).
slabdef(11,n) Initial temperature for slabs on south boundary(applied instead of tslab0).
slabdef(12,n) Initial temperature for slabs on top boundary(applied instead of tslab0).
slabdef(13,n) Initial temperature for slabs on bottom boundary(applied instead of tslab0).
slabdef(14,n) Temperature BC for slabs on east boundary(applied instead of tslabbca).
slabdef(15,n) Temperature BC for slabs on west boundary(applied instead of tslabbca).
slabdef(16,n) Temperature BC for slabs on north boundary(applied instead of tslabbca).
slabdef(17,n) Temperature BC for slabs on south boundary(applied instead of tslabbca).
slabdef(18,n) Temperature BC for slabs on top boundary(applied instead of tslabbca).
slabdef(19,n) Temperature BC for slabs on bottom boundary(applied instead of tslabbca).
slabdef(20,n) Material type for slabs on east boundary(applied instead of matbdy).
slabdef(21,n) Material type for slabs on west boundary(applied instead of matbdy).
slabdef(22,n) Material type for slabs on north boundary(applied instead of matbdy).
slabdef(23,n) Material type for slabs on south boundary(applied instead of matbdy).
slabdef(24,n) Material type for slabs on top boundary(applied instead of matbdy).
slabdef(25,n) Material type for slabs on bottom boundary(applied instead of matbdy).
islablin Flag to set an approximate linear initial temperature profile in each slab cell based on temperature of slab BC#2 and fluid cell contiguous with BC#1 (default is 0, no linear initial temperature profile).
hslablin Heat-transfer coefficient on slab BC#1. Used in evaluating the linear slab cell temperature profile (default is 1000).
dxslabc
dxslabc = 0.0 results in uniform mesh spacing for all concrete slabs.
dxslabc ≠ 0 results in a variable mesh spacing with for all concrete slabs. The first δx for each concrete slab will be dxslabc (default is zero).
matbdy Material type (uniform) for the mesh boundary slabs in all blocks. Can be overridden for specific blocks and boundaries using slabdef. matbdy = 0 results in no boundary slabs.
A material number > 0 specified for a boundary of the computational mesh implies that this particular boundary side is simulated as a slab of the material represented by the specified number.
If nothing more is specified, a flat temperature profile with tslab0 (default 300 K) is initiated and the inner side of the slab is maintained adiabatic.
If tslab0 < 0, a flat profile with the adjacent fluid temperature is specified and an adiabatic BC is applied at the inside.
If a value greater than zero is input for tslabbc, the BC on the inner (positive) surface of the slab uses a constant surface temperature tslabbc.
The slabdef statements allow different definitions for each of the six boundaries of the computational mesh of the block they are defined for. But they apply at the same time also to the obstacle planes inside. The conditions for the computational boundary on the east side define the west side of the boundary slab and are also used to simulate the west side of the obstacle slabs inside. In the same way, the conditions for the top boundary define the bottom side of the top boundary slabs and the bottom side of the internal obstacle slabs.
3.9.6. Background for Defining Stady-State Temperature Profiles
The steady-state temperature profile in the heat-conducting structures can either be flat or have an initial gradient. If one side of the structure is modeled as adiabatic, the initial temperature profile is always flat and defined from the surface temperature of the opposite side. Steady-state temperature profiles are only simulated for nonadiabatic boundary conditions on either side of the structure. Different thermal conductivities for composite layers must be accounted for in the initial profile, if a gradient is simulated.
The steady-state heat ratings and the surface temperatures depend on the selected boundary conditions.
3.9.6.1. Steady-State Fluid Conditions Input for the Structure
GASFLOW-MPI allows input of some outer fluid condition on one structure side by specifying an outer fluid temperature, a heat-transfer coefficient, and a heat flux. This applies to the center of a sink but is also possible on either side of a wall. If the fluid conditions are specified on the positive side (positive side implies the high number side of the heat structure or right side where increasing node numbers go from left to right), the steady-state heat flux for planar geometry is calculated from.
For the same conditions, the correlation for the linear heat rate in cylindrical coordinates is
T__fe, q_ce and h__e are the input values for the fluid temperature, the steady-state heat flux, and the convective heat-transfer coefficient on the east side.
Using the total heating rate, the structure surface temperature on the east/positive/right side is defined as:
Note that the heat flux going into the wall on either side is assigned a positive sign in GASFLOW-MPI.
The convention for calculating steady-state profiles in slabs is slightly different. In this case, with islablin = 1 and hslablin > 0 (as explained in Section 6.5), the initial fluid temperature is specified on the negative side of the slab and is only considered as an initial condition. The surface temperature tslabbc is defined on the positive side and held constant as a boundary condition. The slab surface temperature on the negative side is then adjusted to be consistent with the steady-state heat flux.
3.9.6.2. Direct Input of Steady-State Heat Flux on the Structures
One can also specify only the heat flux and the surface temperature on one side of the structure. In this case, the steady-state surface temperature on the side of the heat flux is consistently defined for this heat flux using the given surface temperature on the opposite side. If the heat flux and one surface temperature are specified, then the surface temperature on the opposite side is calculated consistently.
The input heat fluxes determine the heat flux for planar and cylindrical walls by
The input currently requires the user to specify the steady-state surface temperature on the opposite side as the heat flux. The missing surface temperature on the heat flux side is then calculated:
Instead of inputting the surface temperature on the opposite side, it would be possible to specify the steady-state surface temperature on the same side as the heat flux. But this condition would require prior hand calculations to arrive at the desired surface temperature on the fluid side; therefore, it has not been put into the code.
3.9.7 Heat Fluxes into Slabs, Walls, and Sinks
The heat rate absorbed in the different structures is evaluated in subroutine outheat and printed for each slab, wall, and sink at the user-specified time interval prtdt. This subroutine also evaluates the heat fluxes which the structure take out the GASFLOW-MPI fluid cells. These heat fluxes are summed up for each structure type and are also included in the general plot output from PlotHist.nc. They can be applied in an overall energy balance if the system is closed. The transient temperature changes are also evaluated separately in the surface elements of both structure sides. This allows the calculation of transient heat fluxes associated with boundary conditions that only specify structure surface temperatures.
3.9.8. Balancing of Heat Structure Surfaces
The code automatically sums up all structure surfaces for slabs, walls, and sinks, split up into concrete, steel, and total surface. This information is printed out to the file gfout. Additionally, by setting the input parameter in rheat to
lprarea =1,
a data set area is defined at the start of the calculation under Unit 99 that contains the following: all affected m nodes
Type is: 1=slab, 2=sink, 3=wall;
Mat is the material number;
Thickness is the thickness applied for heat conduction;
Area is the surface area of the respective structure.
There are instances when the GASFLOW-MPI calculated heat transfer surface areas that are computed from the internal geometry are not exactly in agreement with plant, experiment, or other code data. For example, in the current GKN analysis, we are attempting to match the heat transfer surface area of the GRS/RALOC analysis. In the following Table, we see the GRS data and the GASFLOW-MPI calculated areas:
The third column of this Table, the GASFLOW area, is found from the screen output when ihtflag > 0.
The first entry in GASFLOW column of the Table is 35119 m2 which is shown in Figure 6-5 as the total concrete surface. The next two entries, 17485 m2 and 366 m2, are shown as material 2 as sinks and walls, respectively. The last GASFLOW entry in Table 6-2, 8074 m2, is found as material 4
We have added an option in GASFLOW-MPI that will allow the user to exactly balance the heat transfer areas by heat transfer surface type and material number. This option is best demonstrated by continuing the use of the example already started above. We can signal the heat transfer setup routines that we wish to rebalance the heat transfer surfaces by providing the following input in NAMELIST rheat:
iareabal Flag must be set > 0 to activate heat transfer rebalancing option (default = 0).
refaslab(*) Reference area for slabs by material type.
refasink(*) Reference area for sinks by material type.
refawall(*) Reference area for walls by material type.
To produce exactly the heat transfer surface area as the GRS/RALOC data, GASFLOW-MPI would therefore require the following input:
$rheat
...
ihtflag = 1,
iareabal = 1,
refaslab = 1.97991e+08, refasink = 0.00000e+00, 1.74850e+08, 0.00000e+00, 0.79190e+08,
refawall = 1.13409e+08, 3.66350e+06,
...
$end
3.9.9. Modify material Numbers of Slab Structures
It is mostly for 3D visualization that the user wants to omit certain structures to get a better view on results in inner regions hidden by obstacles. The user can open up a view into such regions by giving the hidden structures the same properties as the visible ones but associate them to a different material number. In most cases, the user distinguishes visible and invisible structures with different material numbers already when setting up the geometry model with obstacles and walls. To allow the user to make certain structures invisible also during the run one can change the material number of certain slabs even during the run with the parameter matdef from $rheat.
This parameter works for slabs only and is defined on the surfaces of the affected slabs as
matdef(1,*) Beginning i mesh of the slab surface.
matdef(2,*) Ending i mesh of the slab surface.
matdef(3,*) Beginning j mesh of the slab surface.
matdef(4,*) Ending j mesh of the slab surface.
matdef(5,*) Beginning k mesh of the slab surface.
matdef(6,*) Ending k mesh of the slab surface.
matdef(7,*) Block number (must be 1 for GASFLOW-MPI).
matdef(8,*) Material Number attributed to this slab.
Example
The input matbdy defines the material on the computational boundary. One can define a different material number for the boundary slabs of a cylindrical mesh in the angle between 90 and 270 degrees:
$rheat
...
ihtflag = 1,
matbdy = 6,
matdef = 30, 30, 16, 46, 01, 26, 1, 7, ; opens 180 degree view
i1,i2 = 30, 30, ; defines the outer radial boundary in the mesh
j1,j2 = 16, 46, ; defines the angle with the new material 90 and 270 degrees from ygrid
k1,k2 = 1, 26 defines the height of the opened up boundary cylinder
matpanel = 6, ;only displays material 6 and omits 7.
…
$end
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