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This section describes how to define the thermal network to QTRAN. All resistors and capacitors will be defined in this section. The parameters and options controlled by input are listed below.

1. Thermal Resistor Assignments.

2. Nodal Capacitance Data.


Note:	PATQ normally generates all of the resistor and capacitor data automatically via menu pick 2.

Thermal Resistor Assignments

This section describes how to enter the thermal resistor data that will be used to describe a given problem. The allowed resistor types are identified as follows:


C	-	Conductive Resistor	(p. 276)
H	-	Convective Resistor	(p. 280)
R	-	Radiative Resistor	(p. 283)
W	-	Wavelength-Dependent Radiative
Resistor			(p. 291)
L	-	Automatic 1-D Conduction Mesh
Generation			(p. 300)
A	-	Advective Resistor	(p. 305)
F	-	Hydraulic Resistor	(p. 306)

To enter a data set for any given thermal resistor type, proceed to the appropriate section in any arbitrary order, enter all required data for the resistor, and then proceed to the next resistor to be defined. When all of the resistor information has been entered for the problem, place a dollar sign ($) in column one of the input data file and proceed to Capacitor Data, 320.

Conductive Resistor Data


RES -TYPE	NODE1	NODE2	MPID	LENGTH	AREA

This sections describes how to enter data that describe single conductive resistors. To define a conductive resistor, follow the procedure outlined below.

Enter all data for the resistor from this section. This data defines the resistor as a conduction resistor, defines the nodal connectivity of the resistor, defines the resistor as one-way or two-way (two-way is the normal usage), identifies the material property to be used for thermal conductivity, and defines the effective length/area data for the resistor.

If no more thermal resistor data of any kind is to be entered, enter a dollar sign ($) in column 1 of the input data file and proceed to Capacitor Data, 320. As a result for the PATQ translation (menu pick 2) these declarations are placed in the CONDUCDAT file. If more thermal resistors are to be defined, proceed to the appropriate section ((p. 276) to (p. 306)) and continue with resistor data input.

Example


C	4	7	23	1.4	23.7

This defines a conductive resistor between nodes 4 and 7 with a thermal conductivity MPID of 23, a length of 1.4, and an area of 23.7.


Parameter	Description
RES-TYPE	An alpha character that defines the resistor type. In this case, RES-TYPE is entered as C to identify a conductive resistor.
NODE1	Node 1 of the conductive resistor.
NODE2	Node 2 of the conductive resistor. Notice: You may specify these resistors as one-way resistors if you wish. This means that they may be made to transmit heat in one direction but not in the other. If you wish to do this, input the node that you do not wish heat to flow to as a negative number. Heat will then be allowed to flow from the negative node to the positive node, but not from the positive node to the negative node.
MPID	The MPID number of the material property that is to be used to calculate the thermal conductivity of the resistor. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263. To define a time-dependent thermal conductivity, enter MPID as the negative of the MPID to be used.
LENGTH	Length of the conductive resistor.
AREA	Cross-sectional area associated with flux through the conductive resistor. For Cartesian conductive resistors, the thermal resistance for such a resistor is given by the following expression: where R is the resistor value, Length is the distance between nodes, k is the thermal conductivity, and Area is the cross-sectional area available for heat to flow through between the nodes. This expression may be factored and rewritten in the following form, which separates the geometric data and the thermal conductivity as follows: where CSF is a conduction shape factor. For non-Cartesian resistors, you may enter the analogous values for Length (LENGTH) and Area (AREA) that will result in the calculation of the appropriate CSF for your non-Cartesian resistor. For example, the resistance of a cylindrical wall is given by the expression:
	where: R[1] = inner radius of the cylindrical section you are modeling, R[2] = outer radius of the cylindrical section you are modeling, PI = usual quantity related to circles (3.1415 etc.), L[c] = length of the cylindrical section you are modeling, and k = material’s thermal conductivity. Thus, a correct and equivalent method to enter this resistor’s value is to let AREA = 1.000 and to let This yields a correct CSF value, which is the only information that is of mathematical significance.

Convective Resistor Data

The following sections are used to define convective resistors. As a result of the PATQ translation (menu pick 2), these declarations are placed in the CONVECDAT file. The procedure that you will use to define a convective resistor is explained below.

1. To enter all data for the convective resistor see Convective Resistor Header Data, 281. This data identifies the resistor as a convective resistor, defines the resistor node numbers, and defines the resistor configuration (which must be selected from the convective resistor catalogue in Convection Configurations (Ch. 9)).

2. Enter the data for the resistor for Convective Resistor Geometric Properties, 281. This data defines all Geometric Properties (GP) such as characteristic lengths, surface areas, and fluid free-stream velocities. See Convection Library (Ch. 9) for more information about specific resistor configurations and the required GP data for each configuration.

3. Enter all data for the resistor for Convective Resistor Material Properties, 282. This data is used to identify which of the material properties that you defined in MPID Number, Function Type, Temperature Scale, Factor and Label, 263 will be used to define this convective resistor. See Convection Configurations (Ch. 9) for more information about specific resistor configurations and the required MPID data for each configuration.

4. When all of the thermal resistors are defined, place a dollar sign ($) in column 1 of the input data file and proceed to Capacitor Data, 320. To define another thermal resistor, proceed to the resistor data section ((p. 276) to (p. 306)) that applies to the next resistor to be defined.

Convective Resistor Header Data


RES -TYPE	NODE1	NODE2	NODE3	CFIG

This section allows a given thermal resistor to be identified as a convective resistor, to define its node numbers, and to specify the resistor configuration.

Example

H     1      3      0      14

This heads the resistor data for a convective resistor between nodes 1 and 3 (no third node), and specifies convection configuration number 14.


Parameter	Description
RES-TYPE	An alpha character that defines the resistor type. In this case, RES-TYPE is entered as H to identify a convective resistor.
NODE1	Node 1 of the convective resistor.
NODE2	Node 2 of the convective resistor.
NODE3	Node 3 of the convective resistor. Although most convective resistors have only two node numbers, certain of the convective resistors require that you define three nodes. If the convective resistor that is being defined requires only two nodes, enter a zero for the NODE3 value.
CFIG	Convective resistor configuration identification number, where configuration is defined as the class of convection correlations that would be used for a given problem. For example, flat plates would be one type of resistor configuration, and flow across horizontal cylinders would be another configuration type. For specifics, consult the convective resistor catalogue in Convection Library (Ch. 9) for available configurations. Allowed CFIG values are 1 to 37 inclusive, in addition to numbers greater than or equal to 1000. CFIG values of 1000+ are used to refer to user-supplied convection configuration subroutine.

Convective Resistor Geometric Properties


RES -GP(1)	GP(2)	GP(n)

Example

24.7	23.2	0.0	14.8	29.9

15.6		18.9

This enters 7 GP values of 24.7, 23.2, 0.0, 14.8, 29.9, 15.6, and 18.9, in that order using free format input.


Parameter	Description
GP	Convective resistor’s Geometric Properties such as length, diameter, surface area, or gravitational constants. The exact meaning of each GP value varies for each configuration. See Convective Resistor Header Data, 281. Consult Convection Library (Ch. 9) for specific configurations and GP meanings. QTRAN will continue reading GP values until it encounters a slash (/) in column 1 of the input data file. The procedure for entering GP values is to enter all GP values followed by an input data file line with a slash in column 1. It should be noted that any number GP values may be placed on an 80 character line, or multiple lines may be used. The maintaining of the order is the important consideration. Proceed on to Convective Resistor Material Properties, 282.

Convective Resistor Material Properties


MPID(1)	MPID(2)	MPID(n)

Example


1	7	4	6	15	23

This declares MPID values of 1, 7, 4, 6, 15, and 23.


Parameter	Description
MPID	Material property identification numbers for the convective resistor. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263 for more information. For specifics, consult the convective resistor catalogue in Chapter 6. The material properties that correspond to each MPID entry are listed for each configuration in the catalogue. When done entering MPID values, enter a slash (/) in column 1 of the next line of the input data file.

Example Convective Resistor Definition

The following is an example of a complete convective resistor definition.

Example

H	  23	  45  	0  	14

  	1.23  	9.8	  15

  45  72  88  99  1024

This QTRAN input data defines a configuration 14 convective resistor between nodes 23 and 45. The GP values are 1.23, 9.8, and 15. The MPID numbers are 45, 72, 88, 99 and 1024.

Gray Radiative Resistor Data

The following two sections allow gray or black-body thermal radiation resistors to be identified to QTRAN. These resistors can be either variable or constant and are allowed to be functions of time or temperature but not wavelength. QTRAN will use σ * T4 as the potential across these thermal resistors in accordance with normal network conventions, and the value of T used will be an absolute temperature. If calculations are being performed in degrees Fahrenheit (that is, if ICCALC was defined as F in Temperature Scale and Time Units Definition, 230), Rankine will be used for T. If calculations are being performed in Celsius (that is, if ICCALC was defined as C), Kelvin will be used for T. This convention will be used even if the temperature nodes to which the resistor is connected is a view factor radiosity node rather than a surface temperature node. As a result of the PATQ translation (menu pick 2) and VIEW FACTOR execution (menu pick 3), these declarations are placed in the VFRESDAT file. The procedure used to define a gray thermal radiation resistor is explained below.

1. Enter all data for the gray thermal radiation resistor for Gray Type Specification, Node Assignments, and MPID, 283. This data identifies the resistor as a gray thermal radiation resistor, defines the resistor nodal connectivity, defines the resistor subtype, and identifies the material property MPID numbers for emissivity or transmissivity.

2. Enter the data for the resistor for Gray Radiative Resistor View factors, Areas, and Distances, 288. This data defines the view factor and/or surface area associated with the resistor as well as the view factor distance, if appropriate.

3. To terminate the definition of a thermal resistor of any type, place a dollar sign ($) in column one of the input data file and proceed to Capacitor Data, 320. To define another thermal resistor, proceed to the resistor data section ((p. 276) to (p. 306)) that applies to the next resistor to be defined.

Gray Type Specification, Node Assignments, and MPID


RES -TYPE	NODE1	NODE2	NODE3	SUB-TYPE	MPID

This section describes how to identify a given thermal resistor as a black-body/gray-body radiative resistor and to define the resistor node numbers. These resistors conduct heat according to the following relation:

where σ is the Stefan-Boltzmann constant, T[1] and T[2] are the temperatures of nodes 1 and 2 of the resistor in degrees absolute (QTRAN will perform the conversion to degrees absolute no matter which temperature scale is being used for calculations), and R is the value of the radiative resistor.

Example

R	  1	  3  	4  	2  	15

This defines a gray radiative resistor between nodes 1 and 3 with the transmissivity evaluated at the temperature of node 4, resistor subtype 2, and the transmissivity evaluated from MPID 15.


Parameter	Description
RES-TYPE	A character that defines the resistor type. In this case, RES-TYPE is entered as R to identify a gray thermal radiation resistor.
NODE1	Node 1 of the radiative resistor.
NODE2	Node 2 of the radiative resistor.
NODE3	Node 3 of the radiative resistor (if applicable). If input as zero, it will be set to NODE1. If a resistor subtype does not require a NODE3 value, enter a 0 for NODE3.

The following table is a brief summary of resistor node assignments.

Table 8‑1
Resistor Subtype	Node 1	Node 2	Node 3
1	Non-Black Surface	Radiosity	N/A
2	Radiosity	Radiosity	PM
3	PM	Radiosity	PM
4	Any	Any	N/A
5	Any	Any	N/A
6	Any	Any	N/A
7	Radiosity	Radiosity	PM
8	PM	Radiosity	PM
9	Radiosity	Radiosity	PM
10	PM	Radiosity	PM
11	Radiosity	Radiosity	PM
12	PM	Radiosity	PM
13	Any	Any	N/A
14	Any	Any	N/A
15	Any	Any	N/A
N/A = Not applicable - no entry is necessary for Node 3. PM = Participating Media - the node should be assigned participating media (e.g., participating gas) temperature node.


SUB-TYPE	This is the resistor subtype, where:
	Subtype: 1
	This resistor type is used between a gray surface and a radiosity node, with an emissivity that is taken from a material property (MPID).
	Subtype: 2
	This resistor type is used between radiosity nodes, and with a time or temperature dependent participating media whose transmissivity is taken directly from a material property (MPID).
	Subtype: 3
	This resistor type is used between a radiosity node and a participating media node. The view factor is between the surface i and the gas (or other participating media node). The transmissivity of the gas (or participating media) is taken from a material property.
	Subtype: 4
	This resistor type may be used anywhere that material properties are constant. It would normally be used as a view factor resistor between radiosity nodes, but the F and A values are entered as simple constants and hence could be anything appropriate for a radiative resistor of this formulation. Since there is no data for transmissivity, the transmissivity of the resistor is implicitly assumed to be 1.0.
	Subtype: 5
	This resistor type may be used anywhere that material properties are constant. It would normally be used as a view factor resistor between two radiosity nodes, but the F value is a simple constant and hence could be anything appropriate for a radiative resistor of this formulation. Note: This resistor type is used when a minimum of calculations are desired, thus for this type only the reciprocal of the resistance is input.
	Subtype: 6
	This resistor type may be used as a surface resistor, with the value given for e being the emissivity. This resistor subtype may be used anywhere the emissivity is constant. Because the emissivity is assumed to be constant, it is faster to evaluate than Subtype 1.
	Subtype: 7
	This resistor type is used between radiosity nodes. τ is calculated from an extinction coefficient identified by the resistor’s MPID and from a view factor distance. Specifically, τ[gas] = EXP(-S * P), where S is the view factor distance and P is the extinction coefficient calculated from the material property (MPID) of the resistor.
	Subtype: 8
	This resistor type is used between a radiosity node and a participating media node. τ is calculated from an extinction coefficient identified by the resistor’s MPID and from a view factor distance. The transmissivity value τ is calculated in the same manner as for Subtype 7.
	Subtype: 9
	This resistor type is used between radiosity nodes, and with a temperature dependent participating media whose transmissivity is taken directly from a material property (MPID). This is the same as Subtype 2, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 10
	This resistor type is used between a radiosity node and a participating media node. The view factor is between the surface i and the gas (or other participating media node). The transmissivity of the gas (or participating media) is taken from a material property. This is the same as Subtype 3, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 11
	This resistor type is used between radiosity nodes. τ is calculated from an extinction coefficient identified by the resistor's MPID and from a view factor distance. Specifically, τ[gas] = EXP(-S * P), where S is the view factor distance and P is the extinction coefficient calculated from the material property (MPID) of the resistor. This is the same as Subtype 7, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 12
	This resistor type is used between a radiosity node and a participating media node. τ is calculated from an extinction coefficient identified by the resistor’s MPID and from a view factor distance. The transmissivity value τ is calculated in the same manner as for Subtype 7. This is the same as Subtype 8, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency. In the equations above: R = is the value of the gray thermal radiation resistor, e = is the gray emissivity of a radiating surface, A = is the surface area of the radiating surface, F = s the surface’s view factor, AF = is the product of the surface's area and the view (subtypes 9-12) factor, and τ[gas] = is the transmissivity of the participating media.
	Subtype: 13
	This resistor type may be used between any nodes. The F[i,j] term is defined by a material property (MPID) whose independent variable is either time or the temperature of the i-th node in calculation units. This is normally used to define dynamic viewfactor and thus would couple radiation between radiosity nodes. However, if both surfaces have constant emissivities then the F term can be thought of as a script F which includes any non black characteristics. The area term is a constant for this evaluation. Since there is no data for transmissivity, the transmissivity of the resistor is implicitly assumed to be 1.0. If diagnostic output is requested the F[i,j] term is output as an emissivity value.
	Subtype: 14
	This resistor type may be between used any nodes. The AF[i,j] term is defined by a material property (MPID) whose independent variable is either time or the temperature of the i-th node in calculation units. This is normally used to define dynamic viewfactor and thus would couple radiation between radiosity nodes. However, if both surfaces have constant emissivities then the AF term becomes a script F which includes any non black characteristics. The area term is a constant for this evaluation. Since there is no data for transmissivity, the transmissivity of the resistor is implicitly assumed to be 1.0. If diagnostic output is requested the F[i,j] term is output as an emissivity value. Although the area term is not used, it can be specified for reference purposes and is assumed to be the area of the i-th node.
MPID	Emissivity or Transmissivity MPID number. MPID should be zero for resistor Subtype 4, Subtype 5, or Subtype 6.
	Subtype: 15
	The variable gap resistor is between two surfaces where both emissivities are defined by a material property even if one is a constant. Since the form factor will be one for this equation to be valid as used, it is not necessary to input a form factor, one will be assumed.

Gray Radiative Resistor View factors, Areas, and Distances


VIEW FACTOR	AREA	VFDIST

codeindent10

0.73118     43.2     15.7

This defines a VIEW FACTOR value of 0.73118, AREA = 43.2, and VFDIST = 15.7.


Parameter	Description
VIEW FACTOR	Radiative resistor’s view factor (Subtype 2, Subtype 3, Subtype 7, and Subtype 8) is one of two constants multiplied together to compute the resistor’s value (Subtype 4), the product of the resistor area and the view factor (Subtype 9 through Subtype 12), the reciprocal of resistor’s value (Subtype 5), or is the resistor’s emissivity (Subtype 6 only). VIEW FACTOR may not be left blank for any of the subtypes. A numeric value must be entered (i.e., enter a 0 if VIEW FACTOR is not applicable to the resistor subtype, e.g., Subtype 1).
AREA	Surface area associated with the radiative resistor (Subtype 1 through Subtype 3 and Subtype 6 through Subtype 8), or else is simply one of two constants multiplied together to compute the resistor’s value (Subtype 4), it could also be ignored (or left blank) for Subtype 5 and Subtype 9 through Subtype 12.
VFDIST	View factor distance used with an extinction coefficient to calculate transmissivity for resistor Subtype 7, Subtype 8, Subtype 11, and Subtype 12. VFDIST is ignored for the other resistor subtypes and may be left blank.

Examples of Gray Radiative Resistors

The following are examples of various gray radiative resistors for QTRAN.


Subtype: 1	R 11 2 0 1 102345 0.0 21.73
Defines a gray resistor between surface node 11 and radiosity node 2. MPID 102345 will be used to calculate the temperature-dependent emissivity. The view factor field is given as 0.0 and will be ignored by QTRAN (but must be there as a spacer), and the surface area is given as 21.73.
Subtype: 2	R 21 23 99 2 45 0.0124 15.78
Defines a gray radiative resistor between radiosity nodes 21 and 23. The temperature of node 99 and MPID 45 will be used to compute the participating media transmissivity. The view factor is given as 0.0124 and the surface area for the resistor is given as 15.78.
Subtype: 3	R 14 15 14 3 88 0.0124 0.187
Defines a gray radiative resistor between participating media node 14 and radiosity node 15. The transmissivity will be calculated from material property 88 using the temperature of node 14 (given as both NODE1 and NODE3 here). The view factor is given as 0.0124 and the surface area is given as 0.187.
Subtype: 4	R 77 78 0 4 0 0.89 23.78
Defines a gray radiative resistor between nodes 77 and 78. Nodes 77 and 78 may be any type of radiation network node (surface, radiosity, or participating media). The view factor value (or first constant) is given as 0.89 and the surface area (or second constant) is given as 23.78.
Subtype: 5	R 88 8991 0 5 0 89.76
Defines a gray radiative resistor between nodes 88 and 8991. The input value is 89.76, which is the reciprocal of the resistance.
Subtype: 6	R 101 9 0 6 0 7.890E-01 23.889
Defines a gray radiative resistor between nodes 101 and 9. The constant emissivity has been given as 7.890E-01 and the surface area has been given as 23.889.
Subtype: 7	R 66 77 67 7 89089 0.00123 85.776 1.045E+02
Defines a gray radiative resistor between radiosity nodes 66 and 77. The temperature of node 67 will be used with MPID 89089 to calculate an extinction coefficient. The view factor has been given as 0.00123, the surface area as 85.776, and the view factor distance as 1.045E+02.
Subtype: 8	R 655 656 0 8 2525 0.12 8.9E+02 84.88E+03
Defines a gray radiative resistor between participating media node 655 and radiosity node 656. The temperature of node 655 will be used to calculate the extinction coefficient since NODE3 was entered as 0. The MPID of the extinction coefficient is 2525. The view factor is given as 0.12, the surface area as 8.9E+02, and the view factor distance as 84.88E+03.
Subtype: 9	R 21 23 99 9 45 0.0124
Defines a gray radiative resistor between radiosity nodes 21 and 23. The temperature of node 99 and MPID 45 will be used to compute the participating media transmissivity. The product of the surface area and the view factor is given as 0.0124.
Subtype: 10	R 14 15 l14 10 88 0.0124
Defines a gray radiative resistor between participating media node 14 and radiosity node 15. The transmissivity will be calculated from material property 88 using the temperature of node 14 (given as both NODE1 and NODE3 here). The product of the surface area and the view factor is given as 0.0124.
Subtype: 11	R 66 77 67 11 89089 0.00123 0.0 1.045E+02
Defines a gray radiative resistor between radiosity nodes 66 and 77. The temperature of node 67 will be used with MPID 89089 to calculate an extinction coefficient. The product of the surface area and the view factor has been given as 0.00123, the AREA parameter (not used for this resistor subtype, but still necessary as a placeholder) has been given as 0.0, and the view factor distance as 1.045E+02.
Subtype: 12	R 655 656 0 12 2525 0.120 84.88E+03
Defines a gray radiative resistor between participating media node 655 and radiosity node 656. The temperature of node 655 will be used to calculate the extinction coefficient since NODE3 was entered as 0. The MPID of the extinction coefficient is 2525. The product of the surface area and the view factor is given as 0.12, the AREA parameter (not used for this resistor subtype, but necessary as a placeholder) is given as 0.0, and the view factor distance as 84.88E+03.
Subtype: 13	R 266 277 0 13 35721 0.00 44.4
Defines a gray radiative resistor between nodes 266 and 277. Although time will usually be the independent variable for material properties with this option, if temperature is the independent variable, node 266 will be used to calculate view factor or script F. The view factor has been given as 0.0 value as a place holder. The surface area is 44.4. If the independent variable is temperature for MPID 35721 it must be specified in calculation units.
Subtype: 14	R 366 377 0 14 55721 0.00 55.5
Defines a gray radiative resistor between nodes 366 and 377. Although time will usually be the independent variable for material properties with this option, if temperature is the independent variable, node 366 will be used to calculate view factor or script F. The view factor has been given as 0.0 value as a place holder. The surface area of 55.5 is not used in determining the resistor value but can be specified for reference purposes. If the independent variable is temperature for MPID 55721 it must be specified in calculation units.
Subtype: 15	R 444 222 0 15 123417 100316 0.2468 100416
This defines a gray radiative resistor between noes 444 and 222 with form factor MPID defined as 123417. Most cases this will be 0 and the default form factor of 1.0 will be used. The emissivity on surface 1 is defined by material property ( MPID 100316), the surface area is 0.2468 units squared and the MPID for the second surface material property is 100416. This option is only available for gray body radiation.

Wavelength-Dependent Radiative Resistors

Type, Nodes, Subtype, MPID, Distance, 292, View factor, Area, and Wave band Definitions, 296 and Example Wavelength-Dependent Radiative Resistors, 297 describe how to input data for QTRAN’s wavelength-dependent thermal radiation resistors. These resistors account for wavelength, temperature and time dependent surface emissivities, and for wavelength, temperature, or time dependent transmissivities of participating media (e.g., optically thin gases). Thermal networks of this type can be constructed from any of the resistor subtypes described in Type, Nodes, Subtype, MPID, Distance, 292. As a result of the PATQ translation (menu pick 2) and VIEW FACTOR execution (menu pick 3), these declarations are placed in the VFRESDAT file.

To define a wavelength-dependent radiative resistor, use the following procedure.

1. Enter all data for the wave band resistor for Type, Nodes, Subtype, MPID, Distance, 292. This data identifies the resistor as a wavelength, temperature and/or time dependent thermal radiation resistor, defines the resistor’s nodal connectivity, the resistor subtype, the material property (to be used for emissivity (e), transmissivity (τ), or the extinction coefficient), and also defines the view factor distance to be used with the extinction coefficient (for resistor Subtypes 7, 8, 11 and 12 only).

2. Enter all data for the resistor for View factor, Area, and Wave band Definitions, 296. This data defines the resistor’s view factor, constant emissivity, constant transmissivity (if applicable), surface area, and wave band.

3. When all the thermal resistors are defined, place a dollar sign ($) in column 1 of the input data file and proceed to Capacitor Data, 320. To define another resistor, proceed to the resistor data section (Thermal Resistor Assignments, 276 ) that applies to the next resistor to be defined.

The potential used for calculating the heat flow across wavelength-dependent resistors is not the usual σ * T4 used for gray radiative resistors. Instead, the potential that is used is FRAC * σ * T4, where FRAC is a number between 0.0 and 1.0 and is a fractional multiplier that represents the amount of energy in the wave band η-1 to η-2 for which the resistor is valid. The net rate of heat from node 1 to node 2 is thus seen to be given by the following expression:

FRAC[1] is the fraction of the black-body radiation potential to be found between η-1 and η-2 at temperature T[1], and FRAC[2] is the fraction for T[2]. Strictly speaking, there is no way to incorporate the value of FRAC[1] and FRAC[2] into the R value. This has been a fairly common mistake for many users of other existing thermal programs in the past.

Type, Nodes, Subtype, MPID, Distance


RES -TYPE	NODE1	NODE2	NODE3	SUBTYPE	MFID	VFDIST

Example

W 	 10	  20 	30	 2	 15 	23.7

This declares that a wavelength-dependent resistor is connected to nodes 10 and 20, that the transmissivity will be evaluated according to the temperature of node 30, the resistor subtype is 2, the MPID number for the resistor is 15, and the distance between surfaces is 23.7.


Parameter	Description
RES-TYPE	A character that defines the resistor type. In this case, RES-TYPE is entered as W to identify a wavelength and temperature or time dependent thermal radiation resistor.
NODE1	Node 1 of the wavelength and temperature or time-dependent thermal radiation resistor. For resistor Subtype 1, NODE1 should be a surface node. For Subtype 2, NODE1 should be a radiosity node. For Subtype 3, NODE1 should be a participating media node (e.g., a gas temperature node). The temperature of NODE1 is used to evaluate the temperature-dependent wave band emissivity (E) for Subtype 1.
NODE2	Node 2 of the wavelength and temperature or time-dependent thermal radiation resistor. NODE2 must be a radiosity node, participating media node, or black-body node for all of the resistor subtypes.
NODE3	Node 3 of the wavelength and temperature or time-dependent thermal radiation resistor. NODE3 is used only as a reference temperature for computing the participating media temperature-dependent wave band transmissivity (t). If input as zero, it will be set to NODE1. If a resistor subtype does not require a NODE3 value, enter a 0 for NODE3.

The following table is a brief summary of resistor node assignments.

Table 8‑2
Resistor Subtype	Node 1	Node 2	Node 3
1	Non-Black Surface	Radiosity	N/A
2	Radiosity	Radiosity	PM
3	PM	Radiosity	PM
4	Any	Any	N/A
5	Any	Any	N/A
6	Any	Any	N/A
7	Radiosity	Radiosity	PM
8	PM	Radiosity	PM
9	Radiosity	Radiosity	PM
10	PM	Radiosity	PM
11	Radiosity	Radiosity	PM
12	PM	Radiosity	PM
13	Any	Any	N/A
14	Any	Any	N/A
N/A = Not applicable - no entry is necessary for Node. PM = Participating Media - the node should be assigned participating media (e.g., participating gas) temperature node.


SUB-TYPE	This is the resistor subtype, where:
	Subtype: 1
	This resistor type is used between a gray surface and a radiosity node, with an emissivity that is taken from a material property (MPID).
	Subtype: 2
	This resistor type is used between radiosity nodes, and with a time or temperature dependent participating media whose transmissivity is taken directly from a material property (MPID).
	Subtype: 3
	This resistor type is used between a radiosity node and a participating media node. The view factor is between the surface i and the gas (or other participating media node). The transmissivity of the gas (or participating media) is taken from a material property.
	Subtype: 4
	This resistor type may be used anywhere that material properties are constant. It would normally be used as a view factor resistor between radiosity nodes, but the F and A values are entered as simple constants and hence could be anything appropriate for a radiative resistor of this formulation. Since there is no data for transmissivity, the transmissivity of the resistor is implicitly assumed to be 1.0.
	Subtype: 5
	This resistor type may be used anywhere that material properties are constant. It would normally be used as a view factor resistor between two radiosity nodes, but the F value is a simple constant and hence could be anything appropriate for a radiative resistor of this formulation. Important: This resistor type is used when a minimum of calculations are desired, thus for this type only the reciprocal of the resistance is input.
	Subtype: 6
	This resistor type may be used as a surface resistor, with the value given for e being the emissivity. This resistor subtype may be used anywhere the emissivity is constant. Because the emissivity is assumed to be constant, it is faster to evaluate than Subtype 1.
	Subtype: 7
	This resistor type is used between radiosity nodes. τ is calculated from an extinction coefficient identified by the resistors MPID and from a view factor distance. Specifically, τ[gas] = EXP(-S * P), where S is the view factor distance and P is the extinction coefficient calculated from the material property (MPID) of the resistor.
	Subtype: 8
	This resistor type is used between a radiosity node and a participating media node. τ is calculated from an extinction coefficient identified by the resistor’s MPID and from a view factor distance. The transmissivity value τ is calculated in the same manner as for Subtype 7 above.
	Subtype: 9
	This resistor type is used between radiosity nodes, and with a temperature dependent participating media whose transmissivity is taken directly from a material property (MPID). This is the same as Subtype 2, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 10
	This resistor type is used between a radiosity node and a participating media node. The view factor is between the surface i and the gas (or other participating media node). The transmissivity of the gas (or participating media) is taken from a material property. This is the same as Subtype 3, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 11
	This resistor type is used between radiosity nodes. τ is calculated from an extinction coefficient identified by the resistor’s MPID and from a view factor distance. Specifically, τ[gas] = EXP(-S * P), where S is the view factor distance and P is the extinction coefficient calculated from the material property (MPID) of the resistor. This is the same as Subtype 7, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 12
	This resistor type is used between a radiosity node and a participating media node. τ is calculated from an extinction coefficient identified by the resistor’s MPID and from a view factor distance. The transmissivity value τ is calculated in the same manner as for Subtype 7. This is the same as Subtype 8, except that F[i,j] and A[i] have been combined as AF[i,j] for computational efficiency.
	Subtype: 13
	This resistor type may be used between any nodes. The F[i,j] term is defined by a material property (MPID) whose independent variable is either time or the temperature of the i-th node in calculation units. This is normally used to define dynamic viewfactor and thus would couple radiation between radiosity nodes. However, if both surfaces have constant emissivities then the F term can be thought of as a script F which includes any non black characteristics. The area term is a constant for this evaluation. Since there is no data for transmissivity, the transmissivity of the resistor is implicitly assumed to be 1.0. If diagnostic output is requested the F[i,j] term is output as an emissivity value.
	Subtype: 14
	This resistor type may be used between any nodes. The AF[i,j] term is defined by a material property (MPID) whose independent variable is either time or the temperature of the i-th node in calculation units. This is normally used to define dynamic viewfactor and thus would couple radiation between radiosity nodes. However, if both surfaces have constant emissivities then the AF term becomes a script F which includes any non black characteristics. The area term is a constant for this evaluation. Since there is no data for transmissivity, the transmissivity of the resistor is implicitly assumed to be 1.0. If diagnostic output is requested the F[i,j] term is output as an emissivity value. Although the area term is not used, it can be specified for reference purposes and is assumed to be the area of the i-th node.
MPID	This is the material property identification (MPID Number, Function Type, Temperature Scale, Factor and Label, 263 number that is used here to identify the emissivity or transmissivity of the wavelength and temperature or time-dependent radiative resistor.
VFDIST	This is the View factor Distance, used for resistor Subtypes 7, 8, 11 and 12, along with the material property identified with MPID to compute a transmissivity for the resistor. For Subtypes 7, 8, 11, and 12, MPID is assumed to identify a material property that will be used as an extinction coefficient. The transmissivity Tau is then computed as τ = EXP( -VFDIST * k ), where k is the extinction coefficient calculated from an MPID.

View factor, Area, and Wave band Definitions


VIEW FACTOR	AREA	η1	η-2

Example

0.0     14.7     1.1     3.3

This enters a VIEW FACTOR value of 0.0, an AREA value of 14.7, a η-1 value of 1.1 microns, and a η-2 value of 3.3 microns.


Parameter	Description
VIEW FACTOR	Wavelength and temperature-dependent resistor’s view factor for Subtypes 2, 3, 7, 8, 11, and 12, constant emissivity (Subtype 6), constant transmissivity (Subtype 4), reciprocal of the resistor’s value (Subtype 5), or the product of the resistor area and the view factor (Subtypes 9-12). VIEW FACTOR is ignored for resistor Subtype 1. If defining resistor Subtype 1, enter a zero for VIEW FACTOR.
AREA	Surface area associated with the wavelength and temperature or time dependent thermal radiation resistor. Area should be entered as 0.0 for Subtypes 9-12.
η-1	Shortest wavelength of the wave band interval for which the wavelength and temperature or time-dependent resistor is to be used. h-1 should be entered in units of micrometers only.
η-2	Longest wavelength of the wave band interval for which the wavelength and temperature or time dependent resistor is to be used. h-2 should be entered in units of micrometers only.

Example Wavelength-Dependent Radiative Resistors

The following are examples of various wavelength-dependent radiative resistors for QTRAN.


Subtype: 1	W 11 2 0 1 102345 0.0 21.73
Defines a resistor between surface node 11 and radiosity node 2. MPID 102345 will be used to calculate the temperature dependent emissivity. The view factor field is given as 0.0 and will be ignored by QTRAN (but must be there as a spacer), and the surface area is given as 21.73. The wave band is defined to lie between 0.0 and 5.0 microns.
Subtype: 2	W 21 23 99 2 45 0.0124 15.78 5.0 9.8
Defines a radiative resistor between radiosity nodes 21 and 23. The temperature of node 99 and MPID 45 will be used to compute the participating media transmissivity. The view factor is given as 0.0124 and the surface area for the resistor is given as 15.78. The wave band is given as 5.0 to 9.8 microns.
Subtype: 3	W 14 15 14 3 88 0.0124 0.187 0.13 0.89
Defines radiative resistor between participating media node 14 and radiosity node 15. The transmissivity will be calculated from material property 88 using the temperature of node 14 (given as both NODE1 and NODE3 here). The view factor is given as 0.0124 and the surface area is given as 0.187. The wave band is defined to be between 0.13 and 0.89 microns.
Subtype: 4	W 77 78 0 4 0 0.89 23.78 9.8 1.0E+10
Defines a gray radiative resistor between nodes 77 and 78. Nodes 77 and 78 may be any type of radiation network node (surface, radiosity, or participating media). The view factor value (or first constant) is given as 0.89 and the surface area (or second constant) is given as 23.78. The wave band is defined to be between 9.8 and 1.0E+10 microns.
Subtype: 5	W 88 8991 0 5 0
	89.76 0.0 1.2 8.9
Defines a radiative resistor between nodes 88 and 8991. The input value is 89.76, which is the reciprocal of the resistance. The AREA value of 0.0 is entered as a required spacer between the VIEW FACTOR value and the LAMBDA-1 value. The wave band is defined to be between 1.2 and 8.9 microns.
Subtype: 6	W 101 9 0 6 0 7.890E-01 23.889 1.0E-01 1.2E+01
Defines a radiative resistor between nodes 101 and 9. The constant emissivity has been given as 7.890E-01 and the surface area has been given as 23.889. The wave band has been defined to be between 1.0E-01 and 1.2E+01 microns.
Subtype: 7	W 66 77 67 7 89089 1.045E+02 0.00123 85.776 0.0 5.7
Defines a radiative resistor between radiosity nodes 66 and 77. The temperature of node 67 will be used with MPID 89089 to calculate an extinction coefficient. The view factor has been given as 0.00123, the surface area as 85.776, and the view factor distance as 1.045E+02. The wave band has been defined to be between 0.0 and 5.7 microns.
Subtype: 8	W 655 656 0 8 2525 84.88E+03 0.12 8.9E+02 1.2 8.9
Defines a radiative resistor between participating media node 655 and radiosity node 656. The temperature of node 655 will be used to calculate the extinction coefficient since NODE3 was entered as 0. The MPID of the extinction coefficient is 2525. The view factor is given as 0.12, the surface area as 8.9E+02, and the view factor distance as 84.88E+03. The wave band has been defined to be between 1.2 and 8.9 microns.
Subtype: 9	W 21 23 99 9 45 0.0124 0.0 5.0 9.8
Defines a radiative resistor between radiosity nodes 21 and 23. The temperature of node 99 and MPID 45 will be used to compute the participating media transmissivity. The area view factor product is given as 0.0124 and the AREA parameter (not used by this resistor subtype) as 0.0. The wave band is given as 5.0 to 9.8 microns.
Subtype: 10	W 14 15 14 10 88 0.0124 0.0 0.13 0.89
Defines a radiative resistor between participating media node 14 and radiosity node 15. The transmissivity will be calculated from material property 88 using the temperature of node 14 (given as both NODE1 and NODE3 here). The area view factor product is given as 0.0124 and the AREA parameter (not used by this resistor subtype) as 0.0. The wave band is defined to be between 0.13 and 0.89 microns.
Subtype: 11	W 66 77 67 11 89089 1.045E+02 0.00123 0.0 0.0 5.7
Defines a radiative resistor between radiosity nodes 66 and 77. The temperature of node 67 will be used with MPID 89089 to calculate an extinction coefficient. The view factor has been given as 0.00123; the AREA parameter (not used by this resistor subtype) as 0.0; and the view factor distance as 1.045E+02. The wave band has been defined to be between 0.0 and 5.7 microns.
Subtype: 12	W 655 656 0 12 2525 84.88E+03 0.120 84.88E+03
Defines a radiative resistor between participating media node 655 and radiosity node 656. The temperature of node 655 will be used to calculate the extinction coefficient since NODE3 was entered as 0. The MPID of the extinction coefficient is 2525. The area view factor product is given as 0.12; the AREA parameter (not used by this resistor subtype) as 0.0; and the view factor distance as 84.88E+03. The wave band has been defined to be between 1.2 and 8.9 microns.
Subtype: 13	W 211 231 0 13 10 0.0 87.65 1.2 19.8
Defines a radiative resistor between nodes 211 and 231. MPID 10 will be used to specify the view factor. The view factor is given as 0.0 only as a place holder and the surface area for the resistor is given as 87.65. The wave band is given as 1.2 to 91.8 microns. The temperature of node 211 will be used if the viewfactor is temperature dependent and the material property must be specified in calculation units. Time is the most probable independent variable for this subtype.
Subtype: 14	W 111 131 0 14 100 0.0 33.33 0.2 1.1
Defines a radiative resistor between nodes 111 and 131. MPID 100 will be used to specify the view factor area product. The view factor is given as 0.0 only as a place holder and the surface area of 33.33 is for reference only. Some value must be specified as a place holder but it is not used to define the resistor. The wave band is given as 0.2 to 1.1 microns. The temperature of node 111 will be used if the viewfactor is temperature dependent and the material property must be specified in calculation units. Time is the most probable independent variable for this subtype.

Automatic 1-D Mesh Generation

Resistor Type, Nodes, MPIDs, Subtype, and PHIDs, 301 and Mesh Geometric Parameters, 303 allow you to enter data for the 1-D conduction automatic mesh generators in QTRAN. The following procedure can be used to automatically generate a 1-D conduction mesh without using Patran.

1. Enter the information for Resistor Type, Nodes, MPIDs, Subtype, and PHIDs, 301. This section identifies the data set as a 1-D mesh generation data set, identifies the starting and ending node numbers of the mesh section and the node number increment to be used between successive nodes. This section also identifies the material properties to be used for the resistors and capacitors of the mesh section and the mesh geometry subtype (Cartesian, polar, etc.), and the phase change set (PHID set) to be used with the mesh section (if any).

2. Enter the information for Mesh Geometric Parameters, 303. This section specifies the geometric parameters of the mesh.

3. When all the thermal resistors are defined, enter a dollar sign ($) in column 1 of the input data file and proceed to Capacitor Data, 320. To define more resistors, proceed to the appropriate section (p. 276) to (p. 306) and continue entering thermal resistor data.


Note:	This data must be input manually. It cannot be generated by Patran and PATQ. It is preferable that these declarations are placed in the QINDAT file. But they may be placed in any file that is referenced by an $INSERT FILE_NAME command in the QINDAT file inside of the resistor definition block only.

Resistor Type, Nodes, MPIDs, Subtype, and PHIDs


RES -TYPE	NODE_1	NODE_N	NODE_INC	K_MPID


RHO_MPID	CP_MPID	SUBTYPE	PHID

Example

L	  7  	20  	1  	2  	3  	4  	3  	0

This begins a 1-D mesh generation data set between nodes 7 and 20 by increments of 1 with MPID numbers of 2, 3, and 4 for conductivity, density, and specific heat (respectively), mesh Subtype 3 (polar), and PHID of 0 (this means no phase change MPID will be assigned).


Parameter	Description
RES-TYPE	Character that defines the resistor type. In this case, RES-TYPE is entered as L to identify a 1-D automatic mesh generation data set.
NODE_1	First node, or starting node, for the 1-D automatically generated mesh section.
NODE_N	Last node, or ending node, for the 1-D automatically generated mesh section.
NODE_INC	Node number increment for the mesh and may be either positive or negative. For example, if NODE_1 = 1 and NODE_N = 7 and NODE_INC = 2, the node numbers of the mesh will be 1, 3, 5, and 7. If NODE_1 = 10 and NODE_N = 6 and NODE_INC = -2, the node numbers will be 10, 8, and 6.
K_MPID	Material property identification number for the thermal conductivity of the mesh section. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263.
RHO_MPID	Material property identification number for the density of the mesh section. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263.
CP_MPID	Material property identification number for the specific heat of the mesh section. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263.
SUBTYPE	Mesh subtype, where: 1. Equally-spaced Cartesian meshes, constant lengths, areas, and volumes (P1 is not used) should be entered as zero or left blank. See Mesh Geometric Parameters, 303. The first and last capacitor volumes are 1/2 of the interior capacitor volumes. 2. Geometric mesh, where each resistor length is scaled geometrically. Constant areas and geometrically scaled volumes are used. The length formula used for this mesh type is L[n] = LENGTH * B(P1(n - 1))
	where: LENGTH is the spacing between the first and second node, P1 is a point packing factor, n is the number of the resistor in the one-dimensional system, and L[n] is the length of the n'th resistor. The length of the first resistor (LENGTH) is related to the total slab length and the number of nodes to be used as follows: LENGTH = RCLI Important: The number of resistors is one less than the number of nodes, LSLAB is the total thickness of the slab being analyzed, and RCLI is a unit thickness which is the distance between the first two nodes, or the thickness of the first resistor which is input to QTRAN as the variable LENGTH. 3. Polar mesh. 4. Spherical mesh. 5. LaGrange Cubic Finite Element Cartesian mesh. Important: The resistors generated by this technique are purely mathematical in nature and do not have a physical significance. For example, a number of the resistors generated will have negative area/length ratios that do not make any physical sense. However, they are quite correct and do yield highly accurate results (i.e., they should approach 6th order accuracy). Do not be alarmed by the generation of negative resistors whenever finite element data is transformed into resistor data. The capacitor volumes, on the other hand, should always be positive.
PHID	Phase change MPID to be associated with the capacitors contained in the automatically generated mesh section. See Material Properties, 263.

Mesh Geometric Parameters


LENGTH	AREA	P1

Example

1.0	2.0	3.0

This enters a value of 1.0 for LENGTH, 2.0 for AREA, 3.0 for P1.


Parameter	Description
LENGTH	Distance between nodes in the mesh section. For SUBTYPE = 2, this is the distance between the first two nodes of this mesh section where all other distances for SUBTYPE = 2 meshes are set as follows: For SUBTYPE = 2 ONLY: L[n] = LENGTH * P1(n - 1), where: L[n] is the length of the n'th resistor.
	The length of the first resistor (LENGTH) is related to the total slab length and the number of nodes to be used as follows: LENGTH = RCLI Important: The number of resistors is one less than the number of nodes, LSLAB is the total thickness of the slab being analyzed, and RCLI is a unit thickness which is the distance between the first two nodes, or the thickness of the first resistor which is input to QTRAN as the variable LENGTH.
AREA	Cross-sectional area of the mesh section for SUBTYPE = 1, 2, or 5. AREA is ignored for SUBTYPE = 3 or 4. Note that Subtypes 3 and 4 assume a full cylinder or full sphere, respectively.
P1	Mesh parameter 1 (ignored for SUBTYPE = 1 or 5). For SUBTYPE = 2, P1 is used to gradually increase the mesh spacing so that the distances between nodes and the length L(n) for the n'th resistor is: L(n) = LENGTH * [ P1 (n - 1) ] For SUBTYPE = 3 or 4, P1 is the radial distance between the first node of the mesh section and the origin of the cylindrical or spherical coordinate system. When defining mesh type (SUBTYPE) 5, note that the starting and ending nodes and node number increment must be compatible with 4-node finite elements. For example, if there are N elements in the mesh section there will be N * 3+1 nodes associated with that section. Any other arrangement will cause an erroneous mesh to be generated.

Advective Resistor Data


RES -TYPE	NODE1	NODE2	CP_MPID	MASS_FLOW_CONSTANT


MASS_FLOW_MPID

This section describes how to define data for an advective resistor. Advective resistors are required when it is necessary to model the energy carried along with a mass stream that is entering a given capacitor’s volume. The heat flow relation is

Q[1-->2] = MASS_FLOW * Cp * (T[1] - T[2])

where the specific heat is based on the effective average value integrated between temperatures T[1] and T[2], and based on a flow of temperature step defined by CPDII5, and MASS_FLOW is the mass rate of flow. Because difference schemes for this type of calculation are generally restricted to one-sided upwind or donor cell schemes due to stability considerations, heat will be carried only to the downstream node and not to the upstream node. Node 1 is the upstream node if the mass flow rate is positive, and Node 2 is the upstream node if the mass flow rate should become negative. As a result of the PATQ translation (menu pick 2), these declarations are placed in the RESDAT file.

To add an advective resistor to the model, simply enter the resistor data as shown in the following examples. When all the thermal resistors are defined, enter a dollar sign ($) in column 1 of the input data file and proceed to Capacitor Data, 320. To define more resistors, proceed to the appropriate Section (p. 276) to (p. 306) and continue to enter thermal resistor data.

Example 1

A	1	17	 23	14.7	24

Example 1 defines an advective resistor between node 1 (upstream) and node 17 (downstream) with a specific heat evaluated according to MPID 23 and a mass flow rate given by the product of 14.7 and the value of material property 24.

Example 2

A 	 21 	 23	  23 	 15.2

Example 2 defines an advective resistor between node 21 (upstream) and node 22 (downstream) with the specific heat evaluated according to MPID 23 and with a constant mass flow rate of 15.2.

The advective resistor data items (RES-TYPE, NODE1, NODE2, CP_MPID,MASS_FLOW_CONSTANT, and MASS_FLOW_ MPID) are defined below.


Parameter	Description
RES-TYPE	Character that defines the resistor type. In this case, RES_TYPE is entered as A to identify an advective resistor.
NODE1	Node 1 of the advection resistor. NODE1 is the upstream or upwind node of the advective resistor if the mass flow rate is positive.
NODE2	Node 2 of the advection resistor. NODE2 is the downstream or downwind node of the advective resistor if the mass flow rate is positive.
CP_MPID	Material property identification number for the specific heat of the mass that is flowing for this resistor. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263.
MASS_FLOW_CONSTANT	Constant mass rate of flow for this resistor if no MASS_FLOW_MPID is given. If a MASS_FLOW_MPID is given, this value will scale the value returned by the “material property” referenced by the MASS_FLOW_MPID.
MASS_FLOW_MPID	Material property which will be used to compute a time or temperature-dependent flow rate. If no MPID is given for MASS_FLOW_MPID, the MASS_FLOW_CONSTANT is used for the flow rate. If MASS_FLOW_MPID is given, the value of the material property referenced by this MPID will be multiplied by MASS_FLOW_CONSTANT to compute a mass flow rate. Heat is allowed to flow only from the upstream node to the downstream node in accordance with stable upwind differencing schemes. If the mass flow is specified as a negative number, the upstream and downstream nodes are reversed and heat flow will be from NODE2 to NODE1.

Hydraulic Resistor Data

Hydraulic resistors model energy carried from one location to another like the advective resistor; however, unlike the advective resistors where the mass flow rate of the fluid is specified, a fluid network is established and solved to determine the fluid flow rates. Several types of fluid resistors can be coupled together to form the hydraulic network. The mathematical nature of these fluid resistors are explained in One Dimensional Flow Network, 213. As a result of the PATQ translation (menu pick 2), these declarations are placed in the FRESDAT file. The procedure used to define a hydraulic resistor is explained below.

1. Enter all data for the hydraulic resistor for Hydraulic Resistor Header Data, 307. This data identifies the resistor as a hydraulic resistor, defines the resistor node numbers, and defines the resistor configuration.

2. Enter the data for the resistor for Hydraulic Resistor Geometric Properties, 308. This data defines all Geometric Properties (GP) such as characteristic diameter, cross-sectional areas, and distance fluid travels etc. The number of entries is dependent on the fluid resistor type.

3. Enter all data for the Hydraulic Resistor Material Properties, 309. This data is used to identify where the material properties that are required for specific resistor configurations are to be found.

4. When all the thermal resistors are defined, place a dollar sign ($) in column 1 of the input data file and proceed to Capacitor Data, 320. To define another thermal resistor, proceed to the resistor data section (p. 276) to (p. 306) that applies to the next resistor that you wish to define.

Hydraulic Resistor Header Data


RES -TYPE	NODE1	NODE2	FCFIG

This section describes how to identify a given thermal resistor as a fluid resistor, to define its node numbers, and to specify the resistor fluid configuration.

Example 1

F	 1 	 17	 3

Example 1 defines a hydraulic resistor between node 1 (upstream) and node 17 (downstream). Hydraulic configuration 3 will be used to interpret the meaning of the geometric parameters and material property ID’s specified.

Example 2

F	  21 	 22	 10

Example 2 defines a hydraulic resistor between node 21 (upstream) and node 22 (downstream) with hydraulic configuration 10 used to interpret the meaning of the geometric parameters and material property IDs specified.


Parameter	Description
RES-TYPE	Character that defines the resistor type. In this case, RES_TYPE is entered as F to identify a hydraulic resistor.
NODE1	Node 1 of the hydraulic resistor. NODE1 is the upstream or upwind node of the hydraulic resistor if the mass flow rate is positive.
NODE2	Node 2 of the hydraulic resistor. NODE2 is the downstream or downwind node of the hydraulic resistor if the mass flow rate is positive.
FCFIG	Fluid configuration for this hydraulic resistor. The configuration denotes the type of fluid resistor and how the geometric properties are to be interpreted and what the material properties are to designate. Valid entries are between 1 and 12.

Table 8‑3
FCFIG Subtype	Description


1	Tubing with constant physical and material properties.
2	Tubing with constant physical and material properties with friction factor evaluated by Patran Thermal Moody equation.
3	Tubing with constant physical and variable material properties.
4	Constant pump head.
5	Variable pump head.
6	Constant turbine head.
7	Variable turbine head.
8	Loss resistor or control value.
9	Check value with constant geometry and material properties.
10	Check value with constant physical and variable material properties.
11	Plenum resistor with constant properties.
12	Plenum resistor with variable material properties.

Hydraulic Resistor Geometric Properties


GP(1)	GP(2)	...	GP(n)

Example

24.7	 23.2 	 0.0	 14.8 	29.9

15.6		 18.9

This enters 7 GP values of 24.7, 23.2, 0.0, 14.8, 29.9, 15.6, and 18.9, in that order using free format input.


Parameter	Description
GP	Hydraulic resistor’s Geometric Properties such as length, diameter, cross-sectional area, or gravitational constants. The exact meaning of each GP value varies for each configuration. QTRAN will continue reading GP values until it encounters a slash (/) in column 1 of the input data file. The procedure for entering GP values is to enter all GP values followed by an input data file line with a slash in column 1. Proceed on to Hydraulic Resistor Material Properties, 309. When GP values at the end of the required list are zero, they need not be input. All intermediate zeroes must be included as placeholders.

Hydraulic Resistor Material Properties


MPID(1)	MPID(2)	...	MPID(n)

Example

1 	 7	  4	  6

15	 23

This declares MPID values of 1, 7, 4, 6, 15, and 23.


Parameter	Description
MPID	Material Property Identification numbers for the hydraulic resistors. See MPID Number, Function Type, Temperature Scale, Factor and Label, 263. Material properties include the fluid density, viscosity, and specific heat plus other flow parameters that can be a function of time or temperature such as loss coefficients, friction factors, pump head, etc. The material properties that correspond to each MPID entry are listed for each fluid configuration option in the following option definition section. After all MPID values have been entered, simply enter a slash (/) in column one of the next line of the input data file. When MPID values at the end of the required list are zero, they need not be input. All intermediate zeroes must be included as placeholders.

Hydraulic Resistor Options

The geometric parameters and material properties for each fluid configuration are:

FCFIG = 1, Tubing with constant physical and material properties


Hydraulic_Diameter,	Cross_Sectional_Area,	Length,
DX,	DY,	DZ,
Density,	Viscosity,	Specific_Heat,
Surface_Roughness,	Loss_Coefficient,	Friction_Factor,
Buoyancy
/
/

where:

• Hydraulic_Diameter is a cross-sectional area divided by the wetted perimeter. Internally a circular cross section is assumed for any calculation which relate area and diameter.

• Cross_Sectional_Area is the area that supports the flowing fluid.

• Length is the total travel of the fluid within a resistor. This does not have to be equal to the distance between the beginning and end of a resistor. One example would be a coiled tubing in which the inlet and outlet are very close but the actual distance the fluid travels is much greater than the distance between the inlet and outlet of the coil.

• DX is the displacement of NODE2 relative to NODE1 in the X global axis direction. This distance is used to determine gravitational head changes.

• DY is the displacement of NODE2 relative to NODE1 in the Y global axis direction. This distance is used to determine gravitational head changes.

• DZ is the displacement of NODE2 relative to NODE1 in the Z global axis direction. This distance is used to determine gravitational head changes.

• Density is the density of the fluid flowing. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• Viscosity is the dynamic viscosity of the fluid.

• Specific_Heat is of the fluid.

• Surface_Roughness is the characteristic roughness of the tubing.

• Loss_Coefficient for determining added head loss due to added flow restrictions such as constrictions, orifices, vanes, bends, etc.

• Friction_Factor is used to calculate head loss due to the viscous effect of the fluid flowing in a tube.

• Buoyancy is the gravitational head created by the temperature gradient working against a gravitational field. Buoyancy can be modeled as the reciprocal of the compressibility factor.

• There are no material properties defined.

FCFIG = 2, Tubing with constant physical and material properties with friction factor evaluated by Patran Thermal Moody equation


Hydraulic_Diameter,	Cross_Sectional_Area,	Length,
DX,	DY,	DZ,
Density,	Viscosity,	Specific_Heat,
Surface_Roughness,	Loss_Coefficient,	Buoyancy
/
/

• Hydraulic_Diameter is cross-sectional area divided by the wetted perimeter. Internally a circular cross section is assumed for any calculation which relate area and diameter.

• Cross_Sectional_Area is the area that supports the flowing fluid.

• DX is the displacement of NODE2 relative to NODE1 in the X global axis direction. This distance is used to determine gravitational head changes.

• DY is the displacement of NODE2 relative to NODE1 in the Y global axis direction. This distance is used to determine gravitational head changes.

• DZ is the displacement of NODE2 relative to NODE1 in the Z global axis direction. This distance is used to determine gravitational head changes.

• Density is the density of the fluid flowing. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• Viscosity is the dynamic viscosity of the fluid.

• Specific_Heat is of the fluid.

• Surface_Roughness is the characteristic roughness of the tubing.

• Loss_Coefficient for determining added head loss due to added flow restrictions such as contractions, orifices, vanes, bends, etc.

• Buoyancy is the gravitational head created by the temperature gradient working against a gravitational field. Buoyancy can be modeled as the reciprocal of the compressibility factor.

• There are no material properties defined.

FCFIG = 3, Tubing with constant physical and variable material properties


Hydraulic_Diameter,	Cross_Sectional_Area,	Length,
DX,	DY,	DZ,
Surface_Roughness,	Loss_Coefficient,	Friction_Factor
/
/MPID_RHO	MPID_MU	MPID_CP
MPID_LOSS_COEFF	MPID_BETA	MPID_F
/

• Hydraulic_Diameter is the cross-sectional area divided by the wetted perimeter. Internally a circular cross section is assumed for any calculation which relate area and diameter.

• Cross_Sectional_Area is the area that supports the flowing fluid.

• DX is the displacement of NODE2 relative to NODE1 in the X global axis direction. This distance is used to determine gravitational head changes.

• DY is the displacement of NODE2 relative to NODE1 in the Y global axis direction. This distance is used to determine gravitational head changes.

• DZ is the displacement of NODE2 relative to NODE1 in the Z global axis direction. This distance is used to determine gravitational head changes.

• Surface_Roughness is the characteristic roughness of the tubing.

• Loss_Coefficient for determining added head loss due to added flow restrictions such as contractions, orifices, vanes, bends, etc. This value is used as a scale factor on the material property value specified by MPID_LOSS_COEFF.

• Friction_Factor is used to calculate head loss due to the viscous effect of the fluid flowing in a tube. This value is used as a scale factor on the material property value specified by MPID_F.

• MPID_RHO is the time or temperature dependent density of the fluid and is defined as a material property. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• MPID_MU is the time or temperature-dependent viscosity of the fluid and is defined as a material property.

• MPID_CP is the time or temperature-dependent specific heat of the fluid and is defined as a material property.

• MPID_LOSS_COEFF is the time or temperature-dependent loss coefficient operating on the fluid and is defined as a material property.

• MPID_BETA is the time or temperature-dependent buoyancy term and is defined as a material property. It represents the gravitational head created by the temperature gradient working against a gravitational field. Buoyancy can be modeled as the reciprocal of the compressibility factor.

• MPID_F is the time or temperature-dependent friction factor used to calculate head loss due to the viscous effect of the fluid flowing in a tube and is defined as a material property. If this value is zero, it is calculated by Patran Thermal using the built-in Moody equations.

FCFIG = 4, Constant Pump Head.


Density,	Viscosity,	Specific_Heat,
Pump_Head
/
/

where:

• Density of the fluid flowing. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• Viscosity is the dynamic viscosity of the fluid.

• Specific_Heat of the fluid.

• Pump_Head - The pump head must always be positive.

• There are no material properties defined.

FCFIG = 5, Variable Pump Head


/
MPID_RHO	MPID_MU	MPID_CP
MPID_HEAD
/

where:

• MPID_RHO is the time or temperature-dependent density of the fluid and is defined as a material property. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• MPID_MU is the time or temperature-dependent viscosity of the fluid and is defined as a material property.

• MPID_CP is the time or temperature-dependent specific heat of the fluid and is defined as a material property.

• MPID_HEAD is the time or temperature-dependent head operating on the fluid and is defined as a material property. The pump head must always be positive.

FCFIG = 6, Constant Turbine Head


Density,	Viscosity,	Specific_Heat,
Turbine_Head
/
/

where:

• Density of the fluid flowing. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• Viscosity is the dynamic viscosity of the fluid.

• Specific_Heat of the fluid.

• Turbine_Head - The turbine head must always be negative.

• There are no material properties defined.

FCFIG = 7, Variable Turbine Head


/
MPID_RHO	MPID_MU	MPID_CP
MPID_HEAD
/

where:

• MPID_MU is the time or temperature-dependent viscosity of the fluid and is defined as a material property.

• MPID_CP is the time or temperature-dependent specific heat of the fluid and is defined as a material property.

• MPID_HEAD is the time or temperature-dependent head operating on a turbine by the fluid and is defined as a material property. The turbine head must always be negative.

FCFIG = 8, Loss Resistor or Control Valve.


Hydraulic_Diameter,	Cross_Sectional_Area,	Length,
DX,	DY,	DZ,
Surface_Roughness,	Loss_Coefficient,	Friction_Factor
/
MPID_DIAM
MPID_RHO	MPID_MU	MPID_CP
MPID_EPS	MPID_LOSS_COEFF	MPID_BETA
MPID_F
/

where:

• Hydraulic_Diameter is the cross-sectional area divided by the wetted perimeter. Internally a circular cross section is assumed for any calculation which relate area and diameter. This is used as a scale factor for the variable diameter specified by MPID_DIAM.

• Cross_Sectional_Area is the area that supports the flowing fluid.

• DX is the displacement of NODE2 relative to NODE1 in the X global axis direction. This distance is used to determine gravitational head changes.

• DY is the displacement of NODE2 relative to NODE1 in the Y global axis direction. This distance is used to determine gravitational head changes.

• DZ is the displacement of NODE2 relative to NODE1 in the Z global axis direction. This distance is used to determine gravitational head changes.

• Surface_Roughness is the characteristic roughness of the tubing. Variable roughnesses are allowed and this entry is a scale factor used in conjunction with the material property MPID_EPS.

• Friction_Factor is used to calculate head loss do to the viscous effect of the fluid flowing in a tube. This value is used as a scale factor on the material property value specified by MPID_F.

• MPID_MU is the time or temperature-dependent viscosity of the fluid and is defined as a material property.

• MPID_CP is the time or temperature-dependent specific heat of the fluid and is defined as a material property.

• MPID_EPS is the time or temperature-dependent roughness coefficient operating on the fluid and is defined as a material property.

• MPID_LOSS_COEFF is the time or temperature-dependent loss coefficient operating on the fluid and is defined as a material property.

FCFIG = 9, Check Valve with Constant Geometry and Material Properties


Hydraulic_Diameter,	Cross_Sectional_Area,	Length,
DX,	DY,	DZ,
Density,	Viscosity,	Specific_Heat,
Surface_Roughness,	Loss_Coefficient,	Buoyancy
/
/

where:

• Hydraulic_Diameter is the cross-sectional area divided by the wetted perimeter. Internally a circular cross section is assumed for any calculation which relate area and diameter. If the fluid is not flowing from NODE1 to NODE2, the diameter of the valve is made zero, shutting off the flow.

• Cross_Sectional_Area is the area that supports the flowing fluid.

• DX is the displacement of NODE2 relative to NODE1 in the X global axis direction. This distance is used to determine gravitational head changes.

• DY is the displacement of NODE2 relative to NODE1 in the Y global axis direction. This distance is used to determine gravitational head changes.

• DZ is the displacement of NODE2 relative to NODE1 in the Z global axis direction. This distance is used to determine gravitational head changes.

• Density is the density of the fluid flowing. Units of specific weight are used to be consistent with the thermal solution. Internal units conversion to mass density are performed as necessary.

• Viscosity is the dynamic viscosity of the fluid.

• Specific_Heat is of the fluid.

• Surface_Roughness is the characteristic roughness of the tubing.

• Loss_Coefficient for determining added head loss due to added flow restrictions such as contractions, orifices, vanes, bends, etc.

• Buoyancy is the gravitational head created by the temperature gradient working against a gravitational field. Buoyancy can be modeled as the reciprocal of the compressibility factor.

• There are no material properties defined.

FCFIG = 10, Check Valve with Constant Physical and Variable Material Properties


Hydraulic_Diameter,	Cross_Sectional_Area,	Length,
DX,	DY,	DZ,
Surface_Roughness,	Loss_Coefficient,	Buoyancy
/
MPID_RHO	MPID_MU	MPID_CP
MPID_LOSS_COEFF	MPID_BETA	MPID_F
/

where:

• Hydraulic_Diameter is the cross-sectional area divided by the wetted perimeter. Internally a circular cross section is assumed for any calculation which relate area and diameter. If the flow is not positive from NODE1 to NODE2, the diameter is reduced to zero to stop the flow through this resistor.