I/O data format for 2D Unsteady Heat Conduction Analysis

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Dwain Patterson
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1 December 2, 2012 I/O data format for 2D Unsteady Heat Conduction Analysis (f90 FEM HEAT.f90) 1. Outline of a program f90 FEM HEAT.f90 This is a program for 2D Unsteady Heat Conduction Analysis. This program can not treat steady problem. Thickness of the element is unit thickness and it is not changeable. As boundary conditions, thermal insulation boundary, temperature given boundary and heat transfer boundary can be considered. Heating material can also be used such as cement concrete. 4 node isoparametric element with 4 Gauss points is used. 1 node has 1 degree of freedom of temperature. In coordinate system, x-direction is defined as right-direction and y-direction is defined as upward direction. Property of heat conduction is isotropic in x and y-directions. Simultaneous linear equations are solved using Cholesky method for banded matrix. Although this solving process has repeating process for time history analysis, matrix for calculation is not changed if the time increment is not changed. Therefore, to create the triangular matrix is carried out only one time, and forward elimination and backward substitution process are repeated during the defined time span. Crank-Nicolson method is used for the discretization of the time. Input/Output file name can be defined arbitrarily with the format of csv and those are inputted from command line of MS-Windows. In addition, it is necessary to prepare the input file for time history of node temperatures of given temperature boundary and side temperatures of heat transfer boundary. Used language for program is Fortran 90 and used compiler is MinGW gfortran. 2. Format of input data file ( csv format) 2 files shown below are required for this analysis. 1 2 Basic data file for input (specified in the batch file) Temperature time history data (specified at second row in the basic data file) 2.1 Basic data Items for input s data file name for temperature time history NODT,NELT,MATEL,KOT,KOC,delta Ak,Ac,Arho,Tk,Al...(1 MATEL)... node-1,node-2,node-3,node-4,matno...(1 NELT)... x,y,t 0...(1 NODT)... nokt...(1 KOT)... nekc 1,nekc 2,alphac...(1 KOC)... nout noout 1...(1 line input)... ntout nntout 1...(1 line input)... Remarks Save in the same directory as basic data file Basic values for analysis Material properties Element connectivity, Material set number (counterclockwise order of node numbers) Coordinates of node, initial temperature of node (x: right-direction, y: upward direction) Node number of temperature given boundary (Omit data input if KOT=0) Element number, node number defined side, heat transfer rate (Omit data input if KOC=0) Number of nodes for output of temperature time history Node number for above frequency of output of temperatures of all nodes Time step number for above (Omit data input if ntout=0) 1

2 NODT : Number of nodes Ak : heat conductivity coefficient of element NELT : Number of elements Ac : Specific heat of element MATEL : Number of material sets Arho : Unit weight of element KOT : Number of temperature given nodes Tk : maximum temperature rise of element KOC : Number of heat transfer sides Al : coefficient of heat release rate of element delta : Time increment alphac : heat transfer rate of side of element matno : Material set number Explanation for heating material Properties of heating materials are inputted as element material characteristics. In this program, heat generation of cement concrete is imitated and the adiabatic temperature rise shown below formula can be considered. T = K (1 e α t ) where, T : adiabatic temperature rise, K: maximum temperature rise, α: coefficient of heat release rate, t: time. In this program, K (Tk) and α(al) become input data and heat generation rate per unit area is calculated in calculation process. Explanation for heat transfer boundary Following items are inputted for defining the heat transfer boundary Element number with heat transfer boundary Node number which define the side in the element Heat transfer rate of the side in the element Although a side of element is consisted of 2 nodes, first node number must be inputted as the node number which define the side in the element. Because node number is defined in counterclockwise order in FEM, if first node number can be known, the side can be identified. Explanation for output of temperature time history at specified nodes Number of nodes for output of time history is specified as variable nout. Node numbers for output of time history are specified as array variable nout(). nout must be greater than or equal to 1, and array nout() must be defined with specified number by nout. Explanation for output of temperatures of all nodes at specified time Frequency for output of temperatures of all nodes is specified as variable ntout. Time step numbers for output of temperature of all nodes are specified as array variable nntout(). In the case of ntout=0, data input of array variable nntout can be omitted. 2.2 Temperature time history data Items for input Remarks 1,TE(1),...,TE(KOT),TC(1),...,TC(KOC) data of 1st time step 2,TE(1),...,TE(KOT),TC(1),...,TC(KOC) data of 2nd time step 3,TE(1),...,TE(KOT),TC(1),...,TC(KOC)...(repeating until end time)... data is read step by step itime,te(1),...,te(kot),tc(1),...,tc(koc) TE(): temperature of node for temperature given boundary TC(): outer temperature of side of element for heat transfer boundary Values from 1st step to final step should be written in data file. Number of step (variable name itime ) is defined by reading the final row of this file. Initial temperatures are the values written in basic data file. It is required to prepare this file even if temperatures are not required such as the case of adiabatic temperature raise. In that case, only step number is required in this file. This is a measure to know step number of calculation. 2

3 3. Format of out put file ( csv format) Items of output NODT,NELT,MATEL,KOT,KOC,delta,nout,ntout,itmax NODT: Number of nodes, NELT: Number of elements, MATEL: Number of material set KOT: Number of temperature given nodes, KOC: Number of heat transfer sides delta: time increment nout: Number of nodes for output of temperature time history ntout: frequency of output for temperatures of all nodes itmax: Number of steps of time history *node characteristics node,x,y,fix-t,tinit node : Node number x,y : Coordinates of node Tini : initial temperature of node fix : Temperature given boundary (1: yes, 0: no)...(1 NODT)... *element characteristics element,node-1,node-2,node-3,node-4,alpc1,alpc2,alpc3,alpc4,ak,ac,arho,tk,al,matno element : Element number node-1,node-2,node-3,node-4 : Element-nodes relationship alpc1 alpc4 : heat transfer rate of sides Ak : Heat conductivity coefficient of element Ac : Specific heat of element Arho : Unit weight of element Tk : Maximum temperature raise of element Al : coefficient of heat release rate of element matno : material set number...(1 NELT)... *Temperature records of selected nodes it,time,node-xx,node-xx,...(1 nout)... step,time, temperature of node...(0 itmax)... (if ntout is greater than or equal to 1) *Temperature of all nodes for selected times Node,initial,step-xx,step-xx,...(1 ntout)... Node number, temperature of node initial means initial temperature of each node...(1 NODT)... *Temperature distributions of selected nodes Node,x,y,initial,step-xx,step-xx,...(1 ntout)... Node number, x-coordinate, y-coordinate, temperature of node initial means initial temperature of each node...(1 nout)... (common items) NODT=xxx nt=xx mm=xx ib=xx Calculation time= x.xxx(sec) Date time= :33:8 (gfortran) 3

4 4. Sample model analysis 4.1 Outline of model Consider a square area with a side of 1m. Material properties are such as cement concrete Size of area Width Height=1 m 1 m Heat conductivity coefficient 2.5 kcal/m h C Specific heat 0.28 kcal/kg C Unit weight 2350 kg/m 3 Heat transfer rate 10 kcal/m 2 h C Formula for T = K (1 e α t ) adiabatic temperature raise K=20 C, α=0.3, t: hour(h) Model size 25 nodes, 16 elements y distance (m) Sample input data (1) Input of basic data x distance (m) Adiabatic-3 t_test00_3.csv File name of temperature time history 25,16,1,0,16,1 NODT,NELT,MATEL,KOT,KOC,delta 2.5,0.28,2350,20,0.3 Ak,Ac,Arho,Tk,Al 1, 6, 7, 2,1 Element-nodes relationship for element No.1 2, 7, 8, 3,1 Element-nodes relationship for element No.2 3, 8, 9, 4,1 Element-nodes relationship for element No.3 4, 9,10, 5,1 Element-nodes relationship for element No.4 6,11,12, 7,1 Element-nodes relationship for element No.5 7,12,13, 8,1 Element-nodes relationship for element No.6 8,13,14, 9,1 Element-nodes relationship for element No.7 9,14,15,10,1 Element-nodes relationship for element No.8 11,16,17,12,1 Element-nodes relationship for element No.9 12,17,18,13,1 Element-nodes relationship for element No.10 13,18,19,14,1 Element-nodes relationship for element No.11 14,19,20,15,1 Element-nodes relationship for element No.12 16,21,22,17,1 Element-nodes relationship for element No.13 17,22,23,18,1 Element-nodes relationship for element No.14 18,23,24,19,1 Element-nodes relationship for element No.15 19,24,25,20,1 Element-nodes relationship for element No ,-0.50,20 Node coordinate and initial temperature of node No ,-0.25,20 Node coordinate and initial temperature of node No , 0.00,20 Node coordinate and initial temperature of node No , 0.25,20 Node coordinate and initial temperature of node No , 0.50,20 Node coordinate and initial temperature of node No ,-0.50,20 Node coordinate and initial temperature of node No ,-0.25,20 Node coordinate and initial temperature of node No , 0.00,20 Node coordinate and initial temperature of node No , 0.25,20 Node coordinate and initial temperature of node No , 0.50,20 Node coordinate and initial temperature of node No ,-0.50,20 Node coordinate and initial temperature of node No ,-0.25,20 Node coordinate and initial temperature of node No , 0.00,20 Node coordinate and initial temperature of node No , 0.25,20 Node coordinate and initial temperature of node No , 0.50,20 Node coordinate and initial temperature of node No ,-0.50,20 Node coordinate and initial temperature of node No ,-0.25,20 Node coordinate and initial temperature of node No , 0.00,20 Node coordinate and initial temperature of node No , 0.25,20 Node coordinate and initial temperature of node No , 0.50,20 Node coordinate and initial temperature of node No ,-0.50,20 Node coordinate and initial temperature of node No ,-0.25,20 Node coordinate and initial temperature of node No , 0.00,20 Node coordinate and initial temperature of node No , 0.25,20 Node coordinate and initial temperature of node No , 0.50,20 Node coordinate and initial temperature of node No.25 1, 1,10 Element No. of heat transfer boundary( 1), node No. of side( 1), heat transfer rate 4

5 5, 6,10 Element No. of heat transfer boundary( 5), node No. of side( 6), heat transfer rate 9,11,10 Element No. of heat transfer boundary( 9), node No. of side(11), heat transfer rate 13,16,10 Element No. of heat transfer boundary(13), node No. of side(16), heat transfer rate 13,21,10 Element No. of heat transfer boundary(13), node No. of side(21), heat transfer rate 14,22,10 Element No. of heat transfer boundary(14), node No. of side(22), heat transfer rate 15,23,10 Element No. of heat transfer boundary(15), node No. of side(23), heat transfer rate 16,24,10 Element No. of heat transfer boundary(16), node No. of side(24), heat transfer rate 16,25,10 Element No. of heat transfer boundary(16), node No. of side(25), heat transfer rate 12,20,10 Element No. of heat transfer boundary(12), node No. of side(20), heat transfer rate 8,15,10 Element No. of heat transfer boundary( 8), node No. of side(15), heat transfer rate 4,10,10 Element No. of heat transfer boundary( 4), node No. of side(10), heat transfer rate 4, 5,10 Element No. of heat transfer boundary( 4), node No. of side( 5), heat transfer rate 3, 4,10 Element No. of heat transfer boundary( 3), node No. of side( 4), heat transfer rate 2, 3,10 Element No. of heat transfer boundary( 2), node No. of side( 3), heat transfer rate 1, 2,10 Element No. of heat transfer boundary( 1), node No. of side( 2), heat transfer rate 5 Number of nodes for output of temperature time history 1,21,25,5,13 Node numbers for output of temperature time history 0 Number of time for output of temperatures of all nodes 5

6 (2) Input file of temperature time history t test00 3.csv Component of file is shown below. 1st column step number 2nd 17th column temperature time histories of 16 sides which is specified as heat transfer boundary In this case, all sides have the same temperature at all steps because of constant temperature condition of outer domain. Temperatures 1,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 2,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 3,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 4,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 5,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 6,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 7,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 8,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 9,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 10,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 11,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 12,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 13,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 14,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 15,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 16,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 17,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 18,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 21,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 22,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 23,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 24,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 25,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 26,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 27,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 28,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 29,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 30,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 31,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 32,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 33,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 34,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 35,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 36,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 37,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 38,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 39,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 40,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 41,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 42,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 43,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 44,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 45,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 46,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 47,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 48,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 49,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 50,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20 6

7 4.3 sample output data Output data sample is shown below. The significant figure is set to 3 due to space arrangement. *Temperature records of selected nodes it, time, node-1, node-21, node-25, node-5, node-13 0,0.000E+00,2.000E+01,2.000E+01,2.000E+01,2.000E+01,2.000E+01 1,1.000E+00,2.442E+01,2.442E+01,2.442E+01,2.442E+01,2.516E+01 2,2.000E+00,2.649E+01,2.649E+01,2.649E+01,2.649E+01,2.896E+01 3,3.000E+00,2.741E+01,2.741E+01,2.741E+01,2.741E+01,3.189E+01 4,4.000E+00,2.771E+01,2.771E+01,2.771E+01,2.771E+01,3.417E+01 5,5.000E+00,2.767E+01,2.767E+01,2.767E+01,2.767E+01,3.592E+01 6,6.000E+00,2.746E+01,2.746E+01,2.746E+01,2.746E+01,3.723E+01 7,7.000E+00,2.715E+01,2.715E+01,2.715E+01,2.715E+01,3.818E+01 8,8.000E+00,2.680E+01,2.680E+01,2.680E+01,2.680E+01,3.881E+01 9,9.000E+00,2.644E+01,2.644E+01,2.644E+01,2.644E+01,3.919E+01 10,1.000E+01,2.610E+01,2.610E+01,2.610E+01,2.610E+01,3.936E+01 11,1.100E+01,2.577E+01,2.577E+01,2.577E+01,2.577E+01,3.935E+01 12,1.200E+01,2.547E+01,2.547E+01,2.547E+01,2.547E+01,3.921E+01 13,1.300E+01,2.519E+01,2.519E+01,2.519E+01,2.519E+01,3.897E+01 14,1.400E+01,2.493E+01,2.493E+01,2.493E+01,2.493E+01,3.865E+01 15,1.500E+01,2.469E+01,2.469E+01,2.469E+01,2.469E+01,3.826E+01 16,1.600E+01,2.447E+01,2.447E+01,2.447E+01,2.447E+01,3.783E+01 17,1.700E+01,2.427E+01,2.427E+01,2.427E+01,2.427E+01,3.737E+01 18,1.800E+01,2.408E+01,2.408E+01,2.408E+01,2.408E+01,3.689E+01 19,1.900E+01,2.391E+01,2.391E+01,2.391E+01,2.391E+01,3.639E+01 20,2.000E+01,2.375E+01,2.375E+01,2.375E+01,2.375E+01,3.590E+01 21,2.100E+01,2.360E+01,2.360E+01,2.360E+01,2.360E+01,3.540E+01 22,2.200E+01,2.346E+01,2.346E+01,2.346E+01,2.346E+01,3.490E+01 23,2.300E+01,2.332E+01,2.332E+01,2.332E+01,2.332E+01,3.441E+01 24,2.400E+01,2.319E+01,2.319E+01,2.319E+01,2.319E+01,3.393E+01 25,2.500E+01,2.307E+01,2.307E+01,2.307E+01,2.307E+01,3.346E+01 26,2.600E+01,2.296E+01,2.296E+01,2.296E+01,2.296E+01,3.300E+01 27,2.700E+01,2.285E+01,2.285E+01,2.285E+01,2.285E+01,3.255E+01 28,2.800E+01,2.275E+01,2.275E+01,2.275E+01,2.275E+01,3.212E+01 29,2.900E+01,2.265E+01,2.265E+01,2.265E+01,2.265E+01,3.170E+01 30,3.000E+01,2.255E+01,2.255E+01,2.255E+01,2.255E+01,3.129E+01 31,3.100E+01,2.246E+01,2.246E+01,2.246E+01,2.246E+01,3.089E+01 32,3.200E+01,2.237E+01,2.237E+01,2.237E+01,2.237E+01,3.051E+01 33,3.300E+01,2.228E+01,2.228E+01,2.228E+01,2.228E+01,3.014E+01 34,3.400E+01,2.220E+01,2.220E+01,2.220E+01,2.220E+01,2.978E+01 35,3.500E+01,2.212E+01,2.212E+01,2.212E+01,2.212E+01,2.944E+01 36,3.600E+01,2.205E+01,2.205E+01,2.205E+01,2.205E+01,2.910E+01 37,3.700E+01,2.197E+01,2.197E+01,2.197E+01,2.197E+01,2.878E+01 38,3.800E+01,2.190E+01,2.190E+01,2.190E+01,2.190E+01,2.847E+01 39,3.900E+01,2.184E+01,2.184E+01,2.184E+01,2.184E+01,2.817E+01 40,4.000E+01,2.177E+01,2.177E+01,2.177E+01,2.177E+01,2.788E+01 41,4.100E+01,2.171E+01,2.171E+01,2.171E+01,2.171E+01,2.760E+01 42,4.200E+01,2.165E+01,2.165E+01,2.165E+01,2.165E+01,2.733E+01 43,4.300E+01,2.159E+01,2.159E+01,2.159E+01,2.159E+01,2.707E+01 44,4.400E+01,2.153E+01,2.153E+01,2.153E+01,2.153E+01,2.682E+01 45,4.500E+01,2.148E+01,2.148E+01,2.148E+01,2.148E+01,2.658E+01 46,4.600E+01,2.143E+01,2.143E+01,2.143E+01,2.143E+01,2.635E+01 47,4.700E+01,2.138E+01,2.138E+01,2.138E+01,2.138E+01,2.612E+01 48,4.800E+01,2.133E+01,2.133E+01,2.133E+01,2.133E+01,2.590E+01 49,4.900E+01,2.128E+01,2.128E+01,2.128E+01,2.128E+01,2.569E+01 50,5.000E+01,2.123E+01,2.123E+01,2.123E+01,2.123E+01,2.549E+01 NODT=25 nt=25 mm=25 ib=7 Calculation time= 0.023(sec) Date_time= _7:52:16_(gfortran) 7

I/O format for 2D Steady Seepage Flow Analysis

I/O format for 2D Steady Seepage Flow Analysis (f90 FEM SEEP.f90) December 2, 2012 1. Outline of a program f90 FEM SEEP.f90 This is a program for 2D Steady Seepage Flow Analysis. This program can not treat