TITLE HEATS: HEAT ENERGY ANALYSIS THROUGH SIMULATION * EULER * DOC * CHECK NOTE NOTE MACRO PART OF MODEL NOTE C PI=3.14159 CONSTANT PI NOTE NOTE VARIABLE SET UP TO KEEP TIME NOTE A A1TIME.K=TIME.K TIME FOR 1ST 24 HOURS HOURS A A2TIME.K=TIME.K-24 TIME FOR 2ND 24 HOURS HOURS A ATIME.K=CLIP(A2TIME.K,A1TIME.K,TIME.K,24) TIME USED IN ANALYSIS HOURS NOTE NOTE NOTE NOTE USER SPECIFIED INPUT NOTE NOTE GENERAL INPUT -- LOCATION,WEATHER DATA,DAY NOTE C DTK=.7 TIME STEP OF THE SIMULATION (DT ON SPEC) HOURS C DAY=195 DAY OF INTEREST ,STARTING AT JAN 1 DAY=JULY 14 C BAROP=29.21 BAROMETRIC PRESSURE INCHES OF MERCURY C LATTUD=.72 LATTUD OF LOCATION RADIANS(DEGREES*PI/180) C ROTATN=0.0 ROTATN OF N-S FROM NORMAL RADIANS C TILT=0.0 TILT TAKEN FROM THE NORMAL RADIANS C QMAX=270 MAX ENERGY FROM SUN ON GIVEN DAY BTU/HR/FT**2 C WINDI=10560 INSIDE AVERAGE WIND VELOCITY FPH (MPH*5280) C WINDO=52800 OUTSIDE AVERAGE WIND VELOCITY FPH (MPH*5280) C LENGTH=30 EITHER HIGHT OF SURFACE OR DISTANCE IN WIND[FEET C EPSLON=.91 EMMISSIVITY FACTOR UNITLESS T TTOUT=527,526,533,539,546,553,551,545 OUTSIDE TEMP PROFILE[RANKINE T TTIN=528,528,528,528 INSIDE TEMP PROFILE RANKINE NOTE NOTE SUN'S ANGLE CALCULATIONS NOTE A DEC.K=TABFL(TDCL,DAY,0,365) DECLINATION ANGLE DEGREES A DECL.K=DEC.K/180*PI DECLINATION ANGLE RADIANS A HOUR.K=PI/180*ABS(90*(12-ATIME.K)/6) HOUR ANGLE RADIANS A BET.K=(COS(LATTUD)*COS(HOUR.K)*COS(DECL.K)+SIN(LATTUD)* X SIN(DECL.K)) DEF BET IS THE ANGLE WHOS ARCCOS IS BETA A BETA.K=TABFL(ARCSIN,BET.K,-1,1) BETA,LATTUD ANGLE RADIANS A GAM.K=(1/COS(BETA.K))*((COS(LATTUD)*SIN(DECL.K))-COS(DECL.K)* X SIN(LATTUD)*COS(HOUR.K)) DEF GAM IS THE ANGLE WHOS ARCSIN SIN IS GAMMA A GAMM1.K=TABFL(ARCCOS,GAM.K,-1,1) GAMMA ANGLE FOR THE WEST PLANE[RADIANS A GAMM2.K=PI*2-GAMM1.K GAMMA ANGLE FOR THE EAST PLANE[RADIANS A GAMMA.K=CLIP(GAMM2.K,GAMM1.K,ATIME.K,12) SELECT GAMMA,AZIMUTH ANGLE[RADIANS A ALPH1.K=ABS(GAMMA.K-ROTATN) ANGLE OF INCIDENCE IN NS PLANE[RADIANS A ALPH2.K=ABS(2*PI-ALPH1.K) POSSIBLE ANGLE OF INCIDENCE RADIANS A ALPHA.K=CLIP(ALPH2.K,ALPH1.K,ALPH1.K,ALPH2.K) ANGLE OF INCIDENCE[RADIANS A TOTAL.K=ABS(SIN(1.57-ALPHA.K)*SIN(1.57-BETA.K-TILT))*TEST1.K*TEST2.K X +ABS(SIN(1.57-BETA.K-TILT))*TEST3.K DEF TOTAL ACTUAL AMOUNT OF AREA OF SURFACE PROJECTED NORMAL TO SUN'S RAY A TEST1.K=CLIP(0,1,TILT,1.57) IS SURFACE HORIZONTAL YES=0 A TEST2.K=CLIP(0,1,ALPHA.K,1.57) IS ANGLE OF INCIDENCE > PI/2 YES=0 A TEST3.K=CLIP(1,0,TILT,1.57) IS SURFACE HORIZONTAL YES=1 A QSUNT.K=QSOLAR.K*TOTAL.K ENEGRY FROM SUN AFFECTING SURFACE[BTU/HR/FT**2 A QSUN.K=SWITCH(QSUNT.K,0,QSUNT.K) IS SUN UP YET NO=0 A ANGLE.K=(-SIN(LATTUD)/COS(LATTUD)*SIN(DECL.K)/COS(DECL.K)) DEF ANGLE PORTION OR MORNING AND NIGHT NIGHT A ANGLES.K=TABFL(ARCCOS,ANGLE.K,-1,1) ARCCOS OF ANGLE A MORNG.K=12-ANGLES.K*180/15/PI TIME OF MORNG A NIGHT.K=12+ANGLES.K*180/15/PI TIME OF NIGHT A QSOLAR.K=QMAX*SIN(PI*(ATIME.K/(NIGHT.K-MORNG.K)-MORNG.K/ X (NIGHT.K-MORNG.K))) DEF QSOLAR SOLAR ENERGY PROFILE DURING THE STUDY DAY BTU/HR/FT**2 NOTE NOTE EXPAND FUNCTION FOR THE CALCULATION OF HEAT TRANSFER COEFFIENTS NOTE MACRO HTC(H,P,K,W,L,R,M,T,C) A P.K=TABFL(TPR,T.K,410,610) PRANDTL NUMBER UNITLESS A M.K=TABFL(TMU,T.K,410,610) (MU) FOR AIR LBM/HR/FT A K.K=TABFL(TK,T.K,410,610) THERMAL CONDUCTIVITY BTU/HR/FT/F A C.K=BAROP*14.696/(53.35*T.K*29.92)*144 DENSITY LBM/FT**3 A R.K=W*L*C.K/M.K RENOLD'S NUMBER UNITLESS A H.K=P.K**.333*(ABS(.036*R.K**.8))*K.K/L HEAT TRANSFER COEFFIENT MEND NOTE NOTE CALCULATIONS FOR BOTH THE INSIDE AND OUTSIDE SURFACES NEED BE NOTE MADE NOTE EXPND HTC(HI,CPI,KI,WINDI,LENGTH,RI,MI,TOUT,CI) DEF HI INSIDE HEAT TRANSFER COEFFIENT BTU/HR/FT**2/F DEF HO OUTSIDE HEAT TRANSFER COEFFIENT BTU/HR/FT**2/F EXPND HTC(HO,PO,KO,WINDO,LENGTH,RO,MO,TOUT,CO) NOTE INSIDE AND OUTSIDE TEMPERATURE CALCULATIONS NOTE A TOUT.K=TABFL(TTOUT,ATIME.K,0,24) OUTSIDE TEMPERATURE RANKINE A TIN.K=TABFL(TTIN,ATIME.K,0,24) INSIDE TEMPERATURE RANKINE NOTE NOTE EXPAND FUNCTIONS FOR THE TEMPERATURE CALCULATIONS NOTE MACRO EXTROR(STEP,T,TT,TT1) A T1.K=(A1*DTK/STEP**2)*(2*HO.K*STEP/K1*TOUT.K+2*TT1.K+ X (-2*HO.K*STEP/K1-2+STEP**2/(A1*DTK))*TT.K) A T.K=T1.K+2*QSUN.K/K1*A1*DTK/STEP*EPSLON N TT=505 INITIAL NODE TEMPERATURE RANKINE R RATE1.KL=T.K-TT.K L TT.K=INTGRL(RATE1.JK) MEND NOTE MACRO INTROR(T,TT,CA,CK,TM1,STEP,RATE) A T.K=(CA*DTK/STEP**2)*(2*HI.K*STEP/CK*TIN.K+2*TM1.K+(-2*HI.K*STEP/ X CK-2+STEP**2/(CA*DTK))*TT.K) N TT=505 R RATE.KL=T.K-TT.K L TT.K=INTGRL(RATE.JK) MEND NOTE NOTE MACRO SECTN(T,TT,CA,CK,TM1,TP1,STEP,RATE) A T.K=(CA*DTK/STEP**2)*(TP1.K+TM1.K)+(1-2*CA*DTK/STEP**2)* X TT.K N TT=505 R RATE.KL=T.K-TT.K L TT.K=INTGRL(RATE.JK) MEND NOTE NOTE MACRO INTRSC(T,TT,T1,T2,CA1,CA2,CK1,CK2,STEP,RATE) A T.K=TT.K+(CK1/STEP*TT.K+CK2/STEP*T1.K-(CK1/STEP+CK2/STEP)*T2.K)/ X (CK1/CA1+CK2/CA2)*STEP/2/DTK N TT=505 R RATE.KL=T.K-TT.K L TT.K=INTGRL(RATE.JK) MEND NOTE NOTE MACRO QFIND(T1,QI,QSUM) A QI.K=(T1.K-TIN.K)*HI.K N QSUM=0 A OUT.K=SWITCH(1,0,A2TIME.K) R QR.KL=QI.K*DTK*OUT.K L QSUM.K=INTGRL(QR.JK) MEND T TMU=.0358,.0394,.0459,.0484 T TK=.0118,.0131,.0157,.0167 T TCP=.239,.240,.240,.240 T TPR=.729,.718,.706,.699 T TDCL=-23.08,-21.15,-17.18,-12.55,-7.15,-2.25,4.16,9.3,14.51,18.41, X 21,23,23,21,18,14.17,8.33,3.19,-2.54,-8.15,-14.12,-18.18,-21.41,-23.08 T ARCCOS=3.14159,2.69,2.49,2.34,2.21,2.09,1.98,1.87,1.77,1.67,1.5709 X ,.1476,1.3694,1.2661,1.1593,1.0472,.9273,.7954,.6435,.4510,0 T ARCSIN=-1.5708,-1.11,-.92,-.77,-.64,-.52,-.41,-.30,-.20,-.10, X 0,.1002,.2014,.3047,.4115,.5236,.6435,.7754,.9272,1.119,1.57 NOTE NOTE C K1=.12 C C1=.57 C A1=.0041 C DX1=.125 C K2=.7 C C2=.2 C A2=.0267 C DX2=.0416 EXPND EXTROR(DX1,TWAL1,TTWAL1,TTWAL2) EXPND INTROR(TWAL5,TTWAL5,A1,K1,TTWAL4,DX1,RATE5) EXPND SECTN(TWAL2,TTWAL2,A1,K1,TTWAL1,TTWAL3,DX1,RATE2) EXPND SECTN(TWAL3,TTWAL3,A1,K1,TTWAL2,TTWAL4,DX1,RATE3) EXPND SECTN(TWAL4,TTWAL4,A1,K1,TTWAL3,TTWAL5,DX1,RATE4) EXPND QFIND(TWAL5,QI,QSUM) NOTE NOTE SPECIFICATIONS PARM DT=.7 PARM START=1 PARM STOP=48 PARM PRTPER=1 PARM PLTPER=1 PRINT ATIME,QSUM,QI,HO,HI PRINT ATIME.2,QSUM.2,QI.2,HO.2,HI.2 PRINT ATIME.3,QSUM.3,QI.3,HO.3,HI.3 PRINT ATIME.4,QSUM.4,QI.4,HO.4,HI.4 PRINT ATIME.5,QSUM.5,QI.5,HO.5,HI.5 PRINT ATIME.6,QSUM.6,QI.6,HO.6,HI.6 PRINT ATIME.7,QSUM.7,QI.7,HO.7,HI.7 PRINT QSUM.* PRINT QSUN.* PRINT QSOLAR.* PLOT QSUN.* PLOT QSOLAR.* PLOT QSUM.* RERUN WINDO=158400 FPH C WINDO=158400 RERUN WINDO=105600 C WINDO=105600 RERUN TO CHANGE THE INSIDE TEMPERATURE C WINDO=52800 T TTIN=520,528,529,520 RERUN WINTER C DAY=41 T TTOUT=460,460,461,464,460,460,460,460 C WINDO=52800 RERUN TO CHANGE THE OUTSIDE TEMPERATURE C DAY=41 C WINDO=105600 T TTOUT=460,460,461,464,460,460,460,460 RERUN C DAY=41 C WINDO=158400 T TTOUT=460,460,461,464,460,460,460,460 RERUN WINTER DAY AND MODIFINED INSIDEE AND OUTSIDE TEMPERATURE C DAY=41 C WINDO=52800 T TTOUT=460,460,461,464,460,460,460,460 T TTIN=520,528,528,520