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*DECK THMCDI
FUNCTION THMCDI(T2K,T1K,BURN,POROS,FRACPU,ICONDF,NCONDF,KCONDF,
> UCONDF,IFRCDI)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Compute the thermal conductivity integral of UOX or MOX fuel.
*
*Copyright:
* Copyright (C) 2012 Ecole Polytechnique de Montreal.
*
*Author(s):
* A. Hebert, V. Salino
*
*Parameters: input
* T2K final temperature in Kelvin.
* T1K initial temperature in Kelvin.
* BURN fuel burnup in MWday/tonne.
* POROS fuel porosity.
* FRACPU plutonium mass fraction in fuel.
* ICONDF fuel conductivity flag (0=Stora-Chenebault or COMETHE/
* 1=user-provided polynomial + inverse term).
* NCONDF degree of user-provided fuel conductivity polynomial.
* KCONDF polynomial coefficients for fuel conductivity in W/m/K^(k+1)
* (except for the two last coefficients which belongs to the
* inverse term).
* UCONDF required unit of temperature in polynomial for fuel
* conductivity (KELVIN or CELSIUS).
* IFRCDI flag indicating if average approximation is forced during
* fuel conductivity evaluation (0=default/1=average
* approximation forced).
*
*Parameters: output
* THMCDI thermal conductivity integral in Watt/m/K.
*
*Reference:
* A. Poncot, "Assimilation de donnees pour la dynamique du xenon dans
* les coeurs de centrale nucleaire", Ph.D Thesis, Universite de
* Toulouse, France, 2008.
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER ICONDF,NCONDF,IFRCDI
REAL T1K,T2K,BURN,POROS,FRACPU,KCONDF(NCONDF+3),THMCDI
CHARACTER UCONDF*12
*----
* LOCAL VARIABLES
* NPAS number of rectangles in the quadrature
* DT rectangle width
* T2T1 temperature difference
* DTMIN cutoff criterion for selecting the approximation
* FPI burnup correcting factor
* CIRRA burnup correction constant
* HV* coefficients of the Stora-Chenebault correlation
* HK* coefficients of the Comethe correlation
*----
INTEGER NPAS,I,K
REAL T1,T2,DT,TM,DTMIN,T2T1,FPI,TT,TMK,TEMP,FTP,CINT,FP,TTK
REAL HV1, HV2, HV3
REAL HK1, HK2, HK4, HK5
REAL ZKELV,CIRRA
*
PARAMETER ( ZKELV=273.15 )
PARAMETER ( HV1= 1.3324E-08 , HV2 = -4.3554E-05 ,
& HV3 = 5.8915E-02 )
PARAMETER ( HK1= 40.05 , HK2 = 129.4 , HK4 = 0.8 ,
& HK5 = 0.6416E-12 )
PARAMETER ( CIRRA= 0.124E-02 )
*
REAL A
DATA NPAS /10/
DATA DTMIN /10./
*
IF(MIN(T1K,T2K).LE.0.0) THEN
CALL XABORT('@THMCDI: NEGATIVE TEMPERATURE.')
ENDIF
T1=T1K-ZKELV
T2=T2K-ZKELV
*
T2T1 = T2-T1
DT = T2T1/NPAS
TM = (T1+T2)/2.0
IF(ICONDF.EQ.1) THEN
* User-given conductivity, as a function of temperature
IF((ABS(T2T1).LT.DTMIN).OR.(IFRCDI.EQ.1)) THEN
* Use the average value approximation
THMCDI=0.0
IF(UCONDF.EQ.'KELVIN') THEN
TMK = TM + ZKELV
DO K=1,NCONDF+1
THMCDI=THMCDI + KCONDF(K)*TMK**(K-1)
ENDDO
THMCDI=THMCDI + KCONDF(NCONDF+2)/(TMK-KCONDF(NCONDF+3))
ELSE
DO K=1,NCONDF+1
THMCDI=THMCDI + KCONDF(K)*TM**(K-1)
ENDDO
THMCDI=THMCDI + KCONDF(NCONDF+2)/(TM-KCONDF(NCONDF+3))
ENDIF
ELSE
* Use the rectangle quadrature approximation
TT=T1-DT*0.5
CINT=0.
DO I=1,NPAS
TT=TT+DT
IF(UCONDF.EQ.'KELVIN') THEN
TTK = TT + ZKELV
DO K=1,NCONDF+1
CINT=CINT + KCONDF(K)*TTK**(K-1)
ENDDO
CINT=CINT + KCONDF(NCONDF+2)/(TTK-KCONDF(NCONDF+3))
ELSE
DO K=1,NCONDF+1
CINT=CINT + KCONDF(K)*TT**(K-1)
ENDDO
CINT=CINT + KCONDF(NCONDF+2)/(TT-KCONDF(NCONDF+3))
ENDIF
ENDDO
THMCDI=CINT/NPAS
ENDIF
ELSE IF(FRACPU.GT.0.) THEN
* Use the Comethe correlation for MOX fuel
FPI=CIRRA*BURN
IF((ABS(T2T1).LT.DTMIN).OR.(IFRCDI.EQ.1)) THEN
* Use the average value approximation
IF(TM.GT.1000.0) THEN
A=2.0
ELSE
A=2.58-0.58E-03*TM
ENDIF
FP=(1.0-A*POROS)/(1.0-A*0.05)
TMK = TM + ZKELV
TEMP = HK2 + (1.0 + HK4*FRACPU*1.E-02) * TMK
FTP = FP * (HK1/TEMP + HK5*TMK*TMK*TMK) *100.0
IF(TM.EQ.0.) THEN
THMCDI=FTP
ELSE
THMCDI=1.0/(1.0/FTP+FPI/TM)
ENDIF
ELSE
* Use the rectangle quadrature approximation
TT=T1-DT*0.5
CINT=0.
DO I=1,NPAS
TT=TT+DT
IF(TT.GT.1000.0) THEN
A=2.0
ELSE
A=2.58-0.58E-03*TT
ENDIF
FP=(1.0-A*POROS)/(1.0-A*0.05)
TTK = TT + ZKELV
TEMP = HK2 + (1.0 + HK4*FRACPU*1.E-02) * TTK
FTP = FP * (HK1/TEMP + HK5*TTK*TTK*TTK) *100.0
IF(TT.EQ.0.0) THEN
CINT=CINT+FTP
ELSE
CINT=CINT+1.0/(1.0/FTP+FPI/TT)
ENDIF
ENDDO
THMCDI=CINT/NPAS
ENDIF
ELSE
* Use the Stora-Chenebault correlation for UOX fuel
* (also called the "HGAP Variable 88" correlation)
FPI=CIRRA*BURN
IF((ABS(T2T1).LT.DTMIN).OR.(IFRCDI.EQ.1)) THEN
* Use the average value approximation
IF(TM.GT.1000.) THEN
A=2.0
ELSE
A=2.58-0.58E-03*TM
ENDIF
FP=(1.0-A*POROS)/(1.0-A*0.034)
FTP=FP*(HV3+HV2*TM+HV1*TM*TM)*100.0
IF(TM.EQ.0.0) THEN
THMCDI=FP*HV3*100.0
ELSE
THMCDI=1.0/(1.0/FTP+FPI/TM)
ENDIF
ELSE
* Use the rectangle quadrature approximation
TT=T1-DT*0.5
CINT=0.
DO I=1,NPAS
TT=TT+DT
IF(TT.GT.1000.) THEN
A=2.0
ELSE
A=2.58-0.58E-03*TT
ENDIF
FP=(1.0-A*POROS)/(1.0-A*0.034)
FTP=FP*(HV3+HV2*TT+HV1*TT*TT)*100.0
IF(TT.EQ.0.0) THEN
CINT=CINT+FP*HV3*100.0
ELSE
CINT=CINT+1.0/(1.0/FTP+FPI/TT)
ENDIF
ENDDO
THMCDI=CINT*DT/T2T1
ENDIF
ENDIF
RETURN
END
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