NUSSELT NUMBER COMPUTATION FOR TURBULENT HEAT TRANSFER

phoenics

NUSSELT NUMBER COMPUTATION FOR TURBULENT HEAT TRANSFER
BY : CHAM Technical Support   
DATE : March 2003
PHOENICS Version : 3.5 (Dec 2002)
INTRODUCTION :
The case considered is a steady, turbulent, axisymmetric heated jet impinging on a block of lightweight concrete. The task is to predict the distribution of the heat-transfer coefficient and Nusselt number along the block.
The Reynolds number of the jet is 20,000 and it discharges at 500 deg C into ambient at 25 deg C. The jet is located 3.75 nozzle diameters above the concrete block, which has a thickness of 1.25 nozzle diameters.
The standard k-e model is used in the calculations.
A polar computational grid of 40 radial and 40 axial cells is used. The outer boundary of the solution domain is located 4 nozzle diameters from the jet axis.
All model settings have been made in a VR-based Q1 of PHOENICS 3.5.
The IN-FORM facility is used to compute both the Nusselt number and heat transfer coefficient distribution along the surface of the block.
DEFINITION OF NUSSELT NUMBER AND HEAT TRANSFER COEFFICIENT :
The Nusselt number is defined as a function of radius r along the surface by:
    Nu (r) = h(r)*d/k
where h is the heat transfer coefficient (HTC), d is the nozzle diameter, and k is the gas laminar thermal conductivity. The HTC is defined by:
    h(r) = qw(r)/(Tw(r) - Tj)
where qw is the wall heat transfer rate per unit area, Tw is the wall temperature, and Tj is the jet discharge temperature. Tw can be computed from a thermal balance at the gas-solid interface, i.e.
    Tw = (bs*Ts + bg*Tg)/(bs + bg)
where Ts and Tg are the solid and gas temperatures with bs = ks/ds and bg = a. Here, ks is the solid thermal conductivity, ds is the wall-to-solid node distance, and a is the local heat transfer coefficient computed by the PHOENICS wall functions, defined by:
   a(r) = qw(r)/[Tg(r) - Tw(r)]

THE USE OF INFORM :
As a pre-cursor to defining the INFORM statements, the following whole-field stores are assigned in the 'Models' section of the VR Editor: HTCO (PHOENICS-recognised name for the surface htc based on local conditions); QWAL (user-defined name for the local wall heat transfer rate); TWAL (defines the surface temperature); HTCB (defines the surface htc based on reference conditions); and NUSS (defines the surface Nusselt number).
The INFORM commands for generation of the surface heat-transfer coefficient HTC and Nusselt number Nu have been inserted after the STOP statement in the Q1 file. This has been done from the VR Environment by clicking on 'File'>'Open file for editing'>'Q1'. The following INFORM sequence is used:

** Compute Nu distribution along plate on the last sweep
CHAR(PART1,PART2)
** +1 refers to high-z slab otherwise current z slab
PART2=((KOND[&&+1]/(0.5*DZW[&&+1]))*TEM1[&&+1]+HTCO*TEM1) PART1=((KOND[&&+1]/(0.5*DZW[&&+1]))+HTCO)
** compute surface temperature
(STORED OF TWAL at SURF is PART2/PART1 with IF(ISWEEP.EQ.LSWEEP))
** compute surface heat flux
(STORED OF QWAL at SURF is HTCO*(TEM1-TWAL) with IF(ISWEEP.EQ.LSWEE$
P))
** compute bulk heat-transfer coefficient
CHAR(TJET,TAMB,DIAM);TJET=500.0;TAMB=25.0;DIAM=0.04
(STORED OF HTCB at SURF is ABS(QWAL/(:TJET:-TWAL)) with IF(ISWEEP.E$
Q.LSWEEP))
** compute bulk nusselt number
(STORED OF NUSS at SURF is HTCB*IAM:/KOND with IF(ISWEEP.EQ.LSWEE$
P))
The relevant Q1 file can be inspected and downloaded by clicking here.

zzz

怎么没有q1文件啊，请phoencis在发一下吧！

zzz

还有这是在3.5版本上运行，3.4可以么？我用的是3.4版本。另外：
where Ts and Tg are the solid and gas temperatures ，其中Ts与Tw有什么区别阿？谢谢各位大虾！

zzz

希望phoenics看到后能把q1文件上传上来，谢谢先！

zzz

ding一下

zzz

最近这么冷清阿/

phoenics

TALK=T;RUN( 1, 1)

************************************************************
   Q1 created by VDI menu, Version 3.5, Date 08/10/02
CPVNAM=VDI;SPPNAM=Core
************************************************************
IRUNN   =       1 ;LIBREF =       0
************************************************************
  Group 1. Run Title
TEXT(INFORM - Nusselt number computation     )
************************************************************
  Group 2. Transience
STEADY  =    T
************************************************************
  Groups 3, 4, 5  Grid Information
    * Overall number of cells, RSET(M,NX,NY,NZ,tolerance)
RSET(M,1,40,40)
    * Cylindrical-polar grid
CARTES=F
************************************************************
  Group 6. Body-Fitted coordinates
************************************************************
  Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS  =    T
    * Non-default variable names
NAME(135) =HTCB ; NAME(137) =ENUL
NAME(138) =TWAL ; NAME(139) =YPLS
NAME(140) =STAN ; NAME(141) =HTCO
NAME(142) =SPH1 ; NAME(143) =DEN1
NAME(144) =ENUT ; NAME(145) =QWAL
NAME(146) =MACH ; NAME(147) =EPKE
NAME(148) =PRPS ; NAME(149) =TEM1
NAME(150) =KOND
    * Solved variables list
SOLVE(P1  ,V1  ,W1  ,TEM1)
    * Stored variables list
STORE(KOND,PRPS,EPKE,MACH,QWAL,ENUT,DEN1,SPH1)
STORE(HTCO,STAN,YPLS,TWAL,ENUL,HTCB)
    * Additional solver options
SOLUTN(P1  ,Y,Y,Y,N,N,Y)
SOLUTN(TEM1,Y,Y,Y,N,N,Y)
TURMOD(KEMODL)

************************************************************
  Group 8. Terms & Devices
NEWRH1  =    T
NEWENL  =    T
DENPCO  =    T
************************************************************
  Group 9. Properties
PRESS0  = 1.000000E+05 ;TEMP0  = 2.730000E+02
SETPRPS(1,  2)
DRH1DP  = GRND5
DVO1DT  = 3.330000E-03
PRNDTL(TEM1) = -2.630000E-02
PRT   (EP  ) =  1.314000E+00
************************************************************
  Group 10.Inter-Phase Transfer Processes
************************************************************
  Group 11.Initialise Var/Porosity Fields
FIINIT(PRPS) = -1.000000E+00
   No PATCHes used for this Group


INIADD  =    F
************************************************************
  Group 12. Convection and diffusion adjustments
   No PATCHes used for this Group
************************************************************
  Group 13. Boundary & Special Sources

PATCH (SURF    ,CELL  ,5,0,0,0,0,0,1,2)

EGWF    =    T
************************************************************
  Group 14. Downstream Pressure For PARAB
************************************************************
  Group 15. Terminate Sweeps
LSWEEP  =     700
SARAH   = 5.000000E-02
RESFAC  = 1.000000E-03
************************************************************
  Group 16. Terminate Iterations
LITER (P1  ) =       50 ;LITER (TEM1) =       50
************************************************************
  Group 17. Relaxation
RELAX(P1  ,LINRLX, 1.000000E+00)
RELAX(V1  ,FALSDT, 1.000000E-02)
RELAX(W1  ,FALSDT, 1.000000E-02)
RELAX(KE  ,LINRLX, 5.000000E-01)
RELAX(EP  ,LINRLX, 5.000000E-01)
RELAX(TEM1,LINRLX, 3.000000E-01)
KELIN   =       3
************************************************************
  Group 18. Limits
VARMAX(V1  ) = 1.000000E+06 ;VARMIN(V1  ) =-1.000000E+06
VARMAX(W1  ) = 1.000000E+06 ;VARMIN(W1  ) =-1.000000E+06
************************************************************
  Group 19. EARTH Calls To GROUND Station
USEGRD  =    T  ;USEGRX =    T
GENK    =    T
ASAP    =    T
IDISPB  =       1 ;IDISPC =      30
************************************************************
  Group 20. Preliminary Printout
ECHO    =    T
************************************************************
  Group 21. Print-out of Variables
************************************************************
  Group 22. Monitor Print-Out
IXMON   =       1 ;IYMON  =      40 ;IZMON  =      30
NPRMON  =  100000
NPRMNT  =       1
TSTSWP  =      -1
************************************************************
  Group 23.Field Print-Out & Plot Control
NPRINT  =  100000
NYPRIN  =       1
IYPRF   =       1 ;IYPRL  =      40
NZPRIN  =       1
IZPRF   =      28 ;IZPRL  =      36
YZPR    =    T
ISWPRF  =       1 ;ISWPRL =  100000
ITABL   =       2
   No PATCHes used for this Group
************************************************************
  Group 24. Dumps For Restarts
NOWIPE  =    T
IDISPA  =       1 ;IDISPB =       1 ;IDISPC =      30
CSG1    ='N'
CSG2    ='C'

GVIEW(P,-9.004471E-01,0.000000E+00,-4.349655E-01)
GVIEW(UP,4.349655E-01,0.000000E+00,-9.004471E-01)

> DOM,    SIZE,        1.000000E-01, 1.600000E-01, 2.000000E-01
> DOM,    MONIT,       5.000000E-02, 1.580000E-01, 1.475000E-01
> DOM,    SCALE,       1.000000E+00, 1.000000E+00, 1.000000E+00
> DOM,    SNAPSIZE,    1.000000E-02

> OBJ,    NAME,        OUTLETSI
> OBJ,    POSITION,    0.000000E+00, 1.600000E-01, 0.000000E+00
> OBJ,    SIZE,        1.000000E-01, 0.000000E+00, 1.500000E-01
> OBJ,    CLIPART,     cube12t
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        OUTLET
> OBJ,    PRESSURE,      0.000000E+00
> OBJ,    TEMPERATURE,   2.500000E+01
> OBJ,    COEFFICIENT,   1.000000E+03
> OBJ,    TURBULENCE,   -1.026000E+04,-1.026000E+04

> OBJ,    NAME,        JET
> OBJ,    POSITION,    0.000000E+00, 0.000000E+00, 0.000000E+00
> OBJ,    SIZE,        1.000000E-01, 2.000000E-02, 0.000000E+00
> OBJ,    CLIPART,     cube3t
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        INLET
> OBJ,    PRESSURE,      0.000000E+00
> OBJ,    VELOCITY,      0.000000E+00, 0.000000E+00, 4.000000E+01
> OBJ,    TEMPERATURE,   5.000000E+02
> OBJ,    TURB-INTENS,   5.000000E+00

> OBJ,    NAME,        CONCRETE
> OBJ,    POSITION,    0.000000E+00, 0.000000E+00, 1.500000E-01
> OBJ,    SIZE,        1.000000E-01, 1.600000E-01, 5.000000E-02
> OBJ,    CLIPART,     cube14
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        BLOCKAGE
> OBJ,    MATERIAL,      122
> OBJ,    INI_TEMP,      2.500000E+01

> OBJ,    NAME,        OUTTOP
> OBJ,    POSITION,    0.000000E+00, 2.000000E-02, 0.000000E+00
> OBJ,    SIZE,        1.000000E-01, 1.400000E-01, 0.000000E+00
> OBJ,    CLIPART,     cube12t
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        OUTLET
> OBJ,    PRESSURE,      0.000000E+00
> OBJ,    TEMPERATURE,   2.500000E+01
> OBJ,    COEFFICIENT,   1.000000E+03
> OBJ,    TURBULENCE,   -1.026000E+04,-1.026000E+04

> OBJ,    NAME,        SURF
> OBJ,    POSITION,    0.000000E+00, 0.000000E+00, 1.500000E-01
> OBJ,    SIZE,        1.000000E-01, 1.600000E-01, 0.000000E+00
> OBJ,    CLIPART,     poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED
STOP
  
  The case considered is a steady, turbulent, axisymmetric
  heated jet impinging on a block of lightweight concrete.
  The task is to predict the distribution of the heat-transfer
  coefficient and Nusselt number along the block. The Reynolds
  number of the jet is 20,000 and it discharges at 500 deg C
  into ambient at 25 deg C. The jet is located 3.75 nozzle
  diameters above the concrete block, which has a thickness of
  1.25 nozzle diameters. The standard k-e model is used in the
  calculations. A polar computational grid of 40 radial and 40
  axial cells is used. The outer boundary of the solution domain
  is located 4 nozzle diameters from the jet axis. All model
  settings have been made in VR-based Q1 of PHOENICS 3.5. The
  IN-FORM facility is used to compute both the Nusselt number
  and heat transfer coefficient distribution along the surface
  of the block.

  
  ** Compute Nusselt number distribution along plate
     on the last sweep
CHAR(PART1,PART2)
  ** +1 refers to high-z slab otherwise current z slab
PART2=((KOND[&&+1]/(0.5*DZW[&&+1]))*TEM1[&&+1]+HTCO*TEM1)
PART1=((KOND[&&+1]/(0.5*DZW[&&+1]))+HTCO)
  ** compute surface temperature
(STORED OF TWAL at SURF is PART2/PART1 with IF(ISWEEP.EQ.LSWEEP))
  ** compute surface heat flux
(STORED OF QWAL at SURF is HTCO*(TEM1-TWAL) with IF(ISWEEP.EQ.LSWEE$
P))                                                                 
  ** compute bulk heat-transfer coefficient
CHAR(TJET,TAMB,DIAM);TJET=500.0;TAMB=25.0;DIAM=0.04
(STORED OF HTCB at SURF is ABS(QWAL/(:TJET:-TWAL)) with IF(ISWEEP.E$
Q.LSWEEP))                                                         
  ** compute bulk nusselt number
(STORED OF NUSS at SURF is HTCB*IAM:/KOND with IF(ISWEEP.EQ.LSWEE$
P))                                                                 

zzz

真是太感谢phoenics了！

zzz

怎么不能运行啊，我运行run=>earth然后屏幕一闪而过，我没有改动模型。模型的问题还是我软件的问题，我的软件只有core，是因为模型中用inform编程的原因么？

zzz

这是result文件中提示：
************************************************************
              message from function l0mat
??? imat=      -1
prps value does not correspond to those
placed by SATELLITE in eardat. INIAD=T ?
If you need this material, insert in Q1
SPEDAT(SET,MATERIAL, -1,L,T)

zzz

我发现在调入q1文件后
，vr中的模型显示只有一个物体模型，其他的根本没有调入，这是什么原因呢？

phoenics

把下面的命令写入Q1文件,试试看
SPEDAT(SET,MATERIAL, -1,L,T)

zzz

写在q1中的那一部分呢？group？是物性设置那一group么？还是任意放置就可以？

zzz

试了一试还是不能运行，我把SPEDAT(SET,MATERIAL, -1,L,T)放在物性设置那一group里面了。