CP1

------- PIL real; default = 1005.0; group 9

Introduction

CP1 is a PIL variable used for specifying the specific heat at constant pressure of the phase-1 material. It is employed within PHOENICS for deducing temperature from enthalpy, or vice versa.

The text-book definition of specific heat is that it is the rate of change of enthalpy with temperature; but PHOENICS makes use of a non-standard definition described here.

The difference of definition is important only when specific heat varies with temperature.

The default value of CP1 is that pertaining to air at standard pressure and temperature.

Setting CP1 by way of the Q1 file

Thus:

1. Setting CP1 in the Q1 file to a positive value dictates that it is that constant value which must be used during the calculation.

2. Alternatively, setting CP1 to GRND1, 2 etc indicates that a formula coded in GXSPEHE is to be used.

3. If, however, the Q1 file contains the command STORE(CP1) or STORE(SPH1) the specific heat which is used will be that which is ascribed, cell-by-cell, to the corresponding 3D-stored variable.

   Such values can be prescribed in the usual ways, namely via:

   1. In-Form,
   2. the use of FIINIT and INIVAL patches,
   3. settings of the material-indicating variable PRPS, or
   4. creation of GROUND coding via PLANT or otherwise.

It is Method 2 i,e, the use of the built-in formulae, which will now be described.

In these formulae, the absolute temperature, Tabs, is equal to the local temperature, TEM1, plus the constant, TEMP0, which is set in the Q1 file.

It should be remarked that the built-in formulae are rather unsophisticated. Users are recommended to use the In-Form method for introducing specific-heat information of any complexity.

The built-in formulae

• CP1 = GRND1 selects: CP = CP1A + CP1B*Tabs

  This implies that the enthalpy is a quadratic function of temperature.

• CP1 = GRND2 selects: CP = CP1A + CP1B*Tabs + CP1C*Tabs**2

  This implies that the enthalpy is a cubic function of temperature.

  For air (280-1500K): A= 917.; B= 0.258; C=-3.98E-5
  For ammonia gas (300-1000K): A= 1520.; B= 1.94; C=-1.79E-4

• CP1 = GRND3 selects:
  CP = CP1A + CP1B/Tabs + CP1C/Tabs**2

  This also implies that the enthalpy is a cubic function of temperature. For CO2 (300-3500K): A= 1540.; B=-3.45E5; C= 4.14E7
  For O2 (300-5000K): A= 1420.; B=-2.73E4; C= 4.94E7
  For N2 (300-5000K): A= 1420.; B=-2.88E5; C= 5.35E7

  Note that the integration is carried out from Tabs=200 upward, because the Cp expression cannot be integrated down to Tabs=0

• CP1 = GRND4 selects:
  CP = CP1A + CP1B*Tabs + CP1C/Tabs**0.5
  For H2 (300-2200K): A= 1.2E4; B= 2.16; C= 3.1E4

• CP1 = GRND5 selects:
  CP1 = CP1A + CP1B*/sqrt(Tabs) + CP1C/Tabs
  For O2 (300-2800K): A= 1.51E3; B=-1.68E4; C= 1.11E5

• CP1 = GRND6 selects:
  CP = CP1A for 0 < Tabs < CP1C, and
  CP = CP1B for CP1C < Tabs,

  where CP1C = Tabs_phase_change, and CP1D = latent heat of phase change The latent heat is released over a 1 degree temperature range.

  If PHNH1B is not equal to zero (say,1.0), the phase change occurs at constant temperature.

• CP1 = GRND8 cause CP1 to be obtained by way of the special data-base attached to the PHOENICS-CVD special-purpose program.

• CP1 = GRND9 activates the calculation of specific heat by way of the CHEMKIN data-base

• CP1 = GRND10 computes the specific heat for a mixture of 3 gases: namely fuel, oxidant and product:
  CP1A*FUEL + CP1B*OXID + CP1C*PROD

  Thus, each of the gases may have its own constant specific heat; so the specific heat of the mixture may depend on composition (alone).

• Prior to the introduction of PLANT and In-Form, if these options failed to meet the user's needs, he or she would have had to set CP1=GRND and to insert an appropriate coding sequence in subroutine GROUND.

  However, PLANT has, for several years, allowed users to express their requirements by way of expressions placed in the Q1 file, where after the GROUND coding has been automatically created.

  Now (early 2001) In-Form has extended the facility for placing formulae in the Q1 file, and dispensed with the GROUND-coding feature entirely.

Other topics

If STORE(CP1) or STORE(SPH1) appears in Q1, then the specific heat will be placed in a 3D store and will be available for printing in RESULT and plotting with PHOTON from PHI.

In GROUND, the integer index ISPH1 should be used in calls to FN routines or as the argument of L0F.

See also PHENC entries, SPECIFIC HEATS and TEM1.

wbs