Encyclopaedia Index

(see Q1)

----- PIL real; default=0.0; group 9, ----

TEMP0....the negative of the absolute zero of temperature on the currently used
temperature scale, *i.e.* the number which must be added to the current temperature to yield
the absolute temperature.

It should be set to 273.15 when the Celsius scale is in use, and to 492 when the Fahrenheit scale is in use.

It is used for the calculation of enthalpy and specific heat when TEM1 and/or TEM2 is solved for, and also for radiative heat- transfer calculations.

----- PIL integer name; group 7 ----------

TEMP1.... is a name which may be used in GROUND coding to access the temperature of the first phase, when this is deduced from the enthalpy. It is not a PIL variable.

----- PIL integer name; group 7 ----------

TEMP1.... is a name which may be used in GROUND coding to access the temperature of the first phase, when this is deduced from the enthalpy. It is not a PIL variable.

--------------------------------

Temperature can be treated in PHOENICS as either a derived property, or a solved-for variable.

In the former case, the enthalpy of the phase in question must be a solved-for variable; then the temperature is derived from it by some such relation as:

temperature = const1 * enthalpy + const2.

In the latter, temperature is the represented by the solved-for variables:

TEM1, for phase 1; and

TEM2, for phase 2.

See PHENC entries for: H1, TMP1, TMP1A, TMP1B, TMP1C, TEM1, CP1,

Further relevant information can be found in the entries on: PRPS and PROPS.

Integer used in GXTEMPR to denote temperature of the first phase .

Integer used in GXTEMPR to denote temperature of the second phase.

----- Command; in group 8 ------------

The command to determine which terms are active in the balance equation for variables solved is:

TERMS(variable index,Y or N,Y or N,.. six times) (if no change desired, enter P for
pass)

The six questions answered by the Y's and N's are:

- Built-in sources active?
- Convection active?
- Diffusion active?
- Transient term active?
- Variable belongs to first phase?
- Interphase transport active?

This may be used to cut out the built-into-EARTH sources; it has no effect on GROUND-set sources. A list of the built-in sources is provided under the SOURCE entry.

The transient term is automatically inactive when STEADY=T

These entries are inactive when ONEPHS is T, in which case all variables are associated with the first phase, except U2, V2, W2, H2, R2 and RS which may be solved when ONEPHS=F only. The variables for which the default 5 entry is N, when ONEPHS=F, are: R2,RS,H2,C2,C4,C6,C8,C10,C12,C14,C16,C18,C20,C22,C24,C26,C28,C30,C32 and C34,

ie those with indices,

10,11,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47 and 49.

(see TERMS command, Group 8)

------ PIL logical; default=F; group 25 --- -

TEST....activates calls to the SEARCH subroutines at certain locations in the algorithm-controlling subroutines. Set this T when SEARCHing.

---- PIL real; default= 0.0; group 2 --- -

TFIRST....initial value of time in the calculation of a time-dependent process.

----- PIL real array; default= 100*1.0; gr -

See PHENC

TFRAC is a PIL-language array for setting the time-step intervals. There are three ways of using TFRAC to set the time intervals namely:

These methods are detailed below.

When successive values of the TFRAC array are set to a series of monotonically increasing values, the time at the end of each time step will be equal to TLAST times the value in the array, minus TFIRST. Thus, if TLAST=10.0 (seconds), TFIRST=0 and LSTEP=4 (implying that four time intervals will be calculated), the following settings of TFRAC have the implications shown:-

TFRAC(1)= | 0.1 implies that the first calculation is from 0.0 to 1.0 sec; |

TFRAC(2)= | 0.25 implies that the second calculation is from 1.0 to 2.5 sec; |

TFRAC(3)= | 0.75 implies that the third calculation is from 2.5 to 7.5 sec; |

TFRAC(4)= | 1.42 implies that the fourth calculation is from 7.5 to 14.2 sec. |

Although TFRAC is properly interpreted as being a fraction, in that it multiplies TLAST, there is no objection to its taking values in excess of 1.0. provided each successive member of the array exceeds the one before it. If the last value of TFRAC is 1.0 then TLAST is the duration of the run and the initial time TFIRST is added to the time printed in the output.

When TFRAC(1) is set to a negative number, PHOENICS-EARTH is informed that the method of pairs is in use. Thereafter, the minus sign is ignored.

In this method, the odd-numbered TFRAC's must be given whole- number values; but the even-numbered TFRAC's can take any positive values. The interpretation by EARTH of the following settings:

TFRAC(1)=-4.0 , TFRAC(2)=0.25 ,

TFRAC(3)= 1.0 , TFRAC(4)=0.137 ,

TFRAC(5)=42.0 , TFRAC(6)=1.2E-4 ,

will be that time will be divided into:- 4 intervals each equal to 0.25 times TLAST, followed by 1 interval equal to 0.137 times TLAST, followed by 42 intervals each equal to 0.00012 times TLAST.

GRDPWR(T,number of intervals, total time, exponent)

automatically sets TLAST, LSTEP and TFRAC. See GRDPWR for information.

---------- Advanced PIL command --- -

THEN is an element of the PIL IF construct. See the HELP entry on IF for further details.

- Description
- Energy-equation source terms
- Radiation-equation source terms
- Determination of the plate surface temperatures
- Concluding remarks

The THINPLT object represents a grid-aligned zero-thickness obstacle to flow,
which may be porous, and has a nominal thickness and material for heat transfer
through the plate by conduction. The object accounts for radiative and
convective heat transfer from either side of the plate, and in transient cases
__without radiation__, the thermal capacitance of the plate is taken into account.
The advantage of a THINPLT object over a participating BLOCKAGE object is that
it accounts for heat conduction through the plate without the need to mesh the
thickness of the plate itself, which would be the case for a BLOCKAGE object.

The THINPLT object differs from a PLATE object only in that it allows for heat transfer through the plate. The object can be used with the energy equation solved in terms of either temperature (TEM1) or specific enthalpy (H1), and radiative heat transfer can be taken into account by means of the IMMERSOL variable T3. The user can specify a different surface emissivity for each side of the THINPLT.

The THINPLT object is implemented in PHOENICS by:

- breaking the default diffusive links in the energy and radiation equations between the mesh nodes on either side of the cell face coincident with the THINPLT; and
- then introducing the appropriate energy and radiation sources and sinks on either side of the plate.

For the latter a thermal balance is applied at the surfaces on either side of the object so as to determine the surface temperatures on the two sides. These surface temperatures are used to apply diffusive and radiative source terms on either side of the THINPLT.

The creation of a THINPLT object generates two PATCH's, one on the low-coordinate side of the thin plate named PLT*1, and the other on the high coordinate side named PLT_1. PHOENICS will print to the RESULT every NPRINT sweeps, the convective and radiative heat transfer rates (in W) entering and leaving the thin plate. For example:

*Nett source of TEM1 at patch named: PLT*1 (THINP ) = 1.883105E+02*

*Nett source of TEM1 at patch named: PLT_1 (THINP ) =-4.884870E+02*

*Nett source of T3 at patch named: PLT*1 (THINP ) = 5.539259E+02*

*Nett source of T3 at patch named: PLT_1 (THINP ) =-2.543786E+02*

The whole-field variable TWAL may be used to store the surface temperature on each side of the plate for output purposes.

The THINPLT object adds the following source terms to the energy (TEM1) equation:

S_{T1,m}= H_{m}A(T_{wm}-T_{1m}) (1)

S_{T1,p}= H_{p}A(T_{wp}-T_{1p}) (2)

where the subscripts m and p denote the low and high fluid sides of the plate surface, respectively; A is the cell surface area of the plate, and the H's are the fluid-side heat transfer coefficients, which are defined by:

H_{j}= St_{j}Re_{j}σ_{l,j}k_{j}/δ_{j}(3)

where the subscript j denotes m or p; σ_{l} is the laminar
Prandtl number; k is the fluid thermal conductivity; Re is the local
Reynolds number parallel to the plate; δ_{j} is the node-to-wall normal
distance; and St is the Stanton number, which is defined by:

St ≡ H/(ρC_{p}U_{r}) (4)

where ρ is the fluid density; C_{p} is the fluid specific heat;
and U_{r} is the resultant velocity parallel to the wall. For laminar
flow next to the plate, the Stanton number is calculated from
St=1/(σ_{l}Re), whereas for turbulent flow it is calculated from
the wall functions.

For IMMERSOL, the following source terms are added to the radiation (T3) equation:

S_{T3,m}= H_{r,m}A(T_{wm}-T_{3m}) (5)

S_{T3,p}= H_{r,p}A(T_{wp}-T_{3p}) (6)

where H_{r,m} and H_{r,p} are the radiative heat transfer coefficients
defined by:

H_{r,j}= 4σβ_{j}T_{3j,m}^{3}(7)

Here, the subscript j denotes the fluid-side of the plate m or p; σ is
Stefan Boltzmann's constant = 5.6704.10^{-8} W m^{-2}K^{-4}; β_{j}
is a radiative resistance term for the surface j, defined by

β_{j}=[δ_{j}{0.75(ε_{j}+s_{j})+1/G_{j}}+(1.-ε_{w,j})/ε_{w,j}]^{-1}(8)

and T_{3j,m} is the mean temperature between w and j, which is evaluated from:

T_{3j,m}^{3}=(T_{wj}^{2}+T_{3j}^{2})(T_{wj}+T_{3j})/4 (9)

In equation (8), ε_{w,j} is the wall emissivity for the surface j;
ε_{j} is the fluid emissivity (in m^{-1}); s_{j}
is the fluid scattering coefficient (in m^{-1};) and G_{j} is the
fluid-side gap distance.

Equation (9) follows from linearising the wall heat flux
q_{wj}=σβ_{j}(T_{wj}^{4}-T_{3j}^{4}) in terms of
(T_{wj}-T_{3j}), so that q_{wj}=4σβT_{3j,m}^{3}(T_{wj}-T_{3j}).

For cases with radiation, the two surface temperatures are determined from the two simultaneous equations which arise from considering the total heat transfer through the plate from one side to the other. For transient cases, the thermal capacitance of the plate is ignored. Thus,

Γ_{m}(T_{3m}^{4}-T_{wm}^{4})+H_{m}(T_{1m}-T_{wm})=C_{tp}(T_{wm}-T_{wp}) (10)

Γ_{p}(T_{wp}^{4}-T_{3p}^{4})+H_{p}(T_{wp}-T_{1p})=C_{tp}(T_{wm}-T_{wp}) (11)

where the subscripts m and p denote the low and high fluid sides of the plate
surface, respectively; and C_{tp}=k_{p}/t_{p} is the plate
thermal-conductance coefficient with k_{p} the plate conductivity and
t_{p} the plate thickness. The H's in equations (10) and (11) are the
fluid-side heat-transfer coefficients; and the Γ's are the radiative
heat-exchange coefficients, defined by:

Γ_{j}= σβ_{j}= σ/([δ{0.75(ε_{j}+s_{j})+G_{j}^{-1}}]+(1.-ε_{w,j})/ε_{w,j}) (12)

Equations (10) and (11) above can be manipulated to produce the following two
simultaneous equations for solution of the two surface temperatures T_{wm}
and T_{wp}:

f_{1}= H_{m}(T_{wm}-T_{1m})+Γ_{m}(T_{wm}^{4}-T_{3m}^{4})

+ Γ_{p}(T_{wp}^{4}-T_{3p}^{4})+H_{p}(T_{wp}-T_{1p}) = 0 (13)

f_{2}= H_{m}(T_{wm}-T_{wp})+Γ_{m}(T_{wm}^{4}-T_{3m}^{4})

+ C_{tp}(T_{wm}-T_{wp}) = 0 (14)

Equations (13) and (14) are solved for T_{wm} and T_{wp} by using Newton's method in two dimensions, i.e:

f_{1}[x,y] = 0 f_{2}[x,y] = 0 (15)

x_{k+1}= x_{k}+∆x_{k}y_{k+1}= y_{k}+∆y_{k}(16)

∆x_{k}= -f_{1}/J ∆y_{k}= -f_{2}/J (17)

J[x,y] =| ∂f_{1}/∂x ∂f_{1}/∂y | | ∂f_{2}/∂x ∂f_{2}/∂y | (18)

where x ≡ T_{wm}, y ≡ T_{wp}
and the subscript k denotes the kth Newton iteration, and J is the Jacobian matrix.

For cases without radiation, the thermal capacitance of the thin plate is included in the local heat balance for the plate, as follows:

(T_{m}-T_{W})/R_{m}=(T_{W}-T_{p})/R_{p}+(T_{W}-T_{Wo})/R_{t}(19)

where T_{W} and T_{Wo} are the effective plate temperatures
at the current and previous time steps, respectively. The thermal resistances in
the foregoing equation are defined by:

where dt is the local time step, tR_{p}=r_{p}+r_{w}(20) R_{m}=r_{m}+r_{w}(21) R_{t}=dt/(ρ_{tp}C_{p,tp}t_{p}) (22) r_{m}=1/H_{m}(23) r_{p}=1/H_{p}(24) r_{w}=t_{p}/(2k_{p})=1/(2C_{tp}) (25)

For **transient cases**, the effective plate temperature T_{W} is
determined by re-arrangment of equation (19), as follows:

T_{W}=(R_{p}R_{t}T_{m}+R_{t}R_{m}T_{p}+R_{p}R_{m}T_{Wo})/(R_{p}R_{m}+R_{p}R_{t}+R_{t}R_{m}) (26)

whereas for **steady cases**, equation (19) can be simplified to compute
the effective plate temperature from:

T_{W}=(R_{p}T_{m}+R_{m}T_{p})/(R_{p}+R_{m}) (27)

Finally, the surface temperatures of the thin plate are recovered from the following local heat-balance equations:

T_{wm}=(r_{w}T_{m}+r_{m}T_{W})/(r_{m}+r_{w}) (28)

T_{wp}=(r_{w}T_{p}+r_{p}T_{W})/(r_{p}+r_{w}) (29)

In future work the thin-plate object will be extended to allow for the thermal capacity of the plate in transient cases with radiation.

Further description of the THINPLT object is given in the PHOENICS_VR Reference Guide, TR326

(see TR218)

Integer used in GXTHRMX to denote 1st phase volumetric thermal-expansion coefficient.

Integer used in GXTHRMX to denote 2nd phase volumetric thermal-expansion coefficient.

Cause axis tick marks to be drawn on other side of axes. Revert to original by repeating TICK.

See also HELP on: AXES, BOX, FRAME

TIM is a Fortran real variable used in GROUND. It represents the current time.

---------- PIL real; group 13 -----------

TIMA... is used to specify the wave amplitude of a periodic source term. See the help and encyclopaedia entries on ???, and GXTIM for further information.

PHOENICS permits users to set the maximum clock time of a simulation calculation, by setting the PIL variable MAXSEC to the maximum allowable number of seconds.

It was introduced for the convenience of users of CHAM's pay-by-use Remote Computing Service. However, it may of course be used in stand-alone installations also.

The coding which effects this is in the open-source file:

grex3.for.

This employs the following call to an in-EARTH sub-routine:

CALL SECONDS(NUMSEC)

which returns the number of seconds of time which have elapsed since the EARTH run started to execute.

In the GREX3 sequence provided by CHAM, NUMSEC is simply compared with ISG20, in order to determine whether execution is to cease. Users who incorporate it in their own coding may well find other uses for it.

If NZ=1, and STEADY=F, it is possible to dump field values which can be plotted by PHOTON, with the time dimension replacing Z. In order to activate this feature, it is necessary only to set IDISPA > 0 in the Q1 file; then, because of the statement:

IF(.NOT.STEADY.AND.IDISPA.GT.0.AND.PNAM.EQ.' ') CALL GXPARA

in Group 19 Section 8 of GREX3.F, a call is made to subroutine GXPARA. IDISPA dictates the frequency (in terms of time steps) of dumping.

The file containing the dumped information is called PARPHI, if PHIDA=F in PREFIX, and otherwise PARADA.

The first time step at which dumping occurs is IDISPB and the last is IDISPC. However, if these are left as zero, dumping occurs for the whole time range.

(see LSTEP)

(see STEADY)

(see NPRMNT)

(see TFRAC)

(see GROUP 2)

---------------------------------------

Real flag; value=1.E-20.

TINY....a small real number, defaulted to 1.E-20 which is used in EARTH to guard against division by zero. This value may be too small for machines with short word length, and would normally be set to an appropriate value at the time of installation.

When TINY.LE.1.E-20, underflow trapping occurs at various locations in the calculation. Setting TINY to a higher value therefore saves some time, and is acceptable for most problems on most machines.

------ PIL character ---------------------

TITLE....is a special character variable which contains the character string generated by the TEXT command. Its default setting is:

NAME TITLE OF RUN HERE. MAX OF 40 CHARS.

This variable should be treated as a "read only" PIL variable. Only the TEXT command should be used to modify it.

-------------------------------------- Photon Help ----

After pressing the button, type in the title of the current frame to be saved in the PHOTON save-file.

----- PIL real; default= 1.0; group 2 --- -

TLAST....multiplier of TFRAC. If TLAST is set to GRND, EARTH visits group 2 of GROUND for a setting of the time-step size DT, rather than DT being determined from the settings of TFRAC.

See the Encyclopaedia for full details.

----------------------------------------- Photon Help ----

The last GEOMETRY element to be [DELETE]ed or turned ON/OFF.

All such objects do so by default.

Three 'tolerance' values can be set, one for each of the Cartesian-coordinate directions. By default, all three are set to 0.001 (m).

'Affecting the grid' means requiring the Satellite to create 'region' boundaries co-incident with the edges of the object's bounding box. The grid can then be specified within each region, either automatically or manually.

If the distance between two region boundaries, or a region boundary and the domain edge, is less than the tolerance in that direction, the second region boundary will not be created.

If it is desired that an object should not create region boundaries, the part of the Q1
file which pertains to it should contain:

> OBJ, GRID, NO

if the object is not to affect the grid in any direction, or

> OBJ, GRID, p,p,p

where 'p' is Y (for Yes) or N (for No) for the X, Y and Z co-ordinate directions respectively.

Tolerance values can be specified by the user either interactively or by editing the RSET(M,......) line in the Q1 file.

Judicious settings for the tolerance can help eliminate very thin 'spaghetti' cells formed when objects almost - but not quite - line up.

----------- PIL logical, default F -------

When set equal to T, TRACE switches on a primitive tracing facility in the Q1 file which functions as an aid to debugging complicated Q1 files.

After the command TRACE=T has been read, each line of PIL is written either to the VDU or to the file lupvr (depending on the PHOENICS version) with the message ... 123.45 TRACING ... prefixed to it, before it is interpreted by the Satellite.

The numerical value prefixing the line shows the current machine clock time in seconds. The line-printing procedure is switched off when the command TRACE=F is encountered.

------------------------------- Photon Help ----

The direction in which the streamlines are being tracked; it can be either UP or DOWN.

The TRANSFER object transfers sources between calculations. See the description in the PHOENICS_VR Reference Guide, TR326, and click here for more information on transferring sources.

(see GSET(T,...))

(see GROUP 2, GRDPWR, RSET) (See also TR326 Section 10, Space and Time Grids - Time)

(see STEADY=F) (See also TR326 Section 10, Space and Time Grids - Time)

The partial differential equations which govern fluid flow and heat transfer, for example those described here.

A computer works to only a limited number of significant figures. It is therefore advisable to avoid producing calculated results of the following kinds:

- Enthalpy values of the order of 1.E6, when differences of the order of 1.E1 are significant.
- Pressures of the order of 1.E5, when dynamic heads are below 1.E1.

These can be avoided by use of suitable datum levels for the enthalpy or pressure (see PRESS0) respectively, or by non- dimensionalisation.

---- PIL integer; default=1; group 22 --- -

TSTSWP....dictates frequency (in terms of sweeps, or of hydrodynamic iterations for PARAB) with which sums of the residuals of the equations solved are written to the VDU, for the purpose of on-line monitoring of the convergence path of the solution. Note that the printed quantities are divided by the RESREFs.

If TSTSWP is set to a negative number and USEGRX=T, then EARTH will activate GXMONI. This will open a graphics window and display spot values and residuals both graphically and numerically.

TSTSWP=-1 dictates that changes are displayed every sweep or iteration,

TSTSWP=-2,-3,... means that changes are displayed every 2,3... sweeps or iterations.

An example of what appears on the screen can be seen by clicking here.

Present-day computers lack the power which they would need were they required to compute the small-scale details of turbulence; therefore 'models' of turbulence have been provided which permit then to compute **some** aspects of turbulence, **sometimes** to be **approximately** computed.

The problem then becomes one of calculating the increase ratio.

The widely-used so-called 'k-epsilon' model does this by supposing that the 'effective viscosity' depends on the 'turbulence energy', k, and its rate of dissipation, epsilon, for each of which soluble transport equations have been devised.

The 'two-fluid' model and 'multi-fluid model', with which PHOENICS is supplied, are of this kind.

A broad-brush answer to which some would subscribe is:

- effective-viscosity models have a fairly-good track record for simulating hydrodynamic and convective-heat-transfer phenomena; but
- population models are best for handling combustion and radiative heat transfer.

See also PHENC entry Turmod.

This is effected when a variable named GEN1 is stored by means of STORE(GEN1) in the Q1 file, and the default print-out provisions are used. In addition, printout of the total rate of strain is effected when a variable named GENK is stored in the Q1 file.

See ENUT and

(see PRT)

---- Command; group 9 ---------------

TURMOD....command to activate a turbulence model. The syntax is:

TURMOD(model name) where model name is one of:-

LVEL KLMODL, KEMODL, KEMODL-YAP, KERNG, KECHEN, KOMODL, KOMODL-LOWRE, TSKEMO, KECHEN-LOWRE, KEMODL-LOWRE, KEMODL-LOWRE-YAP, KEMODL-2L, MIXLEN, MIXLEN-RICE, SGSMOD, REYSTRS

WARNING! TURMOD's actions begin by wiping out all prior settings of enut, el1, etc. The TURMOD command must therefore be followed by any desired EL1 settings.

TURMOD is not used for the constant-effective-viscosity model, for which it suffices to set, in the Q1 file:

ENUT = whatever value is chosen.

>>> See the PHENC entry 'Turbulence Models in PHOENICS'.

TWO-EQUATION turbulence models are those which solve two differential equations for the prediction of statistical properties of a turbulent flows, typically the "effective viscosity" and the "dissipation rate".

The most widely known model of this class is the so-called k-epsilon model, first proposed by Harlow and Nakayama.

There are many variants.

See PHENC entry: Turbulence models in PHOENICS

(see ONEPHS=F)

See PHENC entry Two-layer KE-EP turbulence model

See PHENC entry Two-scale KE-EP turbulence model

TYPE....the second argument of PATCH, used in Groups 11, 13 and 23.

The complete list of TYPEs, with their index equivalents and their significances, is provided below.

Group | TYPE | value | meaning |

11 | INIVAL | 26 | initial value |

11 | LINVLX | 27 | linear with IX |

11 | LINVLY | 28 | linear with IY |

11 | LINVLZ | 29 | linear with IZ |

---- | ------- | ----- | -------- |

23 | PROFIL | 24 | line-printer profile |

23 | CONTUR | 25 | line-printer contour |

---- | ------- | ----- | -------- |

13 | multiplier | ||

13 | CELL | 1 | 1.0 |

13 | EAST | 2 | east cell area |

13 | WEST | 3 | west cell area |

13 | NORTH | 4 | north cell area |

13 | SOUTH | 5 | south cell area |

13 | HIGH | 6 | high cell area |

13 | LOW | 7 | low cell area |

13 | VOLUME | 8 | cell volume |

13 | FREEE | 9 | free east area |

13 | FREEN | 10 | free north area |

13 | FREEH | 11 | free high area |

13 | FREEVL | 12 | free volume |

13 | PHASEM | 13 | mass of phase |

13 | RGRAD | 14 | volume-fraction gradient |

13 | OUTFLO | 15 | 1.0, or 0.0 if mass flow is inward |

13 | EWALL | 17 | area * gamma /distance |

13 | WWALL | 18 | area * gamma /distance |

13 | NWALL | 19 | area * gamma /distance |

13 | SWALL | 20 | area * gamma /distance |

13 | HWALL | 21 | area * gamma /distance |

13 | LWALL | 22 | area * gamma /distance |

13 | INFLO | 23 | 1.0, or 0.0 if mass flow is outward |

Notes:

- "Multiplier", for group 13 patches (i.e. sources and boundary conditions) signifies that by which CO * ( VAL - phi ) should be multiplied in order to create the required source;
- "gamma" signifies the near-wall value of viscosity divided by Prandtl number;
- "distance" signifies the distance from the near-wall cell centre to the wall.

wbs