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

Ground logical.

ENUFIT....set .TRUE. by EARTH when enough slab-wise iterations (ie the outer loop at the slabs governed by LITHYD) have been performed.

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

Ground logical.

ENUFSW....set .TRUE. by EARTH at the end of the solution procedure at the last slab (or last but 1 for W1 & W2) when enough sweeps have been performed to satisfy the convergence criteria.

Real PIL variable; default= 1.E-5; group 9, sect 6 ENUL

ENUL, when positive, is the reference laminar kinematic viscosity
*nu*.
When it is set to one of the GRNDx options, this property is set by way of
the formula indicated in the following table.

ENUL = | nu = |

GRND1 | ENULA + ENULB * t1 where t1 is phase-1 temp. |

GRND2 | ENULA + ENULB * t1 + ENULC * t1 ** 2 |

GRND3 | ENULA + ENULB * t1 ** ENULC. |

GRND4 | [ENULA * (LGEN1) ** (ENULB-1.0)/2.0]/RHO |

GRND5 | [ENULA + ENULB/SQRT(LGEN1)] / RHO |

GRND6 | ENULA * t1 **1.5 /(ENULB + t1)/RHO |

Further notes are as follows:

- For the first three options, t1 is taken as equal to TEM1, if that
variable is solved. Otherwise it is deduced from the enthalpy.
- When the GRND4 option is selected,
the calculation of strain-rate squared, LGEN1, is activated automatically, but can also
be controlled by DUDX, DUDY etc.
The strain rate can be stored for plotting and printout by STORE(GENK).

Note also that the laminar viscosity MUST be stored whole-field for this option by STORE(ENUL).

Further, if this viscosity option is activated from the PROPS file, the user must set GENK=T (or DUDX, DUDY etc) explicitly.

This viscosity option is suitable for a non-Newtonian power-law fluid.

- The GRND5 option is appropriate for a non-Newtonian Bingham plastic fluid, where ENULA is the
rigidity coefficient and ENULB is the yield stress.
When STORE(BTAU) appears in the Q1 file, the local values of the magnitudes of the stress tensor are stored for plotting and printing, thereby permitting comparison with the yield stress.

As with the ENUL=GRND4 option:

- (a) the laminar viscosity must be stored;
- (b) the strain rate can be stored for plotting and printing; and
- (c) this option can be activated from the PROPS file.

- The GRND6 option dictates the use of Sutherland's formula for gases at atmospheric pressure, where t1 is the absolute
temperature in Kelvin, and the constants ENULA and ENULB take the following values:
Gas t1 range ENULA ENULB Air 280-1500K 1.46E-6 110. Ammonia 300-1000K 1.54E-6 472. CO2 300-3500K 1.56E-6 233. CO 300-5000K 1.40E-6 109. Helium all t1 1.52E-6 98. H2 300-2200K 0.65E-6 71. N2 300-5000K 1.39E-6 102. O2 300-2800K 1.65E-6 110.

>>>See also the Encyclopedia entry ' NON_Newtonian fluids'.

----- PIL real; default= 1.E-5; group 9, -

ENULA....parameter used in formulae for laminar kinematic viscosity. Further parameters of the same kind are: ENULB, ENULC.

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

ENUT sets the turbulent kinematic viscosity. Options are:

ENUT | = const. (>0) sets turb.kin.visc. | = const. | |

ENUT | =GRND1 sets turb.kin.visc. | = ENUTA + ENUTB * len1 | |

ENUT | =GRND2 sets turb.kin.visc. | = sqrt(abs(lgen1)) * len1 ** 2 | |

ENUT | =GRND3 sets turb.kin.visc. | = CMU * len1 * KE ** 0.5 | |

ENUT | =GRND4 sets turb.kin.visc. | = ENUTA * len1 * | ABS(average (V1 - V2)) * R1 * R2 |

ENUT | =GRND5 sets turb.kin.visc. | = CMU * (KE ** 2) / EP | |

ENUT | =GRND6 sets turb.kin.visc. | = CMU * (KE / VOSQ)** 0.5 | |

ENUT | =GRND7 sets turb.kin.visc. | = CMU * (KE ** 0.5) / OMEGA |

ENUT represents the contribution to the effective kinematic viscosity (E followed by Greek letter NU) made by the local turbulence (T).

The simplest representation is made by setting ENUT to a positive constant, the value
of which can be plausibly estimated from the formula:

ENUT = 0.01 * Vs * Ls , where Vs is a typical velocity, and Ls is a typical length, for
the flow and geometry in question.

ENUT may be estimated from the following formula:

ENUT = 0.035 * SQRT(FRIC/8) * REY * ENUL

where: REY is the duct Reynolds number based on the mass-averaged velocity and hydraulic diameter; and FRIC is the friction factor, which is a function of REY (the definition of which entails that REY * ENUL is the above-mentioned velocity * length product).

The following formula provides a fairly good fit to the data for turbulent flow in smooth pipes:

FRIC = [1.82 * LOG10(REY) - 1.64] ** (-2)

ENUT may be taken as approximately: 0.0012 * distance from start of layer * velocity difference across it, or as: 0.0044 * width of layer times velocity difference across it.

ENUT may be taken as approximately: 0.015 * distance from symmetry plane to jet "edge" * velocity at the symmetry plane.

ENUT may be taken as approximately:

0.01 * distance from symmetry axis to jet "edge" * velocity at the symmetry axis.

The following ENUT options have been provided in subroutine GXENUT called from GREX, and selected as indicated:

ENUT=GRND1 selects turbulent kinematic viscosity equal to, ENUTA + ENUTB * len1, where len1 denotes the mixing-length scale that pertains to the first phase fluid, calculated by means of a formula selected by setting of EL1.

ENUT=GRND2 selects turbulent kinematic viscosity equal to, sqrt(abs(lgen1)) * len1 ** 2 , ie the "generalised" Prandtl mixing-length formula, where in general the generation function lgen1 is given by: lgen1=[DUi/DXj*(DUi/DXj+DUj/DXi)]

The rate-of-strain formula is selected in the Q1 file by activating the appropriate velocity spatial derivatives for inclusion in the generation function, which is the square of the rate of strain. The available derivatives are: DUDX, DUDY, DUDZ, DVDX, DVDY, DVDZ, DWDX, DWDY and DWDZ, and they can be selected independently.

By setting GENK=T the user can activate all terms. This model, when used in combination with EL1=GRND10, serves as the Smagorinsky sub-grid-scale model for use in Large eddy simulations (LES) of turbulence (see the Encyclopaedia entry EL1).

ENUT=GRND3 selects turbulent kinematic viscosity equal to, CMU * len1 * KE ** 0.5 , ie the Prandtl-Kolmogorov formula.

ENUT=GRND4 selects turbulent kinematic viscosity equal to, ENUTA * len1 * ABS(average (V1-V2)) * R1 * R2 , for use with the two-fluid model of turbulence. R1 and R2 are the volume fractions of fluid-1 and fluid-2 respectively.

ENUT=GRND5 selects turbulent kinematic viscosity equal to, CMU * (KE ** 1.5) / EP , ie the Harlow-Nakayama formula.

ENUT=GRND6 selects turbulent kinematic viscosity equal to, CMU * (KE / VOSQ)** 0.5 , where VOSQ denotes the vorticity-fluctuations-squared.

ENUT=GRND7 selects turbulent kinematic viscosity equal to, CMU * (KE ** 0.5) / OMEGA , ie Kolmogorov's frequency model.

GXENUT also provides a modification to the turbulent viscosity for use at low Reynolds' numbers, which multiplies the nominal (high-Re) turbulent kinematic viscosity by the factor:

AMIN1(1.0 , ( A * VIST_NOM / VISL ) ** B)

where VIST_NOM denotes nominal turbulent kinematic viscosity and VISL is the laminar viscosity. Set IENUTA=6 to activate this feature, and then ENUTA and ENUTB equal to A and B respectively (suggested values are A=0.01 and B=4.0).

If these options fail to meet the user's needs, he should set ENUT=GRND and insert the appropriate coding sequence in subroutine GROUND and/or GXENUT.

See also PHENC entry: LVEL

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

ENUTA....parameter used in formulae for turbulent kinematic viscosity.

Further parameters of the same kind are: ENUTB, ENUTC.

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

ENUTB... is a constant used by GXENUT in the calculation of turbulent viscosities.

See the help on Turbulence models in PHOENICS and ENUT for further information.

wbs