Encyclopaedia Index

EL1

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

EL1....the mixing length-scale of the first-phase fluid. The following options have been provided in the open-source subroutine GXMXLEN, and may be selected as indicated below:

• EL1=GRND1 selects a mixing-length scale equal to,
EL1A + EL1B * XG, where XG is the distance from the west boundary to the grid node, obtained from EARTH by means of the index XG2D.

Further, if EL1C is set to a value greater than zero, the length scale is taken as the minimum of:
(EL1A + EL1B * XG) and EL1C.

This form defines the Escudier ramp function, which is suitable for use in calculations of wall boundary layers.

For this prescription the user sets:

• EL1A = 0.0,
• EL1B = 0.41 (von Karman's constant) and
• EL1C = 0.09 * boundary-layer width.

• EL1=GRND2 acts similarly to GRND1, except that the y-direction distance replaces that of the x-direction.

• EL1=GRND3 acts similarly to GRND1 and GRND2, except that the z-direction distance is used.

• EL1=GRND4 selects the mixing length scale derived from the turbulent kinetic energy and its dissipation rate, i.e.,
CD*KE**1.5 / EP .

• EL1=GRND5 selects the mixing-length scale derived from the turbulent kinetic energy and either:
• for EL1A greater than 0.5, the mean square of the vorticity fluctuations, thus:
CD*KE**0.5 / VOSQ **0.5 .
or:
• for EL1A less than 0.5, the Kolmogorov "frequency" variable omega, thus:
KE**0.5 / ( CMU) * OMEG )

• EL1=GRND6 selects the following mixing-length scale, which may be suitable for parabolic calculations of free jets:
( jet width ) * ( EL1A or EL1B )

In this formula:

• EL1A, is the mixing-length constant in the mixing-layer region of the jet and
• EL1B is the constant in the jet region of the flow.

If the jet centre-line velocity falls below the jet- discharge velocity EL1E, then EL1B is used rather than EL1A.

Suitable values for EL1A and EL1B, respectively, are:

• for plane jets, 0.07 and 0.1, and
• for round jets, 0.05 and 0.075.

The jet width is calculated at each z according to the parameters EL1C, EL1D and EL1E, as explained below for the EL1=GRND7 option.

For further details, the user should consult core-input-library cases 150 and 153, and the Fortran coding sequences in gxmxlen.htm.

• EL1=GRND7 selects the Escudier mixing-length scale in a form suitable for parabolic calculations of wall boundary layers,
min ( EL1A+EL1B*YG, 0.09*width )
where YG is measured from the south-wall boundary to the grid node, and the boundary-layer width is computed at each z in subroutine GXLEN.

The width calculation is made in accordance with the user settings for:

• EL1C (the fraction of the maximum velocity difference),
• EL1D (the free-stream velocity) and
• EL1E which is set to
• 0.0 for a boundary layer, or to
• the jet-discharge velocity for a free jet.

The coding for the width calculation presumes NX=1; and the user sets EL1A=0. and EL1B=0.41 (von Karman's constant).

• EL1=GRND8 selects Nikuradze's mixing-length scale, in a form suitable for 2-dimensional channel and pipe flows, namely:
0.14*YVLAST - 0.08*YG**2/YVLAST - 0.06*YG**4/YVLAST**3,
where YG is measured from the symmetry axis to the grid node.

This form of Nikuradse's expression is suitable for flows with a plane or axis of symmetry and with the wall located at the north boundary.

The user sets:

• EL1A=0.14*YVLAST,
• EL1B=-0.08/YVLAST and
• EL1C=-0.06/YVLAST**3.

• EL1=GRND9 selects Nikuradse's mixing-length scale in a form suitable for 2d channel flows with a wall located at the north AND south boundaries,
0.4*YG - 0.88*YG**2/YVLAST + 0.96*YG**3/YVLAST**2 - 0.48*YG**4/YVLAST**3,
where YG is measured from the south-wall boundary to the grid node.

• EL1=GRND10 is used to select all other length-scale formulae according to the setting of EL1E, as follows:
• EL1E=0.0 selects a length scale suitable for use in the Smagorinsky subgrid-scale (SGS) eddy-viscosity model:
MIN(EL1A*H,EL1B*WDIS)
with H=SQRT[(DX**2+DY**2+DZ**2)/3.0], where:
• EL1A is Smagorinsky's constant (typically=0.17);
• H is a representative grid interval;
• DX, DY and DZ are the local mesh widths in the different coordinate directions;
• EL1B is a constant (typically 0.41); and
• WDIS is the minimum wall distance, the calculation of which is activated by the PIL command DISWAL.

The SGS model may be activated by:
TURMOD(SGSMOD),
which is equivalent to:

• ENUT=GRND2,
• EL1=GRND10,
• GENK=T,
• EL1A=0.17,
• EL1B=0.41 and
• DISWAL.

The minimum function is not applied if DISWAL is not set, or if EL1B=0.0, in which case the length scale reduces to EL1A*H.

For more details see the PHENC entry: SUBGRID-SCALE turbulence model.

• EL1E=1.0 selects the mixing-length scale of Geary and Rice
(AIChE Journal, Vol.36, No.9, p1339) for bubbly two-phase flows:
(CFIPB/EL1A)*rd/{rd,av},
where:
• CFIPB=bubble diameter (see the option CFIPS=GRND7 of the Encyclopaedia entry CFIPS);
• EL1A is a correction factor for bubble deformation;
• rd is the void fraction of the dispersed phase; and
• {rd,av} is the area-averaged value of rd at the current Z slab.

The implementation presumes that z is the main flow direction.

The model is suitable for the simulation of bubble column reactors; and it presumes that bubble-induced turbulence dominates shear-induced turbulence.

• For the options EL1=GRND1, GRND2 and GRND3, the facility exists for the distances XG, YG and ZW to be replaced by the minimum wall distance, the calculation of which is activated by the PIL command DISWAL.

• For low-Reynolds-number flow regions next to walls, Van Driest's damping modification is provided as an extension to the y-direction mixing-length expressions EL1=GRND2, GRND7, GRND8 and GRND9.

The damping modification takes the form:
LM = LM0*(1.-EXP(Y+/A+) ,
where:

• LM0 is the unmodified mixing length,
• Y+=UTAU*YG/ENUL,
• A+=26.0,
• UTAU is the friction velocity at the wall ( = SQRT(TAUW/RHO) ) and
• ENUL is the laminar kinematic viscosity.

Van-Driest damping is activated by setting IENUTA=5 in the Q1 file and using GRND2 as the COefficient in the velocity COVALs used for the wall-friction PATCHs.

For more information on Van-Driest damping and low-Reynolds-number turbulence modelling in general, the user is referred to the Encyclopaedia entries provided under LOW-REynolds-number turbulence models and VAN-Driest damping model.

• 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 EL1=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, wherafter 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.

EL1A

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

EL1A....parameter used in phase-1 length-scale formulae. Further parameters of the same kind are: EL1B,EL1C.

EL1D

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EL1D... is used to specify the first-phase free-stream fluid velocity in certain turbulence model options. See the help and encyclopaedia entries on TURBUL, and GXLEN for further information.

EL1E

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EL1E... is used to specify the first-phase nozzle-discharge velocity in certain turbulence model options. See the help and encyclopaedia entries on TURBUL, and GXLEN for further information.

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