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4.1.4 Boundary and Initial Conditions

Wall Boundaries

At wall boundaries, 'equilibrium' log-law wall functions are applied to: the velocity components parallel to the wall; the mean-flow energy and scalar variables; and EP. These conditions, which use the friction velocity as the wall-function velocity scale, are discussed in detail under the PHOENICS Encyclopaedia entry 'Wall_Functions'. As with the PHOENICS eddy-viscosity models, the wall functions take von Karman's constant k=0.41, the roughness parameter E=0.86, and the default values of the laminar and turbulent Prandtl/Schmidt numbers as unity.

For the turbulent stresses and fluxes, the default treatment is to calculate these quantities directly from their respective transport equations at the near-wall grid point. This treatment is equivalent to the 'non-equilibrium' wall-function treatment adopted for KE in the KE-EP turbulence model ( see the PHENC 'Wall_Functions' ).

The option exists in PHOENICS for the user to activate a equilibrium treatment for the turbulent stresses, in which their near-wall values are fixed by assuming that the turbulence is in local equilibrium, i.e:

u2/KE=0.65; v2/KE=0.25; w2/KE=1.1; uiuj/KE=0.255. .... (4.1)

This option is not recommended for general use, as it presumes that: v2 is normal to the wall; w2 is parallel to the wall in the streamwise direction; u2 is parallel to the wall in the lateral direction; and that sign of the near-wall shearing stress is always positive.

Planes of Symmetry

At symmetry planes, the appropriate turbulent shear stresses and fluxes should be set to zero, i.e:

at west and east boundaries - uw and/or uv, ut and uc are zero; at south and north boundaries - vw and/or uv, vt and vc are zero; at high and low boundaries - uv and/or uw, wt and wc are zero.

As will be discussed shortly, PHOENICS provides for the user to set these conditions automatically from the Q1 file.

Inlet Boundary Conditions

For each inlet boundary, values must be prescribed for the turbulent stresses and fluxes, and the dissipation, EP. If these are not known from experimental data, then a simple expedient is to define uniform inlet profiles of these quantities in terms of a representative mixing length and relative turbulence intensity, as follows:

KE,in = (VS*TI)**2 ; EP,in = 0.1643*(KE,in)**1.5/LM .... (4.2)

u2 = v2 = w2 = 2.*(KE,in)/3 .... (4.3)

where: u2, v2 and w2 are the turbulent normal stresses; TI is the relative turbulence intensity ( typically between 0.05 and 0.1 for duct flow ); and LM is the mixing length, which can be taken as 0.1*D, where D is the characteristic inlet dimension (e.g. the inlet hydraulic diameter for duct flow ).

The turbulent shearing stresses and fluxes can be taken as zero, which is consistent with a zero-gradient normal condition for these quantities, and uniform inlet profiles of the mean flow quantities. For non-uniform inlet profiles of mean-flow quantities, the inlet values can be specified via the eddy-viscosity/diffusivity concept. Thus, the Reynolds fluxes can be calculated from equations (3.9) to (3.11), and the shearing stresses from:

-uiuj = ENUT*(Ui,j + Uj,i) .... (4.4)

where ENUT is given by equation (3.12). Even more elaborate formulae may be derived and used by neglecting nett transport in the stress and flux transport equations and presuming equilibrium. However, the simple practice of assuming zero inlet values is likely to be sufficient, because the transport of these correlations is usually unimportant at inlet boundaries.

Initial Conditions

For transient simulations initial values should be set for all variables, including the turbulent stresses and fluxes.

For steady-state simulations, the initial values will not affect the final results, but they may influence the speed of convergence. The recommendation is that the turbulence field be initialised by using the method described above for the inlet boundary conditions. The possibility also exists to use as initial fields, the solution fields resulting from a KE-EP turbulence-model simulation. However, this option has not been provided as standard option in PHOENICS in so far as the user would have to introduce GROUND coding to compute the initial values of the Reynolds stresses and fluxes by way of the eddy-viscosity/diffusivity closure models just discussed above for inlet boundaries.