4.2.2. Scalable Wall Functions

Scalable wall functions overcome one of the major drawbacks of the standard wall function approach in that they can be applied on arbitrarily fine meshes. If the boundary layer is not fully resolved, you will be relying on the logarithmic wall function approximation to model the boundary layer without affecting the validity of the scalable wall function approach. If you are not interested in the details of the boundary layer, then it may not be worth fully resolving it. However, if you have produced a very fine near-wall mesh to examine details of the boundary layer, then you should use the SST model with Automatic near-wall treatment to take advantage of the additional effect in the viscous sublayer.

4.2.2.1. Shear Velocity Scaling Model

You can select Shear Velocity Scaling Model to use the Marie wall function for multiphase flow.

The Marie wall function aims to improve solution accuracy by providing special treatment for turbulence at walls in bubbly/annular flows.

The settings associated with the Marie wall function normally do not require any adjustment:

  • Minimum Non Dimensional Wall Film Height and Wall Film Interface Height have no effect and should therefore not be used.

  • The remaining settings are for advanced users. Some information about those settings is provided below.

The usual near wall turbulence treatment by means of the log law of the wall

(4–13)

is not valid in the case of bubbly/annular flows. From measurements in a bubbly boundary layer at low volume fractions, Marie et al. [238] showed that the effect of buoyancy on the liquid velocity profile near the wall can be modeled with a modified law of the wall. To do so, a new (internal) variable called "Wall Buoyancy Shear Velocity Factor" is computed by a scaling function, . Variable "Wall Buoyancy Shear Velocity Factor" is then used to scale turbulence quantities that are used to compute turbulent boundary layer fluxes. In a boundary layer with bubbles, the buoyancy of the bubbles modifies the wall shear layer by modifying the standard logarithmic profile, in effect, shifting a variable in the profile. This shift is modeled via the scaling function proposed by Marie.

Variable "Wall Buoyancy Shear Velocity Factor" is used to modify the friction velocity, (see Mathematical Formulation in the CFX-Solver Theory Guide), and to scale and . The shift in the log law profile is then computed as

(4–14)

with

(4–15)

in agreement with the shift derived in Marie et al. [238].

Alternatively, the shift in the log law profile can be user-defined by using the Velocity Profile Shift option.

The "Wall Buoyancy Shear Velocity Factor" is now a primitive variable using a diffusion equation.

(4–16)

with the wall values specified through CCL as boundary conditions, enforcing a value of tending toward (default = 1) away from the walls [238]. Zero flux conditions are used at boundaries other than walls.

The following is an example of CCL that applies values of "Wall Buoyancy Shear Velocity Factor" on a boundary:

FLUID: Water
  BOUNDARY CONDITIONS:
    MASS AND MOMENTUM:
      Option = No Slip Wall
    END
    WALL BUOYANCY SHEAR VELOCITY FACTOR:
      Option = Value
      Buoyancy Shear Velocity Factor = MarieBeta
    END
  END
END

The diffusivity of the equation can be customized by using the Buoyancy Shear Velocity Factor Diffusivity option.

Use of the Marie option might modify turbulence production in the turbulence equations by adding the following terms:

  • for the k-epsilon model, or

  • for the k-omega model

In both cases, you can scale using the Turbulence Production Factor.

Wall Node Distance Factor enables you to scale the values of at the wall. Changing the specified Factor away from 1.0 is not recommended except for very advanced users.

You can select Variable Sigma to apply a set of alternative formulations that affect:

  • The calculated turbulent Schmidt number for the epsilon/omega equations,

  • The implementation of the cross diffusion term for the omega equation, when using the SST turbulence model,

  • The implementation of the first blending function for SST.