∇

Description

The sorptionWallFunction is a boundary condition that provides a wall boundary condition to specify scalar/concentration gradient for turbulent and laminar flows.

The governing equation of the boundary condition is:

\[\nabla C = \frac{C^* - C_p}{\Delta_y} = \frac{F}{a \Delta_y}\]

with:

\[C^* = \frac{C_{surf}}{K}\]

and with the mass-transfer coefficient is calculated for turbulent flows:

\[a = \frac{C_\mu^{0.25} k_p^{0.5}}{y^+_{blended}}\]

or for laminar-flow and molecular-diffusion-only states:

\[a = \frac{D_m}{y_1}\]

where:

Property Description
\(\nabla C\) Gradient of concentration
\(C^*\) Wall-adjacent concentration
\(C_p\) Near-wall cell concentration
\(\Delta_y\) First-cell centre wall distance
\(F\) Flux of concentration
\(a\) Mass-transfer coefficient
\(C_{surf}\) Wall-surface concentration
\(K\) Adsorption or absorption/permeation coefficient
\(C_\mu\) Empirical model coefficient
\(k_p\) Turbulent kinetic energy in near-wall cell
\(y^+_{blended}\) Non-dimensional blended near-wall cell height
\(D_m\) Molecular-diffusion coefficient
\(y_1\) First-cell centre wall distance

References

Standard model for exponential blending (tag:FDC):

Foat, T., Drodge, J., Charleson, A., Whatmore, B.,
Pownall, S., Glover, P., ... & Marr, A. (2022).
Predicting vapour transport from semi-volatile organic
compounds concealed within permeable packaging.
International Journal of Heat and Mass Transfer, 183, 122012.
DOI:10.1016/j.ijheatmasstransfer.2021.122012

Standard model for stepwise blending (tag:F):

Foat, T. (2021).
Modelling vapour transport in indoor environments for
improved detection of explosives using dogs.
Doctoral dissertation. University of Southampton.
URI:http://eprints.soton.ac.uk/id/eprint/456709

Usage

The condition requires entries in both the boundary and field files.

Boundary file 

<patchName>
{
    type            patch;
    ...
}

Field file 

<patchName>
{
    // Mandatory entries
    type            compressible::sorptionWallFunction;
    Sc              <scalar>;
    Sct             <scalar>;
    kAbs            <PatchFunction1<scalar>>;

    // Optional entries
    laminar         <bool>;
    D               <scalar>;
    kName           <word>;
    nuName          <word>;

    // Inherited entries
    Cmu             <scalar>;
    kappa           <scalar>;
    E               <scalar>;
    blending        <word>;
    ...
}

where:

Property Description Type Required Default
type Type name: compressible::sorptionWallFunction word yes -
Sc Schmidt number scalar yes -
Sct Turbulent Schmidt number scalar yes -
kAbs Adsorption or absorption/permeation coefficient PatchFunction1<scalar> yes -
laminar Flag to calculate mass-transfer coefficient under the laminar-flow or -diffusion-only states bool no false
kName Name of operand turbulent kinetic energy field word no k
nuName Name of operand kinematic viscosity field word no nu

The inherited entries are elaborated in:

  • fixedGradientFvPatchField.H
  • wallFunctionCoefficients.H
  • wallFunctionBlenders.H
  • PatchFunction1.H

Further information

Tutorial:

  • N/A

Source code:

API:

History:

  • Introduced in version v2212