Turbulence Damping

In the vicinity of a large scale interface, a boundary layer develops and the flow is close to laminar. To mimic this physical phenomenon, the turbulence close to the interface needs to be damped. This is achieved by prescribing turbulence production and/or a dissipation rate near the large scale interface.

Egorov Turbulence Damping Treatment for the K-Omega Model

Following Egorov [517] and Lo & Tomasello [506], a symmetric damping procedure is used to model the interface as a moving wall for both of the phases in the interface region.

The interface turbulence damping model uses low Re treatment to prescribe the specific dissipation rate near the large scale interface:

Figure 1. EQUATION_DISPLAY

ω_{i} = B \frac{6 μ_{i}}{β^{*} ρ_{i} l_{d}^{2}}

(2317)

where:

the subscript $i$ is for the $i$ th phase for phasic turbulence or mixture for mixture turbulence.
$l_{d}$ is the large interface distance (see Interface Distance Specification)
$β^{*}$ is the turbulence model coefficient (see K-Omega Model).
$B$ is the turbulence damping constant. When the aspect ratio of the interface is too high, the turbulence damping constant $B$ must account for that factor.

To enforce

ω_{i}

as a boundary condition, a source term is added to the specific dissipation rate equation as:

Figure 2. EQUATION_DISPLAY

S_{ω} = α_{i} | \nabla α | \cdot l_{d} β^{*} ρ_{i} {(ω_{i})}^{2}

(2318)

where:

$α_{i}$ is the volume fraction of the $i$ th phase.
$| \nabla α |$ is the interfacial area density of the large interface. This property is non-zero only close to the large interface, which ensures that the source term is added for that region only.

Wall Type Turbulence Damping Treatment for the K-Omega and K-Epsilon Models

An alternative to Egorov's turbulence treatment is the use of high Re wall treatment at near-interface cells to specify turbulence quantities directly. This approach uses the Large Interface Detection model to determine one-cell thick interface. A stencil is created for each large interface cell consisting a near wall cell on each side of the interface.

When the K-Omega model is used, the specific dissipation rate $ω_{i}$ and the production rate $P_{i}$ are calculated as:

Figure 3. EQUATION_DISPLAY

ω_{i} = C \frac{u_{*, i}}{\sqrt{β^{*}} κ l_{d}}

(2319)

Figure 4. EQUATION_DISPLAY

P_{i} = \frac{ρ_{i} u_{*, i} {(u_{t, \lim, i})}^{2}}{κ l_{d}}

(2320)

When the K-Epsilon model is used, the turbulent dissipation rate $ε_{i}$ production rate $P_{i}$ are calculated as:

Figure 5. EQUATION_DISPLAY

ε_{i} = C \frac{{(u_{*, i})}^{3}}{κ l_{d}}

Figure 5. EQUATION_DISPLAY

P_{i} = \frac{ρ_{i} u_{*, i} {(u_{t, \lim, i})}^{2}}{κ l_{d}}

(2322)

(2321)

where

$C$ is the damping calibration constant.
$κ$ is the von Karman constant.
$u_{t, \lim}$ is the limited tangential velocity, calculated as $u_{t, \lim} = \min (u_{t}, u_{t, \max})$ . $u_{t, \max}$ is a user-specified maximum tangential velocity. The tangential velocity at a near cell is calculated as $u_{t} = u - u Δ α$ .
$u^{*}$ is the velocity scale (see Wall Functions).