Wall Dryout Area Fraction

Weisman and Pei [570] postulated that, in wall boiling, a bubbly layer exists near the wall and, at DNB (Departure from Nucleate Boiling), this layer reaches a critical bubble concentration. At this concentration, liquid transport is no longer sufficient to remove the heat flux that is applied at the wall. Weisman-Pei found that the maximum value of average volume fraction was 0.82 in a bubbly layer 5.5 departure diameters thick.

A basic application of this DNB criterion to a CFD calculation, is that:

The CFD computation replaces Weisman-Pei’s analysis of radial transport.
The computed distribution of bubble volume fraction, averaged over some prescribed bubbly layer thickness, reaches some critical value.

Such a computation would not expect to use the same coefficients as the original Weisman-Pei model. Also, reassess these coefficients if alternative models are selected for the bubble departure diameter.

In Simcenter STAR-CCM+, there are three options for specifying the bubbly layer thickness for the dryout criterion:

Wall Cell—the layer thickness is the width of the grid cell next to the wall
Fixed Number of Diameters—the layer thickness is a factor of the number of bubble departure diameters
Fixed Yplus—the layer thickness is a factor of the wall turbulence scales for the vapor phase

An output field function, Bubbly Layer Volume Fraction is computed on the wall. This can be easily plotted for comparison on different grids and also used in user expressions for modeling wall dryout.

There is no justification for assuming a logarithmic profile exists for bubble volume fraction, $α_{g} (y)$ , near the wall when approaching DNB conditions. Instead, the distribution is approximated by a one-term expansion about the first cell center at distance $y_{c}$ from the wall, using the wall-normal component of the volume fraction derivative, $α_{g}'$ . This distribution can then be averaged over a layer thickness $δ$ .

Figure 1. EQUATION_DISPLAY

α_{δ} = \frac{1}{δ} \int_{0}^{δ} d y {α_{g} (y_{c}) + α_{g}' (y_{c}) (y - y_{c})} = α_{g} (y_{c}) + α_{g}' (y_{c}) (δ / 2 - y_{c})

(2122)

The simplest model for local wall dryout is that heat transfer from the wall to the vapor begins when the vapor volume fraction exceeds a specified value. At the same time, heat transfer from the wall to the liquid convection and liquid evaporation declines. This is expressed as an effective wall contact area fraction for the vapor:

Figure 2. EQUATION_DISPLAY

K_{d r y} = {\begin{matrix} 0 & α_{δ} \leq α_{d r y} \\ f (β) & α_{δ} > α_{d r y} \end{matrix}

(2123)

where:

$α_{d r y}$ is the wall dryout break-point or the volume fraction at which dryout begins
$α_{δ}$ is the vapor volume fraction averaged over the bubbly layer thickness.
$f (β)$ is the function:

Figure 3. EQUATION_DISPLAY

f (β) = β^{2} (3 - 2 β)

(2124)

Which transitions symmetrically and smoothly from 0 through 1 over $0 \leq β \leq 1$ , where $β$ is the ratio:

Figure 4. EQUATION_DISPLAY

β = \frac{α_{δ} - α_{d r y}}{1 - α_{d r y}}

(2125)

Which varies from 0 through 1 for $α_{d r y} \leq α_{δ} \leq 1$ ,

$α_{δ}$ is the vapor volume fraction averaged over the bubbly layer thickness.

The default value for $α_{d r y}$ is 0.9. This value prevents instabilities in the computation due to unintentional dryout, as it reduces the heat flux that is directed to the liquid as the amount of liquid reduces.

Weisman and Pei [570] geometrically derived a maximum vapor volume fraction of 0.82 for use in their critical heat flux model. Adjust the wall dryout break-point, $α_{d r y}$ , when studying the transition to DNB conditions.