Drift Flux

To account for the kinematic effects of relative motion between the phases, the Simcenter STAR-CCM+ provides the drift flux model. The relative motion is defined using kinematic constitutive equations for the particular flow regime and thermal-hydraulic conditions.

Here, ${\bar{v}}_{dr}$ is the mean drift velocity of the vapor phase, which is defined as:

Figure 1. EQUATION_DISPLAY

{\bar{v}}_{dr} = v_{v} - j

(2940)

where $v_{v}$ is the velocity of the vapor phase and $j$ is the volume-weighted mixture velocity:

Figure 2. EQUATION_DISPLAY

j = α_{v} v_{v} + (1 - α_{v}) v_{l}

(2941)

The drift velocity can be specified using kinematic constitutive equations [637], which can be written as:

Figure 3. EQUATION_DISPLAY

{\bar{v}}_{dr} = {\bar{v}}_{dr} (α_{v}, σ, g, v_{m}, p_{m}, etc.)

(2942)

where $σ$ is the surface tension coefficient and $g$ is gravity.

Knowing the drift velocity, the volume-fraction-weighted mean velocity of individual phases can be estimated:

Figure 4. EQUATION_DISPLAY

\begin{array}{l} v_{v} = v_{m} + \frac{ρ_{l}}{ρ_{m}} {\bar{v}}_{dr} \\ v_{l} = v_{m} - \frac{{α_{v} ρ}_{v}}{(1 - α_{v}) ρ_{m}} {\bar{v}}_{dr} \end{array}

(2943)

The mean drift velocity ${\bar{v}}_{dr}$ can also be expressed as:

Figure 5. EQUATION_DISPLAY

{\bar{v}}_{dr} = \frac{[(C_{0} - 1) v_{m} + v_{dr}] ρ_{m}}{C_{0} α_{v} ρ_{v} + (1 - C_{0} α_{v}) ρ_{l}}

(2944)

where:

$C_{0}$ is a distribution factor that reflects non-uniformity in the volume fraction and velocity distribution
$v_{dr}$ is the volume-weighted mean drift velocity which could be estimated using appropriate constitutive equations.

The velocity or slip ratio $S$ between the phases can be calculated as:

Figure 6. EQUATION_DISPLAY

S = \frac{v_{m} ρ_{m} + {\bar{v}}_{dr} ρ_{l}}{v_{m} ρ_{m} + {\bar{v}}_{dr} ρ_{v} \frac{α_{v}}{1 - α_{v}}}

(2945)

Lellouche-Zolotar Correlation

These correlations were derived for tubular heat exchangers. In a bubbly, or a churn turbulent bubbly, flow regime, Lellouche and Zolotar [638] recommended the following correlations:

Figure 7. EQUATION_DISPLAY

v_{dr} = C_{2} {[\frac{(ρ_{l} - ρ_{g})}{{ρ_{l}}^{2}} \cdot σ g]}^{1 / 4} \frac{{(1 - α_{v})}^{1 / 2}}{(1 + α_{v})}

(2946)

where:

$C_{2} = 1.41$ in the tube bundle region
$C_{2} = 4.5$ above the tube bundle
$g$ is gravity
$σ$ is the surface tension coefficient

Figure 8. EQUATION_DISPLAY

C_{0} = \frac{L}{(κ_{l} + (1 - κ_{l}) {α_{v}}^{γ})}

(2947)

where:

Figure 9. EQUATION_DISPLAY

κ_{l} = κ_{0} + (1 - κ_{0}) {(ρ_{g} / ρ_{l})}^{1 / 4}

(2948)

Figure 10. EQUATION_DISPLAY

κ_{0} = {[1 + e^{- Re / 10^{5}}]}^{- 1}

(2949)

Figure 11. EQUATION_DISPLAY

L = \frac{1 - e^{- c_{l} α_{v}}}{1 - e^{- c_{l}}}

(2950)

Figure 12. EQUATION_DISPLAY

c_{l} = \frac{4.0 {p_{cr}}^{2}}{p (p_{cr} - p)}

(2951)

Figure 13. EQUATION_DISPLAY

γ = [\frac{1 + 1.57 \frac{ρ_{g}}{ρ_{l}}}{1 - κ_{0}}]

(2952)

$p_{cr}$ is the critical pressure, which has a value of $221.14 \cdot 10^{5} N/ m^{2}$ for steam and water.

Also, as recommended in [638], the value of $κ_{0}$ is bounded such that:

κ_{0} = min (0.8, κ_{0})

Re = min (Re, 1.3863 \cdot 10^{5})

The Reynolds number $Re$ is calculated as:

Figure 14. EQUATION_DISPLAY

Re = \frac{G d}{μ_{m}}

(2953)

where:

$d$ is either the equivalent hydraulic diameter inside the tube bundle or the inner shell diameter above the tubes.
$G$ is the mass flux entering the secondary-side of the generator.
$μ_{m}$ is the dynamic viscosity of the mixture