A Review of Void Drift Models in Subchannel Analysis

Abstract

Subchannel analysis is widely used in nuclear reactor core thermal-hydraulic calculation and safety analysis. In subchannel analysis, the axial flow is usually treated as the dominant one-dimensional flow, and the lateral flow is simplified as the intersubchannel interactions and is modeled by introduction of semiempirical source terms or separate models. The accuracy of the subchannel analysis is strongly dependent on the modeling of intersubchannel interactions between adjacent subchannels. The intersubchannel interaction can be decomposed into three components: diversion cross flow that occurs due to imposed transverse pressure gradients, turbulent mixing that occurs due to stochastic pressure and flow fluctuations, and void drift that results from lateral migration of the gaseous phase (void) due to a strong tendency of the two-phase system approaching the equilibrium state of phase distribution. This critical review focuses on void drift research. Both experimental observation of the void drift phenomenon and the proposed void drift models are reviewed. The improvements and corresponding assessments of the void drift models are summarized. Following that, further improvements on the void drift model are proposed.

Keywords:

• Void drift models
• model improvements
• intersubchannel mixing
• two-phase flow

Nomenclature

$D_{H_{ave}}$ =	=	average equivalent diameter of subchannels $i$ and $j$
$D_{H_i}$ =	=	equivalent diameter of subchannel $i$
$D_{H_j}$ =	=	equivalent diameter of subchannel $j$
$D_{VD}$ =	=	void diffusion coefficient
$\bar{G}$ =	=	average mass flux of subchannels $i$ and $j$
$l$ =	=	effective mixing length
$P$ =	=	local pressure
$P_C$ =	=	critical pressure of the flow regime transition from bubbly-slug flow to annular flow
$\mathrm{P}\mathrm{e}$ =	=	Peclet number
$\mathrm{P}\mathrm{r}$ =	=	Prandtl number
$P_r$ =	=	reduced pressure (system pressure divided by critical pressure)
$\mathrm{R}{\mathrm{e}}_l$ =	=	dimensionless liquid phase Reynolds number
$S_{ij}$ =	=	gap clearance between subchannels $i$ and $j$
$\bar{U}$ =	=	average axial velocity of the two interacting subchannels
${\bar{U}}_l$ =	=	average liquid phase velocity
$V_l$ =	=	velocity of liquid phase
$V_r$ =	=	phasic relative velocity
$V_v$ =	=	velocity of vapor phase
$x_M$ =	=	quality at the slug-annular transition point
${\mathrm{\nabla }}_y$ =	=	lateral difference operator

Greek

${\alpha }_{eq}$ =	=	equilibrium void fraction
$\bar{\alpha }$ =	=	average void fraction of subchannels $i$ and $j$
${\beta }_{VD}$ =	=	void drift coefficient
$\mathrm{\Delta }{D}_{h,rel}$ =	=	relative hydraulic diameter difference
$\epsilon$ =	=	eddy diffusivity
${\left(\epsilon /l\right)}_{TP}$ =	=	void diffusion coefficient
$\theta$ =	=	two-phase multiplier
${\theta }_M$ =	=	two-phase multiplier at the slug-annular transition point
$\mu$ =	=	dynamic viscosity
${\mu }_l$ =	=	dynamic viscosity of the single liquid phase
${\rho }_l$ =	=	density of the single liquid phase
$\chi$ =	=	local quality
${\chi }_C$ =	=	critical quality of the flow regime transition from bubbly-slug flow to annular flow
${\chi }_{OSV}$ =	=	quality at the onset of significant void