Two phase flow fundamental (vapor-liquid, gas-liquid) ● Static quality, is the fraction of vapor in a saturated mixture. No flow or closed system.
g
g g st g l g g l l M A x M M A A ρρρ==++
● Flow quality, or vapor quality in two phase flow, it’s convenient to use flow quality instead of the static quality. Open system. g g g g g l g g g l l l m u A x m m u A u A ρρρ==++
● Thermodynamic equilibrium quality (thermodynamic vapor quality). It can be used only for single-component mixtures (e.g. water with steam), and can take values x<0 (for sub-cooled fluids) and x>1 (for super-saturated vapours)
m l g l
h h x h h -=- All of the quality above coincide if the two phases are at thermodynamic equilibrium (i.e. HEM). Once taking subcooled boiling model into consideration, the thermodynamic equilibrium quality is not equal with flow quality.
● The void fraction
i. T he fraction of the channel volume that is occupied by the gas phase. This void fraction is known as the volumetric void fraction.
g
V g l V V V α=+
ii. T he fraction of the channel cross-sectional area that is occupied by the gas phase. This void fraction is known as the cross-sectional void fraction. It is the widely utilized void fraction definition.
, g
A g l A or A A αα=+
iii. T he local void fraction refers to that at a one single point or very small volume. Therefore it takes the values of 1 or 0.
● Phase velocity and superficial velocity
Superficial velocity is a hypothetical flow velocity calculated as if the given phase or fluid were the only one flowing or present in a given cross sectional area. The velocity of the given phase is calculated as if the second phase was ignored. In engineering of multiphase flows and flows in porous media, superficial velocity (j ) is commonly used, because it is the value which is unambiguous, while real velocity is often spatially dependent and subject to many assumptions.
e
,(1)(1)phas phase phase phase phase g g l l
l g l g
Q Q u j A A
j u j u j j j u u αααα====-=+=-+， ● Drift velocity of gas phase with respect to the volumetric center of the mixture: gj g V u j =-
求孔隙率模型
● Homogeneous equilibrium model (HEM)
111()g s
x x αρρ=-+ The velocity ratio is a concept utilized in separated flow types. Introducing the idea
into the HEM void fraction equation results in
111()g s
x S x αρρ=-+ Where Slip ratio, or velocity ratio is the ratio of the velocity of the vapor phase to the velocity of the liquid phase. (g
l u S u =)
With slip void fraction model, the cross-sectional void fraction and volumetric void fraction is derived:1
(1)V S α
ααα=+-。