2.1. Conventional Two-Phase Pressure Drop Models
The pressure drop of single-phase flow can be divided into frictional pressure drop from viscous dissipation between the fluid and the wall, gravitational pressure drop from the flow direction, and irreversible pressure drop (or form loss) from a sudden change in the flow direction or the cross-sectional area of the flow. In the case of two-phase flow, pressure loss from the interface between two phases is additionally generated. There are several methods to predict the pressure drop of two-phase flow in a pipe; pressure drop depends on the two-phase flow pattern, or how the flow pattern is assumed.
Conventional methods for predicting the frictional pressure drop of two-phase flow can be classified into the following three categories: the homogeneous flow model, the separated flow model, and the drift-flux model [
4].
The homogeneous flow model is a simple method that assumes that the velocities of the liquid and gas phases are the same, indicating homogeneous velocity; the pressure drop is estimated using a suitably defined homogenous friction factor for two-phase flow. In the homogeneous flow model, it is important to properly choose the two-phase viscosity correlation, which is expressed in terms of the quality and viscosities of both phases.
The separated flow model considers the phases to be artificially segregated into two streams. This model predicts the two-phase pressure drop by calculating the pressure drop for one of the two phases and then multiplying it by a two-phase friction multiplier (ϕ2). There are several correlations for the two-phase friction multiplier, which are usually deduced empirically.
The drift-flux model considers the relative velocity between the two phases as the most important parameter. In predicting the pressure drop, it is important to properly model the two-phase distribution coefficient and the gas drift velocity. Several models have been reported, and these usually depend on the two-phase flow pattern; Ishii’s models [
5] are widely used.
2.2. Flow Characteristics in Moisture Separator and Two-Phase Pressure Drop Model Development Strategy
The flow path from the inlet to the outlet of the moisture separator has a very complex shape. In the case of a CE-type separator, which is the subject of the present study, the flow introduced into the inlet experiences abrupt direction change when it passes through a spinner blade, and sudden flow area change when it passes through the holes in the outer wall of the separator. When passing through such a complicated flow path, even in the case of a single-phase flow, form loss is mainly expected to occur, rather than frictional pressure drop.
The form loss of single-phase flow is usually expressed in terms of a dynamic pressure component and a loss coefficient (
K), with different models depending on the type of flow path. Several widely used models exist for standardized flow paths (i.e., sudden expansion, sudden contraction, orifice, valve) [
6], but the loss coefficient for the complex flow path should be obtained in a separate experiment.
In the case of irreversible pressure drop for two-phase flow, there exist analytic models for certain standardized flow paths. However, these models are not applicable to the complex flow path through the moisture separator, and so it is necessary to use an experimental approach.
Zeghloul et al. [
7] conducted a series of two-phase flow pressure drop experiments using an orifice for the upward flow, and then compared the experimental data with the several two-phase flow pressure drop correlations. Their methodology for experimental data manipulation is briefly introduced, as follows:
They performed a single-phase test using water as the working fluid, so the ratio of the single-phase flow pressure drop to the two-phase pressure drop was defined as the ‘total liquid two-phase pressure drop multiplier (ϕLO2)’ and used for comparison with existing models.
In the present study, using an air-water experimental facility, single-phase and two-phase pressure drop tests were conducted for the CE-type moisture separator. In a manner similar to that used by Zeghloul et al. [
7], experimental data were used to obtain single-phase Euler number and two-phase pressure drop. Then, an empirical correlation of the multiplier was suggested in terms of the influential parameters.
The detailed model development procedure can be summarized as follows:
where Eu
1ϕ is the single-phase Euler number, and Δ
PA is the pressure drop of the air flow.
ρA and
jA are the air density and superficial velocity of the air flow, respectively. The superficial velocity means the volumetric flow rate divided by the cross-sectional area. In the case of the moisture separator models used in the present study, the inner diameter of the separator can was used to estimate the cross-sectional area.
Here, it is assumed that the single-phase Euler number is mutually applicable for both air and water flows.
After obtaining two-phase pressure drop experimental data, ‘total liquid pressure drop’, Δ
PLO, is calculated from Equation (2); this is the pressure drop assuming that the whole flow area is occupied by liquid with its own superficial velocity.
where
ρW and
jW are the water density and superficial velocity of water flow, respectively.
- 2.
From the two-phase pressure drop data and total liquid pressure drop estimated from Equation (2), the total liquid two-phase pressure drop multiplier is calculated as follows:
where Δ
P2ϕ is the two-phase pressure drop, which is obtained from the experiments.
- 3.
Finally, the empirical correlation of the total liquid two-phase pressure drop multiplier is established considering the effect of major variables representing the physical phenomena of the flow inside the moisture separator on the multiplier.
To verify the above methodology, a series of air-water experiments were performed using full-scale and half-scale CE-type moisture separators. In developing the empirical correlation, benchmark data in a full-scale steam-water test facility were also used.