Heat Transfer 1Feb 01, 10 pages doi:
The conservation equations for two-phase flow are a subset of those for Multiphase Flow.
Full derivation of the conservation equations is given in the article Conservation Equations, Two-Phase. For the purposes of this article, we shall use simplified forms of the momentum equations which apply to ducts of constant cross section and for steady state flow.
Extensive background information on the subject of pressure drop is given by Hewitt and a review of pressure drop in orifices, valves, bends and fittings is given by Hewitt Homogeneous Model The simplest approach to the prediction of two-phase flows is to assume that the phases are thoroughly mixed and can be treated as a single-phase flow.
This homogeneous model see Multiphase Flow will obviously work best when the phases are strongly interdispersed i. The three terms on the right-hand side of Eq.
Thus 3 The frictional pressure gradient term in the homogeneous model is often related to a two-phase friction factor fTP as follows: There are some difficulties in defining the latter; a whole variety of forms being suggested in the literature. These are exemplified by the relationship: In fact, though, the homogeneous model departs grossly from experimental data and simply readjusting the definition of viscosity has been found to be totally inadequate in bring agreement.
Many authors have suggested empirical modifications of the friction factor to take account of the two-phase nature of the flow. Perhaps the most widely used of these corrections to the homogeneous model is the correlation of Beggs and Brillwhich corrects the homogeneous model for both flow regime and tube inclination.
However, the preferred option has been to work using the separated flow model, or alternatively, phenomenological models. The separated flow momentum equation reduces, for a duct of constant cross sectional area and steady flow, to: As will be seen from the above equations, calculation of the latter two terms accelerational and gravitational requires, in contrast to the homogeneous model, a value for the void fraction.
Thus, to use the separated flow model, a void fraction correlation has to be invoked see Void Fraction.
Pressure drop multipliers are then defined as follows: Although still widely used, the Lockhart-Martinelli correlation has the disadvantage that it fails to predict adequately the effect of mass flux and other parameters and a whole variety of more sophisticated correlations have been produced as replacements see Hewitt, Typical of these more recent correlations is that of Friedel whose correlation is given by: Correlation of Lockhart and Martinelly Notes.
The use of different gas and liquid phase densities and void fraction at the inlet and outlet is optional; the outlet densities and void fraction will be assumed to .
An expression is obtained for void fraction in two-phase flow based upon a simple physical model. The model assumes an annular flow regime with a liquid phase and a homogeneous mixture phase flowing with equal dynamic head. Excellent correlation is obtained with a wide range of experimental data.
I had used a previous reprint (~ ), titled "Chemical Engineering aspects of two phase flow", where concepts and correlations of two phase flows (horizontal and vertical) were presented.
2. A comment on post No 3: Method of Lockhart and Martinelli is not applicable to laminar flow only.
The model assumes an annular flow regime with a liquid phase and a homogeneous mixture phase flowing with equal dynamic iridis-photo-restoration.coment correlation is obtained with a wide range of experimental data, indicating a significant improvement over current methods.
The two-dimensional correlation (4) for the liquid phase compressibility is approximately valid for pressures between 1 bar and bar and for temperatures from 10 to °C (compressed liquid). It is not valid for values larger than °C, because the error.
() developed a two-phase correlation for turbulent flow (ReSL > ) in vertical pipes. The correlation was curve fitted using four fluid combinations (water-air, silicone-air, water-helium, and water-freon 12) in vertical pipes. The four sets of.