Two-phase flow friction factor

The flow friction of a channel having subcooled local boiling behaves in a manner similar to the flow friction of a channel having a rough surface. From air-water data obtained at low void fractions (Malnes, 1966), the two-phase flow friction factor without bubble departure was found (Tong, 1968b Thorgerson, 1969)to be... 

Step 4. Calculate the two-phase-flow friction factor /TP. First it is necessary to define /Tp from f . In charting fn>lf, against X, Dukler applied the following published equation for fa ... 

Once RL is calculated, two phase flow friction factor, fm, is calculated by following equation fm = tt fx (161)... 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

Annular flow. In annular flow, as mentioned in Section 3.4.6.1, modeling of the interfacial shear remains empirical. For adiabatic two-phase flow, Asali et al. (1985) suggested that the friction factor, fjfs, is dependent on a dimensionless group for the film thickness, 8+, as defined in Eq. (3-136), and the gas Reynolds number, Rec ... 

Taking the reference liquid mass flux to be the same as that for the two-phase flow (GL = Gm) and the friction factors to be the same (/L = /m), then... 

All quantities in equation 7.64 can be readily evaluated with the exception of the friction factor. There are several approaches to estimating the friction factor for two-phase flow. 

As an example of method 3, in bubbly flow with a low quality it would be appropriate to calculate the friction factor based on the properties of the liquid. The frictional component of the pressure gradient for the actual two-phase flow is given by... 

If the approximation is made that the friction factor for the two-phase flow / is equal to that for the hypothetical liquid flow fLO, a very simple relationship is obtained between the frictional pressure gradients for the two flows ... 

Making the approximation that the value of the friction factor for the two-phase flow is equal to fLO> the frictional component of the two-phase pressure gradient is given by... 

Lockhart and Martinelli (1949) used only liquid and only gas reference flows and, having derived equations for the frictional pressure gradient in the two-phase flow in terms of shape factors and equivalent diameters of the portions of the pipe through which the phases are assumed to flow, argued that the two-phase multipliers and 4>g could be uniquely correlated against the ratio X2 of the pressure gradients of the two reference flows ... 

The basic assumptions implied in the homogeneous model, which is most frequently applied to single-component two-phase flow at high velocities (with annular and mist flow-patterns) are that (a) the velocities of the two phases are equal (b) if vaporization or condensation occurs, physical equilibrium is approached at all points and (c) a single-phase friction factor can be applied to the mixture if the Reynolds number is properly defined. The first assumption is true only if the bulk of the liquid is present as a dispersed spray. The second assumption (which is also implied in the Lockhart-Martinelli and Chenoweth-Martin models) seems to be reasonably justified from the very limited evidence available. 

This can be converted to a velocity head loss, 4fL/D, assuming that the friction factor, 4f, is approximately equal to 0.02 for two-phase flow. It can then be added to the head loss for the two bends. 

In view of the many other uncertainties of two phase flow correlations, the friction factors are adequately represented by... 

ICI recommends a safety factor of 1-2 on flow or area. The safety factor associated with the inaccuracies of the flow calculation will depend on the method used, the phase nature of the flow, and the pipe friction. For two-phase flow, use a safety factor of 2 to account for friction or static head. 

Another possibility for the investigation of the pressure drop in two-phase flows exists in the determination of the frictional pressure drop of the gas and the liquid, under the assumption that the total mass of the fluid would be flowing through the tube either as liquid or as gas. In this case the factors L0 and 4>G0 are defined... 

A particularly simple and frequently used method comes from Lockhart and Martinelli [4.84], It is based on measurements of air-water and air-oil mixtures in horizontal tubes at low pressure. However the procedure has also proved itself in upward, vertical flow of two-phase single and multicomponent mixtures. The basic idea of the Lockhart-Martinelli method is that the frictional pressure drop in a two-phase flow can be determined, with use of a correction factor, from the frictional pressure drop in the individual phases. This means that the two-phase multipliers and are defined according to (4.127) and (4.128). 

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