Pressure drop homogenous model

The homogeneous mixture model is the simplest method for ealculating the frictional two-phase pressure drop, and has been found by Ungar and Cornwell (1992) to agree reasonably well with their experimental data representing the flow of two-phase ammonia in channels with d = 1.46—3.15 mm. 

Fig. 5.27 Model-predicted pressure drops normalized with experimentally measured pressure drops for a circular test section (Triplett et al. 1999b). Model predictions represent the homogeneous wall friction model. Reprinted from Triplett et al. (1999b) with permission...

The two-phase pressure drop was measured by Kawahara et al. (2002) in a circular tube of d = too pm. In Fig. 5.30, the data are compared with the homogeneous flow model predictions using the different viscosity models. It is clear that the agreement between the experimental data and homogeneous flow model is generally poor, with reasonably good predictions (within 20%) obtained only with the model from Dukler et al. (1964) for the mixture viscosity. 

A new approach was developed by Lee and Mudawar (2005a) to improve the accuracy of pressure drop prediction in two-phase micro-channels. Since the bubbly and churn flow patterns are rarely detected in high-flux micro-channel flow, the separated flow model was deemed more appropriate than the homogeneous. 

Bowers and Mudawar (1994a) performed an experimental smdy of boiling flow within mini-channel (2.54 mm) and micro-channel d = 510 pm) heat sink and demonstrated that high values of heat flux can be achieved. Bowers and Mudawar (1994b) also modeled the pressure drop in the micro-channels and minichannels, using the Collier (1981) and Wallis (1969) homogenous equilibrium model, which assumes the liquid and vapor phases form a homogenous mixture with equal and uniform velocity, and properties were assumed to be uniform within each phase. 

Estimate the two-phase pressure drop though the tubes, due to friction. Use the homogenous model or another simple method, such as the Lochart-Martenelli equation see Volume 1, Chapter 5. 

At tube exit, pressure drop per unit lengths, using the homogeneous model homogeneous velocity = G/pm = 237/66.7 = 3.55 m/s Viscosity, taken as that of liquid, = 0.12 mN sm 2... 

Later, Weisman et al. (1978) also found that assuming homogeneous flow everywhere provided nearly as good a correlation of the data as the slip flow model. The total pressure drop across a contraction can be approximated by... 

The homogeneous flow model and the separated flow model may be used to estimate the pressure drop for the churn regime but the former is not recommended for use with annular flow. The separated flow model of Martinelli and Nelson (1948), and developments thereof, may be used for annular flow. 

Air and water flow at 8 x 10 3 kg/s and 0.4 kg/s upwards in a vertical, smooth-wall tube of internal diameter dt = 20 mm and length L = 1.3 m. Using the homogeneous flow model, calculate the pressure drop across the tube (neglecting end effects). The fluids are at a temperature of 20 °C and the expansion of the air may be assumed to be isothermal. The exit pressure is 1 bar. 

Integration of equation 7.81 to determine the pressure drop over a length of pipe generally requires a stepwise procedure. As with the homogeneous model, in some cases simplifications may be possible ... 

It should be noted that the frictional drop was calculated by subtracting the hydrostatic head and acceleration losses from the measured total pressure-drop where void data were lacking, a homogeneous flow model was assumed. This modification of X by use of the Froude number appears very similar to the technique used by Kosterin (K2, K3) for horizontal pipes, in which the equivalent of volume-fraction of gas flowing, with mixture Froude number as the correlating parameter. 

Assume that the fibers in a filter are cylindrical they are parallel to each other and are uniformly assembled. Consider cake filtration in which particles are collected with the deposited particles forming a layer of porous structure as shown in Fig. 7.13(a). Thus, to account for the total pressure drop, three basic flow modes are pertinent (1) flow is parallel to the axis of fibers (2) flow is perpendicular to the axis of the cylinder and (3) flow passes through a layer of a homogeneous porous medium. In the analysis of the first two modes given later, Happel s model [Happel, 1959] is used, while for the third mode, Ergun s approach [Ergun, 1952] is used. 

Related Calculations. Homogeneous flow method. Two-phase flow pressure drop can also be calculated using a homogeneous-flow model that assumes that gas and liquid flow at the same velocity (no slip) and that the physical properties of the fluids can be suitably averaged. The correct averages are... 

Triplett et al. (1999) measured pressure drop and void fraction in minichannels with air-water adiabatic flows. They observed bubbly, churn, slug, slug-annular and annular flows as in conventional tubes, but the transitions were very different. Moreover they highlighted that the homogeneous model best predicted their pressure drop measurements for every flow conflguration except the annular one. 

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