Two-phase pressure drop

Fig. 33. Lockhart-MartineUi plot for two-phase pressure drop.

The two-phase pressure drop may be then be estimated from either of the single-phase pressure drops, using... 

The Loekliart and Martinelli [32] eoiTelation is employed to estimate the two-phase pressure drop in the Kenies mixer. The pressure drop... 

The two-phase pressure drop is obtained by multiplying either the liquid-phase drop by (t) or the gas-phase pressure drop by. Figure 7-23 gives the Lockhart-Martinelli correlation between X and ([t s... 

A computer program (TWOPHASE) was developed that uses the Lockliart-Matinelli correlation and determines the total pressure drop based on the vapor phase pressure drop. The total length of the unit depends on the nature of the Reynolds numher. The program also calculates the gas-liquid phase regime employing a modified Baker s map [33]. Table 7-13 gives the results of the two-phase pressure drop. 

TWO-PHASE PRESSURE DROP CALCULATION IN A PIPE LINE PIPE INTERNAL DIAMETER, inch 3.070... 

Calculate two-phase pressure drop, horizontal portions of lines. For all types of flow, except wave and fog or spray ... 

Total two-phase pressure drop, including horizontal and vertical sections of line. Use calculated... 

PTPh = Total two-phase pressure drop for system involving horizontal and vertical pipe, psi per foot of length... 

Probably the most widely used method for estimating the drop in pressure due to friction is that proposed by LOCKHART and Martinelli(,5) and later modified by Chisholm(,8 . This is based on the physical model of separated flow in which each phase is considered separately and then a combined effect formulated. The two-phase pressure drop due to friction — APtpf is taken as the pressure drop — AP/, or — APG that would arise for either phase flowing alone in the pipe at the stated rate, multiplied by some factor 2L or . This factor is presented as a function of the ratio of the individual single-phase pressure drops and ... 

CHENOWETH and Martin 20,21 1 have presented an alternative method for calculating the drop in pressure, which is empirical and based on experiments with pipes of 75 mm and pressures up to 0.7 MN/m2. They have plotted the volume fraction of the inlet stream that is liquid as abscissa against the ratio of the two-phase pressure drop to that for liquid flowing at the same volumetric rate as the mixture. An alternative technique has been described by Baroczy 22). If heat transfer gives rise to evaporation then reference should be made to work by Dukler et al 23). 

An illustration of the method of calculation of two-phase pressure drop is included here as Example 5.1. 

If air is injected so that the mixture velocity is increased to buL, then the total length of liquid slugs in the pipe will be (1 /b)l. Then, neglecting the pressure drop across the air slugs, the two-phase pressure drop — APTp will be given by ... 

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. 

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. 

Ungar EK, Cornwell JD (1992) Two-phase pressure drop of ammonia in small diameter horizontal tubes. In AIAA 17th Aerospace Ground Testing Conference, NashviUe, 6-8 July 1992 Wallis GB (1969) One dimensional two-phase flow. McGraw-Hfll, New York Yang CY, Shieh CC (2001) Flow pattern of air-water and two-phase R-134a in small circular tubes. Int J Multiphase Flow 27 1163-1177... 

Hwan and Kim (2006) investigated the pressure drop in circular stainless steel tubes with inner diameter of 244, 430, and 792 pm. These data show that mass flux strongly affects two-phase pressure drop in micro-channels of different diameters. 

In Table 6.7, C is the Martinelli-Chisholm constant, / is the friction factor, /f is the friction factor based on local liquid flow rate, / is the friction factor based on total flow rate as a liquid, G is the mass velocity in the micro-channel, L is the length of micro-channel, P is the pressure, AP is the pressure drop, Ptp,a is the acceleration component of two-phase pressure drop, APtp f is the frictional component of two-phase pressure drop, v is the specific volume, JCe is the thermodynamic equilibrium quality, Xvt is the Martinelli parameter based on laminar liquid-turbulent vapor flow, Xvv is the Martinelli parameter based on laminar liquid-laminar vapor flow, a is the void fraction, ji is the viscosity, p is the density, is the two-phase frictional... 

Quiben and Thome (2007a,b) presented an experimental and analytical investigation of two-phase pressure drops during evaporation in horizontal tubes. Experiments were performed under diabatic conditions in tubes of d = S and 13 mm in the range of vapor quality x = 0—1, mass velocity G = 70—700kg/m s, heat flux q = 6.0—57.5 kW/m. The test fluids were R-134a, R-22 and R-410A. The results... 

Qu W, Mudawar I (2002) Prediction and measurement of incipient boiling heat flux in micro-channel heat sinks. Int J Heat Mass Transfer 45 3933-3945 Qu W, Mudawar I (2004) Measurement and correlation of critical heat flux in two-phase micro-channel heat sinks. Int J Heat Mass Transfer 47 2045-2059 Quiben JM, Thome JR (2007a) Flow pattern based two-phase pressure drop model for horizontal tubes. Part I. Diabatic and adiabatic experimental study. Int. J. Heat and Fluid Flow. 28(5) 1049-1059... 

Tran TN, Chyu M-C, Wambsganss MW, France DM (2000) Two-phase pressure drop of refrigerants during flow boiling in small channels an experimental investigation and correlation development. Int J Multiphase Flow 26 1739-1754... 

Yen T-H, Kasagi N, Suzuki Y (2003) Forced convective boiling heat transfer in micro-tubes at low mass and heat fluxes. Int J Multiphase Flow 29 1771-1792 Yu W, France DM, Wambsganss MW, Hull JR (2002) Two-phase pressure drop, boiling heat transfer, and critical heat flux to water in a small-diameter horizontal tube. Int J Multiphase Flow 28 927-941... 

This matter was discussed in Sect. 5.8. For channeis of dh = 0.9-3.2 mm, the two-phase pressure drop can be caicuiated using the Lockhart-Martineiii modei with parameter C, ranging from 5 to 20. The parameter C decreases when the hydraulic diameter decreases (Zhao and Bi 2001). For channels of = 100 pm, (Kawahara et al. 2002) two-phase pressure drop can be correlated within an accuracy of 10% using the Lockhart-Martineiii model with C = 0.24. 

This method uses simple, unsophisticated, methods to estimate the two-phase pressure drop through the exchanger and piping, and the convective boiling heat transfer coefficient. The calculation procedure is set out below and illustrated in Example 12.11... 

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. 

More accurate, but more complex, methods could be used to predict the two-phase pressure drop and heat transfer coefficients. 

The tube inside heat transfer coefficients and pressure drop can be calculated using the conventional methods for flow inside tubes see Section 12.8, and Volume 1, Chapter 9. If the unit is being used as a vaporiser the existence of two-phase flow in some of the tubes must be taken into account. Bergman (1978b) gives a quick method for estimating two-phase pressure drop in the tubes of fired heaters. 

Evaluation of p and Km2 requires determination of the void fraction and the two-phase pressure drop. Crossflow is determined from the appropriate lateral momentum balance equation. The interchange due to mixing, represented by w is determined by the turbulent transverse fluctuating flow rate per foot of axial length (lb/hr ft), where... 

Baroczy, C. J., 1966, A Systematic Correlation for Two-Phase Pressure Drop, NAA-SR-Memo-11858, North American Aviation Co., Canoga Park, CA. (3)... 

Chen, J. C., and S. Kalish, 1970, An Experimental Investigation of Two-Phase Pressure Drop for Potassium with and without Net Vaporization, 4th Int. Heat Transfer Conf., Paris-Versailles. (3) Chen, J. C., et al., 1966, Heat Transfer Studies with Boiling Potassium, Nuclear Eng. Dept., Brookhaven Natl. Lab. Annual Report, BNL-50023 (S-69), pp. 52-54, Brookhaven, NY. (4)... 

Weisman, J., A. Husain, and B. Harshe, 1978, Two-Phase Pressure Drop Across Abrupt Changes and Restriction, in Two-Phase Transport and Reactor Safety, T. N. Vezetroglu and S. Kakac, Eds., Taylor Francis, Inc., Washington, DC. (3)... 

Lockhart and Martinelli divided gas-liquid flows into four cases (1) laminar gas-laminar liquid (2) turbulent gas-laminar liquid (3) laminar gas-turbulent liquid and (4) turbulent gas-turbulent liquid. They measured two-phase pressure drops and correlated the value of 0g with parameter % for each case. The authors presented a plot of acceleration effects, incompressible flow (3) no interaction at the interface and (4) the pressure drop in the gas phase equals the pressure drop in the liquid phase. 

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