Pressure Losses in Bends during Two-Phase Gas-Newtonian Liquid Flow S. N. Mandal † and S. K. Das* Department of Chemical Engineering, University of Calcutta, 92 A.P.C. Road, Calcutta 700009, India Experimental investigations have been carried out to evaluate the two-phase pressure drop across different types of bends in the horizontal plane for gas-Newtonian liquid flow. Four different Newtonian liquids were used for the experiments. Correlations have been developed to predict the two-phase friction factor as a function of various physical and dynamic variables of the system. Statistical analysis of the correlation suggests that the correlations are of acceptable accuracy. Introduction Bends are an integral part of any pipeline transport processes, and the flow patterns developed are more complex than those of straight tubes. Fluid motion in a bend is not parallel to the curved axis of the bend. As the flow enters into the bend, the centrifugal force acts outward from the center of curvature on the fluid particles. The slower moving fluid particles move along paths whose radii of curvatures are smaller than those of the faster moving particles. This leads to the onset of secondary flow such that fluid nearer the wall moves toward the inner wall while fluid far from it flows to the outer wall. Das 1,2 discussed in detail the single- phase flow through curved geometry and piping com- ponents. Two-phase flow in a straight pipe is complex, involv- ing a number of flow regimes. However, two-phase flow in a bend is always in the developing stage 3 and is more difficult to analyze than that for a straight pipe. The curvature generates a centrifugal force and causes the denser phase (i.e., liquid) to move away from the center of curvature, while the air flows toward the center of curvature. Separation of phases in this way is likely to give rise to significant slip between the phases. Studies on the bend for a two-phase flow are relatively few in numbers. Sekoguchi et al. 4 have investigated the air- water flow through a 90° bend and analyzed the two- phase pressure drop across the bend data using param- eters φ lb and X b , which are similar to the Lockhart- Martinelli 5 parameters. Maddock et al. 3 studied the flow structure during two-phase flow through different types of bends (30-90°) and concluded that the flow was in the developing region within the bend. Chisholm 6,7 developed equations for pressure drop prediction based on a two-phase multiplier for 90° and 180° bends. Experimental observations of the flow structure and pressure drop have been presented by Hoang and Davis 8 for air-water froth flow in the entrance of 180° bends. They observed that the overall loss coefficients were substantially larger than those in single-phase flow, particularly for bends with a larger radius of centerline curvature, and the flow structure was almost stratified. Norstebo 9 reported the two-phase pressure drop in pipe fittings, the 90° bend, and the return bend in the refrigeration plant. He analyzed the pressure drop data across the pipe fittings by correlating φ lb and X b in a manner similar to that of the Lockhart-Martinelli correlation. He also compared the experimental pressure drop data with the Chisholm 7 method and found a +110% deviation. Subbu et al. 10 studied the air-water flow through different U-bends, and they developed an empirical correlation for the prediction of the two-phase pressure drop. Das et al. 11 studied gas-non-Newtonian liquid flow through bends and developed an empirical equation to calculate the two-phase friction factor. Even today the data or equations for pressure loss in two- phase gas-Newtonian liquid flow through bends are meager, and the present study is an attempt to generate experimental data on pressure drop with respect to certain finite bends in the horizontal plane. Experimental Section The schematic diagram of the experimental apparatus incorporating a 180° bend is shown in Figure 1. For other bends the upstream straight portion was identical, but the downstream portion and the gas-liquid separa- tor were shifted as per bend angle. The experimental setup consisted of a liquid storage tank (0.45 m 3 ), an air supply system, a test section, a gas-liquid separator, control and measuring systems for the flow rates, pressure drops, and other accessories. The test section consisted of a horizontal upstream straight tube of 4.5 m length, a bend portion, and a horizontal downstream straight tube of 3 m length. The internal diameter of * To whom all correspondence should be addressed. E-mail: sudipcuce@hotmail.com. † Present address: Technical Teachers’ Training Institute (ER), Block FC, Sector III, Salt Lake City, Calcutta 700 091, India. E-mail: sailen•engg@hotmail.com. Table 1. Dimensions of Bends angle R (deg) radius of centerline curvature Rc (m) linear length of the bend portion Lb (m) 45 0.1195 0.13 90 0.0505 0.08 135 0.0645 0.13 180 0.1060 0.33 Table 2. Physical Properties of the Test Liquids liquid used density Fl (kg/m 3 ) viscosity μl (kN‚s/m 2 ) surface tension σl (kN/m) water 995.67 0.85 71.23 1% amyl alcohol-water solution (% by volume) 996.37 0.84 50.00 30% glycerin-water solution (% by volume) 1067.95 2.00 63.38 42% glycerin-water solution (% by volume) 1098.20 2.91 68.40 2340 Ind. Eng. Chem. Res. 2001, 40, 2340-2351 10.1021/ie0003988 CCC: $20.00 © 2001 American Chemical Society Published on Web 04/14/2001