New Correlation for Two-Phase Flow in 90 Degree Horizontal Elbows

Abstract

The comparison of experimental data and results obtained from four global models — homogeneous, Dukler, Martinelli and Chisholm, used to evaluate the two-phase flow pressure drop in circular 90° horizontal elbows — is presented in this paper. An experimental investigation was carried out using three galvanized steel 90° horizontal elbows (E1, E2, E3) with internal diameters of 26.5, 41.2 and 52.5 mm, and curvature radii of 194.0, 264.0 and 326.6 mm, respectively. According to the experimental results, the model proposed by Chisholm best fitted them, presenting for each elbow an average error of E1 = 18.27%, E2 = 28.40% and E3 = 42.10%. Based on experimental results two correlations were developed. The first one is the classical Chisholm model modified to obtain better results in a wider range of conditions; it was adjusted by a dimensionless relationship which is a function of the homogeneous volumetric fraction and the Dean number. As a result, the predictions using modified Chisholm model were improved presenting an average error of 8.66%. The second developed correlation is based on the entire two-phase mass flow taken as liquid and adjusted by the homogeneous volumetric fraction ratio. The results show that this last correlation is easier and accurate than the adjusted Chisholm model, presenting an average error of 7.75%. Therefore, this correlation is recommended for two-phase pressure drop evaluation in horizontal elbows.

A computational study of curvature effect on pressure drop of gas-liquid two-phase flow through 90 degree elbow

“…In order to support and validate this computational study and to find similar results that validate this CFD study, pressure drop calculations for pipes and bends were performed using Azzi and Friedel model [28], Chisholm [9] and Benbella [2] empirical models conducted on elbows for similar boundary and flow conditions. Chisholm proposed a model, that includes dimensionless parameters achieved by experimental data for two-phase flow, and prepared equation that is a combination of the homogeneous volumetric form and the Dean number [29]. A multi-phase air-water system was built and managed to validate computational study (CFD simulation) and empirical models results.…”

Experimental Investigation of Three-Phase Flow Regime Transition in a Large Diameter 90° Bend and the Resultant Pressure Drop Prediction

“…The change in the ratio of both forces changes the flow patterns in the bend and, therefore, changes the pressure drop in the flow. The Dean number given by eq 32 has been used by Silva et al 25 in their correlations, which are obtained by multiplying the Reynolds number with the ratio of the pipe diameter to the bend curvature radius. Therefore, both the dimensionless numbers can include the restriction effect of the bend successfully by considering the important factors involved during the flow through the bend.…”

“…The development of the complex flow structures and the high degree of turbulence affect the pressure drop significantly. The pressure drop across the bend is the combination of the losses that occur due to the frictional and the restriction losses offered by the bend. , If the bend is not in the horizontal plane, then the hydrostatic loss adds up to increase the pressure drop. Several researchers developed two-phase flow pressure drop models and correlations for flow through 90° bends.…”

“…The values of C and loss coefficient k have been obtained empirically as 65 and 0.58, respectively. Silva et al worked on three different R / d ratios upward vertical to horizontal 90° bends. They evaluated Dukler et al, Lockhart and Martinelli, and Chisholm, and the homogeneous model by comparing the predicted pressure drop with the experimental results.…”