A method of predicting the two-phase liquid-liquid flow resistance in a horizontal pipe with a layer of metal foam

Abstract

The study reported here is experimental. Its aim was to determine the method applicable for prediction of pressure losses of an unstable two-phase liquid-liquid system flow through a horizontal pipe with a short section of the pipe containing a metal foam packing. However, the flow disturbance resulting from the presence of foam does not lead to a change in the type of the mixture (as there is no phase inversion) nor a permanent emulsification of the flow system. The calculation procedure developed in the study takes into account both the peculiarities that accompany the flow of a two-phase liquid-liquid system in an empty pipe (i.e. type of continuous phase, phase slip, hold-up), as well as geometric parameters of the foam skeleton (i.e. cell and pore dimensions, surface roughness of fibers). The results of experimental research were applied for the purposes of determining the specific form of the equations, consistent with the mathematical model adopted and described in detail in this paper. They were conducted for two foams: aluminum and nickel, which were characterized by the same degree of pore packing (PPI20). The mean dimensions of the elements forming metal foams skeletons were determined by computed tomography. The horizontal flow tube had a diameter of 10 mm and the foam packing occupied it only over a a section with a certain length. In the liquid-liquid system pumped to the pipe, the hydrophilic phase was tap water, while the hydrophobic phase was typical machine oil. The adopted range of flux changes of both liquids corresponded to the conditions at which unstable two-phase systems of the W/O, O/W and W+O type were formed in the empty pipe. The pressure loss of the flowing substance was measured in the foam layer. The values of constants and exponents of the adopted model equation were determined separately for single-phase flow and two-phase systems of various types. The results of the statistical evaluation of the performance of the developed dependencies justify their application in the design procedures of selected heat or mass transfer devices. The equations are dimensionless, and therefore, under the conditions of validity, they should also be effective for other liquid-liquid systems, other foams and flow in a pipe with a different diameter. The developed method is based on a new approach to the description of the two-phase flow resistance through the porous material filling the pipe. In addition, it concerns the flow of a liquid-liquid system, which still forms the area that has been tackled in few publications.