Extension of the effectiveness-NTU Model to Liquid-to-Air Membrane Energy Exchangers (LAMEEs)

Abstract

Liquid-to-air membrane energy exchangers (LAMEEs) enable simultaneous heat and moisture exchange, with a minimal cross-contamination, between air and liquid desiccant solution by separating the streams with porous membranes that are permeable to water vapor. This thesis has two main objectives. The first objective is to identify and introduce a new set of dimensionless parameters to which the effectiveness of LAMEEs for heat and moisture exchange can be correlated. The second objective is to develop methods to predict the effectiveness of LAMEEs based on these new dimensionless parameters. The standard effectiveness-NTU model correlates the effectiveness of heat exchangers to the dimensionless parameters: number of transfer units (NTU) and heat capacity rate ratio (Cr). The standard effectiveness-NTU models is widely used in the industry as a simple method for initial design and sizing of heat exchangers, however, as a result of the coupling between heat and moisture exchange in LAMEEs, this model is not directly applicable to LAMEEs. To extend this model to LAMEEs, two new dimensionless parameters that are analogous to Cr are introduced and defined: effective heat capacity rate ratio (effective Cr) and effective mass flow rate ratio (effective m*). Furthermore, two models (termed the simplified-extended effectiveness models) are introduced as analogs of the standard effectiveness-NTU model. These models correlate the effectiveness of LAMEEs for heat exchange to the dimensionless parameters: number of transfer units (NTU) and effective Cr, and correlate the effectiveness of LAMEEs for moisture exchange to the dimensionless parameters: number of moisture transfer units (NTUm) and effective m*. To verify these models, a number of experimental data previously published for a small-scale LAMEE and also a hollow fiber membrane contactor were used. The discrepancies between the estimations of the simplified-extended effectiveness models and the experimental measurements for heat and moisture effectiveness do not exceed 16%. However, a major drawback of this method is that to calculate the new dimensionless parameters (effective Cr and effective m*), in addition to the inlet operating conditions of both the air and solution streams, the outlet operating conditions of the air stream are also required, which results in an iterative design procedure. To achieve the second objective of this thesis, a set of methods are proposed for estimating effective Cr and effective m* as a function of the inlet operating conditions of the air and solution streams and the LAMEEs' design parameters. To verify that these proposed methods result in accurate estimations, a number of previously published experimental data points and 10,000 numerical data points for different designs of LAMEEs were used. The methods developed in this thesis were used to estimate effective Cr and effective m* for these data points. Then, these estimations for effective Cr and effective m*, along with NTU and NTUm corresponding to each data point, were substituted into the simplified-extended effectiveness models to predict the changes in the temperature and moisture content of the air stream for each of the data points. The estimated changes in the temperature and moisture content of the air stream differed from the experimental measurements and numerical calculations by less than 2.1 °C and 2.8 g/kg. For comparison, the estimations provided by the standard effectiveness-NTU model for the outlet air temperature differed from the numerical calculations by up to 7.2 °C and from the experimental measurements by up to 5.1 °C.