TWO-DIMENSIONAL Mathematical Model of FLows In Thin film Composite Membranes
Aatma Maharajh1, Prakash Persad2, Denver Cheddie3 and Edward Cumberbatch4
1,2,4 Design and Manufacturing Systems, The University of Trinidad and Tobago, Trinidad and Tobago
3 Utilities Engineering Group, The University of Trinidad and Tobago, Trinidad and Tobago
1Email: aatma.maharajh@utt.edu.tt *(Corresponding author)
2Email: prakash.persad@utt.edu.tt
3Email: denver.cheddie@utt.edu.tt
4Email: edward.cumberbatch@utt.edu.tt
Abstract:
Mathematical modelling of reverse osmosis membranes has evolved from simplified one-dimensional simulations to complex three-dimensional simulations using CFD based techniques. These models have been useful in simulating solute and solvent flows across the membrane, the development of the concentration polarisation layer and the effects of spacer and spacer geometry as some examples. Various simplifying assumptions are, however, made in the modelling process that limit their extension to the specific application of directly-coupled wave powered desalination. These include the treatment of the membrane and use of rejection coefficients for solute transport. The model presented in this paper addresses some of the limitations imposed currently on available models. Fully coupled mass-momentum equations are specified for the hydrodynamics within the feed, membrane and permeate channels. Semi-empirical relationships are developed to account for the effects of inlet pressure, cross-flow velocity and inlet concentration on solvent and solute flows across the membrane. The model is validated against published experimental data and the predicted errors for simulations of solvent and solute flows were found to be 0.6% and 0.7% respectively. The effects of three feed spacer types, submerged, cavity and zigzag, on solvent and solute flows are then considered. Larger wall shear stress was seen for the submerged type spacer than for either cavity or zigzag types.
Keywords: Computation Fluid Dynamics, Concentration Polarisation, Diffusion Coefficients, Reverse Osmosis, TFC membranes
https://doi.org/10.47412/GAEH3878
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