Comparison of CFD and one-dimensional Bernoulli solutions of the flow in a plate and frame ultrafiltration module in Z configuration

Abstract

Comparison of CFD and one-dimensional Bernoulli solutions of the flow in a plate and frame ultrafiltration module in Z configuration AbstractPredictions of flow and pressure distributions in one bank of a plate and frame ultrafiltration module with five channels in parallel operating in a Z configuration were predicted using (1) Bernoulli's equation and a momentum balance in one dimension and (2) a threedimensional field solution (Computational Fluid Dynamics) of the Navier-Stokes equation. CFD solutions were taken as the benchmark and used to refine the 1D model being developed to evaluate flow and pressure distributions for different operating conditions and ultimately different module configurations. The 1D model was able to provide quantitatively accurate flow distribution and qualitatively representative pressure distributions. Flow distributions increased monotonically with increasing channel number, maximum/minimum flow ratios in channels increased from 2 to 6.9 with oil (µ = 0.0361 kg/m/s) as the design cross flow velocity increased from 0.5 to 5 m/s. Pressure distributions were well predicted qualitatively but were typically 40% lower than the CFD solution in the distributor. Key to the accuracy of the 1D model were the implementation of (a) variable contraction co-efficients in the distributor orifice, (b) the 1/7th power law for velocity profiles in the plenums (c) a new approach for combining flows in the collector and (d) assuming only one half of the orifice area was being effectively used by the fluid.

Design Considerations for Plate and Frame Ultrafiltration Modules by Computational Fluid Dynamics Analysis

“…Plenum pressure distributions 1-D pressure distributions in the distributor and collector in previous work (Dal-Cin et al, 2006) where 1/3 rd of the module width was modelled agreed qualitatively with CFD predictions but generally under-predicted the overall pressure. Pressures were under-predicted to a greater extent by the 1-D model in the current work in comparison to the CFD simulations.…”

“…The effi cacy of the inlet manifold will be addressed fi rst, followed by comparisons of fl ow and pressure distributions in the 1/3 rd and full width simulations for the plate design that was used in Dal-Cin et al (2006).…”

“…For turbulent cases the RNG version of the k -ε model was used as detailed previously (Dal-Cin et al, 2006).…”

“…This results in a constant orifi ce diameter defi ned by Equation (1) for all the channels and has 10 permeating walls. Note that this was the design used in the 1/3 rd width study (Dal-Cin et al, 2006).…”

“…T his work represents the continuation of a previous study (Dal-Cin et al, 2006) where the pressure and fl ow distributions in an industrial plate and frame ultrafi ltration module were simulated. The motivation for the study was the lack of response of the module's productivity to changes in pressure and average cross-fl ow velocity during the recovery of used motor oil; fl ow and pressure maldistributions were suspected.…”