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

Predictions 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 three-dimensional 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=0.0361kg/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.