The Effect of the Oleophobicity Deterioration of a Membrane Surface on Its Rejection Capacity: A Computational Fluid Dynamics Study

High-Frequency Pulsatile Parameterization Study for the Titania Ceramic Membrane Fouling Mitigation in Oily Wastewater Systems Using the Box-Behnken Response Surface Methodology

In this comprehensive study, a seven-channel ultrafiltration (UF) titania membrane was used to investigate the impact of the pulsatile cleaning process on the crossflow filtration system. Seventeen experimental runs were performed for different operating conditions with a transmembrane pressure (TMP) varying from 0.5 to 1.5 bar, a crossflow velocity (CFV) ranging from 0.5 to 1 m/s, and pulsatile parameters within an interval varying from 60 to 120 s with a duration of 0.8 s, and collecting membrane permeate flux and volume data. The optimized operating conditions revealed that a TMP of 1.5 bar, a CFV of 0.71 m/s, and a pulsatile cycle of 85 s were the best operating conditions to reach the highest steady permeability flux and volume of 302 LMH and 8.11 L, respectively. The UF ceramic membrane under the optimized inputs allowed for an oil-rejection ability of 99%. The Box-Behnken design (BBD) model was used to analyze the effect of crossflow operating conditions on the permeate flux and volume. The analysis of variance (ANOVA) indicated that the quadratic regression models were highly significant. At a 95% confidence interval, the optimum TMP significantly enhanced the flux and permeate volume simultaneously. The results also demonstrated a positive interaction between the TMP and the pulsatile process, enhancing the permeate flux with a slight impact on the permeate volume. At the same time, the interaction between the CFV and pulsatile flow improved the permeability and increased the permeate volume.

Velocity Profile Representation for Fully Developed Turbulent Flows in Pipes: A Modified Power Law

In the design practices of many engineering applications, gross information about the flow field may suffice to provide magnitudes of the parameters that are essential to complete the design with reasonable accuracy. If such design parameters can be estimated following simpler steps, it may be possible to abandon the need to conduct expensive numerical and/or experimental works to produce them. In this work, we are interested in providing a generalized power law that depicts the velocity profile for fully developed turbulent flows. This law incorporates two fitting parameters m and n that represent the exponents of (1) a nondimensional length scale and (2) an overall exponent, respectively. These two parameters may be determined by fitting the experimental and/or computational data. In this work, fitting benchmark experimental and computational fluid dynamics (CFD) data found in the literature reveals that the parameter m changes over a relatively smaller range (between 1 and 2), while the parameter n changes over a wider range (between 1 and 12 for the range of Reynolds number considered). These two parameters (m and n) are, generally, not universal, and they depend on the Reynolds number (Re). A correlation was also developed to correlate n and Re in the turbulent flow region. In order to preserve the continuity of the derivative of the velocity profile at the centerline, a value of m equals 2 over the whole range of Re is recommended. Apart from the near wall area, the new law fits the velocity profile reasonably well. This generalized law abides to a number of favorable stipulations for the velocity profile, namely the continuity of derivatives and reduction to the laminar flow velocity profile for lower values of Re.