Steady three dimensional flow and mass transfer analyses for brackish water desalination by reverse osmosis membranes Ali E. Anqi a,b , Nawaf Alkhamis c , Alparslan Oztekin a,⇑ a Lehigh University, Dept. of Mechanical Engineering & Mechanics, USA b King Khalid University, Dept. of Mechanical Engineering, Saudi Arabia c King Abdulaziz University, Dept. of Mechanical Engineering, Saudi Arabia article info Article history: Received 8 November 2015 Received in revised form 22 May 2016 Accepted 23 May 2016 Keywords: Desalination Reverse osmosis Membrane performance Computational fluid dynamics Mass transfer abstract Reverse osmosis has been emerged as one of the most used technologies to desalinate water. Present study investigates steady three dimensional flows and mass transfer in the feed channel for a brackish water desalination process by using reverse osmosis membranes. Flow and the mass transfer in the feed channel are governed by Navier–Stokes and mass transport equations. The channel containing cylindrical shaped spacers is bounded by membranes. Computational fluid dynamics simulations are conducted for the range of the Reynolds number 100 6 Re 6 800. The laminar flow model is employed when Re ¼ 100 while SST k—x turbulence model is employed when Re P 400. Membranes are treated as a functional surface where water flux is determined from local concentration and pressure by employing the solution-diffusion model of the reverse osmosis. The influence of three dimensional flow structures on the concentration polarization and the potential fouling over the membrane surface is discussed. It is shown that high water flux regions and low concentration regions coincide with low wall shear regions. The high intensity concentration polarization sites correlates directly with the high potential fouling sites. Spacers enhance the membrane performance and they help to alleviate concentration polarization. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction Reverse Osmosis (RO) is one of the leading technologies in fresh water production worldwide. The process requires an applied pres- sure higher than the osmotic pressure caused by dissolved salt. The semi-permeable membrane allows water to pass through while it blocks the passage of dissolved salt ions through the membrane. The membrane permeability and the salt rejection rate influence the membrane performance directly. Pure water production rate increases as the membrane permeability and the salt rejection rate increase. Recent RO membranes are built with higher permeability and nearly 100% salt rejection rate. Such a high water passage rate through membranes and the high salt rejection rates cause salt accumulations at the surface of the membrane. This well-known phenomenon is referred to as concentration polarization or con- centration boundary layer. The concentration polarization at the membrane surface increases the osmotic pressure in the feed chan- nel. As a result, the applied pressure needs to be increased to keep the water passage through the membrane at the same rate. Furthermore, it is well-documented that the concentration polarization is a leading cause of scaling and fouling at the membrane surface [1,2]. The scaling and fouling reduce the process efficiency and shorten the membrane life [1,2]. Spacers are placed between the membranes in the feed channel to keep the membranes a part and to enhance the membrane performance by promoting the momentum mixing and reducing the concentra- tion polarization at the membrane surface. Flows past cylinders confined in a channel have been studied extensively. Some of the findings relevant to the present study are summarized here. Chakraborty et al. [3] documented that the drag coefficient decreases as the Reynolds number (Re) increases, and the drag coefficient increases as the blockage ratio increases at fixed Re. Kanaris et al. [4] reported that the transition from two-dimensional to three-dimensional flows occurs at about 180 < Re < 210 in flows past cylinder with a blockage ratio of 1/5, where Re is based on the centerline velocity and cylinder diameter. Rehimi et al. [5] reported that the onset of the vortex shedding occur at Re ¼ 108 and the onset of transition from two dimensional to three dimensional flow occurs at Re ¼ 159 in flows past a cylinder with a blockage ratio of 1/3. Griffith et al. [6] reported that the flow transitions occur at lower value of Re when the blockage ratio is increased to 1/2. The present paper focuses on the effect of such flow transitions on the membrane performance, http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.05.102 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: alo2@lehigh.edu (A. Oztekin). International Journal of Heat and Mass Transfer 101 (2016) 399–411 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt