Multi-field Simulation Of The Spiral Wound Module By Finite Volume Method

Reverse Osmosis（RO）,also known as inverse osmosis,is the membrane separation process that separates solvent from solution by the driving force of the pressure difference applied across a semi-permeable membrane.It has been widely used in pure and ultra-pure water manufacture,drinking water purification,seawater desalination and other fields.The membrane module is the basic unit to realize the membrane separation process.Currently,there are three main types of membrane modules namely plate and frame module,hollow fiber module and spiral wound module.As an important part of the spiral wound module,the feed spacer not only provides the fluid channel,but also can enhance the local turbulence in the fluid channel,improve the mass transfer on the membrane surface,reduce the solute concentration on the membrane surface and thus decrease the concentration polarization on the membrane surface.Computation Fluid Dynamics（CFD）method can accurately simulate the internal flow of membrane module and provide a theoretical basis for the design and optimization of spiral wound module.In this study,the finite volume method based on Computational Fluid Dynamics was used to simulate the flow field and concentration field distributions inside the spiral wound module.Firstly,in order to find a proper balance between feed flow rate and energy penalty of the spiral wound module,the dumbbell-shaped non-uniform filament was proposed to simulate the effect of spacer mesh angle on the velocity,pressure and wall shear stress on the membrane surface in the flow channel within spiral wound module under the non-permeable wall boundary condition.The results showed that,with the increase of the spacer mesh angle,the fluid velocity in the flow channel increased and the concentration polarization near the membrane surface weakened.With the spacer mesh angle ascended from 60° to 90°,the wall shear stress on the membrane surface was enhanced by 12%and the pressure loss along the flow channel was increased by 10%。When the included angle ascended from 90° to 120°,the wall shear stress on the membrane surface was enhanced by 14%and the pressure drop along the flow channel was increased by 15%.When the feed Reynolds numbers increased from 50 to 200,the average wall shear stress on the top and bottom membrane surface of different spacer mesh angles increased by 4 times,and the pressure loss in the feed channel increased by more than 4 times.Secondly,the 3D CFD numerical model of the reverse osmosis process was established based on the solution-diffusion mass transfer mechanism.Then,the user-defined function（UDF）was adopted to simulate the formation of the concentration polarization on membrane surface through coupling the trans-membrane permeation with the membrane surface concentration.The mass transfer and energy loss characteristics in the flow channel of the spiral wound module were investigate by varying spacer mesh angle（α）,filament diameter ratios（DR,d₂/d₁）and the feed Reynolds numbers under the permeable wall boundary condition.The results showed that the pressure drop rate in the flow channel increased with the increase of the spacer mesh angle,and the pressure loss in the flow channel of the module was within the tolerable range when the spacer mesh angle is between 60° and 120°.When the filament diameter ratio reduced from 1.0 to 0.45,the pressure drop rate decreased significantly by 58.1%,the average wall shear stress on the membrane surface lowered by 38.8%,and the average concentration polarization factor on the membrane surface increased by27%.By increasing the feed Reynolds number from 50 to 200,the averaged wall shear stress on the membrane surface increased by more than 5.6 times,and the average water permeate flux increased by 18.2%.Finally,the image reconstruction and 3D reverse modeling of different types of spacer filament samples were fulfilled via micro-CT scan and were employed to analyze and compare the mass transfer and energy loss characteristics in the flow channels of spiral wound module with four different solid structures of feed spacers under the permeable wall boundary condition.The results showed that,the deviation between the theoretical predicted permeate flux of the reverse osmosis membrane and the experimentally obtained flux through cross-flow flat plate membrane filtration device was within 5%,indicating the feasibility of the mass transport simulation within the spiral wound module based on the image reconstruction and 3D reverse modeling.The energy loss in the flow channel of the membrane module was mainly concentrated at the front end of the spacer filament,and the wall shear stress and solvent permeate flux of the feed spacer A03 were significantly higher than those of the other three spacer configurations.The solvent permeation coefficient of the reverse osmosis membrane affects the solute mass fraction and the ratio of solvent permeation flux on the membrane surface.The permeation flux ratio on the membrane surface decreased by10%when the solvent permeation coefficient increased from 0.5e-11 m·Pa^-1·s^-1 to2.0e-11 m·Pa^-1·s^-1.