CFD for the optimization of spiral wound film assembly

In this paper, a conventional mesh shim for a spiral wound membrane assembly is structurally optimized by adding jet holes to achieve the jet function, and the effect of curvature on fluid flow is investigated. The three different gaskets are compared with each other and the performance of the optimized gaskets is investigated by using computational fluid dynamics (CFD) techniques and analyzed parametrically. This knowledge can be supplemented by the use of CFD techniques for spacers, whereby the geometry of the spacer can be optimized and the corresponding performance of the spiral wound film assembly can be improved.


Introduction
Spiral Wrap Module (SWM) is one of the most commonly used parts in practice and they are also the most commonly used for water treatment.In forward osmosis, due to the different membrane orientations, forward osmosis can be divided into forward osmosis (FO) schema and pressure delayed osmosis (PRO) schema.In the PRO schema, the active surface and its porous support face extraction solution, and the reverse are also true in the FO schema [1].In both modes, there is a corresponding internal and external differential polarisation, which has a varying effect on water flux [2], so improvement in water circulation is a very important goal of the positive osmosis technique [3].This has important implications for the lifetime of spiral wound membrane schema and their development.
This paper aims to establish a realistic picture of the spiral wound membrane assembly, taking into account the curvature of the spiral wound membrane assembly and the permeation factors in FLUENT, to provide a more complete picture of the spiral wound membrane assembly and to compare the performance of a bent shim with that of a non-bent shim.The study will also propose a jet shim by optimizing the conventional shim to some extent.The introduction of a jet structure will improve instability in the feed channel, creating a more desirable flow field [4].

Structure and methodology
This section describes the design of the feed shims, the boundary conditions for the simulation, and the numerical formulation.

Design of feed gaskets and flow channels
The design of the gaskets in this study takes into account the curvature factor, designing the size of the gaskets according to the FILMTEC corporation™ model XLE-4040 mow membrane, as well as the size of the radius of curvature.A simplified diagram of layer elements is shown in Figure 1.In the model XLE-4040 membrane element, the radius is 99 mm and the length is 962.7 mm.Specific dimensions in Figure 1 are shown in Table 1.All of the spacers I are designed in a CAD system using SolidWorks-related software.The spacer that takes the curvature factor into account is named the curvature jet spacer and the spacer that is used as a control without the curvature factor is named the zero curvature jet spacer (same name below).Based on the analysis of the XLE-4040 parameters above, this paper will define both shim heights as being the same as the node thickness of the commercial feed shims.Since the shims designed in this study take the curvature factor into account, both thicknesses are defined as radial thicknesses with a value of 1.2 mm, and the radius of curvature of the central curved plane of the curvature jet shim is defined as 48.9 mm to ensure a feed passage height of 1.2 mm.The angles between the shim characteristic angle, the cross fillet angle , and the incident flow angle are fixed at 45 degrees and 90 degrees (Figure 2).For curvature jet gasket, the characteristic angle, and the cross fillet angle are defined as projection angles, which is reasonable for this assumption.To ensure adequate fluid flow in the flow channel, the flow length is defined as 25 mm in both flow channels [5].

Geometric parameters of the channels.
To provide an adequate representation of the degree of curvature of the curvature jet shim, the curvature dimensionless radius, , will be defined as where R o and R i represent the outer and inner radii of the runner, respectively.According to the above equation, the degree of curvature of the fluid flow channel increases with .When is 0, the flow channel is in non-curved form, so it is a zero curvature jet gasket case.So in this study, a total of two types of are defined, respectively.As the actual flow in the spiral wound membrane is semi-permeable at both the top and bottom walls of the flow channel, it is also important to compare the difference in shear between the inner and outer walls, so this study will define the difference between the two in terms of the dimensionless shear stress , defined as: where o is shear stress in the top wall and i is shear stress in the bottom wall.According to the above equation, shear stress variance across the upper and lower walls increases with the increase, and this increase increases the degree of contamination of the membrane and the concentration polarisation (CP).

CFD simulation
The current research focuses on the calculation of stream flows in flow channels using commercial CFD.
The traffic distribution can be found by addressing the systems of the equations of motion equilibrium under appropriate boundary conditions.The steady-state fluid steam is governed by equations of motion, which are used to calculate the flow in the river channel.The programmable streak and kinetic equations of the system are as follows [6].
.(u )=0 (3) where t is the time, the moment magnitude of the field vectors; P is the pressure; denotes the velocity gradient; and Re is the Reynolds number of fluid flow.= ( is the density of the channel fluid; v i represents the average inlet velocity; d h represents the hydraulic diameter, generally defaults to the channel thickness; is the viscosity coefficient of the channel fluid.)

Influence of feed shims on pressure drop
CFD simulations were carried out for three feed spacers at the same feed rate.In a channel filled with spacer filaments, increased pressure drops due to airflow blockage by spacer wire, as a result of the resistance caused by each spacer filament.This section focuses on the pressure drop and distribution due to the two types of jet spacers and the normal spacers.Figure 3(a) depicts a comparison of the pressure drop for the three shims, and Figure 3(b) depicts pressure distribution across the centreline of the flow channel for the three shims [7].There is a certain difference between pressure drop caused by two types of jet shims at different feed rates, and the difference in pressure drop caused by two types of jet shims becomes progressively larger as the feed rate increases.As a result, the pressure drop caused by the normal shims is much higher than that caused by the two jet shims under the same conditions, which means more energy is consumed [8].At a feed flow rate of 0.188 m/s, the difference in pressure drop between the two jet shims is about 200 Pa, while the pressure drop of the ordinary shims is significantly higher than that of the jet shims, which is about 200-400 Pa.The reason for this is that the jet shims have been designed with a jet channel, which reduces the resistance to the flow of the fluid in the channel to a certain degree, and thus leads to a certain reduction in pressure drop.It can be seen that the design of the jet shim reduces the pressure drop and thus reduces the energy consumption.

Effect of shim-filled channel curvature on velocity distribution in membrane modules
Two surfaces were taken at two different radii of curvature to observe the parameter variation curves, which were used to analyze the effect of factors related to the degree of bending.Figure 4 shows the computed wall shear pressures on the inside and outside walls of curvature-containing injection shims for two feed rates.For the case of a curved channel filled with shims, it can be observed that the curvature shear distribution curve at r = 48.7 mm is higher than the curvature shear distribution curve at r = 49.1 mm, i.e.In addition, shearing stress on face of walls on inner wall are somewhat larger than those on outer wall, and this difference increases further as the feed rate of the shim-filled channel is increased (Figure 4(a)(b) relative to the feed rate of the shim-filled channel) [9].This is mainly because when arched shims fill the channel, the different degrees of curvature of the inner and outer diameters, the region of transaction between the wires and the wall adjacent to the exterior face is higher than the region of transaction adjacent to the interior face.The presence of curvature in the gasket-filled channel can lead to adding the shear forces in the vicinity of the borehole, which in turn leads to a diminution of shear stresses near the outer wall.This conclusion is also supported by Equation (2).
For the inner and outer walls of the curvature channel, it can also be observed from simulations that the wall shear value distributions for different radii of curvature also show different fractional irregularities due to curvature disturbances for the same feed velocity and boundary conditions.The fluid layer near the outer wall passes through a larger area per unit of time than the inner side, and this difference increases with the distance between the two surfaces selected, with a more pronounced phenomenon that can be observed.

Conclusion
This study uses computational fluid dynamics simulation channel radian and infiltration of packed spacers on the hydraulic flow of a helically entangled block.The curvature jet spacer flow channel with different curvature of the surface shear and velocity distribution are compared and illustrated to focus on the effect of curvature on the relevant hydraulic parameters within the flow channel, the results of which show that: Ordinary shims can produce high shear values in the wall at the thin film interface, but this is at the expense of energy consumption and the high shear can provide a good environment for bacteria to survive.The two jet shims provide thermal shear fluctuations on the plane of the body of a film, enhancing the instability of streamlining the passage of fluids in a flow path, which facilitates the removal of fouling from the membrane surface and extends membrane life.For curvature shims, the curvature factor causes the fluid to flow over different curved areas on the interior and exterior walls, which can result in different fluid shear stresses between the different layers.Generally, the outer shear values are usually greater than the inner ones, and the flow velocity distribution shows the same distribution pattern [10].

Figure 2 .
Figure 2. (a) (b) the model and geometric parameters of the zero curvature jet spacer; (c) (d) shows the model of the curvature jet shim.

Figure 3 .
Figure 3.The pressure drops at 0.188 m/s and 0.6 m/s for three shims, (b) show pressure distribution at the feed rate of 0.188 m/s respectively.

Figure 4 .
Figure 4. Distribution of shear force values for surfaces with different radii of curvature, (a) material supply speed of 0.188 m/s (b) feed rate of 0.6 m/s.