Simulation and Research of CFD on Internal Pressure Parallel Hollow Fiber Membrane Module

Membrane bioreactor (MBR) has been widely used in sewage treatment, effectively solving many long-standing problems such as solid-liquid separation. In this paper, the internal pressure parallel type hollow fiber membrane module was taken as the research object. Based on the CFD theory and method, the solid-liquid separation of the flow entering the membrane module was simulated by FLUENT software. Firstly, the geometric model of the internal pressure parallel membrane module was established by the computational fluid dynamics (CFD) preprocessor and structured meshing was performed. Then the volume fraction of suspended solid (SS) at the exit of the model was calculated by Eulerian multi-phase flow model and Phase Coupled SIMPLE algorithm. The calculation results were presented as images in the CFD post processor. In this paper, the simulation calculation for different concentrations of suspended solid showed that the volume fraction of suspended solid at the exit of the model was zero, which was consistent with the actual MBR system operating data. The simulation results indicated that the model established in this paper had higher accuracy. The model can simulate and predict the separation effect of solid-liquid two-phase flow in wastewater treatment, which has certain reference value for MBR engineering design and research.


Introduction
Membrane bioreactor (MBR) has the advantages of good effluent quality, low operating cost, strong system impact resistance, low sludge volume and high degree of automation [1][2]. The presence of the MBR membrane increases the ability of the system to separate solid and liquid, bringing about a significant increase in system effluent, water quality and volumetric loading. Due to the filtration of the membrane, the microorganisms are completely trapped in the MBR that achieves complete separation of water and activated sludge and eliminates the problem of sludge expansion in the traditional activated sludge process [3][4].
Computational fluid dynamics (CFD) is a numerical simulation tool developed with modern computer technology [5]. CFD plays an important role in fluid mechanics, momentum, heat, mass transfer and reaction, multiphase flow and some complex system research. What's more, it has been widely used as a core technology in research and development of technologies and equipment in many engineering fields such as aerospace, automotive, water conservancy, chemical and environmental  [5][6][7]. At the same time, MBR also has some problems that are difficult to solve: complex structure, variable operating conditions, difficult experimental research, high cost, long time and limited experimental results. CFD has the characteristics of less capital investment, fast calculation speed, complete information and strong simulation ability, and is not affected by the size and structure complexity of the research object [8][9][10].
MBR is one of the popular fields of sewage treatment, and has broad application prospects. At present, CFD has been widely used in structural simulation and optimization of MBR [3]. This paper built the MBR membrane module by the CFD tool and achieved the separation of solid-liquid two-phase flow. The CFD provides detailed analysis of the flow field and macroscopic diffusion of materials within the system [11][12]. This article modeled and simplified assumptions for a single filament or a part of the module geometry, reducing computational time.

Membrane Module
The membrane module is the indispensable part of the MBR. According to the structure, the membrane can be divided into four types: hollow fiber, flat, spiral and tubular membrane. The four membranes have different characteristics and the scope of application is also different. The difference is shown in table 1. Internal and external pressure MBR system. In the MBR system, the hollow fiber membrane module can be divided into an internal pressure MBR system and an external pressure MBR system according to the operation mode. Internal pressure MBR system: when the MBR system is operated, the pretreated sewage flows from one end of the hollow fiber tube. After filtration, the filtrate is out from the hollow fiber tube wall. The impurities such as SS in the sewage flow out from the other end of the hollow fiber tube.
External pressure type MBR system: the operation mode is opposite to the internal pressure type MBR system. When the MBR system is operated, the pretreated sewage flows from the hollow fiber tube wall. After filtration, the filtrate flows out from both ends of the hollow fiber tube. And the impurities such as SS are trapped on the tube wall.

Series and parallel connection MBR.
The MBR system can be divided into a series MBR system and a parallel MBR system from the connection mode.
Series MBR system: when the series MBR system treats sewage, the sewage flows through the membrane modules of each stage one by one. The filtrate is collected at the last stage membrane module.
Parallel MBR system: when the parallel MBR system is running, the sewage flows through each membrane module at the same time, and finally the filtrate is collected uniformly. These two MBR systems are equivalent.

Calculation Methods and Conditions
3.1.1. Mathematical model. When the membrane module is simulated by FLUENT software, the Eulerian bidirectional flow model is adopted. And the general form of the control equation is as follows. Mass conservation equation: Where is the volume fraction; is the density, kg • −3 ; is the average velocity vector of the qth phase, m • −1 ; q denotes the liquid phase or solid phase g.
Momentum conservation equation: Where q represents liquid phase (water) or gas phase (air); j represents three directions of x, y, z; t is time, s; is volume fraction; is flow velocity, m • −1 ; is density, kg • −3 ; is the pressure, Pa; is the viscous stress tensor, Pa; is the interphase force of the micro-element, N • −3 ; g is the gravity Acceleration, m • −2 .

Calculation conditions.
The MBR membrane module was simulated by FLUENT software for solid-liquid two-phase flow. Due to the Reynolds number was lower than 2300, the laminar flow model was selected. And the Eulerian model was used as the two-phase flow model. To simplify the calculation, the liquid phase was clean water and the solid phase was set as a suspended solid in the two-phase flow. The initial flow rate of the solid suspension phase and the liquid phase both were set to zero. The inlet boundary condition was defined as the pressure inlet, the velocity direction was perpendicular to the inlet boundary. It was assumed that the sand at the inlet had the same velocity as the water, and the outlet boundary was defined as the pressure outlet. The geometric model was segmented using a structured grid with a standard wall function. In order to make the calculation better, the sub-relaxation factor could be appropriately reduced. The convergence precision was 0.0001, and the number of single-step iterations was 2000.

CFD Modeling Process
3.2.1. ICEM CFD establishes internal pressure parallel MBR and meshing. The geometric model established by the ICEM CFD preprocessor in this paper is shown in figure 1, which represented a twostage parallel MBR system. Only the operation of a single hollow fiber membrane wire was studied on the water tank of each stage of the MBR system. The small cylinder on each membrane tube represented the small hole in the wall of the membrane tube. When the MBR system was running, the sewage flowed into the water pipe from the water inlet. After passing through the water tank of each stage, the permeate flowed out from the small hole in the wall of the membrane tube and flowed out from the outlet 1. The solid particles in the sewage were separated from the outlet 2. In ICEM CFD, there are two types of meshing: structured meshing and unstructured meshing. Structured meshing usually divides the geometric model into several quadrilaterals or hexahedrons; unstructured meshing usually divides the geometric model into several triangles or tetrahedrons. The specific method of partitioning depends on the actual situation. Because the texture distribution of the hollow fiber membrane tube is uniform, this paper used structured meshing. The circular part was Oshaped, and the final grid file was shown in figure 2. Figure 3 showed the grid quality map of the grid file, where the minimum grid quality is 0.401.

Fluent solver calculation.
In the FLUENT solver, the FLUENT model operation tree is mainly composed of solution model description, solution process control and post-calculation processing. Only the first two parts were used in this paper. The solution model description is mainly used to set the initial conditions for the calculation model. After importing the grid file into the FLUENT solver, the first step was to check the grid file for ensuring that the minimum volume was not negative. Transient solver was selected which based on the pressure in the model tree and set the acceleration of gravity. The second step was to select the physical model. Because the research object of this paper was solid-liquid separation, the Eulerian multiphase flow model was selected. The Reynolds number was calculated according to the formula (3). In the third step, water was introduced into the material library as a fluid material. The SS material was established through actual data. The fourth step set the primary and secondary phases. Since the SS was dispersed in the water, the water was the main phase and the SS was the secondary phase. In the fifth step, the inlet and outlet boundary conditions were set. In this paper, the pressure inlet was set as the inlet boundary condition. The volume fraction of SS was input in the secondary phase inlet boundary condition. The pressure outlet was set as the outlet boundary condition.
The work of setting solution model description had been completed. The setting of solution process control was performed below.   In the solution process control model tree, Phase Coupled SIMPLE algorithm was first selected as the solution algorithm, in which the gradient was set to Least Squares Cell Based. The momentum equation and the volume fraction were set to the First Order Upwind. The relaxation factor was set to remain the default. The volume fraction of suspended solids was monitored at the exit of the hollow fiber membrane coil. Finally, the model was initialized and began the iterative calculation. Figure 4 was a residual graph of the solver iterative calculation. Convergence reached at the iteration of 79 steps. Figure 5 indicated the volume fraction of suspended solid at the exit of the hollow fiber membrane tube. It was not difficult to see that the volume fraction of suspended solid at the outlet was substantially zero with the iterative calculation of the solver. The effect of solid-liquid separation is achieved.

3.2.3.
Post-processing cloud image display. This paper used CFD post-processor to perform postcalculation operation for expressing the calculation result as graphics or image. Figure 6 represented the flow of liquid water in an internal pressure parallel MBR model. It was basically consistent with the operation of the actual MBR system. Figure 7 showed the pressure cloud diagram at the XZ section of the model. Similarly, the left color bar indicates that the pressure decreases from top to bottom; on the other side of the water pipe is sealed. On the other side of the water pipeline is sealed. When sewage flows into the other side from the water pipeline, the pressure at the water pipeline seal will increase due to the reaction force at the seal, which is consistent with the principle of the actual MBR system. By observing figure 8, it found that the speed of SS at the exit was basically zero, which was basically consistent with the actual MBR system operation result. It realized the effect of solid-liquid separation and solved the problem of to simulate the internal parallel MBR system for filtering sewage.

Simulation results analysis
In order to verify the correctness and reliability of the above CFD model, this paper selected the actual MBR system operation data of a sewage treatment plant in Shijiazhuang for analysis. In the analysis processing, we selected sewage with different concentration of SS as the experimental sample. The different concentration of SS as the secondary boundary condition of the solver to calculate iteratively.

Conclusion
In this paper, the tool of CFD was used to establish the MBR system model of the internal pressure parallel membrane module. The model was applied to simulate the solid-liquid separation for the sewage entering the membrane module. Using this model, a large number of simulation calculations were performed on different concentrations of SS. Compared with the actual data in a sewage treatment plant, the comparison showed that the data obtained by the internal pressure parallel MBR model established was basically consistent with the actual data. The pressure cloud and streamline diagram of the postprocessor displayed the working condition of the MBR system, so that we could clearly observe the flow of sewage and the situation of stress in the membrane module. The simulation results indicated that the internal pressure parallel MBR model established by CFD is correct and reliable. The internal pressure parallel MBR system can be applied to the actual production of sewage treatment. Applying computational fluid dynamics to MBR system modeling and simulation is also a novel research idea and method. It can not only save a lot of MBR engineering design and engineering implementation cost, but also has certain reference value for MBR field research.