MODELING OF HOLLOW FIBER TRANSVERSE FLOW

MODULES USING CFD Alexandre PAZOS COSTA, Christian JORDAN, Anton FRIEDL, Michael HARASEK

Institute of Chemical Engineering, Vienna University of Technology

Getreidemarkt 9/166, 1060, Vienna, Austria Phone: +43-1-58801/15925. Fax: +43-1-58801-16699

e-mail: mharasek@mail.zserv.tuwien.ac.at

Abstract This work was conducted in collaboration with GKSS Forschungszentrum and TU-Wien (Vienna University of Technology), in order to find the optimal configuration of a hollow-fiber membrane module with the application of computational fluid dynamics. This module is used in a humidification /dehumidification system. The simulated hollow-fiber module is composed of five frames with the fibers placed perpendicular to the main flow direction. Different geometries were compared for different parameters such as fluid dynamics, pressure drop and mass transfer. In order to simulate the mass transfer, an analogy between heat and mass transfer was used. One of the most important issues of this research was mesh generation, involving, as main problems, the quality and the achievement of acceptable number of cells. Realizable k-ε model modeling turbulence and second order discretization scheme for pressure were used, in order to obtain the most accurate results. The optimized parameters were velocity, pressure and temperature; thus allowing to study the energetic necessities and the mass transfer, as well as fluid dynamic properties. Considering all these issues the most efficient geometry for a large operation range was found. This geometry displayed a high flux density and a low pressure drop.

1. Introduction Although membrane technology is well-known for many years, it is now starting to have a place in the industrial applications. Each day there are more applications which are based on this technology with a proved economical and technological viability, and not only in the traditional uses of membranes; in another fields membranes are proving to be able to perform more efficiently. One of most important advantages of membranes is their selectivity. However this advantage, when the unit is designed, becomes a problem, because this means a more complicate process of design involving a lot of specific research. That is why simulation has become an important tool for designers, because it allows sparing a lot of time and money in experimentation. Nowadays with simulation some expensive and slow experiments can be evaded, because in simulations the same operation conditions of real equipment can be

generated. Of course experimentation can not be avoided, because it is necessary to obtain reliable results –all the results obtained via simulation should be compared with experimental data, in order to prove whether they are physically possible and truthful–.

Figure1.1: Presentation of the module

One of the most recent studies in membrane technology concerns air-liquid contactors for air humidification and dehumidification in industrial and civil air-handling applications. Recent publications, such as [Scovazzo et al. (1999)], [Bergero and Chiari (2000)] and [Johnson, D. et al. (2003)], have proved the high efficiency of hollow fibers in this field. In this work the simulated contactors have a modular design. Each module consists of a five frames, in which the fibers are placed. As absorbent lithium chloride solutions (38-40%) are used, which circulate through the lumen of the fibers [Novak et al. (2004)]. The aim of this work was the to find out which is the most appropriate configuration for this module, in order to achieve the best mass transfer and contributing the minimal quantity of energy. 2. Software About thirty years ago, with the development of increasingly powerful computers, numerical simulations of various approximations to the Navier-Stokes equations began supplementing these numerical simulation methods, which became known as Computational Fluid Dynamics (CFD). Usually the method is to discretize the spatial domain into small cells to form a volume mesh or grid, and then apply a suitable algorithm to solve the equations of motion (Euler equations for inviscid and Navier-Stokes equations for viscid flow). The techniques are widely used by engineers designing or analyzing devices that interact with fluid, such as vehicles, pumps, chemical apparatus or ventilation systems. Nowadays there are numerous commercial software packages to solve the Navier Stokes Equations1. In this work the FLUENT/GAMBITTM package was used. GAMBITTM allows creating the mesh, which discretizes the regarded volume into control volumes. FLUENTTM uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically [FLUENT (2005)]. FLUENTTM also allows data post-processing. 1 [Johnson, F. T (2003)] and en.wikipedia.org

3. Simulation In order to find the optimal configuration of the hollow-fibers transverse flow module, five different geometries were compared. These geometries consist of different arrangements of the hollow fibers. The rest of the properties of the module are constant.

Figure 3.1: Schematic representation of the geometry A. Note that the green circles represent the fibers installed in the frames. Geometry A was proposed by GKSS as initial point of the research. The following geometries are variations of this initial scheme, normally changing the distances or the angles. In the following table the main differences between geometries are shown.

Distance Geometry a

(mm) b

(mm)

Angle (°) Sandwich

A 3 3 0/0/0/0/0 - B 3 3 15/0/-15/0/15 - C 2 2 15/0/-15/0/15 - D 3 3 0/0/0/0/0 X E 2 2 0/0/0/0/0 X

Table 3.1: Description of the simulated geometries

Distance a: The distance from the center of a frame to the center of the next one. Distance b: The distance from the center of one fiber to the center of the next one in the same frame. Angle: Angle between the hollow fibers of one frame and the perpendicular axis. Sandwich: This configuration is shown in Figure 3.2.

Figure 3.2: Schematic representation of geometry D with sandwich configuration. The first step of the simulation with the commercial package FLUENT/GAMBITTM is constructing of the geometry in GAMBITTM. Next it comes the creation of a mesh, which allows carrying out the simulation in FLUENTTM. The reliability of the results depends strongly on how these initial steps are made.

Figure 3.3: Detail of the frame mesh

The main characteristics of the searched mesh were:

• Suitable for all geometries • Good quality • Relatively small number of cells

The first point was in order to minimize the mesh influence of the different geometries. The second and the third ones were important to have a good and quick convergence. The main problems of the mesh building lay on the

meshing of round shapes and the connection between the frames. The first inconvenient was solved by dividing the volumes and meshing them separately (see Figure 3.3); and the second one by using connected surfaces (“interface method” of FLUENTTM). The final mesh had 1.500.000 cells. To achieve the convergence of the solution a systematic procedure was employed in all the cases, which involved a step-by-step convergence. Instead of introducing all the simulation conditions together, firstly the simplest conditions were converged and then introducing one by one the new conditions until the convergence criterion was met. This approach was faster than applying all models at once and it assured the convergence. This step-by-step method of convergence, advised in FLUENTTM user’s guide [FLUENTTM (2005)], gave very good results, and approximately two hundred iterations were necessary to converge a whole case. In order to simulate the mass transfer, an analogy between heat and mass transfer was used. Realizable k-ε model modeling turbulence and second order discretization scheme for pressure were used, in order to obtain the most accurate results. 4. Results and discussion

Figure 4.1: Velocity contour-plot of geometry D in

the flow direction (m/s).

The aim of this work was the to find out which is the most appropriate configuration for this

Cooper

Map

module, in order to achieve the best mass transfer contributing the minimal quantity of energy. The most important features of the analysis are pressure drop and concentration. In the reality the operation is isobaric. An important energy necessity is mechanical energy to compensate the pressure drop due to the displacement of the fluid.

Figure 4.2: Pressure contour-plot of geometry D in

the flow direction (Pa).

The concentration profile allows interpretation of mass transfer. Instead of using the concentration directly, the analogy between heat and mass transfer was used. The heat transfer equation was enabled and the behavior of the temperature studied.

Figure 4.3: Temperature contour-plot of geometry

D in the flow direction (K).

The analysis procedure was the same for all parameters, initially using contour-plots of different areas (qualitative analysis) and afterwards using tables and precise X-Y plots (quantitative analysis).

0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

Frame 1 Frame 2 Frame 3 Frame 4 Frame 5

Pres

sure

dro

p (P

a)

Geometry AGeometry BGeometry CGeometry DGeometry E

Figure 4.4: Pressure drop of each frame for the different geometries. In Figures 4.1 - 4.3 different contour-plots of geometry D, as sample, are shown. Actually for all geometries these contour-plots were created. This allowed establishing the first comparison of the performance. However it was not enough to analyze in-depth.

0

50

100

150

200

250

300

Frame 1 Frame 2 Frame 3 Frame 4 Frame 5

Hea

t flu

x de

nsity

(W/m

2 )

Geometry A

Geometry B

Geometry C

Geometry D

Geometry E

Figure 4.5: Heat flux density of each frame for the different geometries.

Therefore the second step of the analysis consisted on the creation of some tables and afterwards its representation (see Figures 4.4 and 4.5). The performance of geometries B, D and E were the most outstanding, overhanging geometry D. This one achieved the good mass transfer having a small pressure drop. 5. Conclusions CFD simulations have proved to be a useful tool for unit design. In this current work, the aid of CFD allowed to find new and better internal arrangements for transversal flow modules. Future work would be to carry out some experiments, especially with the geometries, which have shown a better performance in the simulation, such as geometries B, D or E. 6. References

• Bergero, S. and Chiari A.: Experimental and theoretical analysis of air humidification/dehumidification processes using hydrophilic capillary contactors, Applied Thermal Engineering 21, 1119 - 1135, 2000

• FLUENT inc.: FLUENT 6.2 User’s guide, 2005

• FLUENT inc.: GAMBIT 2.2 User’s guide, 2004

• Johnson, D. W., Yavuzturk, C. and Pruis, J.: Analysis of heat and mass transfer phenomena in hollow fiber membranes used for evaporative cooling, Journal of Membrane Science 227, 159 - 171, 2003

• Johnson, F. T., Tinoco, E. N. and Yu, N. J.: Thirty years of development and applications of CFD at Boeing commercial airplanes, Seattle, 16th AIAA Computational Fluid Dynamics Conference, 2003

• Nowak, S., Kneifel, K., Waldemann, R., Wind, J., Albrecht, W., Just, R. and Peinemann, K.-V.: Hollow Fiber Membrane Contactor for Air Humidity Control, Poster presentation Euromembrane, Hamburg, 2004

• Scovazzo, P., Hoehn, A. and Todd, P.: Membrane porosity and hydrophilic membrane-based dehumidification performance, Journal of Membrane Science 167, 217 – 225, 2000

• http://en.wikipedia.org/wiki/Computational_fluid_dynamics, august 2005