Modeling flow inside a beaker containing coupons and filled with bacterial suspensions
By,
Vijaya Krishna Bodla
S041492
Introduction: 2 Computational Fluid Dynamics (CFD): 3 CFD Analysis: 4 Preprocessing in Gambit: 5 Solver  Fluent Simulations: 7 Post Processing: 8 Conclusion: 15 References: 15 Introduction:
In the past many researchers have investigated the formation and removal of biofilm from coupons of materials in beakers filled with bacterial suspensions. The main causes for the formation of the biofilm over surfaces contaminated with microorganisms are:
The microorganisms must adhere to the exposed surfaces of the device long enough to become irreversibly attached The rate of cell attachment depends on the number and types of cells in the liquid The flow rate of liquid through the device Physicochemical characteristics of the surface
Microbial biofilms develop when microorganisms irreversibly adhere to a submerged surface and produce extra cellular polymers that facilitate adhesion and provide a structural matrix. This surface may be inert, nonliving material or living tissue.
But once these cells irreversibly attach and produce extracellular polysaccharides to develop a biofilm, rate of growth is influenced by flow rate, nutrient composition of the medium, antimicrobialdrug concentration, and ambient temperature.
One of the important aspects which should be accounted for is the effect of wallshear stress which can in cases have a significant effect on the biofilm characteristics locally on the coupons.
Many researchers have discussed this effect in their articles, like Y. Liu and J.H. Tay have studied the effect of ‘Metabolic response of biofilm to shear stress in fixedfilm culture’. Their results suggested that ‘Smooth, dense and stable biofilm formed at relatively high shear stress. Higher dehydrogenase activity and lower growth yield were obtained when the shear stress was raised. Growth yield was inversely correlated with the catabolic activity of biofilm. The reduced growth yield, together with the enhanced catabolic activity, suggests that a dissociation of catabolism from anabolism would occur at high shear stresses’.
While on the other hand in other cases shear seemed to have a negative effect on the attachment of the microbes to the coupons discussed in articles like the PhD dissertation submitted to university of south Hampton on ‘Survival of Helicobacter pylori in drinking water and associated biofilms’. Their results suggested that ‘Decreasing shear forces, however, clearly promote the attachment, with an observable difference noticeable from the beginning of the experiment’.
In some cases shear had a neutral effect on the formation of the biofilm. Researchers like Brent M. Peyton, W. G. Characklis have investigated the ‘A statistical analysis of the effect of substrate utilization and shear stress on the kinetics of biofilm detachment’. Their results indicated that ‘detachment rate is directly related to biofilm growth rate and that factors which limit growth rate will also limit detachment rate. No significant influence of shear on detachment rate was observed.’
Carollo Services: Research and Development Team have conducted the benchscale testing of annular reactors from which biofilm growth and the extent of corrosion was determined. The reactors consisted of a rotor inside a stationary outer cylinder. Hydraulic conditions within the reactor, such as shear stress and water velocity, depend on the rotational speed of the rotor. A rotational speed of 50 rpm was commonly used in drinking water studies. From a further literature survey it was observed that the most biofilms for study were grown in 0.51 liter beakers with a magnetic stirrer at a rotational speed of 100150 rpm.
Researchers like C.H. Nelson, J.A. Robinson and W.G. Characklis have studied the ‘Bacterial Adsorption to smooth surfaces: Rate, Extent and Spatial Pattern’. In their study an experimental system was designed where an outflow from a chemostat is continuously circulated into the BAR (continuous flow bacterial adsorption reactor). The BAR was a Berzelius beaker with a working volume of 450 ml. The relative turbulence of the BAR bulk water was kept constant in all their experiments by maintaining the same stirrer setting. Bacterial cell counts were made in the same relative location on each slide to minimize the effect of nonuniform turbulence over the slide.
But the relative shear on each of the slides can have a considerable impact on the bacterial counts. This study aims at identifying the wall shear stresses at various locations in the beaker, on the slides and the wall. It is considered to make a CFD model of the beaker used which can further be validated with some real time experiments.
Computational Fluid Dynamics (CFD):
Computational Fluid Dynamics can be an effective tool to study the effective wall shear stress and flow pattern. CFD is the science of predicting fluid flow, heat transfer, mass transfer, chemical reactions, and related phenomena by solving mathematical equations that represent physical laws, using a numerical process. The range of applications is very broad and encompasses many different fluid phenomena.
The result of CFD analyses is relevant engineering data, which can be used to:
Conceptual studies of new designs Detailed product development Troubleshooting Redesign
CFD analysis complements testing and experimentation
Reduces the total effort required in the laboratory
The basic equations of the fluid flow are obtained from the conservation of mass and momentum, and combined with the Reynolds transport theorem to obtain the so called Navierstokes theorem which is the basis for the all the calculations. The basic equations of fluid flow can be generalized in the following equation:
Unsteady Convection Diffusion Generation
stands for field variables ( u, v, w, p, H, …)
The flow field and the equations of motion are discretised. The system of algebraic equations is solved to give values at the nodes, approximated in terms of values at nodes:
Differential or Integral equations Algebraic equations (Continuum) (Discrete)
The approximation of a continuouslyvarying quantity in terms of values at a finite number of points is called Discretisation. CFD Analysis:
CFD analysis can be broadly classified into three stages, Preprocessor, Simulations and Postprocessing.
Figure1: CFD Modeling Overview CFD Analysis: Basic Steps
Problem Identification and PreProcessing Defining the modeling goals Identifying the domain to be modeled Designing and creating the grid Solver Execution Setting up the numerical model Computing and monitoring the solution Processing Examining the results Considering revisions to the model
Thus it is decided to make a CFD model of the BAR (continuous flow bacterial adsorption reactor) to study the wall shear stresses inside the BAR using CFD analysis. Preprocessing in Gambit:
Gambit is a single integrated preprocessor for CFD analysis and can perform multiple tasks such as Geometry Construction, Mesh Generation, Mesh quality examination, Boundary Zone Assignment.
Geometry Construction:
A folder titled fluent – work needs to be dedicated as the working directory for gambit operations Gambit is started by typing gambit in the command prompt Gambit opens a default file created in the specified directory referred as .lok file Gambit has various options for creating geometry, mesh generation, assigning boundaries and zones to the created geometry and also various other tools such as sizing function In the solver option, Fluent 5/6 has been selected as the solver In the gambit main window under operationsgeometry, the volume command button was selected to open the ‘Create Real Cylinder’ form where a cylinder has been created in the positive zdirection with dimensions Height 10, r1,r2 – 4 The same form is used to create a smaller cylinder with dimensions, Height – 3, r1,r2 – 2.5 in the positive zdirection Again from the volume command button, brick was created using the ‘Create Real Brick’ form with dimensions, width – 4, height – 1, depth – 1 centered to all three axes Using the ‘Move / Copy volumes’ form the brick was translated to 0.5 units in the positive zdirection to align with the remaining geometry Using the Boolean operations in the volume command button, the subtract volumes option is selected to subtract volume 2, small cylinder, from volume 1, large cylinder retaining the small cylinder and again subtracting the volume 3, brick, from volume 2, the small cylinder while retaining brick Now the three plates were created using the ‘Create Real Brick’ form in the volume command button with dimensions width – 4, depth – 0.5, height – 4 centered to all three axes The ‘Move / Copy volumes’ form has been used to move the newly created plates, rotate with 90 degrees angle to the zdirection and the translate to 6 units with Cartesian coordinate system The same form is used to translate two of the plates to 2.5 units into two directions positive and negative xaxis Using the Boolean operations in the volume command button, all the three plates have been subtracted form volume 1, the bigger cylinder Volumes 4,5,6 and 3, i.e., the plates and the brick have been deleted using the delete volumes form in the volume command button From the ‘Create Real Circular Face’ form in the Face command button two circles were created with dimensions, Radius – 4 The newly created circular faces have been translated using ‘Move / Copy Faces’ to 8 units and 4 units in the positive zdirection The newly created circular faces have been used to split volume 1, the big cylinder into three volumes using the ‘Split Volume form – split with real face’ under volume command button Finally in the ‘Connect Faces’ form from the Face menu in Geometry, the faces 5 and 55, and 6 and 57 have been connected. These are the overlapping faces connecting the inner geometry volume 2 with the outer geometry volume 1 of the lower part and needs to be connected to form a single face
Mesh Generation:
In the ‘Mesh Faces’ form from the Face menu of the OperationMesh, the bottom face of the volume 2 with void for the stirrer has been selected and meshed using the quadpave scheme with 0.2 as the interval spacing The Volume 2, inside geometry of the lower part, has been meshed with the Hex/Wedge – Cooper scheme with 0.2 as the interval spacing using the ‘Mesh Volumes’ form from the volume menu of the OperationMesh Using the same form the volume 3, upper geometry, has been meshed using the Hex/Wedge – Cooper scheme with 0.2 as the interval spacing. Gambit selects the required source faces automatically Using the same form the volume 4, middle geometry, has been meshed using the Hex/Wedge – Cooper scheme with 0.2 as the interval spacing In an attempt to decrease the total number of cells and to mesh maximum possible volume with the Hex/Wedge – Cooper scheme, a face is created in volume 1 and the volume is split using the face into two, one encompassing the volume surrounding volume 2 and other the upper geometry Now the newly created volume 5, encompassing the volume 2, is meshed using the Hex/Wedge – Cooper scheme with 0.2 as the interval spacing The remaining upper geometry, the new transformed volume 1, is now meshed using the Tet/Hybrid – TGrid scheme with 0.2 as the interval spacing
Setting Continuum Types:
Under ‘OperationSpecify Continuum Types’ form Fluid 1 has been defined in volume 2 as the entity Finally the mesh has been exported using the ‘ExportMesh’ option under file menu Solver  Fluent Simulations:
Fluent begins by clicking the fluent icon and choosing the 3d option for the 3dimensional mesh The file is then read in the ‘ReadCase’ menu and selecting the exported mesh file from the directory Fluent then reads the mesh file and displays useful information such as minimum cell volume Initially the grid is checked in the ‘GridCheck’ menu for any inconsistencies. The size of the grid i.e., the number of cells can be checked for in the ‘GridInfoSize’ menu Fluent normally reads the grid scale in SI units, i.e., in meters and now has to be changed to centimeters in the ‘GridScale’ option by selecting cm from the drop down list and pressing the scale button The ‘GridSmooth’ option is selected to refine the grid and then from the ‘GridSwap’ menu it is swapped until the number of swapped faces is zero to further refine the grid. The grid can be checked for manually from the ‘DisplayGrid’ option
Figure 2: Displaying the grid after exporting to Fluent from the ‘DisplayGrid’ menu
Fluent directly selects the volume 2, inside the geometry, as the interior for performing simulations The ‘DefineSolver’ menu is checked for all the defaults. In the ‘DefineViscous’ menu the default kε model is selected to account for turbulence The ‘DefineMaterials’ menu water (liquid) is selected from the Fluent Database as the material flow. The aqueous suspended bacterial liquid is approximated to be having the same density as that of the liquid water In the ‘DefineBoundary Conditions’ menu, water is selected as the ‘Fluidset’ and ‘Fluid1set’ menus. In the ‘Fluid1set’ menu the moving reference frame is selected to define the rotational flow of the fluid in the volume and the rotational speed is set to 15 rad/s In the ‘DefineBoundary Conditions’ menu, wall has to be defined as the rotating wall relative to the rotating fluid 1 in volume 2. This is done in ‘wallset’ menu by selecting the rotating wall option under momentum menu, and setting the relative velocity to zero. In the ‘SolverControls’ menu the second order upwind is selected to increase the approximations in calculating the differential equations The ‘SolverMonitors’ menu is set to plot all the residuals The calculations are initialized in the ‘SolverInitialize’ menu The file is saved to write the case in the ‘FileWriteCase’ menu The number of iterations are started and set to about 7000 in the ‘SolverIterate’ menu to account for convergence Post Processing:
Post Processing is the examining of the results to review solution, extract the useful data and also analyzing the preciseness of the solution. Visualization tools can be used to study the overall flow pattern, separation, shocks, shear layers and also about the consistency of the result from a common knowledge of the system. Numerical reporting tools can be used to calculate quantitative results such as forces, moments, heat transfer coefficients, flux balances.
Post processing further helps in revising the model for more precise solutions like if the turbulent flow is a good approximation, if the boundary conditions are appropriate and if the grid is adequate.
The iterations are run for about 7000 times by still monitoring the residuals and checking for no considerable change. The residual plots indicate the residuals such as velocity in the three directions, turbulence and continuity from all the iterations. Thus convergence can be said to be achieved when there is no considerable difference in the residuals from one iteration to the next.
The velocity vectors over various locations can be seen from the ‘DisplayVectors’ panel by selecting the vectors of velocity. A high value for the scale option, here chosen to be 3, can give a clear view of the direction of the vectors at various locations. a)
b)
Figures 3: a) Showing the velocity vectors on the outer wall b) Showing the velocity vectors in the fluid zone and on the moving wall moving relative to the fluid zone
From a basic visual analysis, the moving fluid zone and the moving wall can be seen in figure b directing the rotational flow inside the volume, can be observed in figure a. It can be seen that in order to obtain more uniform pattern of the velocity vectors for more uniform mixing inside the geometry, the rotational speed of the magnetic stirrer needs to be increased.
From the ‘DisplayContours’ panel select the Display contours of wall fluxes and check the filled in contours option and click ok to display the contours of wall shear stresses on the outer wall and also on the coupons.
a)
b)
Figure 4: a) Displaying the contours of wall fluxes at various locations on the outer wall b) Displaying the contours of wall fluxes at various locations on the coupons From the visual analysis from figure a, it can be observed that wall shear is maximum near and around the stirrer as expected and also the rotational flow of the stirrer can also be visualized from the variations in wall fluxes around the stirrer. It can also be observed that the wall fluxes on the upper part of the beaker are negligible indicating a more rotational speed for a better mixing and uniform shear on the outer wall. However the tangential motion of the fluid resulting from the rotation of the stirrer inside can also be observed.
The wall shear on the coupons can be seen from inside the geometry in figure b. It can be observed that for the bottom edges of the coupons, the shear on the outer plates is higher than that of the middle plate. The tangential flow of the fluid inside makes the outer surface more exposed to the fluid and shear than that of the middle plate.
In order to have clear view of the contours on the coupons or different planes inside the geometry, planes can be created in the ‘SurfacePlane’ panel. Thus planes have been created inside the geometry parallel to the zdirection enclosing the three coupon slides and displaying all the outer surfaces of all the slides. Planes have also been created longitudinally through the geometry which can give an overview of the shear at various locations.
a)
b)
c)
Figure 5: a) & b) Displaying the contours of the wall shear stress on the both the surfaces of all the coupons c) Displaying the contours of the wall shear stress on the bottom edges of the coupons facing the magnetic stirrer
Figures 5)a and 5)b show more wall fluxes and shear between the coupons or slides rather than between the coupons and the outer wall. More or less the same shear and fluxes can be observed on the surfaces of the coupons facing each other and lesser shear is observed on the faces of the coupons facing the outer wall of the beaker. Thus the ununiform distribution of the shear on the surfaces of the outer plates might result in varying characteristics of the biofilm formed on either surface.
The bottom edges of the coupons facing the stirrer can be seen in figure c. The shear on the outer plates can be observed to be higher than that of the middle plates.
From the ‘DisplayContours’ panel selecting the display contours of velocity will display the contours of velocity on various planes inside the geometry.
Figure 6: Displaying the contours of velocity at various planes inside the geometry
The contours of the velocity in figure 6 indicate more or less the same velocity distribution in all the planes indicating more or less uniform mixing, except near the stirrer where the velocity is supposed to be higher.
Conclusion:
From the literature survey, it can be noticed that the shear might have a considerable effect on the biofilm characteristics. The CFD modeling and analysis of the flow inside the BAR (continuous flow adsorption reactor) can be an effective tool for studying the shear and the flow pattern at various locations inside the BAR. Geometry is constructed in Gambit and meshed using the meshing tools for minimum number of cells by meshing maximum possible part of the geometry using Hex/Wedge – Cooper scheme. The continuum types are set to indicate the fluids in the volumes which can further be defined in fluent as the rotating and stationary fluids. The faces of the volume interior to the geometry have been connected to form a single face so that fluid recognizes the volume as the interior. Simulations were performed in Fluent by monitoring the residuals for convergence.
The results indicate a more or less uniform velocity around the coupons though there are quite velocity variations around the rotating magnetic stirrer in the lower geometry below the coupons indicating considerable uniform mixing around the coupons inside the BAR. The wall fluxes vary quite considerably from near the magnetic stirrer to the outer wall to the different surfaces of the coupons. It was observed that the shear on the surfaces of the coupons facing each other were considerable uniform and higher compared to the shear on the outer surfaces of the coupons facing the wall. This might have considerable effect on the biofilm characteristics on either surface of the outer coupons. The middle coupon on the other hand has considerably uniform shear on both its surfaces.
References:
‘An Introduction to Computational Fluid Dynamics – The Finite Volume Method’ by H K Versteeg and W Malalasekera ‘Biofilms and DeviceAssociated Infections’ by Rodney M. Donlan, Centers for Disease Control and Prevention Atlanta, Georgia, USA ‘Bacterial Adsorption to smooth surfaces: Rate, Extent and Spatial Pattern’ by C.H. Nelson, J.A. Robinson and W.G. Characklis ‘Biofilms and DeviceAssociated Infections’ by Rodney M. Donlan ‘Prediction of Flow in mixproof valve by use of CFD – Validation by LDA’ by Bo B.B. Jensen and Alan Friis Gambit and Fluent Tutorials from the Fluent.com website
