# Multiphase Flow - Appendices

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1 Discovery Laboratory Multiphase Flow - Appendices 1. Creating a Mesh 1.1. What is a geometry? The geometry used in a CFD simulation defines the problem domain and boundaries; it is the area (2D) or volume (3D) containing the fluids of interest. Boundary conditions can be assigned to the edges or surfaces outlining the geometry What is a Mesh? CFD relies on the discretisation of equations governing the state of fluids within the computational domain. Meshing a geometry allows the computational domain to be split into numerous elements/cells, within which the discretised equations can be solved. The piecing together of these individual elements gives a complete picture of the fluid flow, at a point in time. In a transient solution such as bubble rise, these elements can be solved repeatedly to show how the flow develops over time. An example 2d mesh is shown below: Figure 1 - an example 2D mesh of a curved pipe section. We note that in addition to space, time is also divided into discrete time-steps. Choosing the size of the time-step is of crucial importance and is related to the choice of spatial grid-size. Generally, in order to increase accuracy, one must refine the spatial grid, which then reduces the stability of the numerical scheme leading to the generation of spurious results (i.e. numerical artefacts that have no physical analogue). Remedying this issue involves the reduction of the time-step, which on the one hand alleviates the stability problem, but on the other hand, leads to longer computational times Some Meshing Terminology Element/cell - one discrete small subsection of a computational domain.

2 Time-step a discrete unit of time, the length of which varies according to various mesh and setup parameters. A series of time steps in the result of discretising the time dependent terms of the equations governing the fluid flow. Node a vertex of an element/cell. The location/number of nodes are often considered when meshing as opposed to elements. Mesh Quality - affects both the accuracy of the CFD solution and the computing power required to reach a solution. Structured Mesh consists of a regular arrangement of quadrilateral (2D) or hexahedral (3D) elements. This is usually achieved through blocking, and often requires less computational resources than unstructured meshing Blocking - a series of quadrilateral or hexahedral blocks can be introduced around the geometry. Each edge on a block can be split into a specified number of points, and associated with an edge on the geometry these points will define the number of cells along each edge of the geometry. In essence, this allows a structured grid to be defined, and distorted to nonrectangular geometries such as pipes. Unstructured mesh consists of irregular elements connected in a non-uniform manner. Can utilise any shaped element. They tend to require more computational power than structured meshes due to the inability of the solver to easily create regular arrays from the irregularly spaced elements 1.4. How to create a structured 2D mesh in ICEM CFD Shown below is the main ICEM CFD display upon launching the software, with the curved pipe Tabs Options Console Graphics Window

3 section geometry shown above. 1) Create the geometry - Construct the boundaries of the solution domain (pipe) using points and curves within the geometry tab in ICEM CFD. At this stage, consider the pipe diameter to be studied, and the appropriate pipe length (given the flow dynamics under investigation). Create a surface from the boundary curves only defined surfaces are meshed in ICEM CFD. 2) Block the surface - Within the blocking tab, use the create block option to create a 2D block from the surface. The pre-mesh params option allows for edge parameters for the block to be defined. Consider both uniform distribution of points, and distribution according to different mesh laws. Before proceeding, associate block edges with the appropriate geometry curves. 3) Generate the mesh - Once the pre-mesh parameters are defined, the mesh can be computed by right-clicking Pre-mesh in the top left panel of ICEM, and clicking recompute. Clicking convert to unstructured mesh will then produce a visible mesh. 4) Define parts for future application of boundary conditions - Right clicking Parts in the top left pane of ICEM allows the creation of parts. This enables the mesh to be split into zones consisting of edges or surfaces. Later, this is useful for the assignment of different boundary conditions to different parts of the mesh. Consider the required boundaries for bubble rise simulation. 5) Export the mesh to a.msh file - Within the output tab, ensure the file is setup for ANSYS FLUENT, and use the write input option to create an appropriately names.msh file. In FLUENT, this can be opened directly How to create an unstructured 2D mesh in ICEM CFD 1) Create the geometry as above. 2) Setup mesh parameters - The objective here is to control the mesh density through adjustment of the maximum and minimum element size. Within the mesh tab, use the part mesh setup option to adjust and apply the mesh parameters. 3) Compute and generate mesh - Use the generate mesh option within the Mesh tab to compute the surface mesh. Some parameters can be experimented with here. 4) Define parts and export the mesh as above Extending the above instructions to 3D domains 3D geometries tend to begin with a series of curves in 2D, which can be modified to produce a 3D surface using the create/modify surface option within the geometry tab. Various options are available for experimentation. Once the desired 3D surface has been produced, blocking can commence as above, but with a 3D bounding box. Whilst blocking with just a 3D bounding box produces a usable pre-mesh, of particular use in pipe flow is the 0-grid tool in the split block option within the blocking tab.

4 Applying an o-grid block to the relevant face splits the bounding block into an array of blocks with new corresponding edges. Experimenting with the transform blocks options to adjust the block size and distribution gives greater control over the element shape and density within the mesh. Above left: a body-fitted grid. Above right: an o-grid The method for defining parts and outputting usable mesh files is comparable to the 2D instructions. Care should be taken to ensure the mesh is output as a 3D.msh file What makes a good mesh for 2 phase flow? Considerations. Sufficiently high mesh density to capture liquid films, vapour-liquid interphase & boundary layer effects a low-resolution mesh may also give an inaccurate solution in areas where there is a significant change in flow characteristics or fluid properties across a small distance. Locally increasing the element density is referred to as mesh refinement. Conversely, a lower mesh density should be used where applicable/possible The point at which refining the mesh has no impact on the given solution is referred to as mesh independence. Refining the mesh beyond this point increases simulation time for two reasons: o It increases the number of elements for which the governing equations need to be solved at each time step. o It reduces the time step size accordingly, since by rough approximation: time step = minimum grid size / maximum velocity in domain i to achieve the same stability & solution accuracy. A max element aspect ratio of 5 this refers to the ratio of length/width in a quadrilateral element for example. Higher aspect ratios lower the mesh quality, increasing computational time. The ideal is 1. A skewness of <0.85 ii the definition of skewness varies depending on the elemental shape, but in general, a skewness closer to 0 increases the likelihood of obtaining an accurate solution and prevents divergence of a simulation. A smooth transition from smaller to larger elements this reduces the probability of an erroneous calculation in an element.

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6 2. Guidance for Problem Setup (FLUENT) 2.1. Solution Setup General The relevant parameters are: Navigation Pane Task Page Graphics Window Console Gravity allows angle of inclination to be specified without changing the mesh Time 2.2. Solution Setup - Models Multiphase Model see hand-out for details. Viscous Model this is key to the manifestation of phenomena observed in the lab. Model k-epsilon. K-epsilon model Standard. Others default Solution Setup - Materials This section requires specification of the fluids present in the simulation. FLUENT s database contains basic fluid properties for numerous fluids, but the user can also create new fluids and input the relevant properties Solution Setup Phases This section considers the discrete phases to be used in the simulation, and interactions between them. Of particular relevant to two phase bubble rise is the influence of surface tension and wall adhesion on flow characteristics, both of which should be addressed here. Ensure the phase material is correctly specified for both the primary and secondary phase.

7 2.5. Solution Setup Boundary Conditions The boundary conditions specified in a model have a significant impact on the final solution, as well as how closely the bubble formation agrees with literature and experimental findings. Factors addressed her should include Boundary condition type Fluid contact angle at the wall especially relevant in setups where it is anticipated that the liquid/vapour interphase will intersect with a wall. The turbulence specification method for each boundary recommended K and Epsilon (Default values) 2.6. Solution Setup Dynamic Mesh Perhaps not a mandatory part of the solution setup, but can be used if desired. Contains useful option which may help automate the simulation process. Only the Events button needs to be addressed in this section ensure the event is defined and on Solution Solution Methods In the section, the solution algorithms FLUENT uses to obtain a solution can be selected. The appropriateness of a solution method is depended on the models used, whether the solution is transient or steady, and the type of fluid flow under consideration. In our case, the default values for spatial discretization are applicable, but could be experimented with. Non-iterative Time Advancement should be applied. The appropriate Pressure-Velocity Coupling is flexible and should be researched. iii 2.8. Solution Solution Controls The default values are satisfactory for this case, but can be adjusted if the simulation is struggling to converge. iv The purpose of these relaxation factors should be known. Altering the relaxation factors can cause the simulation to take a lot longer to converge Solution Solution Initialisation & Patching Patching refers to the manual alteration of an element or region s properties. It enables the elements in a domain to have an initial condition before the simulation begins, as well as the boundaries. Of specific interest in the case of bubble rise is the patching of fluid volume fractions into the domain. From the top navigation bar, selecting Adapt > Region allows a region to be marked, onto which a volume fraction of the secondary fluid can be patched through Solution Initialisation > Patch. By default, the domain is filled with the primary fluid (Air) of volume fraction 1. Patching different shapes to the inlet of the tube may affect the ease of bubble The region adaptation window

8 formation Solution Calculation Activities The patching window This pane allows the capture of solution animations and case/data files at regular time step intervals. The location of these saved files can be selected, allowing different folders to be specified for different simulations. Considering the limited available storage space, it is important to bear in mind the anticipated size of your data files & auto save frequency. The following commands are of great use when capturing images of phase distribution in 2D simulations at regular time step intervals: The simulation time step (incremental change in time after 1 solution iteration) should be specified here. The appropriate time step is related to the mesh density and quality, as well as the desired degree of solution accuracy, which is characterised by the courant number. An appropriate value for the courant number should be selected/obtained through suitable time stepping.

9 Figure 2 - Command window within calculation activities pane. These settings capture a 2D image of the volume fractions across the entire domain Solution Run Calculation Fixed Time Stepping allows the time step to be fixed and the courant number to be varied accordingly. Variable Time Stepping allows the courant number to be fixed and the time step to be varied accordingly. Useful if abrupt changes in flow conditions are expected or a dynamic mesh is in place. The Calculate will begin your simulation, saving auto-saves in the specified folder Report These tabs allow the user to visualise the velocity field, phase distribution and other properties of the fluid across the domain, for the current time step. New surfaces can be created within the graphics panels, allowing for a 2D plane within a 3D domain to be studied.

10 3. Troubleshooting and useful links 3.1. Common Issues My fluids are behaving strangely at the interphase Lower the courant number to maintain stability Reconsider boundary conditions incorrect boundary conditions can create unphysical behaviour. My time step is very low Consider coarsening the mesh in areas where low detailing is necessary and velocities are low. If the simulation is stable and results seem physical, increase the courant number perhaps run these two simulations side by side to ensure there is no variation in the solution. Each iteration is taking a very long time Ensure FLUENT is running in Parallel configuration during launching this utilises multiple computer processors and enables faster solution. As before reduce the element density in the mesh if possible. Reset the relaxation parameters to the default if changing them is not necessary. Reversed flow in _ faces on pressure-inlet/pressure outlet notification This just indicates that the flow direction at a pressure boundary condition varies across its length. The accuracy of the solution will not be effected but computational time is marginally longer. Global courant number is greater than 250. The velocity field is probably diverging error The courant number is a condition which ensures the accuracy of solutions. It is usually a function of the velocity vectors within the domain, and the time step used. An increasing courant number can be rectified by decreasing the time step, but often this is not sufficient. If using variable time stepping, try lowering the minimum step change factor such that the time step can react more sharply to an increasing courant number, or lowering the courant number. In fixed time stepping, simply reducing the time step should reduce the courant number to a level where the velocity field will not diverge Useful Links 1) Learning modules for ANSYS FLUENT mainly uses ANSYS workbench for meshing as opposed to ICEM CFD but the solver (FLUENT) is the same. 2) Explains surface tension & wall adhesion in FLUENT 3) Advises on the use of an appropriate calculation method in FLUENT

11 4) YouTube tutorial for body fitted meshing in a 3D pipe in ICEM CFD. 5) A general guide to modelling multiphase flows in FLUENT 6) Provides numerous potential solutions to a diverging velocity field (Global courant number > 250) 7) Provides potential reasons and solutions for errors encountered when exporting a mesh to FLUENT from ICEM CFD. i ii iii iv

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