M o d e l i n g a n d S i m u l a t i o n s o f F l u i d F l o w

In this section:

•Modeling Strategy

•Geometrical Complexities

•Material Properties

•Defining the Physics

•Meshing

•The Choice of Solver and Solver Settings

•Overview of the Physics Interfaces and Building a COMSOL Model in

the COMSOL Multiphysics User’s Guide

See Also

Modeling Strategy

Modeling and simulating fluid-flow is a cost-effective way for engineers and scientists to understand, develop, optimize, and control designs and processes.

One of the most important considerations that have to be done before setting up a model is the accuracy that will be required in the simulation results. This consideration determines the level of complexity of the model.

Since fluid flow simulations are often computationally demanding, a multi-stage modeling strategy is usually required. This implies using simplified models as a starting point in a modeling project. Complexities can then be introduced gradually so that the influence of each refinement of the model description is well understood before introducing new complexities.

Complexities in the modeling process can be introduced at different stages in order to achieve the desired accuracy. They may be introduced in the description of the geometry, the physical properties, and in the description of the governing equations. The Model Builder, which shows the model set-up as a sequence of operations in the Model Tree, is designed with this modeling strategy in mind.

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In addition to fluid flow, COMSOL Multiphysics and the CFD Module provide predefined couplings of fluid flow and other phenomena. Example of these couplings are heat transfer for free convection and structural mechanics for fluid-structure interaction simulations. Set up your own couplings by defining mathematical expressions of the dependent variables (velocity, pressure, temperature, etc) in the physics interfaces for arbitrary multiphysics combinations.

Geometrical Complexities

A complicated 3D CAD drawing is usually not the best place to start the modeling process. A 2D representation of a cross-section of the geometry may give valuable initial estimates of the flow field that can be used in setting up the full 3D model. For example, you may be able to determine the pressure variations and the nature of the flow, if a turbulence model is needed or not. This provides information on where in the final geometry the most amount of ‘change’ occurs, and require more concentration or resolution, or what parts of the modeling process is more sensitive than others.

Simplifying the geometry itself can also help immensely. Making use of planes of symmetry and reducing the size of the geometry by half or even more is a great first step. Rounding-off corners is another. Small geometric parts require large amounts of mesh to fully resolve them, but the parts themselves probably have negligible effects on the fluid-flow of a system. They can be removed or modified in either the CAD tool or using the CAD Import Module. See the CAD Import Module User’s Guide for more information.

Material Properties

Depending of the accuracy required in a simulation, the effort in obtaining data for fluid properties may also vary. In many cases, the dependency of the fluid properties on pressure and temperature has to be taken into account.

For pressure-driven flow, it is usually a good approach to set up a first model using constant density and viscosity, to get a first estimate of the flow and pressure fields. Once the model works with constant properties, it can be extended by adding the accurate expressions for density and viscosity.

For free convections, the density variations drive the flow and the fluid properties’ dependency of the modeled variables, for example temperature, has to be accounted for from the beginning. In difficult cases, with large temperature variations, it may be

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a good approach to run a time-dependent simulation even if the purpose of the simulation is to get the results at steady-state.

Defining the Physics

The CFD Module contains a number of physics interfaces for single-phase flow, multiphase flow, laminar flow, nonisothermal flow, turbulent flow, and porous media flow.

Also the definition of the physics depends on the accuracy required in a simulation. A fluid may be weakly compressible but could be approximated as incompressible if the required accuracy allows for that. A complex turbulence model may be replaced by a much simpler one, again if the required accuracy is comparably low. A first step in setting up the physics is to consider the simplest possible set-up as the initial step. The results from such a simulation may reveal difficulties that could be useful to be aware of when adding complexities to the physics.

In addition to fluid flow, the fluid flow interfaces may also be coupled to any other physics interface in a multiphysics model.

When setting up a complex multiphysics model involving fluid flow and other coupled physics, it is a good strategy to define and solve one physics at the time first. This allows for verification of the model set-up, for example to check if the intended domain and boundary settings are reflected in the solution of each decoupled physics. The alternative of debugging the model set-up with several coupled physics interfaces could be very time-consuming.

In steady-state multiphysics simulations, it may also be a good strategy to solve the model for each physics in a decoupled set-up as a first step. The solution of the decoupled model can then be used as the initial guess for the fully coupled model. This is specially recommended for highly nonlinear models. The Study node in the Model Tree is designed for this modeling strategy.

Meshing

The mesh used in a fluid flow simulation depends on the fluid flow model and on the accuracy required in the simulation. A fluid flow model may inherently required a dense resolution in order to yield convergence, even though the results may not require a high accuracy. In such case, it may be a good idea to change the fluid model. In other cases, the requirements of the accuracy in the results may set a limit of the maximum element size.

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There are a number of different elements for fluid flow modeling in COMSOL and these are shortly described below:

•Free-meshing techniques generate unstructured meshes that can be used for most types of geometries. The mesh generating algorithms are highly automated, often creating a good quality mesh from minimal user input. This mesh type is therefore a good choice when the geometry of the domain is evident but the behavior of the mathematical model in a it is unknown. Yet, unstructured meshes tend to be isotropic or homogenous in nature, so that they fail to consider the geometry’s size and direction on the behavior of the mathematical model.

•In many ways, the properties of structured meshes complement those of the unstructured type. Structured meshes provide high quality meshes with few elements for sufficiently simple geometries. The properties of a structured mesh can furthermore be used to create very efficient numerical methods. Finally, it is often easier to control the mesh when high anisotropy or large variations in mesh size and distribution is required, as the size of a structured mesh can be easily increased linearly or geometrically with geometric dimensions.

•Swept meshes are generated in 3D by creating a mesh at a source face and then sweeping it along the domain to a destination face, such as from a cut in the cylindrical part of the polymerization reactor to the outlet face. A swept mesh is structured in the sweep direction, while the mesh at the source and destination faces can be either structured or unstructured. As is the case for structured meshes, the model geometry determines if a swept mesh is applicable. Swept meshes are typically ideal when the cross section in the sweep direction is constant, which is the case for channels and pipes, for instance. Revolving a mesh around symmetry axes is another useful sweep operation.

•A boundary layer mesh is a mesh with an element distribution that is stacked or dense in the normal direction of a boundary. It is created by inserting structured layers of elements along specific boundaries that integrate into a surrounding structured or unstructured mesh. This type of mesh is very useful for many applications in fluid-flow applications coupled to mass and energy transfer, where thin boundary layers need to be resolved. This is also the default physics-induced mesh for fluid flow.

Ideally, a mesh convergence analysis should be run in order to estimate the accuracy of a simulation. This means that the mesh should be made twice as fine in each spatial direction and the simulation carried out once again on the refined mesh. If the change in a critical solution parameter for the original mesh and the finer mesh are within the required accuracy, then the solution can be regarded as being mesh-converged. For

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