Mathematical Simulations

An important tool in the thermal and fluidic design of energy components is the mathematical simulation of impulse, heat and mass transfer processes. Typical applications are

• thermal storages (sensitive, latent or sorptive),
• heat exchangers for gases and liquids with or without phase change (evaporators/condensers),
• temperature control systems for electrical energy storage devices or temperature-sensitive components and
• cooling systems for heat generating electrical components.

Among other things, problems of (in)stationary heat conduction, convective heat and mass transfer, heat radiation and pressure loss calculations are solved.

Typically, the following steps are required to simulate a specific problem:

1. Analysis of the problem definition and calculation objectives, preparing the balance equations including simplifications,
2. Provision of initial and boundary conditions, if necessary determination of unknown material and transport quantities in the thermo-technical laboratory,
3. Selection of the solution method (analytical, numerical) - creation of the calculation model (pre-processing)
4. Evaluation and preparation of the calculation results, if necessary experimental validation (post-processing).

Depending on the complexity of the problem to be solved, different calculation tools can be used. The selection is based on the accuracy requirements and available resources:

• analytical or empirical approaches for simple problems with mostly just one dependent variable,
• numerical methods based on own solution algorithms e.g. in MS Excel© for more complex tasks (up to transient 2D problems with phase change, see picture), or
• commercial software packages (especially COMSOL Multiphysics© and OpenFOAM) for any task.

Simplifications must be undertaken and, for example, convective boundary conditions must be simulated by effective transport variables (heat transfer coefficients). For this purpose, measurements can be carried out under practical conditions in the thermo-technical laboratory.

The program package COMSOL Multiphysics© available at Fraunhofer IFAM Dresden is able to perform multiphysics simulations considering flow, heat and mass transport as well as electrical and mechanical parameters.

After the definition of the calculation area - usually by creating or importing a CAD file - the division into solid elements, the so-called meshing or discretization, is carried out. After specifying suitable initial and boundary conditions as well as necessary definition equations, the general balance equations for mass, momentum and energy in each volume element are solved. Necessary definition equations are:

• interaction of flow and wall (friction, heat transfer, mass transfer),
• definition of inlet and outlet openings and planes of symmetry,
• description of mass and transport quantities of solids and fluids (including phase change, e.g. solid/liquid in latent heat storages, if necessary) and
• mathematical modeling of turbulent transport processes.

The results can be processed locally or integrally in the form of velocity and temperature distributions, heat or mass flow densities or heat or mass transfer coefficients.

The freely available simulation software OpenFOAM can be used for various simulations and especially for flow simulations in combination with heat and mass transfer processes.

The surface-based cross-linking process, with which reconstructed surfaces (e.g. from CT scans) can be made directly usable for flow simulations, is particularly interesting.

The available solvers can be viewed in source code and can thus be traced and modified for research and development purposes.