Resolving the Boundary Problem - a Hybrid Cell Technique

29 October, 2018


The increase in power densities coupled with the complexity of product designs in today’s electronics, demands accurate models of heat transfer paths for efficient thermal management. For thermal simulation tools, the first requirement to facilitate this process is the ability to work with complex CAD shapes. We address this capability of 6SigmaET in the following blog.

While the ability to work with CAD data has become a must-have feature in today’s ever-evolving electronics industry, as far as thermal modeling is concerned, it is only an aesthetic feature if the simulation tools are unable to grid the geometry to accurately and efficiently resolve the heat transfer paths. Using the traditional staggered structured grid provides the benefit of the simplicity in implementation, however, it falls short in resolving practical applications that involve complex shapes and varying sizes of parts. One of the methods used to grid complex shapes is a fully unstructured grid that uses tetrahedral or polyhedral grid cells. However, to get the best out of these cell types requires a deep understanding of the specific grid generation techniques available in the mesher and significant time commitments to establish the optimum grid for the solver.

For a few years now, 6SigmaET’s unique “Multi-level Unstructured Staggered Grid (MLUS)” solver has proved to efficiently and intelligently generate grid and provide solutions for complex geometry at unparalleled speed. This technique utilizes a hierarchy of structured and unstructured cartesian grids that can resolve arbitrary shapes while also providing stability and simplicity of implementation. MLUS takes advantage of the robustness of a structured cartesian grid coupled with the grid count efficiency of the unstructured grid to generate finer grid only where needed and avoiding the bleeding of cells.

Although grid generation using cartesian based technique are proven to be efficient, it is interesting to consider how a non-orthogonal solid boundary is represented for heat transfer, at the solid-fluid interface – where the grid cell intersects both a solid and a fluid. This becomes particularly problematic if the heat transfer paths through a complex shape needs to be accurately represented in a case for conjugate heat transfer.

A common technique used by many CFD tools that rely on Cartesian based gridding is a simple stair-step technique1. When using a stair-step treatment, a grid cell is treated completely as a solid cell if the center of the cell is within the solid object, similarly, the cell is treated entirely as a fluid cell if the center of the cell is outside the solid object. This results in a computation shape (the shape that the solver sees) that is a jagged stair-step-like surface. This technique, for the most part, is very useful in handling complex geometries and benefits automation of grid generation. However, to resolve a non-orthogonal geometry very closely, the grid must be heavily refined near the boundaries. Occasionally this stair-step approach can be refined using a cut-cell or porosity treatment to consider cells partially filled with fluid and solid at the same time. This, however, introduces significant added complexity to the equation solving.

 

Figure 1: Temperature plot showing computational geometry of flow through two parallel plates at an angle (a) with hybrid cell turned off, and (b) with hybrid cell turned on.

A new and ground-breaking feature in 6SigmaET is the use of the Boundary Cell Reconstruction Method (BCRM) for treating solid-fluid interfaces. In keeping with 6SigmaET’s principle of automating gridding, this option can be activated by simply checking the Hybrid Cell checkbox in the Solution Control. Activating this option in 6SigmaET marks the grid cells which contain both solid and fluid properties as ‘hybrid’. These grid cells will store all the additional geometrical properties to adjust the control volume fluxes near the interface boundaries2. Then the appropriate part of a hybrid cell is geometrically merged with the neighboring cells (solid to solid and fluid to fluid) by using face splitting and cell merging technique producing a form of polyhedral cells automatically without user intervention. This reconstruction of the boundary cell enforces an accurate treatment of convection – thus ensuring an accurate heat transfer at this interface.

As modern electronics develop with new state of the art technology, 6SigmaET is in the forefront of developing novel techniques for accurately modeling thermal problem arising in these electronics applications. In an ever-stagnant world of thermal modeling, 6SigmaET is proving that there is a better option available.

Figure 2. Merging scheme for solid-fluid boundary cells

Figure 3. Inviscid flow between two parallel solid surfaces for stair-step and hybrid cell treatments


Blog written by: Priam Fernandes, Sales Manager

Footnotes:

1.Handbook of Numerical Analysis, Vol. 18, 2017, Pages 1-22: Cut Cells: Meshes and Solvers https://www.sciencedirect.com/science/article/pii/S1570865916300394

2.Semin, V. et al, “Application of a multilevel unstructured staggered solver to thermal electronic simulations”, 2015 31st Thermal Measurement, Modeling & Management Symposium (SEMI-THERM) https://ieeexplore.ieee.org/document/7100174/citations#citations