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Top tips for modeling electronics

Edited by Paul Dvorak; Machine Design magazine, February 24, 2000.

The 3.5-kW device was designed by CAS Ltd. and built by Charlotteís Web Networks Ltd. Having gained experience with thermal software by following the modeling tips in this article, engineers with the companies optimized the product for smallest size. CFD optimization in software called Coolit from Daat Research, let the company trim the number of anticipated fans by creating the optimal airflow in the system with judicious placement of components, boards, and vents. All this was done without building physical prototypes.

Specialized computational fluid dynamics or CFD software provides a wide range of capabilities for computer prototyping of electronics in enclosures. The software lets thermal engineers shorten design cycles, and eliminate building and testing physical prototypes. The software also lets designers quickly and efficiently evaluate "what if" scenarios, it simulates conditions not reproducible in a lab, and provides more detailed information than do lab experiments. Finally, the technology improves the operation and endurance of electronics and optimizes placement, size, and parameters of components. In short, it helps get a design right the first time.

CFD technology involves solving transport equations of fluid flow and heat transfer on computers. To solve the equations, they must be represented so computers can handle them. This is usually done with so-called finite volume or finite-element methods. The latter were successful only in specialized CFD applications, such as slow flows and non-Newtonian flows. Most all production CFD programs currently use finite-volume methods and we will refer only to them.

Putting the latest CFD technology to best use takes practice and a few unavoidable mistakes. The problems here are solved with software called Coolit from Daat Research and the following guidelines have been compiled from observations of new users. Learning from their mistakes may shorten your learning curve.

Start with simple models. Gain confidence in your modeling abilities and the softwareís capability, start with simple problems, and compare results to analytical solutions and experimental data. One of the easiest problems to set up includes laminar natural convection in a square cavity with vertical heated walls and adiabatic conditions at top and bottom.

The problem should take a few minutes to set up and even less to solve.A solution to this problem appears in the accompanying illustration Flow in a square cavity. The same problem can be slightly modified to obtain another well-researched solution of turbulent natural convection in a rectangular cavity.

To get familiar with the software and build confidence in its use, work on simple well-documented models such as the flow in a square cavity with heated walls.

Finding out how your numerical solution stacks up against the real world is easy with these examples because readily available reliable data makes for an easy comparison. If you experimented with the model by setting different grids and convergence criteria, you noticed the solution changed along with the parameters.

Determining a sufficient grid for an accurate numerical solution means finding the coarsest grid or mesh that provides good answers. This discussion applies both to unstructured and structured grid systems. In general, a finer grid produces more accurate solutions than a coarser one on the same models. In mathematical terms, the numerical solution will tend to the solution of the underlying partial differential equations as the grid is refined.

In practice, however, a uniform grid refinement for 3D problems is virtually impossible as the total number of grids grows exponentially. For instance, if a model has n = 70 grid cells in each direction, increasing the number by only 10% will increase the total number of grid cells 33% from 343,000 to 456,533. Increasing n by 50% in each direction expands the grid to over a million cells for a 238% growth.

Another simple but important problem is the backward-facing step flow. In fact, every obstacle in the path of airflow is a backward-facing step. Many experimental and numerical results are available for comparison.

Fortunately, the solution error depends on both the total number of grid cells and their distribution. Correctly distributed grids go a long way toward getting an accurate solution. A simple example illustrates the point. Consider an exponentially fast varying boundary layer, which is obtained as a result of solving a convection diffusion equation:

Solving this problem on uniform grid with R=10 produces 14% maximum error when 10 cells are used in the boundary layer. To reduce that error to less than 5%, at least 100 uniform grid cells are needed in the boundary layer.

The image is an example of a laminar temperature boundary layer developing on a flat plate. Itís another important problem because itís encountered frequently, itís easy to set up, and solutions are readily available.

A better way to reduce the error is to use non-uniform grids, with smaller cells towards the wall, where the solution changes rapidly. In the case of the boundary layer, an optimum solution uses a logarithmic distribution of grids. Such grid will yield the exact solution with only two cells in the boundary layer!

Obtaining exact solutions on specially designed grids is not an easy feat for general 3D problems. Sufficiently accurate grids, however, are possible. Software, such as Coolit, will automatically produce grids optimized in that regard.

But the question still remains: In the absence of experimental data, how can one determine a sufficient grid? The only method is to recompute the same problem on finer grid and compare results. When the solution in the points of interest does not appreciably change, the previous grid was sufficient. Otherwise, youíll need to repeat the process until changes to the solution become small.

Define the simulationís goal before you start modeling.A goal could be to reduce the number of fans, keep the temperature of a particular package or component within limits, or select a heat sink. Objectives change as projects progress.

Use coarse grid simulations to determine the sensitivity of design decisions on critical components, such as fan parameters or placement. The same applies to optimization problems that require comparing different designs to find a best one. This case would call for examining relative rather than absolute numbers. If an objective is to determine heat-transfer coefficients on the surface of an enclosure, there is no need to specify internal details. The only important element is the position and power of heat sources. The accuracy of a predicted heat transfer coefficient would not be affected.

Do a triage on your CAD model. In most cases, one cannot simply press a button and move a CAD model to thermal software. Too much detail overwhelms computers without a corresponding improvement in accuracy. Simplify the model by deciding what is important in the simulation.

For example, consider an enclosure with several pin fin heat sinks, each with 11x11 pins. A coarse grid - about two grid cells per pin, three per space between the pins, and 20 cells in the direction normal to the base - requires 500,000 grid cells. Add other components and you quickly run out of computer resources.

Ask if the model needs an accurate solution everywhere, or only in certain parts of the model. Be realistic. Greater accuracy requires more time to build a more detailed model and finer grid with correspondingly longer solution times.

Itís worth the effort to trade unneeded detail in a model for a shorter solution time. With regard to pin-fin heat sinks, when itís critical to find a solution around only one sink, then replace the other two with lumped-parameter versions, such as a porous media model available in most CFD codes. The effect of the lumped-parameter heat sinks on the rest of the problem should be close to that of the detailed model, so the solution around the important sink is not adversely affected. Donít forget that partially converged solutions are one way to quickly check a model setup for its accuracy. A complex model usually takes considerable time to reach a fully converged solution, and a mistake in the setup wastes that time. Instead, solve the problem for a few iterations and look at results. Recognizing modeling errors early allows correcting them before the case converges. You may, for example, see that a component is unexpectedly hot - a good indicator that you mistyped its power dissipation or thermal conductivity value. Or, check the fan curves when a flow seems too fast. Itís a good idea to use this technique every time you start a complex model.

 

The avionics equipment built by Miltope Corp. Boulder, CO, was also optimized using CFD software. The model used several lumped parameter submodels and successfully predicted temperatures of critical components to within a few degrees.

The heat sinks look similar but analysis with CFD software showed that one is 50% less efficient than the other. Reports accompanying the analysis further detail the study with quantitative information.

Use a coarse-grid solution when faced with optimization or sensitivity studies. Looking for an optimum component arrangement usually requires comparing several different designs to determine their relative performance. Coarse-grid analysis is the perfect tool for the task. It allows quickly and efficiently predicting whether one design is better than another. NEC engineers, for example, used the method to quickly determine that a heat sink from one manufacturer is 50% less effective than a similar one from another.

Sensitivity studies with coarse grids make sense when you donít have all the information to build a CFD model, or when some of the information is suspect. It becomes important to determine whether or not the suspect quantity appreciably affects the prediction of critical parameters. When it turns out the missing data is unimportant, the analyses can safely continue using estimates.

The same approach works when itís necessary to determine sensitivity to lumped parameter models. After replacing a component or a group with their simplified versions, it is important to determine how the change affects critical parts. Coarse-grid analyses let users judge whether important components in the model are sensitive to the parameters selected for the lumped parameter model.

Check the mass and energy balance using hand-calculated estimates. Itís a good way to see whether or not a CFD model has gross errors. Do the mass and energy balances hold? Does the order of magnitude predicted using hand-calculations and numerical simulations agree? If any of these are not true, look for an error in the setup or the model.

Identify turbulence. All CFD programs require that users specify whether the flow is turbulent or laminar before doing the simulation and, if the flow is defined as turbulent, require you select a turbulence model. (Turbulence models are approximations of the original equations that allow simulations on regular grids.) Turbulence models are necessary because even though the CFD governing equations correctly capture turbulence, very fine grids are required to do so accurately. This approach of modeling turbulence on fine grids is called a direct simulation and is used primarily in academia for basic research.

Selecting the right type of flow is important because assuming laminar flow instead of turbulent may significantly under-predict heat transfer. Robust turbulent eddy mixing results in the effective thermal conductivity in electronics applications ten to hundred times greater than it is for laminar flow.

Many commercial CFD codes provide on-line advice based on specified boundary conditions. But the advice is often misleading. For example, one suggestion says when a system has a fan, flow is turbulent. That is indeed true next to the fan. The question is whether the flow is still turbulent as it goes through the rack of closely spaced PCBs carrying heat-sensitive components. It probably is not. Most of the airflow will bypass the rack along paths with less resistance. And whatever goes through the rack becomes laminar as the flow squeezes in the narrow passageways between boards.

Using a turbulence model with wall functions is likely to over-predict the amount of heat transfer from the board. That means the model will predict lower than actual temperatures for board components. A better choice is to avoid the turbulence model or use advanced turbulence models without wall functions, which work reasonably well in both the laminar and turbulent regions of the flow.

The simulation for an electronics equipment manufacturer was computed using a turbulence model in Coolit that is capable of modeling mixed flows. It correctly predicts transition of flow from highly turbulent (white) to laminar (violet) and again to turbulent.

A special case is free convection flows that have no steady state solution. For example, in the flow shown below, the air plume at the point of impact where the rising warm air hits the ceiling of the enclosure oscillates. You wonít be able to find a steady state solution to this laminar flow problem. The solution residuals, that measure the departure of solution from steady state after reaching a plateau oscillate with the flow. Users have several options after recognizing that the plumeís oscillations have almost no effect on the temperature of the plate fin below:. accept the solution with oscillating residuals as ďconvergedĒ; use a turbulence model without wall functions to dampen the oscillations and obtain a steady state solution, or solve the problem as time-dependent, obtain results over a period, and average them. All three approaches are legitimate and produce similar results. But unless you are writing a scientific paper, the third approach is not practical because it takes a lot longer than the other methods.


Coolit simulation of the Nokia benchmark experiment in which a rising plume oscillates.



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