What does the word “optimization” mean to you? To many, it is a broad definition applied rather abstractly, describing a process whereby a system is made to perform better through incremental advancements in understanding and subsequent implementation of improvements. But in the world of data scientists, engineers, and mathematicians, the word “optimization” has a very specific and profound definition.

Merriam-Webster defines optimization as “an act, process, or methodology of making something *as fully perfect, functional, or effective as possible*, specifically the mathematical procedures (such as finding the maximum of a function) involved in this.” Engineers hear the phrase “maximum of a function” and immediately begin to envision their system or design as a complex multi-variate function relating the outputs to the input variables. Instead of hunting and pecking at individual improvements, what if we could understand the entirety of how the input variables affect the result, and then simply select the maximum?

In one or two dimensions, it is a relatively easy exercise to envision this. Take flow around a bent channel, for instance. If somebody asked you “how does pressure drop change as I increase the radius of the bend?” You may think for a minute, but then confidently say “increasing the radius of curvature decreases pressure drop.”

All other things being equal, this is of course a well-known relationship. But what if somebody said, “What aspect ratio duct has the lowest sensitivity of pressure drop to radius of curvature?” You’d be forgiven for not immediately answering; this requires the establishment of several more relationships and the complex interdependencies between them. Now, extend that question to “In order to achieve the highest uniformity of heat transfer while also requiring the lowest pressure drop, which combination of duct aspect ratio and radius of curvature should I choose?” and now you are sure that this cannot be answered manually.

Luckily, a question such as this is easily answerable via mathematical optimization methods. All that it requires is a means to gather a table of data: a series of inputs and their corresponding outputs. Experimental methods have historically been used to derive this data, but modern simulation methods are much more effective. Since most of these variables tend to be geometric, modifying them on an experimental basis can be prohibitively expensive, while simulation methods can modify geometry instantaneously and derive new results in minutes. And since ANSYS Workbench provides a perfect platform for scripting simulations through changing parameters, the construct is already in place. Furthermore, the optimization methods available in ANSYS are completely agnostic to the simulation type and complexity; as far as they are concerned, it is a table being generated of input parameters and results. This means that every design proposed within an optimization method can easily be sent through any of the physical tests within the ANSYS toolset, and the outputs from all of those tests can be collated into multi-objective studies.

In the above heat exchanger example, this is only a two input/two objective optimization problem. A modest laptop can solve it in roughly 15-20 minutes using ANSYS CFD, and it turns out the performance functions look like this.

And the pareto front looks like this.

Indicating a clear tradeoff between heat transfer uniformity and pressure drop; since there were two objectives, a designer can now pick a point on that blue curve which best balances the two objectives, read off the chart which input parameters created that point and use that for her design. But perhaps more importantly, she can visualize exactly how the change in input parameters affects her design within these ranges. For instance, she can also state “It looks like the duct with aspect ratio of 1.6 has the lowest sensitivity of pressure drop to radius of curvature”.

This bent duct problem was a very simple one, but the opportunity for solving larger problems can be much more lucrative. Say she is working on a design for an air-cooling manifold and chamber after a metalworking operation. She has four nozzles pointed down at a conveyor with a hot plate on it and wants to know what the optimum shape and position of those nozzles would be to evenly distribute the heat and minimize required airflow. Once she adds up all the variables (length, width, depth, angle, aspect ratio, spacing, etc.) for all four nozzles, she realizes she has a couple dozen input variables. She certainly wants to see the highest cooling rate possible but also needs it to be relatively uniform, so she has multiple objectives. Perhaps she also wants to analyze the thermal stresses such a cooling scheme would place on her metal and minimize those. If she can set up one simulation, why not tag those dimensional input parameters and set up an optimization study?

At the cost of 20 more minutes of setup and a couple days of computational time, she could save weeks or months of trial and error design work.

Many people think of CFD as a sort of replacement for experimental prototype development, but it really goes much further than that. Due to the rapid turnaround time of changing geometries, and the inherent ability of scripting, optimization methods offer an extremely powerful set of tools to bring into the product design process, both in terms of arriving at the optimal design quicker and in educating the designers and users on the relationships inherent in their designs.

If you are looking to extend your simulation capabilities to include optimization, reach out to Rand SIM and we’ll be happy to showcase this ability.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.