Aero­dy­namic Shape Opti­miza­tion: A Prac­ti­cal Guide

When it comes to fluid- or aero­dy­namic shape opti­miza­tion, we have been talking a lot about very specific appli­ca­tions in our recent blog posts, such as the design of race car rear wings or the shape opti­miza­tion of turbine blades. Sim­u­la­tion engi­neers from the aero­space, auto­mo­tive or tur­bo­ma­chin­ery sector are inter­ested in finding optimal designs with superior per­for­mance but also with a high robust­ness in terms of oper­at­ing points. They inves­ti­gate quan­ti­ties such as lift and drag coef­fi­cients, vortex struc­tures, pressure, shear stress and velocity dis­tri­b­u­tions, and try to improve the flow and struc­tural char­ac­ter­is­tics of their products. Thanks to the afford­able hardware resources, engi­neers can now scale their design process with a few clicks to explore hundreds or even thou­sands of design variants.

This article now focuses on giving you a rather quick and prac­ti­cal guide to shape opti­miza­tion with CFD (Com­pu­ta­tional Fluid Dynamics) and other sim­u­la­tion tools. We’ll look into require­ments for the geometry models, the meshing and sim­u­la­tion setup, but also at opti­miza­tion strate­gies and dis­trib­ut­ing sim­u­la­tions on HPC systems.

Para­met­ric Models for Aero­dy­namic Shape Optimization

In many orga­ni­za­tions, the existing CAD models of their products (e.g. aircraft bodies and wings, turbines, car com­po­nents, etc.) are typ­i­cally para­met­ric. However, when it comes to variable geometry that needs to be robust and ready for an opti­miza­tion loop, many of the tra­di­tional CAD systems fail at some stage. The regen­er­a­tion of geometry some­times unex­pect­edly breaks or returns an error. The reason could be as an example a failing inter­sec­tion or fil­let­ing process. This is only one bot­tle­neck. If you have to auto­mat­i­cally create a mesh for new design can­di­dates, all face IDs (e.g. colors with names) need to be the same for each design because the IDs are often ref­er­enced in meshing tools.

So, the first thing you need is a para­met­ric model of your product that is ready for automa­tion. If you have to pick a CAD software or geometry modeler, you should ideally consider the fol­low­ing issues:

Ded­i­cated to Automation

Make sure you use flexible para­met­ric tech­nolo­gies and tools that are geared towards automa­tion. Note that some of the CAD tools on the market were ini­tially not made for this task or do not target such a design process at all.

Robust­ness

Your geometry should be 100% robust, i.e., the regen­er­a­tion of new geometry can­di­dates should never break or fail.

Inno­va­tion

As an aero­dy­namic engineer, you should be able to quickly build inno­v­a­tive new ideas into your geometry model (e.g. flow-related features), either together with the CAD depart­ment or on your own. This is impor­tant espe­cially for the long-term com­pet­i­tive­ness of your product.

Para­me­ter Reduction

Your CAD tool should give you smart tech­niques for para­me­ter reduc­tion, to minimize the overall sim­u­la­tion time in the opti­miza­tion. This can be either smart para­met­ric modeling tech­niques or inte­grated method­olo­gies such as PCA (Prin­ci­pal Com­po­nent Analysis), etc.

Iden­ti­fiers

The face IDs and names are pre­served for all gen­er­ated designs to automate the meshing and sim­u­la­tion. This is required e.g. for some meshing tools, in order to be able to run a recorded script.

Con­straints

The geometry con­straints are auto­mat­i­cally sat­is­fied for each design. This includes cross-section areas, thick­nesses, and minimum dis­tances (pack­ag­ing), etc. For these tasks, your CAD tool needs to offer inte­grated opti­miza­tion methods that can be used for defining geometry.

Auto­mated Pre-Processing

Finally, a few CAE tools expect good-quality STL geometry so you need some controls for the exported surface mesh quality.

Automate Meshing and Simulation

Once you have the geometry ready for automa­tion, you need to decide on your meshing and sim­u­la­tion strategy. Probably, you have your sim­u­la­tion setups already, and you simply need to automate it.

In some cases, the first phase of design explo­rations can be con­ducted with simpler sim­u­la­tion approaches, e.g., poten­tial flow codes or other pre­lim­i­nary eval­u­a­tion tools. These cal­cu­la­tions are much faster than full-blown RANS (Reynolds-averaged Navier-Stokes) codes and help you to find a promis­ing direc­tion. You need to make sure that your ​“simple” solution really gives you the infor­ma­tion you need, within the quality range that you require for the explo­ration phase, and based on your expe­ri­ence as a sim­u­la­tion engineer.

No matter which approach or software you choose: All these sim­u­la­tion tools need to be auto­mated, and this is increas­ingly easy for most of the solu­tions in the market. Usually, they run in batch mode as well. You have to do the record­ing before­hand, i.e., some kind of script­ing, which replaces the baseline geometry with the new design can­di­date. Examples of meshing and sim­u­la­tion tools that can be auto­mated are ANSYS software, STAR-CCM+, NUMECA tools, TCFD, GridPro, POINT­WISE, etc.

Adjoint CFD

Besides poten­tial flow codes and standard RANS solu­tions, there is also adjoint CFD which gets more traction in engi­neer­ing appli­ca­tions. Tools such as CAESES can also link the para­met­ric model to the adjoint CFD solution in order to find the most impor­tant geometry para­me­ters for your opti­miza­tion. Automat­ing adjoint CFD is pretty straight­for­ward as well. In most cases just an addi­tional result file needs to be taken into account.

Struc­tural Analysis

If you are not just con­sid­er­ing the flow char­ac­ter­is­tics of your com­po­nent, but also the struc­tural behavior, you need to inte­grate these addi­tional com­pu­ta­tions as well (here is a tur­bo­ma­chin­ery example). Since these tools have dif­fer­ent require­ments, it might take some time to inte­grate it into the full loop. But you will win a lot if you manage to finally go the holistic track. From our expe­ri­ence, orga­ni­za­tions can save up to several months of engi­neer­ing time only if the CFD and the struc­tural depart­ments tightly col­lab­o­rate within shape opti­miza­tion tasks.

Choosing the Right Opti­miza­tion Strategy

Most of the engi­neer­ing appli­ca­tions today are pretty expen­sive when it comes to the overall sim­u­la­tion time of a single design can­di­date. Hence, you need an effi­cient opti­miza­tion strategy to accel­er­ate the design process, and to find your optimal design in shortest time. Here is one rec­om­mended strategy for typical fluid or aero­dy­namic shape opti­miza­tion tasks:

Sen­si­tiv­ity Analysis

Depend­ing on your sim­u­la­tion time, conduct a design explo­ration phase with a set of samples where you learn about your opti­miza­tion problem. Which of the free vari­ables are impor­tant, and which of them can be deac­ti­vated for the next phase of the opti­miza­tion? Check the cor­re­la­tions and under­stand what’s going on. Your exper­tise counts in this phase! As an example, let’s say we create and analyze 100 dif­fer­ent designs.

Global Opti­miza­tion

Run a global opti­miza­tion based on the data col­lected in the sen­si­tiv­ity analysis. Create a response surface model where you recycle e.g. the 100 designs, and run a genetic algo­rithm on this sur­ro­gate. This can be fully auto­mated, and you can decide how many iter­a­tions you want to run, depend­ing on your hardware and license resources. The sur­ro­gate models are often gen­er­ated on the basis of either Neural Network concepts, Radial Basis Func­tions, Kriging, or just simple poly­no­mial functions.

Local Opti­miza­tion

In some sit­u­a­tions, and if there is still some time left, it can be ben­e­fi­cial to take the best design(s) from the global opti­miza­tion and run a few more iter­a­tions by using a local search. In most industry-relevant cases, deriv­a­tive-free methods are rec­om­mended and do a good job in fine-tuning your designs.

For more infor­ma­tion about sur­ro­gate models, see the article ​“Global opti­miza­tion using response surfaces”. Of course, there are many other strate­gies possible: For instance, run the sen­si­tiv­ity analysis as explained above and then directly apply a local opti­miza­tion to a few promis­ing design can­di­dates (using the reduced para­me­ter set). Finally, some of the opti­miza­tion tools in the market offer one-click opti­miza­tion strate­gies where a com­bi­na­tion of the methods from above are coupled. And since AI (Arti­fi­cial Intel­li­gence) and machine learning are a big movement, we will also see new opti­miza­tion solu­tions coming up in the market that intro­duce inno­v­a­tive approaches to aero­dy­namic shape optimization.

Make Use of HPC Clusters

If you have the setup ready on your local machine, it is often a rea­son­ably small effort to let it run on remote hardware resources. The sim­u­la­tion and geometry tools such as CAESES run in batch mode, i.e., without the need of a graph­i­cal user inter­face. Exactly what you need to run the entire setup on HPC clusters, for instance.

Grid engines help you to dis­trib­ute your analyses (check out more infor­ma­tion about opti­miza­tion and grid engines), and tools such as ANSYS even have their own solution for that (Remote Solve Manager RSM). To be on the safe side, make sure your CAE tools support Linux. 

By the way: Weekends are really great for running opti­miza­tions! Many engi­neers all over this planet set up and trigger their runs on Friday so that first results can be already assessed on Monday. Sure, this works only for a subset of appli­ca­tions, but it’s def­i­nitely worth­while pointing it out at least as a side note… has anybody already written an article about energy con­sump­tion in the CAE sector on weekends? ;-)

More Infor­ma­tion

CAESES is a spe­cial­ized solution for robust and flexible para­met­ric design and shape opti­miza­tion with sim­u­la­tion tools. If you also work on aero­dy­namic shape opti­miza­tion for aircraft com­po­nents, race cars, wings, channels, ducts etc., and you are inter­ested in trying out CAESES within your team, then please don’t hesitate to get in touch with us.