NatureDesignedbytheFlow 1536x847 1

Panta rhei – Everything Flows

The world flows! Literally. There are fluids and flow all around us, and there are amazing solutions from nature to tackle associated flow problems. Take the shark nose: Nature came up with the most streamlined nose for this guy to be fast in the water. Same for the Penguin; Did not do a good job on flying for that one, to be honest…  But there‘s more: Rivers find the best possible way through a given terrain, even shaping it for better throughput. Wind shapes trees to minimize the drag on them. Dunes form from nothing but sand driven by the wind, creating an aerodynamic bulk of grains. Our very own heart is a flow-optimized solution to transport blood through our body in the most economical way etc. etc.

Now – as an engineer – why do I tell you this?

In recent decades, engineers have started to look at nature and technically leverage the solutions nature came up with! They started to understand those solutions’ power in nature and began to mimic them to solve engineering problems. Very famous stuff. Called Biomimicry or Bionics.

SimcenterConf The Mighty Duct with HP
Designed by the flow – The Revolution of Evolution 10

Admittedly this is exceptional engineering, no doubt about it. But there is a bunch of issues associated with it…

  1. It takes ages for nature to come up with those solutions.
  2. What if nature has not (yet) solved your flow engineering problem?
  3. What if the solution is great in nature but can’t be manufactured?

Now imagine what would happen if we don’t mimic the few flow-optimized designs that evolution came up with but instead.

we mimic the evolutionary process itself – but an evolution a million times !

DarwinDay TopologyOptimization 1536x743 1
Designed by the flow – The Revolution of Evolution 11

Well, to do so, just like for your coffee this morning, you need only two ingredients… Number one:

Computational Fluid Dynamics (CFD) Simulation

No worries, I will not discuss the equations. But let me tell you this one thing: There is a mathematical equation called the Navier-Stokes Equation that describes liquids and gases’ behavior in all its kinds. And, that one is among the most important equations on this planet. Its Business impact is probably the highest of all equations; I would guess it‘s at least heads up with Maxwell equation for electrodynamics. It‘s probably more business-relevant than the well-known E=mc2. (it‘s hard to measure, to be honest, and I may be biased- but undoubtedly, the thing is huge!)

But in any case, some find that thing so cool they have it engraved on their arm.


Now, CFD in two sentences is just this: Split the space of interest into millions of small volumes, called cells, solve the Navier stokes equation in each of them, and transfer the physical quantities from one cell to the other. That way, you will be able to predict the physical behavior of the fluid numerically.

Anyways, let‘s scratch math here… and come straight to ingredient number two, which is probably less famous:

Topology Optimization and the “Adjoint of Marathon”

To understand how Topology Optimization works, imagine you would like to become a six-star medal winner, i.e., finish all big marathons of this earth successfully.

In a nutshell, Topology Optimization for CFD (and six-star medaling) is an algorithm that works like this:

  1. For a given domain that the fluid may enter, we run the flow simulation using CFD.

(You run any marathon)

  1. Then we assess something called the adjoint: A mathematical function that gives us an idea of which local area impacts the cost function, e.g., the pressure loss or the flow rate.
Adjoint1 1536x646 1
Designed by the flow – The Revolution of Evolution 12

(For the marathon, the adjoint goes like this:

Adjoint2 1536x731 1
Designed by the flow – The Revolution of Evolution 13
  1. Next, we let the algorithm make those areas inaccessible for the flow (by a wall or solidification) that negatively impact the performance function.

(You start training those parts of your body that were showing the most significant negative impact on your run time, detected by those parts that hurt the most. Yes, pain can be a good teacher!)

  1. In the Simulation, we start running the CFD with the newly formed remaining flow domain. So you are back at step 1 but with an updated environment. This time, the cost function – when reassessed – should show an improved value.

(You are going to run the next Marathon after training the most relevant parts of your body. This time your finishing time should have improved.)

  1. We do these steps 1 to 4 in loops until the flow path’s shape does not change significantly.

(You run one marathon after the other until all parts of your body are trained such that pain is minimized/sufficiently low and in return finishing, times are the best possible within the given constraints – aka  your physiological preconditions

Topology Optimization – the shortcut

If that was too much…

It‘s just like… a River defining its way! BUT in hours, not ages!

River 1536x508 1
Designed by the flow – The Revolution of Evolution 14

So, with these two ingredients, you will have a tool at hand that comes up with optimal solutions for a yet unsolved engineering flow problem within a few hours.

However, there is still issue #3:

Topology Optimization? Great! But that thing can’t be manufactured!

Ten years ago, this story would probably have stopped here. I will always remember my Ph.D. supervisor tell his story about his freeform surface optimization of a turbine blade. As a young engineer, he was super-thrilled about the significant performance gains the edge showed in the CFD simulation, so in excitement, he went to his boss, who then went to the designers, who then said:

“Well, no. We can’t manufacture this. Let’s make this a proper circle and this straight and this straightforward and …. Boom! Gone was the excitement! Gone was the performance gain! Gone was freeform-based surface optimization!

But the times they have changed!

Meanwhile CAE got a big buddy: Additive Manufacturing

CFD engineers, I am not sure if you all realized yet, but this is a game-changer! The moment that unchains our creativity delivers finally unseen freedom in looking at possible flow solutions. It’s the moment we can dig out the old freeform surface optimized shape for the turbine blade.

And, it is the moment where the flow becomes the new designer. It is the revolution of CAE based evolution.

But then, I hear you say, while this digital process sounds great in theory and you tell me I can print the wildest shapes now, I still have some doubt:

Why would I trust topology optimization for real-life product development?

Well, it’s Darwin Day, so what better test to see if eight million years of evolution can be imitated by a few hours of Simulation than what’s closest to our hearts? Take a look at this:


For reference, we took an aorta geometry from We then generated a sufficiently big box around it as the starting domain, constrained the inlets and outlets according to where they are for the real aorta, then added some (admittedly simplified boundary conditions – blood can be a nightmare in CFD)  and let the magic happen.

Check this out, Charles.

Admittedly it’s not perfect, but given it took a few hours on a Laptop, I think we can call it en-par with 8 million years of evolution.

But again, I hear you say. All right, a nice toy! But, I am an engineer, not a biologist.

Why would I care about this methodology?

Now, I don’t tell you why! I just let you see what has happened to those engineers that already did care.

On 4: Siemens – The brake cooling duct

Breaks of cars can get quite hot. So cooling them through air guided to them is crucial but may cost aerodynamic performance. In the study at hand, the goal was to improve the heat rejection of a front-wheel brake disk through a brake cooling duct design. Topology optimization was set up to optimize heat transfer, thereby constrain pressure loss in the duct to be ~90% of the original design. Moreover, as a constraint, 10-20 % of design space should remain fluid space.

Compared to the reference duct, the new cooling duct design showed a 4.4 percent improved cooling performance (heat transfer) at a 21 percent reduced pressure drop. All that achieved within a few days of autonomous CFD simulation.

On 3: EDAG – The scaleable battery pack cooling device

Electrification in automotive is currently a hot topic of discussion. Electric vehicle batteries are continuously improving, delivering more power, and having greater autonomy. Still, one of the biggest challenges is battery safety and the ability to design an effective cooling system. EDAG as mobility engineering experts explored, with the help of Siemens, additive manufacturing and topology optimization to develop an optimized battery pack water cooling system.

Employing the topology optimization method leads to a 6.4% increase in the inlet duct’s mass flow and a 46.9% reduction in the pressure drop of the outlet duct. All this in just 2 days of simulation time (~50 hours in 336 cores). See the video for the amazing new organic design.

On 2: HP – The mighty duct

On 1: What is your flow problem?

In Simcenter STAR-CCM+, the Siemens multiphysics CFD solution, version 2020.3, we introduced an integrated solution for fluid/thermal adjoint-based topology optimization. The success inspired this and the lessons learned from the “Mighty Duct” project, one of the early pilot projects applying the technology. Streamlined and easy to set up, the newly implemented Topology Optimization feature mitigates any need for complicated JAVA macros or third-party tools. It features an integrated constrained optimization method. This allows you to solve engineering problems with competing attributes. By defining one objective and multiple flows and thermal constraints and volume constraints, it offers numerous possibilities for flow topology optimization.

So the only question left is

When will the flow become your new designer?

Find out more about topology optimization in Simcenter STAR-CCM+

and join the cult! Which cult? Well, the story goes like this: in the early days of a comparably tough-to-use JAVA-based methodology implemented by my colleague Steve, another colleague, Rodolfo, came up and asked: “And you really believe in this topology optimization stuff?” “Yeah, sure. Why wouldn’t I?” said Steve. Rodolfo thought about it for a second, and as he was about to walk away, he said:

“Adjointology” that’s what this should be called then. And nobody could explain that phrase better than my colleague Mani:

Disclaimer: I am the author at PLM ECOSYSTEM, focusing on developing digital-thread platforms with capabilities across CAD, CAM, CAE, PLM, ERP, and IT systems to manage the product data lifecycle and connect various industry networks. My opinions may be biased. Articles and thoughts on PLMES represent solely the author's views and not necessarily those of the company. Reviews and mentions do not imply endorsement or recommendations for purchase.

Leave a Comment

Your email address will not be published. Required fields are marked *