Minimizing Pressure Drop in Cast and Molded Parts
Shawn Wasserman posted on March 18, 2014 | | 4384 views

Solving CFD challenges with the adjoint method has theoretically been around for some time and is well known by experts in industries like Aerospace.  What’s new is that this technology can now be applied to more common problems, like pressure drop simulation in ventilation systems or cast parts.

Pressure drop in rear cabin HVAC optimized 33% using adjoint solver. [1]


What can adjoint solvers tell you?

The adjoint solver is a smart optimization technology which quickly iterates towards an optimal solution.  It can tell you:
  • What areas of your model geometry are causing
          the greatest pressure drop
  • Which direction to modify the geometry to improve
          the fluid or gas flow
  • A prediction of how much of an improvement to
          expect from making the change

And it will do all that with surprisingly light computing resources and few iterations. 

For example, on the left is a before and after image of an automotive ventilation system by Volvo.  Note that the adjoint technology identified the y-junction area as the most restrictive area and recommended changes to the geometry of the duct, producing a 33% reduction in pressure drop from their original baseline.

If you are interested in the math behind the adjoint method, read this paper on aerodynamic shape improvement or even this early paper by Antony Jameson on Aerodynamic Design via Control Theory.  For those of you who might be more interested in how the method applies to pressure drop analysis and other CFD optimizations read on.  Adjoint technology can be applied to a wide range of CFD problems from aerospace to common pressure drop scenarios. 

Gilles Eggenspieler Sr. Fluid Product Line Manager at ANSYS said, “With adjoint solvers you never define a parameter, you just define a goal. In Volvo’s case described above the goal was to minimize the pressure drop. First setup is to run the first simulation as usual. Then use the adjoint solver to determine what section of the geometry impacts (negatively) the pressure drop the most. In the same time, the adjoint solver will also suggest how to modify the geometry to reduce the pressure drop and estimate the effect this change will have on the goal.”


Optimizing Parameterized Models takes a lot of Resources

It’s not unusual for analysts to parameterize their designs and run multiple simulations to optimize for pressure drop or other desired outcomes.  In many cases that means a work-flow process that looks like this:

Even when there are scripts running several iterations, this process still places a big demand on human and computing resources.  “This is a good strategy,” says Eggenspieler, “but the iteration of modifying your geometry, mesh, and then restarting your simulation takes time. Additionally, how do you know you are testing all the parameters you need?”


Adjoint Method is Fundamentally Different

To iterate towards an optimal solution, one first solves the typical Navier-Stokes equations to determine a baseline solution. The adjoint solver then solves and converges an auxiliary field equation and determines a sensitivity gradient. This gradient will then tell the program the changes which, if implemented, will improve the system and by how much. The system can then be solved using the improved geometry. 

This video on Youtube sets out how the Ansys Adjoint software works in a simple example.  This aerospace example clearly shows how the software identifies the areas of improvements and recommends changes to morph the geometry.  The video was recorded using a laptop and only one core.  Ansys says the computing requirements for adjoint solving are no more than with traditional CFD.

“The added benefit to this method is that the program will not just suggest an improved geometry. The program can automatically morph the geometry to this improved shape (note: there is no meshing or re-meshing operation). Morphing takes the initial mesh and morphs it to the new shape. Assuming the initial mesh was optimal, your new one should be as well,” said Eggenspieler. He added, “What is even better is that your next simulation will have a perfect starting point for its iteration - the solution of the previous simulation. These two factors will reduce the optimization process considerably.”


Optimizing with an Adjoint Method Solver

The initial work towards optimization is the same with an adjoint method solver as for typical CFD.  You need to create the geometry, create the mesh and then solve it.  This then becomes your base case.  But rather than iterating back to the beginning, you can now get a list of recommendations to morph your model along with the estimated improvements in your target output.  So if your target output is reduced pressure drop, the various recommended design changes would be ranked by their impact on said goal.


Who Should use an Adjoint Method Solver?

“We see a very large market interest in minimizing pressure drop. Everything that can be made using casting and plastics is fair game for the adjoint solver. But there are other applications: for examples, applications where heat transfer needs to be optimized. Also automotive companies can use the adjoint solver to reduce car drags. Competitive racing companies (e.g. Formula One), can use the adjoint solver to maximize down forces,” clarified Eggenspieler.

However, if you don’t have control over the geometry, such as may be the case if you are working with piping, then an adjoint solver won’t speed your path to optimization. 

The concept of adjoint solvers was once only a high-end solution for aerospace. Now this method is becoming more mainstream and can be applied to a wide range of design and engineering challenges in many industries. 


Ansys has sponsored promotion of their simulation solutions on They have no editorial input to this post - all opinions are mine, Shawn Wasserman. 

Volvo Image courtesy of:

1. Wade, A. (2012). 52 ansys advantage volume vi | issue 1 | 2012 turning optimization on its head. Ansys Advantage, VI(1), 52-53. Retrieved from