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Published January 13, 2025

Balancing Speed With Accuracy: an FSI–MRF Coupling Approach

Author:
Allie Yuxin Lin

Marketing Writer

In today’s fast-paced and ever-evolving world, industries face increasing pressure to deliver precise results quickly—and CFD simulations are no exception. Instead of buckling in the face of this challenge, one organization rose up and decided they were not going to settle for the typical trade-off between accuracy and speed; they wanted both, and they were determined to figure out how to get it. Researchers at Southwest Research Institute (SwRI) developed an innovative coupled approach between two common techniques in the CFD industry, and their results combined high-fidelity simulations with fast computational runtimes. In this blog, we explore their journey, from the identification of the problem to the creation of a solution, along with the appropriate testing, analysis, and general relevance.

The Trouble With Traditional Techniques

A 3D CFD simulation for a turbocharger is typically conducted in one of two ways. The simplest approach is the multiple reference frame (MRF) strategy, also known as the frozen rotor. This technique keeps the impeller stationary and simulates movement using a rotating coordinate system; as such, the simulation accommodates the moving geometry without needing to regenerate the mesh at every time-step. However, the existing literature indicates this approach may be limited in several capacities. In their CFD analysis of an automotive pulse system turbocharger, a research team in London found the MRF model could not numerically capture the hysteresis curves of mass flow rate and efficiency.1 The MRF approach is also known to overpredict the non-uniformity of the flow field, as demonstrated by CFD studies of turbo compressors.2 

The most accurate framework is achieved through transient fluid-structure interaction (FSI) modeling, in which forces are calculated by the numerical integration of pressure and shear stress over the impeller surface. With these calculations and Newton’s Second Law, the rotational speed of the impeller can be predicted. This approach is a predictive method where the rotation of the impeller is determined by the fluid-impeller interaction; therefore, any flow field change can result in a different rotational speed. While this approach accurately predicts all necessary parameters and creates a comprehensive simulation, it is computationally time-consuming. 

“Typically, for CFD simulations of compressors and turbines, we use an FSI modeling approach. This works relatively well, since the device’s rotational speed is low, around 1,000–4,000 RPM, which means the computational expense is not so extreme,” said Zainal Abidin, Powertrain Analysis Manager at SwRI. “But for a turbocharger, where the speed is comparatively much higher, in the order of 100,000 RPM, the simulation can get very expensive, very fast. So we needed to do something differently.”

The New Approach

To accommodate the limitations they found, the team at SwRI developed a two-way coupled MRF and FSI approach using CONVERGE CFD software. The FSI solver within CONVERGE simulates the impeller motion using the constrained 1-degree of freedom (1-DOF) model, where the motion is restricted to rotational movement about the impeller axis. A specific region is identified around the moving turbine impeller, where the equations are modeled in the local rotating reference frame. The governing equations are then modified to incorporate the velocity of the rotating region that arises due to the fluid forces on the moving surface, which in turn affect the flow field.3

“When we were considering CFD solvers to use for this case, CONVERGE was the obvious choice,” explained Zainal. “In the years that we’ve worked with the software, we’ve found CONVERGE provides the highest accuracy for simulations with a complicated mesh, which is definitely the case for this turbocharger.”

Insights and Outcomes

The test platform used was a 2010 heavy-duty on-highway 15L engine with a twin-scroll compressor. To collect CFD calibration data, high-speed pressure transducers were installed on both sides of the divided turbine inlet, turbine outlet, compressor inlet, and compressor outlet, as shown in Figure 1.

Figure 1: Locations of the high-speed pressure transducers.

The team at SwRI then created a 3D CFD model to test the new coupling method; the 3D geometry is shown in Figure 2.

Figure 2: 3D geometry of the CFD setup.

CONVERGE automatically generates a cut-cell Cartesian grid at runtime, eliminating user meshing time. At each intersection surface, the software trims the cells so the intersection information, including metrics such as surface area and normal vectors, is reduced before storage. The Redlich-Kwong equation-of-state was employed to couple density, pressure, and temperature variables, and a modified Pressure Implicit with Splitting of Operators (PISO) algorithm assisted with pressure-velocity coupling. Due to its simplicity and low computational runtimes, the researchers chose to employ the k-ε turbulence model over more complicated options like a Reynolds Stress Model or large eddy simulation model. The setup also leveraged a law of the wall boundary condition to bridge the under-resolved flow in the viscous sublayer between the wall and the fully turbulent region.3

To compare the FSI-MRF coupling approach with its pure FSI counterpart, a pure FSI model was built and run to simulate the impeller rotation. The numerical setup used for both strategies was the same, but due to the long runtimes, the pure FSI simulation was not run for as many crank angle degrees. Results, as pictured in Figure 3, showed both approaches had very similar predictions of impeller rotational speed. Additionally, the computational time for the coupled FSI-MRF process is around 16 times faster than the pure FSI solution. 

Figure 3: Impeller rotational speed comparison between the pure FSI and FSI-MRF coupling approaches.

To further assess the validity of the new approach, the SwRI researchers wanted to compare the predicted values for pressure upstream of the turbine against experimental data. To do so, they introduced an energy sink (represented by a resistant torque) to the governing equations to account for the energy transfer from the turbine to the compressor. Calculated pressure values from the coupled approach matched well with test data, as shown in Figure 4.

Figure 4: Pressure comparisons between modeling data and experimental results, shown for the front and rear sides of the turbine.

The validated coupling approach can now be used in design optimization studies to maximize turbine efficiency. The adapter and exhaust manifold were modified to assess their influence on turbine power. The adapter connects the exhaust manifold to the turbine entrance; therefore, an improvement on turbine power is represented by an increase in impeller speed. The modified adapter resulted in slightly increased rotational speed, while the modified manifold had the opposite effect, as seen below in Figure 5.

Figure 5: A comparison of impeller rotational speed between the baseline model, the turbine with a modified adapter, and the turbine with a modified manifold.

Looking Ahead

The coupled FSI-MRF approach successfully bridges the gap between accuracy and speed, offering a powerful solution for complex simulations that require both precision and efficiency. Calculations reminiscent of a pure FSI approach were iteratively passed back to the solver to update an MRF-type system. Early testing demonstrated this approach not only aligns closely with experimental results but also achieves a 16-fold speed increase for the simulation process. As future research continues to refine this method, it has the potential to play a pivotal role in driving faster, more accurate simulations across various applications.  

“We discovered this new coupling approach, but we’ve only really scratched the surface. There is a lot of room for improvement, especially to increase the efficiency of the exhaust port,” Zainal noted. “Still, this method has a lot of potential; it can be applied to any simulation that could benefit from a faster computational speed while avoiding the pitfalls of a less accurate solution.”

References

[1] Palfreyman, D. and Martinez-Botas, R. F., “The Pulsating Flow Field in a Mixed Flow Turbocharger Turbine: An Experimental and Computational Study .” J. Turbomach. 2005; 127(1), 144–155. doi:10.1115/1.1812322.

[2] Liu, Z. and Hill, D. L., “Issues Surrounding Multiple Frames of Reference Models for Turbo Compressor Applications,” International Compressor Engineering Conference. Paper 1369. 2000. 

[3] Abidin, Z., Morris, A., Miwa, J., Sadique, J., et. al., “FSI – MRF Coupling Approach For Faster Turbocharger 3D Simulation,” SAE Technical Paper 2019-01-0007, 2019, doi:10.4271/2019-01-0007.

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