Reduced Order Modeling for Automotive Aerodynamics

40% scale DrivAer model (notchback configuration) in wind channel A

The recent improvement of high-performance computing hardware has enabled the utilization of unsteady computational fluid dynamics (CFD) for industrial product development. Unsteady CFD can accurately simulate the transient phenomena of the flow field, moreover, highly accurate steady-state results can also be obtained through appropriate averaging. Especially in the field of automotive aerodynamics, the transient flow phenomena around the vehicle can strongly affect driving stability and ride comfort. A difficulty in the analysis of the transient flow field by CFD is that the time series of flow field data typically needs to be saved to disk during and after a simulation. This often requires massive storage space, as the transient flow field data around a vehicle is spatially highly resolved to capture complex flow structures consisting of various time and length scales. One possible solution to reduce the total amount of data is to approximate a transient flow field in reduced order. Proper orthogonal decomposition (POD) is a well-known data-driven modal analysis method that is often used for reduced-order modeling of the flow field. Especially the on-the-fly algorithm of POD, such as incremental proper orthogonal decomposition (IPOD) or incremental singular value decomposition, requires much less RAM and disk space, since it updates modes incrementally when new snapshot data is available.

As an example, the IPOD modes are computed from the simulated transient flow field around the DrivAer notchback model. The numerical simulation is validated with the wind tunnel experiment (figure above). The computed IPOD modes successfully approximate the complex transient flow field around the vehicle with respect to both transient characteristics and instantaneous flow structures (figure below). Furthermore, this unsteady flow field data approximated in reduced order can be processed by dynamic mode decomposition (DMD) to extract the dominant transient flow structures.

Consequently, the amount of transient flow field data is reduced to 11% of the original size with the setups presented. This IPOD computation occupies roughly 80% less memory than the conventional POD algorithm.

A snapshot of the instantaneous vertical velocity on the x-z-plane at y=0.2m from the reconstructed field (above) and the original field (below).

Publications

  • Matsumoto, D., Kiewat, M., Niedermeier, C., & Indinger, T. (2018). Reduction of transient flow field data using Incremental Proper Orthogonal Decomposition. Proceedings in 2018 JSAE Annual Congress (Spring) 
  • Matsumoto, D., Kiewat, M., Haag, L., & Indinger, T. (2018). Online Dynamic Mode Decomposition Methods for the Investigation of Unsteady Aerodynamics of the DrivAer Model (First Report). International Journal of Automotive Engineering, Vol. 9, Issue 2, pp. 64-71
  • Kiewat, M., Matsumoto, D., Haag, L., Zander, V., & Indinger, T. (2018). Online Dynamic Mode Decomposition Methods for the Investigation of Unsteady Aerodynamics of the DrivAer Model (Second Report). International Journal of Automotive Engineering, Vol. 9, Issue 2, pp. 72-78
  • Haag, L., Kiewat, M., Indinger, T., & Blacha, T. (2017, July). Numerical and experimental investigations of rotating wheel aerodynamics on the DrivAer model with engine bay flow. In ASME 2017 Fluids Engineering Division Summer Meeting (pp. V01BT12A005- V01BT12A005). American Society of Mechanical Engineers
  • Collin, C., Mueller, J., Islam, M., & Indinger, T. (2017). On the Influence of Underhood Flow on External Aerodynamics of the DrivAer Model. Proceedings of the 11th FKFS Conference, Progress in Vehicle Aerodynamics and Thermal Management, Stuttgart,Germany, pp. 201-215, ISBN 978-3-319-67822-1