This content is not included in your SAE MOBILUS subscription, or you are not logged in.
Application of Dynamic Mode Decomposition to Influence the Driving Stability of Road Vehicles
ISSN: 0148-7191, e-ISSN: 2688-3627
Published April 02, 2019 by SAE International in United States
Annotation ability available
The recent growth of available computational resources has enabled the automotive industry to utilize unsteady Computational Fluid Dynamics (CFD) for their product development on a regular basis. Over the past years, it has been confirmed that unsteady CFD can accurately simulate the transient flow field around complex geometries. Concerning the aerodynamic properties of road vehicles, the detailed analysis of the transient flow field can help to improve the driving stability. Until now, however, there haven’t been many investigations that successfully identified a specific transient phenomenon from a simulated flow field corresponding to driving stability. This is because the unsteady flow field around a vehicle consists of various time and length scales and is therefore too complex to be analyzed with the same strategies as for steady state results. Dynamic Mode Decomposition (DMD) extracts the coherent structures from complex, transient flow fields, which can help to identify certain target phenomena. However, one issue in the practical application of DMD is the difficulty to find a connection between a computed mode and an actual aerodynamic effect on the body. To overcome this issue, we propose an extension of existing DMD algorithms that enables the interpretation of DMD modes such that they can be connected to the aerodynamic design. Here, we applied this extended DMD algorithm on the numerically simulated flow field around a simplified vehicle model. The DMD was able to identify the transient flow structures which potentially correspond to driving stability. Based on the DMD results, we developed a body kit that was expected to reduce the aerodynamic force fluctuations in the target frequency range. Finally, we verified that this body kit effectively controls the fluctuations. In summary, the proposed extended DMD algorithm can support the effective development of body kits for road vehicles to improve their transient aerodynamic characteristics.
CitationMatsumoto, D., Nakae, Y., Niedermeier, C., Tanaka, H. et al., "Application of Dynamic Mode Decomposition to Influence the Driving Stability of Road Vehicles," SAE Technical Paper 2019-01-0653, 2019, https://doi.org/10.4271/2019-01-0653.
- Theissen, P., Wojciak, J., Heuler, K., Demuth, R. et al., “Experimental Investigation of Unsteady Vehicle Aerodynamics under Time-Dependent Flow Conditions - Part 1,” SAE Technical Paper 2011-01-0177, 2011, doi:10.4271/2011-01-0177.
- Wojciak, J., Theissen, P., Heuler, K., Indinger, T. et al., “Experimental Investigation of Unsteady Vehicle Aerodynamics under Time-Dependent Flow Conditions - Part2,” SAE Technical Paper 2011-01-0164, 2011, doi:10.4271/2011-01-0164.
- Rowley, C.W., Mezić, I., Bagheri, S., Schlatter, P. et al., “Spectral Analysis of Nonlinear Flows,” Journal of Fluid Mechanics 641:115-127, 2009, doi:10.1017/S0022112009992059.
- Schmid, P.J., “Dynamic Mode Decomposition of Numerical and Experimental Data,” Journal of Fluid Mechanics 656:5-28, 2010, doi:10.1017/S0022112010001217.
- Muld, T.W., Efraimsson, G., and Henningson, D.S., “Flow Structures around a High-Speed Train Extracted Using Proper Orthogonal Decomposition and Dynamic Mode Decomposition,” Computers & Fluids 57:87-97, 2012, doi:10.1016/j.compfluid.2011.12.012.
- Peichl, M., Mack, S., Indinger, T., and Decker, F, “Numerical Investigation of the Flow around a Generic Car Using Dynamic Mode Decomposition,” in Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting - FEDSM 2014, Chicago, Aug. 3-7, 2014, doi:10.1115/FEDSM2014-21255.
- Hemati, M.S., Rowley, C.W., Deem, E.A., and Cattafesta, L.N., “De-Biasing the Dynamic Mode Decomposition for Applied Koopman Spectral Analysis of Noisy Datasets,” Theoretical and Computational Fluid Dynamics 31(4):349-368, 2017, doi:10.1007/s00162-017-0432-2.
- Williams, M.O., Kevrekidis, I.G., and Rowley, C.W., “A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition,” Journal of Nonlinear Science 25(6):1307-1346, 2015, doi:10.1007/s00332-015-9258-5.
- Jovanović, M.R., Schmid, P.J., and Nichols, J.W., “Sparsity-Promoting Dynamic Mode Decomposition,” Physics of Fluids 26(2):024103, 2014, doi:10.1063/1.4863670.
- Hemati, M.S., Williams, M.O., and Rowley, C.W., “Dynamic Mode Decomposition for Large and Streaming Datasets,” Physics of Fluids 26(11):111701, 2014, doi:10.1063/1.4901016.
- Duke, D., Soria, J., and Honnery, D., “An Error Analysis of the Dynamic Mode Decomposition,” Experiments in Fluids 52(2):529-542, 2012, doi:10.1007/s00348-011-1235-7.
- Sirovich, L., “Turbulence and the Dynamics of Coherent Structures. I. Coherent Structures,” Quarterly of Applied Mathematics 45(3):561-571, 1987, doi:10.1090/qam/910462.
- Sirovich, L., “Turbulence and the Dynamics of Coherent Structures. II. Symmetries and Transformations,” Quarterly of Applied Mathematics 45(3):573-582, 1987, doi:10.1090/qam/910463.
- Sirovich, L., “Turbulence and the Dynamics of Coherent Structures. III. Dynamics and Scaling,” Quarterly of Applied Mathematics 45(3):583-590, 1987, doi:10.1090/qam/910464.