Identification of the vortex around a vehicle by considering the pressure minimum

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R E G UL A R P A P E R

Yusuke Nakamura • Takuji Nakashima Yasuaki Doi • Hidemi Mutsuda



Takenori Hiraoka • Keigo Shimizu • Takahide Nouzawa



Identification of the vortex around a vehicle by considering the pressure minimum

Received: 1 December 2019 / Revised: 25 March 2020 / Accepted: 27 May 2020 Ó The Visualization Society of Japan 2020

Abstract This paper proposes a method to identify low-pressure vortices with swirling motions around a vehicle by considering the two-dimensional pressure minimum. The existing sectional-pressure-minimumand-swirl method combined with the finite difference method can be used to identify low-pressure vortices with swirling motions in homogeneous isotropic turbulence. To apply this method to the flow field around a vehicle, a method that extends the existing method to the finite volume method on unstructured grids and prevents the fragmentation of the vortex core lines was developed. To verify the proposed method, it was applied to the von Ka´rma´n vortices of the square cylinder on the unstructured grids. The results indicate that the von Ka´rma´n vortices, which involve low-pressure vortices with swirling motions, could be effectively captured using the proposed method. Finally, the proposed method was applied to the flow field around a vehicle. Compared with the existing method, the proposed method could better prevent the fragmentation of the vortex core lines. In addition, four known vortex structures around the vehicle could be identified by using the proposed method in combination with the isosurface method. Compared to other generally used methods in the field of vehicle aerodynamics, the proposed method could better identify the vortex core lines within a few minutes. These results demonstrate that the proposed method is effective for identifying the vortices around a vehicle. Keywords Vehicle aerodynamics  Vortex structure around vehicles  Vortex identification  Vortex visualization

1 Introduction Identifying vortices around a vehicle is important to reduce the aerodynamic drag, and the relationship between the vortices and the drag has been extensively studied. Using experimental techniques, the effects of the wake vortex structures on the drag and shape parameters were clarified using a simple car model (Hucho and Sovran 1993). Another study indicated that four characteristic vortices occurred with increasing the drag (Nouzawa et al. 2009); the vortices are the front pillar vortex, body side vortex, floor vortex, and trailing vortex. Moreover, the study found that the vortices around a sedan vehicle were low-pressure vortices with swirling motions. Recently, details pertaining to the vortices were clarified using computational fluid dynamics (CFD) simulations; for instance, Shimizu et al. (2017) reported on the vortex structures around a rolling front tire. Y. Nakamura  T. Nakashima (&)  Y. Doi  H. Mutsuda Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima-shi, Hiroshima, Japan E-mail: [email protected] T. Hi