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Space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation

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Abstract

We present a space–time (ST) isogeometric analysis framework for car and tire aerodynamics with road contact and tire deformation and rotation. The geometries of the computational models for the car body and tires are close to the actual geometries. The computational challenges include i) the complexities of these geometries, ii) the tire rotation, iii) maintaining accurate representation of the boundary layers near the tire while being able to deal with the flow-domain topology change created by the road contact, iv) the turbulent nature of the flow, v) the aerodynamic interaction between the car body and the tires, and vi) NURBS mesh generation for the complex geometries. The computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) method, and the element-based mesh relaxation (EBMR). The ST context provides higher-order accuracy in general, the VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, and the moving-mesh feature of the ST context enables high-resolution flow computation near the moving fluid–solid interfaces. The ST-SI enables moving-mesh computation with the tire rotating. The mesh covering the tire rotates with it, and the SI between the rotating mesh and the rest of the mesh accurately connects the two sides of the solution. The ST-TC enables moving-mesh computation even with the TC created by the contact between the tire and the road. It deals with the contact while maintaining high-resolution flow representation near the tire. Integration of the ST-SI and ST-TC enables high-resolution representation even though parts of the SI are coinciding with the tire and road surfaces. It also enables dealing with the tire–road contact location change and contact sliding. By integrating the ST-IGA with the ST-SI and ST-TC, in addition to having a more accurate representation of the tire geometry and increased accuracy in the flow solution, the element density in the tire grooves and in the narrow spaces near the contact areas is kept at a reasonable level. The NSVGMG enables NURBS mesh generation for the complex car and tire geometries, and the EBMR improves the quality of the meshes. The car and tire aerodynamics computation we present shows the effectiveness of the analysis framework we have built.

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Acknowledgements

This work was supported in part by Rice–Waseda research agreement and International Technology Center Indo-Pacific (ITC IPAC) Contract FA520921C0010. The work was also supported in part by ARO Grant W911NF-17-1-0046 and Contract W911NF-21-C-0030 (first and fourth authors), and Top Global University Project of Waseda University (fourth author). The tire geometry in Sect. 3.1 was provided by the YOKOHAMA RUBBER CO., LTD.

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Authors and Affiliations

  1. Mechanical Engineering, Rice University – MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Takashi Kuraishi & Tayfun E. Tezduyar

  2. Department of Modern Mechanical Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Satoshi Yamasaki, Kenji Takizawa, Zhaojing Xu & Ryutaro Kaneko

  3. Faculty of Science and Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo, 169-8555, Japan

    Tayfun E. Tezduyar

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Correspondence to Kenji Takizawa.

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Kuraishi, T., Yamasaki, S., Takizawa, K. et al. Space–time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation. Comput Mech 70, 49–72 (2022). https://doi.org/10.1007/s00466-022-02155-0

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