Tire aerodynamics with actual tire geometry, road contact and tire deformation

Abstract

Tire aerodynamics with actual tire geometry, road contact and tire deformation pose tough computational challenges. The challenges include (1) the complexity of an actual tire geometry with longitudinal and transverse grooves, (2) the spin of the tire, (3) 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 and tire deformation, and (4) the turbulent nature of the flow. A new spacetime (ST) computational method, "ST-SI-TC-IGA," is enabling us to address these challenges. The core component of the ST-SI-TC-IGA is the ST Variational Multiscale (ST-VMS) method, and the other key components are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and the ST Isogeometric Analysis (ST-IGA). The VMS feature of the ST-VMS addresses the challenge created by the turbulent nature of the flow, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid-solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-SI enables moving-mesh computation with the tire spinning. The mesh covering the tire spins with it, and the SI between the spinning 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. We present computations with the ST-SI-TC-IGA and two models of flow around a rotating tire with road contact and prescribed deformation. One is a simple 2D model for verification purposes, and one is a 3D model with an actual tire geometry and a deformation pattern provided by the tire company. The computations show the effectiveness of the ST-SI-TC-IGA in tire aerodynamics.

Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change

“…The challenges are mainly addressed with the space-time (ST) computational method "ST-SI-TC-IGA" [1,2]. The ST-SI-TC-IGA integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method [3][4][5], which subsumes its precursor "ST-SUPS" (see Sect.…”

A node-numbering-invariant directional length scale for simplex elements

“…119 for the coupled incompressible-flow and thermal-transport equations retains the high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces. These ST-SI methods have been applied to aerodynamic analysis of vertical-axis wind turbines, 98,48,49 thermo-fluid analysis of disk brakes, 119 flow-driven string dynamics in turbomachinery, [120][121][122] flow analysis of turbocharger turbines, [123][124][125][126] flow around tires with road contact and deformation, 115,[127][128][129][130] fluid films, 131,130 aerodynamic analysis of ram-air parachutes, 132 and flow analysis of heart valves. 116,117,111,113 In the ST-SI version presented in Ref.…”

“…That in turn enables using larger time-step sizes while keeping the Courant number at a desirable level for good accuracy. It has been used in ST computational flow analysis of turbocharger turbines, [123][124][125][126] flow-driven string dynamics in turbomachinery, 121,122 ram-air parachutes, 132 spacecraft parachutes, 134 aortas, [111][112][113] heart valves, 116,117,111,113 tires with road contact and deformation, [128][129][130] and fluid films. 131,130 Using IGA basis functions in space is now a key part of some of the newest arterial zero-stress-state estimation methods [138][139][140][141]113 and related shell analysis.…”

Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

“…It has been used in ST computational flow analysis of turbocharger turbines, 8,111-113 flow-driven string dynamics in turbomachinery, 109,110 ram-air parachutes, 117 spacecraft parachutes, 119 aortas, 101,102 heart valves, 101,105,106 and tires with road contact and deformation. 115,116 The imagebased arterial geometries used in patient-specific arterial FSI computations do not come from the zero-stress state (ZSS) of the artery. A number of methods 20,22,[121][122][123][124][125][126][127][128][129][130] have been proposed for estimating the ZSS required in the computations.…”

“…10 for the coupled incompressible-flow and thermal-transport equations retains the high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces. These ST-SI methods have been applied to aerodynamic analysis of vertical-axis wind turbines, 9,41,42 thermo-fluid analysis of disk brakes, 10 flow-driven string dynamics in turbomachinery, [108][109][110] flow analysis of turbocharger turbines, 8,111-113 flow around tires with road contact and deformation, 104,[114][115][116] aerodynamic analysis of ram-air parachutes, 117 and flow analysis of heart valves. 101,105,106 In the ST-SI version presented in Ref.…”