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Space-time computational analysis of tire aerodynamics with actual geometry, road contact, tire deformation, road roughness and fluid film. (English) Zbl 1465.74130

Summary: The space-time (ST) computational method “ST-SI-TC-IGA” has recently enabled computational analysis of tire aerodynamics with actual tire geometry, road contact and tire deformation. 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). These ST methods played their parts in overcoming the computational challenges, including (i) the complexity of an actual tire geometry with longitudinal and transverse grooves, (ii) the spin of the tire, (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, and (iv) the turbulent nature of the flow. The combination of the ST-VMS, ST-SI and the ST-IGA has also recently enabled solution of fluid film problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality. This was accomplished with the computational flexibility to go beyond the limitations of the Reynolds-equation model. Here we include and address the computational challenges associated with the road roughness and the fluid film between the tire and the road. The new methods we add to accomplish that include a remedy for the trapped fluid, a method for reducing the number of control points as a space occupied by the fluid shrinks down to a narrow gap, and a method for representing the road roughness. We present computations for a 2D test problem with a straight channel, a simple 2D model of the tire, and a 3D model with actual tire geometry and road roughness. The computations show the effectiveness of our integrated set of ST methods targeting tire aerodynamics.

MSC:

74M15 Contact in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S99 Numerical and other methods in solid mechanics
74S22 Isogeometric methods applied to problems in solid mechanics
76D08 Lubrication theory

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References:

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[89] Takizawa, K.; Henicke, B.; Tezduyar, TE; Hsu, M-C; Bazilevs, Y., Stabilized space-time computation of wind-turbine rotor aerodynamics, Comput Mech, 48, 333-344 (2011) · Zbl 1398.76127 · doi:10.1007/s00466-011-0589-2
[90] Takizawa, K.; Henicke, B.; Montes, D.; Tezduyar, TE; Hsu, M-C; Bazilevs, Y., Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics, Comput Mech, 48, 647-657 (2011) · Zbl 1334.74032 · doi:10.1007/s00466-011-0614-5
[91] Takizawa, K.; Tezduyar, TE; McIntyre, S.; Kostov, N.; Kolesar, R.; Habluetzel, C., Space-time VMS computation of wind-turbine rotor and tower aerodynamics, Comput Mech, 53, 1-15 (2014) · Zbl 1398.76129 · doi:10.1007/s00466-013-0888-x
[92] Takizawa, K.; Bazilevs, Y.; Tezduyar, TE; Hsu, M-C; Øiseth, O.; Mathisen, KM; Kostov, N.; McIntyre, S., Engineering analysis and design with ALE-VMS and space-time methods, Arch Comput Methods Eng, 21, 481-508 (2014) · Zbl 1348.74104 · doi:10.1007/s11831-014-9113-0
[93] Takizawa, K., Computational engineering analysis with the new-generation space-time methods, Comput Mech, 54, 193-211 (2014) · doi:10.1007/s00466-014-0999-z
[94] Takizawa, K.; Henicke, B.; Puntel, A.; Kostov, N.; Tezduyar, TE, Space-time techniques for computational aerodynamics modeling of flapping wings of an actual locust, Comput Mech, 50, 743-760 (2012) · Zbl 1286.76179 · doi:10.1007/s00466-012-0759-x
[95] Takizawa, K.; Henicke, B.; Puntel, A.; Kostov, N.; Tezduyar, TE, Computer modeling techniques for flapping-wing aerodynamics of a locust, Comput Fluids, 85, 125-134 (2013) · Zbl 1290.76170 · doi:10.1016/j.compfluid.2012.11.008
[96] Takizawa, K.; Kostov, N.; Puntel, A.; Henicke, B.; Tezduyar, TE, Space-time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle, Comput Mech, 50, 761-778 (2012) · Zbl 1286.76180 · doi:10.1007/s00466-012-0758-y
[97] Takizawa, K.; Tezduyar, TE; Kostov, N., Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV, Comput Mech, 54, 213-233 (2014) · doi:10.1007/s00466-014-0980-x
[98] Takizawa, K.; Tezduyar, TE; Buscher, A., Space-time computational analysis of MAV flapping-wing aerodynamics with wing clapping, Comput Mech, 55, 1131-1141 (2015) · doi:10.1007/s00466-014-1095-0
[99] Takizawa, K.; Bazilevs, Y.; Tezduyar, TE; Long, CC; Marsden, AL; Schjodt, K., ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling, Math Models Methods Appl Sci, 24, 2437-2486 (2014) · Zbl 1296.76113 · doi:10.1142/S0218202514500250
[100] Takizawa, K.; Schjodt, K.; Puntel, A.; Kostov, N.; Tezduyar, TE, Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent, Comput Mech, 50, 675-686 (2012) · Zbl 1311.76157 · doi:10.1007/s00466-012-0760-4
[101] Takizawa, K.; Schjodt, K.; Puntel, A.; Kostov, N.; Tezduyar, TE, Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms, Comput Mech, 51, 1061-1073 (2013) · Zbl 1366.76106 · doi:10.1007/s00466-012-0790-y
[102] Suito, H.; Takizawa, K.; Huynh, VQH; Sze, D.; Ueda, T., FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta, Comput Mech, 54, 1035-1045 (2014) · Zbl 1311.74044 · doi:10.1007/s00466-014-1017-1
[103] Suito, H.; Takizawa, K.; Huynh, VQH; Sze, D.; Ueda, T.; Tezduyar, TE; Bazilevs, Y. (ed.); Takizawa, K. (ed.), A geometrical-characteristics study in patient-specific FSI analysis of blood flow in the thoracic aorta, 379-386 (2016), Berlin · Zbl 1356.76471 · doi:10.1007/978-3-319-40827-9_29
[104] Takizawa, K.; Tezduyar, TE; Uchikawa, H.; Terahara, T.; Sasaki, T.; Shiozaki, K.; Yoshida, A.; Komiya, K.; Inoue, G.; Tezduyar, TE (ed.), Aorta flow analysis and heart valve flow and structure analysis, 29-89 (2018), Berlin · doi:10.1007/978-3-319-96469-0_2
[105] Takizawa, K.; Tezduyar, TE; Uchikawa, H.; Terahara, T.; Sasaki, T.; Yoshida, A., Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization, Comput Fluids, 179, 790-798 (2019) · Zbl 1411.76184 · doi:10.1016/j.compfluid.2018.05.025
[106] Takizawa, K.; Tezduyar, K.; Bazilevs, Y. (ed.); Takizawa, K. (ed.), New directions in space-time computational methods, 159-178 (2016), Berlin · Zbl 1356.76291 · doi:10.1007/978-3-319-40827-9_13
[107] Takizawa, K.; Tezduyar, TE; Terahara, T.; Sasaki, T.; Wriggers, P. (ed.); Lenarz, T. (ed.), Heart valve flow computation with the space-time slip interface topology change (ST-SI-TC) method and isogeometric analysis (IGA), 77-99 (2018), Berlin · doi:10.1007/978-3-319-59548-1_6
[108] Takizawa, K.; Montes, D.; McIntyre, S.; Tezduyar, TE, Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers, Math Models Methods Appl Sci, 23, 223-248 (2013) · Zbl 1261.76037 · doi:10.1142/s0218202513400022
[109] Takizawa, K.; Tezduyar, TE; Hattori, H., Computational analysis of flow-driven string dynamics in turbomachinery, Comput Fluids, 142, 109-117 (2017) · Zbl 1390.76011 · doi:10.1016/j.compfluid.2016.02.019
[110] Komiya K, Kanai T, Otoguro Y, Kaneko M, Hirota K, Zhang Y, Takizawa K, Tezduyar TE, Nohmi M, Tsuneda T, Kawai M, Isono M (2019) Computational analysis of flow-driven string dynamics in a pump and residence time calculation. In: IOP conference series earth and environmental science, vol 240, p 062014. https://doi.org/10.1088/1755-1315/240/6/062014 · doi:10.1088/1755-1315/240/6/062014
[111] Kanai, T.; Takizawa, K.; Tezduyar, TE; Komiya, K.; Kaneko, M.; Hirota, K.; Nohmi, M.; Tsuneda, T.; Kawai, M.; Isono, M., Methods for computation of flow-driven string dynamics in a pump and residence time, Math Models Methods Appl Sci, 29, 839-870 (2019) · Zbl 1425.76139 · doi:10.1142/S021820251941001X
[112] Otoguro, Y.; Takizawa, K.; Tezduyar, TE, Space-time VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method, Comput Fluids, 158, 189-200 (2017) · Zbl 1390.76345 · doi:10.1016/j.compfluid.2017.04.017
[113] Otoguro, Y.; Takizawa, K.; Tezduyar, TE; Tezduyar, TE (ed.), A general-purpose NURBS mesh generation method for complex geometries, 399-434 (2018), Berlin · doi:10.1007/978-3-319-96469-0_10
[114] Otoguro, Y.; Takizawa, K.; Tezduyar, TE; Nagaoka, K.; Mei, S., Turbocharger turbine and exhaust manifold flow computation with the space-time variational multiscale method and isogeometric analysis, Comput Fluids, 179, 764-776 (2019) · Zbl 1411.76070 · doi:10.1016/j.compfluid.2018.05.019
[115] Takizawa, K.; Tezduyar, TE; Asada, S.; Kuraishi, T., Space-time method for flow computations with slip interfaces and topology changes (ST-SI-TC), Comput Fluids, 141, 124-134 (2016) · Zbl 1390.76358 · doi:10.1016/j.compfluid.2016.05.006
[116] Kuraishi, T.; Takizawa, K.; Tezduyar, TE; Tezduyar, TE (ed.), Space-time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation, 337-376 (2018), Berlin · doi:10.1007/978-3-319-96469-0_8
[117] Takizawa, K.; Tezduyar, TE; Terahara, T., Ram-air parachute structural and fluid mechanics computations with the space-time isogeometric analysis (ST-IGA), Comput Fluids, 141, 191-200 (2016) · Zbl 1390.76359 · doi:10.1016/j.compfluid.2016.05.027
[118] Takizawa, K.; Tezduyar, TE; Kanai, T., Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity, Math Models Methods Appl Sci, 27, 771-806 (2017) · Zbl 1361.76017 · doi:10.1142/S0218202517500166
[119] Kanai, T.; Takizawa, K.; Tezduyar, TE; Tanaka, T.; Hartmann, A., Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization, Comput Mech, 63, 301-321 (2019) · Zbl 1462.76145 · doi:10.1007/s00466-018-1595-4
[120] Tezduyar, TE; Ganjoo, DK, Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: applications to transient convection-diffusion problems, Comput Methods Appl Mech Eng, 59, 49-71 (1986) · Zbl 0604.76077 · doi:10.1016/0045-7825(86)90023-X
[121] Beau, GJ; Ray, SE; Aliabadi, SK; Tezduyar, TE, SUPG finite element computation of compressible flows with the entropy and conservation variables formulations, Comput Methods Appl Mech Eng, 104, 397-422 (1993) · Zbl 0772.76037 · doi:10.1016/0045-7825(93)90033-T
[122] Tezduyar, TE; Senga, M., Stabilization and shock-capturing parameters in SUPG formulation of compressible flows, Comput Methods Appl Mech Eng, 195, 1621-1632 (2006) · Zbl 1122.76061 · doi:10.1016/j.cma.2005.05.032
[123] Corsini, A.; Menichini, C.; Rispoli, F.; Santoriello, A.; Tezduyar, TE, A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms, J Appl Mech, 76, 021211 (2009) · doi:10.1115/1.3062967
[124] Rispoli, F.; Saavedra, R.; Menichini, F.; Tezduyar, TE, Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZ \(\beta\) shock-capturing, J Appl Mech, 76, 021209 (2009) · doi:10.1115/1.3057496
[125] Corsini, A.; Iossa, C.; Rispoli, F.; Tezduyar, TE, A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors, Comput Mech, 46, 159-167 (2010) · Zbl 1301.76045 · doi:10.1007/s00466-009-0441-0
[126] Hsu, M-C; Bazilevs, Y.; Calo, VM; Tezduyar, TE; Hughes, TJR, Improving stability of stabilized and multiscale formulations in flow simulations at small time steps, Comput Methods Appl Mech Eng, 199, 828-840 (2010) · Zbl 1406.76028 · doi:10.1016/j.cma.2009.06.019
[127] Corsini, A.; Rispoli, F.; Tezduyar, TE, Stabilized finite element computation of NOx emission in aero-engine combustors, Int J Numer Methods Fluids, 65, 254-270 (2011) · Zbl 1426.76240 · doi:10.1002/fld.2451
[128] Corsini, A.; Rispoli, F.; Tezduyar, TE, Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique, J Appl Mech, 79, 010910 (2012) · doi:10.1115/1.4005060
[129] Corsini, A.; Rispoli, F.; Sheard, AG; Tezduyar, TE, Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations, Comput Mech, 50, 695-705 (2012) · Zbl 1311.76121 · doi:10.1007/s00466-012-0789-4
[130] Kler, PA; Dalcin, LD; Paz, RR; Tezduyar, TE, SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems, Comput Mech, 51, 171-185 (2013) · Zbl 1312.76062 · doi:10.1007/s00466-012-0712-z
[131] Corsini, A.; Rispoli, F.; Sheard, AG; Takizawa, K.; Tezduyar, TE; Venturini, P., A variational multiscale method for particle-cloud tracking in turbomachinery flows, Comput Mech, 54, 1191-1202 (2014) · Zbl 1311.76030 · doi:10.1007/s00466-014-1050-0
[132] Rispoli, F.; Delibra, G.; Venturini, P.; Corsini, A.; Saavedra, R.; Tezduyar, TE, Particle tracking and particle-shock interaction in compressible-flow computations with the V-SGS stabilization and YZ \(\beta\) shock-capturing, Comput Mech, 55, 1201-1209 (2015) · Zbl 1325.76121 · doi:10.1007/s00466-015-1160-3
[133] Cardillo, L.; Corsini, A.; Delibra, G.; Rispoli, F.; Tezduyar, TE, Flow analysis of a wave-energy air turbine with the SUPG/PSPG stabilization and discontinuity-capturing directional dissipation, Comput Fluids, 141, 184-190 (2016) · Zbl 1390.76295 · doi:10.1016/j.compfluid.2016.07.011
[134] Castorrini, A.; Corsini, A.; Rispoli, F.; Venturini, P.; Takizawa, K.; Tezduyar, TE, Computational analysis of wind-turbine blade rain erosion, Comput Fluids, 141, 175-183 (2016) · Zbl 1390.76298 · doi:10.1016/j.compfluid.2016.08.013
[135] Takizawa, K.; Tezduyar, TE; Otoguro, Y., Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations, Comput Mech, 62, 1169-1186 (2018) · Zbl 1462.76128 · doi:10.1007/s00466-018-1557-x
[136] Castorrini, Alessio; Corsini, Alessandro; Rispoli, Franco; Venturini, Paolo; Takizawa, Kenji; Tezduyar, Tayfun E., Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion, Computational Mechanics, 64, 1133-1153 (2019) · Zbl 1467.74083 · doi:10.1007/s00466-019-01697-0
[137] Tezduyar, TE; Aliabadi, SK; Behr, M.; Mittal, S., Massively parallel finite element simulation of compressible and incompressible flows, Comput Methods Appl Mech Eng, 119, 157-177 (1994) · Zbl 0848.76040 · doi:10.1016/0045-7825(94)00082-4
[138] Takizawa, K.; Tezduyar, TE, Space-time computation techniques with continuous representation in time (ST-C), Comput Mech, 53, 91-99 (2014) · doi:10.1007/s00466-013-0895-y
[139] Takizawa, K.; Tezduyar, TE; Sasaki, T.; Wriggers, P. (ed.); Lenarz, T. (ed.), Estimation of element-based zero-stress state in arterial FSI computations with isogeometric wall discretization, 101-122 (2018), Berlin · doi:10.1007/978-3-319-59548-1_7
[140] Takizawa, K.; Tezduyar, TE; Sasaki, T., Aorta modeling with the element-based zero-stress state and isogeometric discretization, Comput Mech, 59, 265-280 (2017) · doi:10.1007/s00466-016-1344-5
[141] Sasaki, T.; Takizawa, K.; Tezduyar, TE, Aorta zero-stress state modeling with T-spline discretization, Comput Mech, 63, 1315-1331 (2019) · Zbl 1465.74125 · doi:10.1007/s00466-018-1651-0
[142] Sasaki, Takafumi; Takizawa, Kenji; Tezduyar, Tayfun E., Medical-image-based aorta modeling with zero-stress-state estimation, Computational Mechanics, 64, 249-271 (2019) · Zbl 1469.74085 · doi:10.1007/s00466-019-01669-4
[143] Takizawa, K.; Tezduyar, TE; Sasaki, T., Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping, Comput Mech, 63, 681-700 (2019) · Zbl 1464.74107 · doi:10.1007/s00466-018-1616-3
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