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Space-time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle. (English) Zbl 07147411
Summary: Many of the computational challenges encountered in turbocharger-turbine flow analysis have been addressed by an integrated set of space-time (ST) computational methods. The core computational method is the ST variational multiscale (ST-VMS) method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST slip interface (ST-SI) method enables moving-mesh computation of the spinning rotor. The mesh covering the rotor 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 Isogeometric Analysis enables more accurate representation of the turbine geometry and increased accuracy in the flow solution. The ST/NURBS Mesh Update Method enables exact representation of the mesh rotation. A general-purpose NURBS mesh generation method makes it easier to deal with the complex geometries involved. An SI also provides mesh generation flexibility in a general context by accurately connecting the two sides of the solution computed over nonmatching meshes, and that is enabling the use of nonmatching NURBS meshes in the computations. The computational analysis needs to cover a full intake/exhaust cycle, which is much longer than the turbine rotation cycle because of high rotation speeds, and the long duration required is an additional computational challenge. As one way of addressing that challenge, we propose here to calculate the turbine efficiency for the intake/exhaust cycle by interpolation from the efficiencies associated with a set of steady-inflow computations at different flow rates. The efficiencies obtained from the computations with time-dependent and steady-inflow representations of the intake/exhaust cycle compare well. This demonstrates that predicting the turbine performance from a set of steady-inflow computations is a good way of addressing the challenge associated with the multiple time scales.

MSC:
74 Mechanics of deformable solids
Software:
SUPG
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[98] Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647-657. https://doi.org/10.1007/s00466-011-0614-5 · Zbl 1334.74032
[99] Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space-time methods. Arch Comput Methods Eng 21:481-508. https://doi.org/10.1007/s11831-014-9113-0 · Zbl 1348.74104
[100] Takizawa K (2014) Computational engineering analysis with the new-generation space-time methods. Comput Mech 54:193-211. https://doi.org/10.1007/s00466-014-0999-z
[101] Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2013) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput Fluids 85:125-134. https://doi.org/10.1016/j.compfluid.2012.11.008 · Zbl 1290.76170
[102] Takizawa K, Tezduyar TE, Kostov N (2014) Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213-233. https://doi.org/10.1007/s00466-014-0980-x
[103] Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time interface-tracking with topology change (ST-TC). Comput Mech 54:955-971. https://doi.org/10.1007/s00466-013-0935-7 · Zbl 1311.74045
[104] Takizawa K, Tezduyar TE, Buscher A (2015) Space-time computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55:1131-1141. https://doi.org/10.1007/s00466-014-1095-0
[105] Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437-2486. https://doi.org/10.1142/S0218202514500250 · Zbl 1296.76113
[106] Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50:675-686. https://doi.org/10.1007/s00466-012-0760-4 · Zbl 1311.76157
[107] Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061-1073. https://doi.org/10.1007/s00466-012-0790-y · Zbl 1366.76106
[108] Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T (2014) FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54:1035-1045. https://doi.org/10.1007/s00466-014-1017-1 · Zbl 1311.74044
[109] Suito, Hiroshi; Takizawa, Kenji; Huynh, Viet Q. H.; Sze, Daniel; Ueda, Takuya; Tezduyar, Tayfun E., A Geometrical-Characteristics Study in Patient-Specific FSI Analysis of Blood Flow in the Thoracic Aorta, 379-386 (2016), Cham · Zbl 1356.76471
[110] Takizawa, Kenji; Tezduyar, Tayfun E.; Uchikawa, Hiroaki; Terahara, Takuya; Sasaki, Takafumi; Shiozaki, Kensuke; Yoshida, Ayaka; Komiya, Kenji; Inoue, Gaku, Aorta Flow Analysis and Heart Valve Flow and Structure Analysis, 29-89 (2018), Cham
[111] Takizawa K, Tezduyar TE, Uchikawa H, Terahara T, Sasaki T, Yoshida A (2019) Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization. Comput Fluids 179:790-798. https://doi.org/10.1016/j.compfluid.2018.05.025 · Zbl 1411.76184
[112] Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time fluid mechanics computation of heart valve models. Comput Mech 54:973-986. https://doi.org/10.1007/s00466-014-1046-9 · Zbl 1311.74083
[113] Takizawa, Kenji; Tezduyar, Tayfun E., New Directions in Space-Time Computational Methods, 159-178 (2016), Cham · Zbl 1356.76291
[114] Takizawa, Kenji; Tezduyar, Tayfun E.; Terahara, Takuya; Sasaki, Takafumi, Heart Valve Flow Computation with the Space-Time Slip Interface Topology Change (ST-SI-TC) Method and Isogeometric Analysis (IGA), 77-99 (2017), Cham · Zbl 1390.76944
[115] Takizawa K, Tezduyar TE, Terahara T, Sasaki T (2017) Heart valve flow computation with the integrated space-time VMS, slip interface, topology change and isogeometric discretization methods. Comput Fluids 158:176-188. https://doi.org/10.1016/j.compfluid.2016.11.012 · Zbl 1390.76944
[116] Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013) Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223-248. https://doi.org/10.1142/s0218202513400022 · Zbl 1261.76037
[117] Takizawa K, Tezduyar TE, Hattori H (2017) Computational analysis of flow-driven string dynamics in turbomachinery. Comput Fluids 142:109-117. https://doi.org/10.1016/j.compfluid.2016.02.019 · Zbl 1390.76011
[118] 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. IOP Conf Seri Earth Environ Sci 240:062014. https://doi.org/10.1088/1755-1315/240/6/062014
[119] Kanai T, Takizawa K, Tezduyar TE, Komiya K, Kaneko M, Hirota K, Nohmi M, Tsuneda T, Kawai M, Isono M (2019) Methods for computation of flow-driven string dynamics in a pump and residence time. Math Models Methods Appl Sci. https://doi.org/10.1142/S021820251941001X
[120] Takizawa K, Tezduyar TE, Asada S, Kuraishi T (2016) Space-time method for flow computations with slip interfaces and topology changes (ST-SI-TC). Comput Fluids 141:124-134. https://doi.org/10.1016/j.compfluid.2016.05.006 · Zbl 1390.76358
[121] Kuraishi, Takashi; Takizawa, Kenji; Tezduyar, Tayfun E., Space-Time Computational Analysis of Tire Aerodynamics with Actual Geometry, Road Contact, and Tire Deformation, 337-376 (2018), Cham · Zbl 07053716
[122] Kuraishi T, Takizawa K, Tezduyar TE (2019) Tire aerodynamics with actual tire geometry, road contact and tire deformation. Comput Mech 63:1165-1185. https://doi.org/10.1007/s00466-018-1642-1 · Zbl 07053716
[123] Kuraishi T, Takizawa K, Tezduyar TE (2019) Space-Time isogeometric flow analysis with built-in Reynolds-equation limit. Math Models Methods Appl Sci. https://doi.org/10.1142/S0218202519410021 · Zbl 07053716
[124] Takizawa K, Tezduyar TE, Terahara T (2016) Ram-air parachute structural and fluid mechanics computations with the space-time isogeometric analysis (ST-IGA). Comput Fluids 141:191-200. https://doi.org/10.1016/j.compfluid.2016.05.027 · Zbl 1390.76359
[125] Takizawa K, Tezduyar TE, Kanai T (2017) Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. Math Models Methods Appl Sci 27:771-806. https://doi.org/10.1142/S0218202517500166 · Zbl 1361.76017
[126] Kanai T, Takizawa K, Tezduyar TE, Tanaka T, Hartmann A (2019) Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization. Comput Mech 63:301-321. https://doi.org/10.1007/s00466-018-1595-4 · Zbl 07037442
[127] Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119:157-177. https://doi.org/10.1016/0045-7825(94)00082-4 · Zbl 0848.76040
[128] Takizawa K, Tezduyar TE (2014) Space-time computation techniques with continuous representation in time (ST-C). Comput Mech 53:91-99. https://doi.org/10.1007/s00466-013-0895-y
[129] Tezduyar TE, Cragin T, Sathe S, Nanna B (2007) FSI computations in arterial fluid mechanics with estimated zero-pressure arterial geometry. In: Onate E, Garcia J, Bergan P, Kvamsdal T (eds) Marine, CIMNE, Barcelona, Spain · Zbl 1276.76043
[130] Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space-time fluid-structure interaction technique. Int J Numer Methods Biomedl Eng 57:601-629. https://doi.org/10.1002/fld.1633 · Zbl 1230.76054
[131] Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space-time finite element computation of arterial fluid-structure interactions with patient-specific data. Int J Numer Methods Biomedl Eng 26:101-116. https://doi.org/10.1002/cnm.1241 · Zbl 1180.92023
[132] Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid-structure interaction modeling of cerebral aneurysms. Int J Numer Methods Biomedl Eng 65:308-323. https://doi.org/10.1002/fld.2360 · Zbl 1203.92044
[133] Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space-time fluid-structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomedl Eng 27:1665-1710. https://doi.org/10.1002/cnm.1433 · Zbl 1244.92036
[134] Takizawa K, Takagi H, Tezduyar TE, Torii R (2014) Estimation of element-based zero-stress state for arterial FSI computations. Comput Mech 54:895-910. https://doi.org/10.1007/s00466-013-0919-7 · Zbl 1398.74096
[135] Takizawa K, Torii R, Takagi H, Tezduyar TE, Xu XY (2014) Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates. Comput Mech 54:1047-1053. https://doi.org/10.1007/s00466-014-1049-6 · Zbl 1311.76158
[136] Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi, Estimation of Element-Based Zero-Stress State in Arterial FSI Computations with Isogeometric Wall Discretization, 101-122 (2017), Cham
[137] Takizawa K, Tezduyar TE, Sasaki T (2017) Aorta modeling with the element-based zero-stress state and isogeometric discretization. Comput Mech 59:265-280. https://doi.org/10.1007/s00466-016-1344-5
[138] Sasaki T, Takizawa K, Tezduyar TE (2019) Aorta zero-stress state modeling with T-spline discretization. Comput Mech 63:1315-1331. https://doi.org/10.1007/s00466-018-1651-0 · Zbl 07053724
[139] Sasaki T, Takizawa K, Tezduyar TE (2019) Medical-image-based aorta modeling with zero-stress-state estimation. Comput Mech.https://doi.org/10.1007/s00466-019-01669-4 · Zbl 07073977
[140] Takizawa K, Tezduyar TE, Sasaki T (2019) Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping. Comput Mech 63:681-700. https://doi.org/10.1007/s00466-018-1616-3 · Zbl 07053688
[141] Takizawa K, Tezduyar TE, Otoguro Y (2018) Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations. Comput Mech 62:1169-1186. https://doi.org/10.1007/s00466-018-1557-x · Zbl 06981055
[142] Tezduyar TE, Ganjoo DK (1986) 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. https://doi.org/10.1016/0045-7825(86)90023-X · Zbl 0604.76077
[143] Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104:397-422. https://doi.org/10.1016/0045-7825(93)90033-T · Zbl 0772.76037
[144] Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36:191-206. https://doi.org/10.1016/j.compfluid.2005.02.011 · Zbl 1177.76202
[145] Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195:1621-1632. https://doi.org/10.1016/j.cma.2005.05.032 · Zbl 1122.76061
[146] Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ \[\beta\] β shock-capturing. Comput Fluids 36:147-159. https://doi.org/10.1016/j.compfluid.2005.07.009 · Zbl 1127.76029
[147] Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ \[\beta\] β shock-capturing. Comput Mech 38:469-481. https://doi.org/10.1007/s00466-005-0025-6 · Zbl 1176.76077
[148] Tezduyar TE, Sathe S (2006) Enhanced-discretization selective stabilization procedure (EDSSP). Comput Mech 38:456-468. https://doi.org/10.1007/s00466-006-0056-7 · Zbl 1187.76712
[149] Corsini A, Rispoli F, Santoriello A, Tezduyar TE (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38:356-364. https://doi.org/10.1007/s00466-006-0045-x · Zbl 1177.76192
[150] Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput Fluids 36:121-126. https://doi.org/10.1016/j.compfluid.2005.07.004 · Zbl 1181.76098
[151] Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57:1189-1209. https://doi.org/10.1002/fld.1743 · Zbl 1140.76024
[152] Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ \[\beta\] β shock-capturing. Int J Numer Methods Fluids 54:695-706. https://doi.org/10.1002/fld.1447 · Zbl 1207.76104
[153] Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2007) YZ \[\beta\] β discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. Int J Numer Methods Fluids 54:593-608. https://doi.org/10.1002/fld.1484 · Zbl 1207.76049
[154] Corsini A, Menichini C, Rispoli F, Santoriello A, Tezduyar TE (2009) A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms. J Appl Mech 76:021211. https://doi.org/10.1115/1.3062967
[155] Rispoli F, Saavedra R, Menichini F, Tezduyar TE (2009) Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZ \[\beta\] β shock-capturing. J Appl Mech 76:021209. https://doi.org/10.1115/1.3057496
[156] Corsini A, Iossa C, Rispoli F, Tezduyar TE (2010) A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors. Comput Mech 46:159-167. https://doi.org/10.1007/s00466-009-0441-0 · Zbl 1301.76045
[157] Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199:828-840. https://doi.org/10.1016/j.cma.2009.06.019 · Zbl 1406.76028
[158] Corsini A, Rispoli F, Tezduyar TE (2011) Stabilized finite element computation of NOx emission in aero-engine combustors. Int J Numer Methods Fluids 65:254-270. https://doi.org/10.1002/fld.2451 · Zbl 1426.76240
[159] Corsini A, Rispoli F, Tezduyar TE (2012) Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique. J Appl Mech 79:010910. https://doi.org/10.1115/1.4005060
[160] Kler PA, Dalcin LD, Paz RR, Tezduyar TE (2013) SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems. Comput Mech 51:171-185. https://doi.org/10.1007/s00466-012-0712-z · Zbl 1312.76062
[161] Rispoli F, Delibra G, Venturini P, Corsini A, Saavedra R, Tezduyar TE (2015) Particle tracking and particle-shock interaction in compressible-flow computations with the V-SGS stabilization and YZ \[\beta\] β shock-capturing. Comput Mech 55:1201-1209. https://doi.org/10.1007/s00466-015-1160-3 · Zbl 1325.76121
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