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Turbocharger turbine and exhaust manifold flow computation with the space-time variational multiscale method and isogeometric analysis. (English) Zbl 1411.76070
Summary: We address the computational challenges encountered in turbocharger turbine and exhaust manifold flow analysis. The core computational method is the space-time variational multiscale (ST-VMS) method, and the other key methods are the ST isogeometric analysis (ST-IGA), ST slip interface (ST-SI) method, ST/NURBS mesh update method (STNMUM), and a general-purpose NURBS mesh generation method for complex geometries. The ST framework, in a general context, provides higher-order accuracy. The VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow in the manifold and turbine, and the moving-mesh feature of the ST framework enables high-resolution computation near the rotor surface. The ST-SI 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-IGA enables more accurate representation of the turbine and manifold geometries and increased accuracy in the flow solution. The STNMUM enables exact representation of the mesh rotation. The general-purpose NURBS mesh generation method makes it easier to deal with the complex geometries we have here. An SI also provides mesh generation flexibility in a general context by accurately connecting the two sides of the solution computed over nonmatching meshes. That is enabling us to use nonmatching NURBS meshes here. Stabilization parameters and element length definitions play a significant role in the ST-VMS and ST-SI. For the ST-VMS, we use the stabilization parameters introduced recently, and for the ST-SI, the element length definition we are introducing here. The model we actually compute with includes the exhaust gas purifier, which makes the turbine outflow conditions more realistic. We compute the flow for 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. The computation demonstrates that the methods we use here are very effective in this class of challenging flow analyses.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65D07 Numerical computation using splines
76N15 Gas dynamics, general
76T15 Dusty-gas two-phase flows
Software:
SUPG
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References:
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[116] Akin, J. E.; Tezduyar, T. E., Calculation of the advective limit of the SUPG stabilization parameter for linear and higher-order elements, Comput Methods Appl Mech Eng, 193, 1909-1922, (2004) · Zbl 1067.76557
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[118] Tezduyar, T. E.; Osawa, Y., Finite element stabilization parameters computed from element matrices and vectors, Comput Methods Appl Mech Eng, 190, 411-430, (2000) · Zbl 0973.76057
[119] Hsu, M.-C.; Bazilevs, Y.; Calo, V. M.; Tezduyar, T. E.; Hughes, T. J.R., 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
[120] Tezduyar, T. E., Adaptive determination of the finite element stabilization parameters, Proceedings of the ECCOMAS Computational Fluid Dynamics Conference 2001 (CD-ROM), Swansea, Wales, United Kingdom, (2001)
[121] Tezduyar, T. E., Finite element methods for fluid dynamics with moving boundaries and interfaces, (Stein, E.; Borst, R. D.; Hughes, T. J.R., Encyclopedia of computational mechanics, chapter 17, volume 3: fluids, (2004), Wiley)
[122] Tezduyar, T. E., Determination of the stabilization and shock-capturing parameters in SUPG formulation of compressible flows, Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004 (CD-ROM), Jyvaskyla, Finland, (2004)
[123] Tezduyar, T. E., Finite elements in fluids: stabilized formulations and moving boundaries and interfaces, Comput Fluids, 36, 191-206, (2007) · Zbl 1177.76202
[124] Rispoli, F.; Corsini, A.; Tezduyar, T. E., Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD), Comput Fluids, 36, 121-126, (2007) · Zbl 1181.76098
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[126] Tezduyar, T. E.; Senga, M., SUPG finite element computation of inviscid supersonic flows with YZβ shock-capturing, Comput Fluids, 36, 147-159, (2007) · Zbl 1127.76029
[127] Tezduyar, T. E.; Senga, M.; Vicker, D., Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZβ shock-capturing, Comput Mech, 38, 469-481, (2006) · Zbl 1176.76077
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[130] Tezduyar, T. E.; Sathe, S., Enhanced-discretization selective stabilization procedure (EDSSP), Comput Mech, 38, 456-468, (2006) · Zbl 1187.76712
[131] Corsini, A.; Rispoli, F.; Santoriello, A.; Tezduyar, T. E., Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation, Comput Mech, 38, 356-364, (2006) · Zbl 1177.76192
[132] Tezduyar, T. E.; Ramakrishnan, S.; Sathe, S., Stabilized formulations for incompressible flows with thermal coupling, Int J Numer Methods Fluids, 57, 1189-1209, (2008) · Zbl 1140.76024
[133] Rispoli, F.; Saavedra, R.; Corsini, A.; Tezduyar, T. E., Computation of inviscid compressible flows with the V-SGS stabilization and YZβ shock-capturing, Int J Numer Methods Fluids, 54, 695-706, (2007) · Zbl 1207.76104
[134] Bazilevs, Y.; Calo, V. M.; Tezduyar, T. E.; Hughes, T. J.R., YZβ discontinuity-capturing for advection-dominated processes with application to arterial drug delivery, Int J Numer Methods Fluids, 54, 593-608, (2007) · Zbl 1207.76049
[135] Corsini, A.; Menichini, C.; Rispoli, F.; Santoriello, A.; Tezduyar, T. E., A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms, J Appl Mech, 76, 021211, (2009)
[136] Rispoli, F.; Saavedra, R.; Menichini, F.; Tezduyar, T. E., Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZβ shock-capturing, J Appl Mech, 76, 021209, (2009)
[137] Corsini, A.; Iossa, C.; Rispoli, F.; Tezduyar, T. E., A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors, Comput Mech, 46, 159-167, (2010) · Zbl 1301.76045
[138] Corsini, A.; Rispoli, F.; Tezduyar, T. E., Stabilized finite element computation of NOx emission in aero-engine combustors, Int J Numer Methods Fluids, 65, 254-270, (2011) · Zbl 1426.76240
[139] Corsini, A.; Rispoli, F.; Tezduyar, T. E., Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique, J Appl Mech, 79, 010910, (2012)
[140] Kler, P. A.; Dalcin, L. D.; Paz, R. R.; Tezduyar, T. E., SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems, Comput Mech, 51, 171-185, (2013) · Zbl 1312.76062
[141] Rispoli, F.; Delibra, G.; Venturini, P.; Corsini, A.; Saavedra, R.; Tezduyar, T. E., Particle tracking and particle-shock interaction in compressible-flow computations with the V-SGS stabilization and YZβ shock-capturing, Comput Mech, 55, 1201-1209, (2015) · Zbl 1325.76121
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