Isogeometric Modeling and Experimental Investigation of Moving-Domain Bridge Aerodynamics
Publication: Journal of Engineering Mechanics
Volume 145, Issue 5
Abstract
Computational fluid dynamics (CFD) and fluid–structure interaction (FSI) are growing disciplines in the aeroelastic analysis and design of long-span bridges, which, with their bluff body characteristics, offer major challenges to efficient simulation. In this paper, we employ isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) to numerically simulate turbulent flows over moving bridge sections in three dimensions (3D). Stationary and dynamic analyses of two bridge sections, an idealized rectangular shape with aspect ratio and a model of the Hardanger bridge, were performed. Wind tunnel experiments and comparative finite-element (FE) analyses of the same sections were also conducted. Studies on the convergence, static dependencies on the angle of attack, and self-excited forces in terms of the aerodynamic derivatives show that IGA successfully captures the bluff-body flow characteristics and exhibits superior per-degree-of-freedom accuracy compared to the more traditional lower-order FE discretizations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was carried out with financial support from the Norwegian Public Roads Administration. All simulations were performed on resources provided by UNINETT Sigma2, the National Infrastructure for High Performance Computing and Data Storage in Norway. The authors greatly acknowledge this support.
References
Akkerman, I., Y. Bazilevs, V. M. Calo, T. J. R. Hughes, and S. Hulshoff. 2008. “The role of continuity in residual-based variational multiscale modeling of turbulence.” Comput. Mech. 41 (3): 371–378. https://doi.org/10.1007/s00466-007-0193-7.
Bai, Y., D. Sun, and J. Lin. 2010. “Three dimensional numerical simulations of long-span bridge aerodynamics, using block-iterative coupling and DES.” Comput. Fluids 39 (9): 1549–1561. https://doi.org/10.1016/j.compfluid.2010.05.005.
Bazilevs, Y., and I. Akkerman. 2010. “Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method.” J. Comput. Phys. 229 (9): 3402–3414. https://doi.org/10.1016/j.jcp.2010.01.008.
Bazilevs, Y., V. M. Calo, J. A. Cottrell, T. J. R. Hughes, A. Reali, and G. Scovazzi. 2007a. “Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows.” Comput. Methods Appl. Mech. Eng. 197 (1–4): 173–201. https://doi.org/10.1016/j.cma.2007.07.016.
Bazilevs, Y., V. M. Calo, T. J. R. Hughes, and Y. Zhang. 2008. “Isogeometric fluid-structure interaction: Theory, algorithms, and computations.” Comput. Mech. 43 (1): 3–37. https://doi.org/10.1007/s00466-008-0315-x.
Bazilevs, Y., J. R. Gohean, T. J. R. Hughes, R. D. Moser, and Y. Zhang. 2009. “Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device.” Comput. Methods Appl. Mech. Eng. 198 (45–46): 3534–3550. https://doi.org/10.1016/j.cma.2009.04.015.
Bazilevs, Y., M.-C. Hsu, and M. Scott. 2012a. “Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines.” Comput. Methods Appl. Mech. Eng. 249–252: 28–41. https://doi.org/10.1016/j.cma.2012.03.028.
Bazilevs, Y., M.-C. Hsu, K. Takizawa, and T. E. Tezduyar. 2012b. “ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction.” Supplement, Math. Models Methods Appl. Sci. 22 (S2): 1230002. https://doi.org/10.1142/S0218202512300025.
Bazilevs, Y., and T. J. R. Hughes. 2007. “Weak imposition of Dirichlet boundary conditions in fluid mechanics.” Comput. Fluids 36 (1): 12–26. https://doi.org/10.1016/j.compfluid.2005.07.012.
Bazilevs, Y., A. Korobenko, X. Deng, and J. Yan. 2015a. “Novel structural modeling and mesh moving techniques for advanced fluid–structure interaction simulation of wind turbines.” Int. J. Numer. Methods Eng. 102 (3–4): 766–783. https://doi.org/10.1002/nme.4738.
Bazilevs, Y., A. Korobenko, J. Yan, A. Pal, S. M. I. Gohari, and S. Sarkar. 2015b. “ALE-VMS formulation for stratified turbulent incompressible flows with applications.” Math. Models Methods Appl. Sci. 25 (12): 2349–2375. https://doi.org/10.1142/S0218202515400114.
Bazilevs, Y., C. Michler, V. M. Calo, and T. J. R. Hughes. 2010. “Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes.” Comput. Methods Appl. Mech. Eng. 199 (13–16): 780–790. https://doi.org/10.1016/j.cma.2008.11.020.
Bazilevs, Y., C. Michler, V. M. Calo, and T. J. R. Hughes. 2007b. “Weak Dirichlet boundary conditions for wall-bounded turbulent flows.” Comput. Methods Appl. Mech. Eng. 196 (49–52): 4853–4862. https://doi.org/10.1016/j.cma.2007.06.026.
Bazilevs, Y., K. Takizawa, and T. E. Tezduyar. 2013a. “Challenges and directions in computational fluid-structure interaction.” Math. Models Methods Appl. Sci. 23 (2): 215–221. https://doi.org/10.1142/S0218202513400010.
Bazilevs, Y., K. Takizawa, and T. E. Tezduyar. 2013b. Computational fluid-structure interaction. Chichester, UK: Wiley.
Bazilevs, Y., K. Takizawa, and T. E. Tezduyar. 2015c. “New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods.” Math. Models Methods Appl. Sci. 25 (12): 2217–2226. https://doi.org/10.1142/S0218202515020029.
Bazilevs, Y., K. Takizawa, T. E. Tezduyar, M.-C. Hsu, N. Kostov, and S. McIntyre. 2014. “Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods.” Arch. Comput. Methods Eng. 21 (4): 359–398. https://doi.org/10.1007/s11831-014-9119-7.
Brooks, A. N., and T. J. R. Hughes. 1982. “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations.” Comput. Methods Appl. Mech. Eng. 32 (1–3): 199–259. https://doi.org/10.1016/0045-7825(82)90071-8.
Brusiani, F., S. de Miranda, L. Patruno, F. Ubertini, and P. Vaona. 2013. “On the evaluation of bridge deck flutter derivatives using RANS turbulence models.” J. Wind Eng. Ind. Aerodyn. 119: 39–47. https://doi.org/10.1016/j.jweia.2013.05.002.
Buffa, A., G. Sangalli, and R. Vázquez. 2014. “Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations.” J. Comput. Phys. 257: 1291–1320. https://doi.org/10.1016/j.jcp.2013.08.015.
Chen, X., and A. Kareem. 2002. “Advances in modeling of aerodynamic forces on bridge decks.” J. Eng. Mech. 128 (11): 1193–1205. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1193).
Cottrell, J. A., T. J. R. Hughes, and Y. Bazilevs. 2009. Isogeometric analysis. Chichester, UK: Wiley.
Cottrell, J. A., A. Reali, Y. Bazilevs, and T. J. R. Hughes. 2006. “Isogeometric analysis of structural vibrations.” Comput. Methods Appl. Mech. Eng. 195 (41–43): 5257–5296. https://doi.org/10.1016/j.cma.2005.09.027.
De Lorenzis, L., I. Temizer, P. Wriggers, and G. Zavarise. 2011. “A large deformation frictional contact formulation using NURBS-based isogeometric analysis.” Int. J. Numer. Methods Eng. 87 (13): 1278–1300. https://doi.org/10.1002/nme.3159.
de Miranda, S., L. Patruno, F. Ubertini, and G. Vairo. 2014. “On the identification of flutter derivatives of bridge decks via RANS turbulence models: Benchmarking on rectangular prisms.” Eng. Struct. 76: 359–370. https://doi.org/10.1016/j.engstruct.2014.07.027.
Golshan, R., A. E. Tejada-Martínez, M. Juha, and Y. Bazilevs. 2015. “Large-eddy simulation with near-wall modeling using weakly enforced no-slip boundary conditions.” Comput. Fluids 118: 172–181. https://doi.org/10.1016/j.compfluid.2015.06.016.
Gómez, H., V. M. Calo, Y. Bazilevs, and T. J. Hughes. 2008. “Isogeometric analysis of the Cahn-Hilliard phase-field model.” Comput. Methods Appl. Mech. Eng. 197 (49–50): 4333–4352. https://doi.org/10.1016/j.cma.2008.05.003.
Helgedagsrud, T. A., Y. Bazilevs, A. Korobenko, K. M. Mathisen, and O. A. Øiseth. Forthcoming. “Using ALE-VMS to compute aerodynamic derivatives of bridge sections.” Comput. Fluids. https://doi.org/10.1016/j.compfluid.2018.04.037.
Helgedagsrud, T. A., K. M. Mathisen, Y. Bazilevs, O. Øiseth, and A. Korobenko. 2017. “Using ALE-VMS to compute wind forces on moving bridge decks.” In Proc., MekIT’17 9th National Conf. on Computational Mechanics, edited by B. Skallerud and H. I. Andersson, 169–189. Barcelona, Spain: International Center for Numerical Methods in Engineering.
Hsu, M. C., I. Akkerman, and Y. Bazilevs. 2011. “High-performance computing of wind turbine aerodynamics using isogeometric analysis.” Comput. Fluids 49 (1): 93–100. https://doi.org/10.1016/j.compfluid.2011.05.002.
Hsu, M.-C., I. Akkerman, and Y. Bazilevs. 2012. “Wind turbine aerodynamics using ALE-VMS: Validation and the role of weakly enforced boundary conditions.” Comput. Mech. 50 (4): 499–511. https://doi.org/10.1007/s00466-012-0686-x.
Hsu, M.-C., I. Akkerman, and Y. Bazilevs. 2014a. “Finite element simulation of wind turbine aerodynamics: Validation study using NREL Phase VI experiment.” Wind Energy 17 (3): 461–481. https://doi.org/10.1002/we.1599.
Hsu, M.-C., Y. Bazilevs, V. M. Calo, T. E. Tezduyar, and T. J. R. Hughes. 2010. “Improving stability of stabilized and multiscale formulations in flow simulations at small time steps.” Comput. Methods Appl. Mech. Eng. 199 (13–16): 828–840. https://doi.org/10.1016/j.cma.2009.06.019.
Hsu, M.-C., D. Kamensky, Y. Bazilevs, M. S. Sacks, and T. J. R. Hughes. 2014b. “Fluid–structure interaction analysis of bioprosthetic heart valves: Significance of arterial wall deformation.” Comput. Mech. 54 (4): 1055–1071. https://doi.org/10.1007/s00466-014-1059-4.
Hughes, T. J. R., J. A. Cottrell, and Y. Bazilevs. 2005. “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement.” Comput. Methods Appl. Mech. Eng. 194 (39–41): 4135–4195. https://doi.org/10.1016/j.cma.2004.10.008.
Hughes, T. J. R., L. P. Franca, and M. Balestra. 1986. “A new finite element formulation for computational fluid dynamics: V. Circumventing the babuška-brezzi condition: A stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations.” Comput. Methods Appl. Mech. Eng. 59 (1): 85–99. https://doi.org/10.1016/0045-7825(86)90025-3.
Hughes, T. J. R., W. K. Liu, and T. K. Zimmermann. 1981. “Lagrangian-Eulerian finite element formulation for incompressible viscous flows.” Comput. Methods Appl. Mech. Eng. 29 (3): 329–349. https://doi.org/10.1016/0045-7825(81)90049-9.
Hughes, T. J. R., and G. Sangalli. 2007. “Variational multiscale analysis: The fine scale green’s function, projection, optimization, localization, and stabilized methods.” SIAM J. Numer. Anal. 45 (2): 539–557. https://doi.org/10.1137/050645646.
Karypis, G., and V. Kumar. 1998. “A fast and high quality multilevel scheme for partitioning irregular graphs.” SIAM J. Sci. Comput. 20 (1): 359–392. https://doi.org/10.1137/S1064827595287997.
Korobenko, A., M.-C. Hsu, I. Akkerman, J. Tippmann, and Y. Bazilevs. 2013. “Structural mechanics modeling and FSI simulation of wind turbines.” Math. Models Methods Appl. Sci. 23 (02): 249–272. https://doi.org/10.1142/S0218202513400034.
Larsen, A., and J. H. Walther. 1998. “Discrete vortex simulation of flow around five generic bridge deck sections.” J. Wind Eng. Ind. Aerodyn. 77–78: 591–602. https://doi.org/10.1016/S0167-6105(98)00175-5.
Le Maître, O. P., R. H. Scanlan, and O. M. Knio. 2003. “Estimation of the flutter derivatives of an NACA airfoil by means of Navier-Stokes simulation.” J. Fluids Struct. 17 (1): 1–28. https://doi.org/10.1016/S0889-9746(02)00111-1.
Mathisen, K. M., K. M. Okstad, T. Kvamsdal, and S. B. Raknes. 2015. “Simulation of contact between subsea pipeline and trawl gear using mortar-based isogeometric analysis.” In Proc., 6th Int. Conf. on Computational Methods in Marine Engineering, 290–305. Barcelona, Spain: International Center for Numerical Methods in Engineering.
Mills, R., J. Sheridan, and K. Hourigan. 2002. “Response of base suction and vortex shedding from rectangular prisms to transverse forcing.” J. Fluid Mech. 461: 25–49. https://doi.org/10.1017/S0022112002008534.
Motlagh, Y. G., and H. T. Ahn. 2012. “Laminar and turbulent channel flow simulation using residual based variational multi-scale method.” J. Mech. Sci. Technol. 26 (2): 447–454. https://doi.org/10.1007/s12206-011-1209-y.
Nieto, F., J. S. Owen, D. M. Hargreaves, and S. Hernández. 2015. “Bridge deck flutter derivatives: Efficient numerical evaluation exploiting their interdependence.” J. Wind Eng. Ind. Aerodyn. J. 136: 138–150. https://doi.org/10.1016/j.jweia.2014.11.006.
Øiseth, O., A. Rönnquist, and R. Sigbjörnsson. 2010. “Simplified prediction of wind-induced response and stability limit of slender long-span suspension bridges, based on modified quasi-steady theory: A case study.” J. Wind Eng. Ind. Aerodyn. 98 (12): 730–741. https://doi.org/10.1016/j.jweia.2010.06.009.
Otoguro, Y., K. Takizawa, and T. E. Tezduyar. 2017. “Space-time VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method.” Comput. Fluids 158: 189–200. https://doi.org/10.1016/j.compfluid.2017.04.017.
Patruno, L. 2015. “Accuracy of numerically evaluated flutter derivatives of bridge deck sections using RANS: Effects on the flutter onset velocity.” Eng. Struct. 89: 49–65. https://doi.org/10.1016/j.engstruct.2015.01.034.
Piegl, L., and W. Tiller. 1995. The NURBS book. Monographs in visual communications. Heidelberg, Germany: Springer.
Rabiner, L. R., and B. Gold. 1975. Theory and application of digital signal processing. Englewood Cliffs, NJ: Prentice Hall.
Šarkić, A., R. Fisch, R. Höffer, and K. U. Bletzinger. 2012. “Bridge flutter derivatives based on computed, validated pressure fields.” J. Wind Eng. Ind. Aerodyn. 104–106: 141–151. https://doi.org/10.1016/j.jweia.2012.02.033.
Scanlan, R. H., and J. Tomko. 1971. “Airfoil and bridge deck flutter derivatives.” J. Eng. Mech. Div. 97 (6): 1717–1737.
Scotta, R., M. Lazzari, E. Stecca, J. Cotela, and R. Rossi. 2016. “Numerical wind tunnel for aerodynamic and aeroelastic characterization of bridge deck sections.” Comput. Struct. 167: 96–114. https://doi.org/10.1016/j.compstruc.2016.01.012.
Siedziako, B., O. Øiseth, and A. Rønnquist. 2017. “An enhanced forced vibration rig for wind tunnel testing of bridge deck section models in arbitrary motion.” J. Wind Eng. Ind. Aerodyn. 164: 152–163. https://doi.org/10.1016/j.jweia.2017.02.011.
Takizawa, K., Y. Bazilevs, T. E. Tezduyar, M.-C. Hsu, O. Øiseth, K. M. Mathisen, N. Kostov, and S. McIntyre. 2014a. “Engineering analysis and design with ALE-VMS and space-time methods.” Arch. Comput. Methods Eng. 21 (4): 481–508. https://doi.org/10.1007/s11831-014-9113-0.
Takizawa, K., Y. Bazilevs, T. E. Tezduyar, C. C. Long, A. L. Marsden, and K. Schjodt. 2014b. “ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling.” Math. Models Methods Appl. Sci. 24 (12): 2437–2486. https://doi.org/10.1142/S0218202514500250.
Takizawa, K., B. Henicke, A. Puntel, N. Kostov, and T. E. Tezduyar. 2012. “Space-time techniques for computational aerodynamics modeling of flapping wings of an actual locust.” Comput. Mech. 50 (6): 743–760. https://doi.org/10.1007/s00466-012-0759-x.
Takizawa, K., B. Henicke, A. Puntel, N. Kostov, and T. E. Tezduyar. 2013a. “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.
Takizawa, K., D. Montes, S. McIntyre, and T. E. Tezduyar. 2013b. “Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers.” Math. Models Methods Appl. Sci. 23 (02): 223–248. https://doi.org/10.1142/S0218202513400022.
Takizawa, K., and T. E. Tezduyar. 2011. “Multiscale space-time fluid-structure interaction techniques.” Comput. Mech. 48 (3): 247–267. https://doi.org/10.1007/s00466-011-0571-z.
Takizawa, K., T. E. Tezduyar, S. Asada, and T. Kuraishi. 2016a. “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.
Takizawa, K., T. E. Tezduyar, and H. Hattori. 2017a. “Computational analysis of flow-driven string dynamics in turbomachinery.” Comput. Fluids 142: 109–117. https://doi.org/10.1016/j.compfluid.2016.02.019.
Takizawa, K., T. E. Tezduyar, T. Kuraishi, S. Tabata, and H. Takagi. 2016b. “Computational thermo-fluid analysis of a disk brake.” Comput. Mech. 57 (6): 965–977. https://doi.org/10.1007/s00466-016-1272-4.
Takizawa, K., T. E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan, and K. Montel. 2015. “Space-time VMS method for flow computations with slip interfaces (ST-SI).” Math. Models Methods Appl. Sci. 25 (12): 2377–2406. https://doi.org/10.1142/S0218202515400126.
Takizawa, K., T. E. Tezduyar, and Y. Otoguro. 2018. “Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations.” Comput. Mech. 62 (5): 1169–1186. https://doi.org/10.1007/s00466-018-1557-x.
Takizawa, K., T. E. Tezduyar, Y. Otoguro, T. Terahara, T. Kuraishi, and H. Hattori. 2017b. “Turbocharger flow computations with the space-time isogeometric analysis (ST-IGA).” Comput. Fluids 142: 15–20. https://doi.org/10.1016/j.compfluid.2016.02.021.
Takizawa, K., T. E. Tezduyar, T. Terahara, and T. Sasaki. 2017c. “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.
Tezduyar, T. E. 2003. “Computation of moving boundaries and interfaces and stabilization parameters.” Int. J. Numer. Methods Fluids 43 (5): 555–575. https://doi.org/10.1002/fld.505.
Tezduyar, T. E., and Y. Osawa. 2000. “Finite element stabilization parameters computed from element matrices and vectors.” Comput. Methods Appl. Mech. Eng. 190 (3–4): 411–430. https://doi.org/10.1016/S0045-7825(00)00211-5.
Tezduyar, T. E., and Y. Park. 1986. “Discontinuity-capturing finite element formulations for nonlinear convection-diffusion-reaction equations.” Comput. Methods Appl. Mech. Eng. 59 (3): 307–325. https://doi.org/10.1016/0045-7825(86)90003-4.
Yan, J., A. Korobenko, X. Deng, and Y. Bazilevs. 2016. “Computational free-surface fluid-structure interaction with application to floating offshore wind turbines.” Comput. Fluids 141: 155–174. https://doi.org/10.1016/j.compfluid.2016.03.008.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 5 • May 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Feb 26, 2018
Accepted: Oct 15, 2018
Published online: Feb 23, 2019
Published in print: May 1, 2019
Discussion open until: Jul 23, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.