Abstract
Many aerospace applications involve complex multiphysics in compressible flow regimes that are challenging to model and analyze. Fluid–structure interaction (FSI) simulations offer a promising approach to effectively examine these complex systems. In this work, a fully coupled FSI formulation for compressible flows is summarized. The formulation is developed based on an augmented Lagrangian approach and is capable of handling problems that involve nonmatching fluid–structure interface discretizations. The fluid is modeled with a stabilized finite element method for the Navier–Stokes equations of compressible flows and is coupled to the structure formulated using isogeometric Kirchhoff–Love shells. To solve the fully coupled system, a block-iterative approach is used. To demonstrate the framework’s effectiveness for modeling industrial-scale applications, the FSI methodology is applied to the NASA Common Research Model (CRM) aircraft to study buffeting phenomena by performing an aircraft pitching simulation based on a prescribed time-dependent angle of attack.
Similar content being viewed by others
References
Abbas A, Vicente J, Valero E (2013) Aerodynamic technologies to improve aircraft performance. Aerosp Sci Technol 28:100–132
Heinz A, Haszler A, Keidel C, Moldenhauer S, Benedictus R, Miller WS (2000) Recent development in aluminium alloys for aerospace applications. Mater Sci Eng, A 280:102–107
Immarigeon J-P, Holt RT, Koul AK, Zhao L, Wallace W, Beddoes JC (1995) Lightweight materials for aircraft applications. Mater Charact 35:41–67
Lee BHK (2000) Vertical tail buffeting of fighter aircraft. Prog Aerosp Sci 36:193–279
Sharma V, Walker J, Sweet M, Weimerskirch T (2001) P-3 aircraft buffet response characterization. In 39th AIAA Aerospace Science Meeting & Exhibition, AIAA 2001-0711, Reno, Nevada
Giannelis NF, Vio GA, Levinski O (2017) A review of recent developments in the understanding of transonic shock buffet. Prog Aerosp Sci 92:39–84
Molent L, Jones R, Barter S, Pitt S (2006) Recent developments in fatigue crack growth assessment. Int J Fatigue 28:1759–1768
Liu N, Rajanna MR, Johnson EL, Lua J, Phan N, Hsu M-C (2022) Isogeometric blended shells for dynamic analysis: simulating aircraft takeoff and the resulting fatigue damage on the horizontal stabilizer. Comput Mech 70:1013–1024
Marshall JG, Imregun M (1996) A review of aeroelasticity methods with emphasis on turbomachinery applications. J Fluids Struct 10:237–267
Dowell EH, Hall KC (2001) Modeling of fluid-structure interaction. Annu Rev Fluid Mech 33:445–490
Kamakoti R, Shyy W (2004) Fluid-structure interaction for aeroelastic applications. Prog Aerosp Sci 40:535–558
Shyy W, Aono H, Chimakurthi SK, Trizila P, Kang C-K, Cesnik CES, Liu H (2010) Recent progress in flapping wing aerodynamics and aeroelasticity. Prog Aerosp Sci 46:284–327
Lee-Rausch EM, Batina JT (1995) Wing flutter boundary prediction using unsteady Euler aerodynamic method. J Aircraft 32(2):416–422
Farhat C, Lesoinne M (2000) Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problem. Comput Methods Appl Mech Eng 182:499–515
Smith MJ, Hodges DH, Cesnik CES (2000) Evaluation of computational algorithms suitable for fluid-structure interactions. J Aircraft 37(2):282–294
Abras JN, Lynch CE, Smith MJ (2012) Computational fluid dynamics-computational structural dynamics rotor coupling using an unstructured Reynolds-averaged Navier-Stokes methodology. J Am Helicopter Soc 57(1):1–14
Rajanna MR, Johnson EL, Liu N, Korobenko A, Bazilevs Y, Hsu M-C (2022) Fluid-structure interaction modeling with nonmatching interface discretizations for compressible flow problems: computational framework and validation study. Math Models Methods Appl Sci 32:2497–2528
Bazilevs Y, Hsu M-C, Scott MA (2012) 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
Xu F, Moutsanidis G, Kamensky D, Hsu M-C, Murugan M, Ghoshal A, Bazilevs Y (2017) Compressible flows on moving domains: Stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Comput Fluids 158:201–220
Rajanna MR, Johnson EL, Codoni D, Korobenko A, Bazilevs Y, Liu N, Lua J, Phan N, Hsu M-C (2022) Finite element methodology for modeling aircraft aerodynamics: development, simulation, and validation. Comput Mech 70:549–563
Kiendl J, Bletzinger K-U, Linhard J, Wüchner R (2009) Isogeometric shell analysis with Kirchhoff–Love elements. Comput Methods Appl Mech Eng 198:3902–3914
Kiendl J, Hsu M-C, Wu MCH, Reali A (2015) Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials. Comput Methods Appl Mech Eng 291:280–303
Herrema AJ, Johnson EL, Proserpio D, Wu MCH, Kiendl J, Hsu M-C (2019) Penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches with application to composite wind turbine blades. Comput Methods Appl Mech Eng 346:810–840
Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821–833
Wu MCH, Kamensky D, Wang C, Herrema AJ, Xu F, Pigazzini MS, Verma A, Marsden AL, Bazilevs Y, Hsu M-C (2017) Optimizing fluid-structure interaction systems with immersogeometric analysis and surrogate modeling: Application to a hydraulic arresting gear. Comput Methods Appl Mech Eng 316:668–693
Xu F, Johnson EL, Wang C, Jafari A, Yang C-H, Sacks MS, Krishnamurthy A, Hsu M-C (2021) Computational investigation of left ventricular hemodynamics following bioprosthetic aortic and mitral valve replacement. Mech Res Commun 112:103604
Neighbor GE, Zhao H, Saraeian M, Hsu M-C, Kamensky D (2023) Leveraging code generation for transparent immersogeometric fluid-structure interaction analysis on deforming domains. Eng Comput 39:1019–1040
Vassberg J, Dehaan M, Rivers M, Wahls R (2008) Development of a Common Research Model for applied CFD validation studies. In AIAA 2008-6919, Honolulu, Hawaii. 26th AIAA Applied Aerodynamics Conference
Rivers MB, Dittberner A (2014) Experimental investigations of the NASA Common Research Model. J Aircr 51:1183–1193
NASA Common Research Model. https://commonresearchmodel.larc.nasa.gov/. [Accessed 31 March 2022]
Shakib F, Hughes TJR, Johan Z (1991) A new finite element formulation for computational fluid dynamics: X. The compressible Euler and Navier-Stokes equations. Comput Methods Appl Mech Engrg 89:141–219
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
Aliabadi SK, Tezduyar TE (1993) Space-time finite element computation of compressible flows involving moving boundaries and interfaces. Comput Methods Appl Mech Eng 107:209–223
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
Hauke G, Hughes TJR (1994) A unified approach to compressible and incompressible flows. Comput Methods Appl Mech Eng 113:389–396
Wren GP, Ray SE, Aliabadi SK, Tezduyar TE (1995) Space-time finite element computation of compressible flows between moving components. Int J Numer Meth Fluids 21:981–991
Wren GP, Ray SE, Aliabadi SK, Tezduyar TE (1997) Simulation of flow problems with moving mechanical components, fluid-structure interactions and two-fluid interfaces. Int J Numer Meth Fluids 24:1433–1448
Mittal S, Tezduyar T (1998) A unified finite element formulation for compressible and incompressible flows using augumented conservation variables. Comput Methods Appl Mech Eng 161:229–243
Ray SE, Tezduyar TE (2000) Fluid-object interactions in interior ballistics. Comput Methods Appl Mech Eng 190:363–372
Hauke G (2001) Simple stabilizing matrices for the computation of compressible flows in primitive variables. Comput Methods Appl Mech Eng 190:6881–6893
Hughes TJR, Scovazzi G, Tezduyar TE (2010) Stabilized methods for compressible flows. J Sci Comput 43:343–368
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
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
Takizawa K, Otoguro Y, Tezduyar TE (2023) Variational multiscale method stabilization parameter calculated from the strain-rate tensor. Math Models Methods Appl Sci 33:1661–1691
Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59:307–325
Hughes TJR, Mallet M, Mizukami A (1986) A new finite element formulation for computational fluid dynamics: II. Beyond SUPG. Comput Methods Appl Mech Eng 54:341–355
Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput Methods Appl Mech Eng 58:329–339
Almeida RC, Galeão AC (1996) An adaptive Petrov–Galerkin formulation for the compressible Euler and Navier-Stokes equations. Comput Methods Appl Mech Eng 129:157–176
Hauke G, Hughes TJR (1998) A comparative study of different sets of variables for solving compressible and incompressible flows. Comput Methods Appl Mech Eng 153:1–44
Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195:1621–1632
Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ\(\beta \) shock-capturing. Comput Mech 38:469–481
Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ\(\beta \) shock-capturing. Comput Fluids 36:147–159
Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ\(\beta \) shock-capturing. Int J Numer Meth Fluids 54:695–706
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\(\beta \) shock-capturing. J Appl Mech 76:021209
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\(\beta \) shock-capturing. Comput Mech 55:1201–1209
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
Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized-\(\alpha \) method. J Appl Mech 60:371–75
Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319
Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3–37
Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space-time finite element techniques for computation of fluid-structure interactions. Comput Methods Appl Mech Eng 195:2002–2027
Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid-structure interactions with the space-time formulations. Comput Methods Appl Mech Eng 195:5743–5753
Tezduyar TE, Sathe S (2007) Modelling of fluid-structure interactions with the space-time finite elements: Solution techniques. Int J Numer Meth Fluids 54(6–8):855–900
Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94
Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid-structure interactions with large displacements. J Appl Mech 70:58–63
Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193:2019–2032
Fluid-structure interaction modeling with composite blades (2011) Y. Bazilevs, M.-C. Hsu, J. Kiendl, R. Wüchner, K.-U. Bletzinger. 3D simulation of wind turbine rotors at full scale. Part II. Int J Numer Meth Fluids 65:236–253
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
Terahara T, Takizawa K, Tezduyar TE, Tsushima A, Shiozaki K (2020) Ventricle-valve-aorta flow analysis with the Space-Time Isogeometric Discretization and Topology Change. Comput Mech 65:1343–1363
Bazilevs Y, Takizawa K, Wu MCH, Kuraishi T, Avsar R, Xu Z, Tezduyar TE (2021) Gas turbine computational flow and structure analysis with isogeometric discretization and a complex-geometry mesh generation method. Comput Mech 67:57–84
Aydinbakar L, Takizawa K, Tezduyar TE, Matsuda D (2021) U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization. Comput Mech 67:823–843
Kuraishi T, Xu Z, Takizawa K, Tezduyar TE, Yamasaki S (2022) High-resolution multi-domain space-time isogeometric analysis of car and tire aerodynamics with road contact and tire deformation and rotation. Comput Mech 70:1257–1279
Bazilevs Y, Takizawa K, Tezduyar TE, Korobenko A, Kuraishi T, Otoguro Y (2023) Computational aerodynamics with isogeometric analysis. J Mech 39:24–39
Kudela L, Kollmannsberger S, Almac U, Rank E (2020) Direct structural analysis of domains defined by point clouds. Comput Methods Appl Mech Eng 358:112581
Balu A, Rajanna MR, Khristy J, Xu F, Krishnamurthy A, Hsu M-C (2023) Direct immersogeometric fluid flow and heat transfer analysis of objects represented by point clouds. Comput Methods Appl Mech Eng 404:115742
Wang X, Jaiswal M, Corpuz AM, Paudel S, Balu A, Krishnamurthy A, Yan J, Hsu M-C (2023) Photogrammetry-based computational fluid dynamics. Comput Methods Appl Mech Eng 417:116311
Acknowledgements
This work is supported by the Naval Air Systems Command (NAVAIR) Funding Agreement No. N68335-20-C-0899. This support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Rajanna, M.R., Jaiswal, M., Johnson, E.L. et al. Fluid–structure interaction modeling with nonmatching interface discretizations for compressible flow problems: simulating aircraft tail buffeting. Comput Mech (2024). https://doi.org/10.1007/s00466-023-02436-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00466-023-02436-2