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Fluid-structure interaction solver for compressible flows with applications to blast loading on thin elastic structures. (English) Zbl 1480.74062

Summary: In this study, we report the development and application of a fluid-structure interaction (FSI) solver for compressible flows with large-scale flow-induced deformation of the structure. The FSI solver utilizes a partitioned approach to strongly couple a sharp interface immersed boundary method-based flow solver with an open-source finite-element structure dynamics solver. The flow solver is based on a higher-order finite-difference method using a Cartesian grid, where it employs the ghost-cell methodology to impose boundary conditions on the immersed boundary. Higher-order accuracy near the immersed boundary is achieved by combining the ghost-cell approach with a weighted least squares error method based on a higher-order approximate polynomial. We present validations for two-dimensional canonical acoustic wave scattering on a rigid cylinder at a low Mach number and for flow past a circular cylinder at a moderate Mach number. The second order spatial accuracy of the flow solver was established in a grid refinement study. The structural solver was validated according to a canonical elastostatics problem. The FSI solver was validated based on comparisons with published measurements and simulations of the large-scale deformation of a thin elastic steel panel subjected to blast loading in a shock tube. The solver correctly predicted the oscillating behavior of the tip of the panel with reasonable fidelity and the computed shock wave propagation was qualitatively consistent with the published results. In order to demonstrate the fidelity of the solver and to investigate the coupled physics of the shock-structure interaction for a thin elastic plate, we employed the solver to simulate a 6.4 kg TNT blast loading on the thin elastic plate. The initial conditions for the blast were taken from previously reported field tests. Using numerical schlieren, the shock front propagation, Mach reflection, and vortex shedding at the tip of the plate were visualized during the impact of the shock wave on the plate. We discuss the coupling between the nonlinear dynamics of the plate and blast loading. The plate oscillates under the influence of blast loading and the restoration of elastic forces. The time-varying displacement of the tip of the plate is the superimposition of two dominant frequencies, which correspond to the first and second modes of the natural frequency of a vibrating plate. The effects of the material properties and length of the plate on the flow-induced deformation are briefly discussed. The proposed FSI solver is a versatile computational tool for simulating the impact of a blast wave on thin elastic structures and the results presented in this study may facilitate the design of thin structures subjected to realistic blast loadings.

MSC:

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76L05 Shock waves and blast waves in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
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[1] Bhardwaj, R.; Zeigler, K.; Seo, J. H.; Ramesh, K. T.; Nguyen, T. D., A computational model of blast loading on human eye, Biomech. Model. Mechanobiol., 13, 1, 123-140 (2014)
[2] Bailoor, S.; Bhardwaj, R.; Nguyen, T. D., Effectiveness of eye armour during blast loading, Biomech. Model. Mechanobiol., 14, 6, 1227-1237 (2015)
[3] Ganpule, S.; Alai, A.; Plougonven, E.; Chandra, N., Mechanics of blast loading on the head models in the study of traumatic brain injury using experimental and computational approaches, Biomech. Model. Mechanobiol., 12, 3, 511-531 (2013)
[4] Kambouchev, N.; Noels, L.; Radovitzky, R., Nonlinear compressibility effects in fluid-structure interaction and their implications on the air-blast loading of structures, J. Appl. Phys., 100, Article 063519 pp. (2006), (1-11)
[5] Wang, E.; Gardner, N.; Shukla, A., The blast resistance of sandwich composites with stepwise graded cores, Int. J. Solids Struct., 46, 18, 3492-3502 (2009)
[6] Zheng, X.; Xue, Q.; Mittal, R.; Beilamowicz, S., A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation, J. Biomech. Eng., 132, Article 111003 pp. (2010), (1-12)
[7] Dunne, T.; Rannacher, R., Adaptive finite element approximation of fluid-structure interaction based on an Eulerian variational formulation, (Bungartz, H.-J.; Schaefer, M., Lecture Notes in Computational Science and Engineering (2006), Springer Verlag) · Zbl 1323.74082
[8] Bhardwaj, R.; Mittal, R., Benchmarking a coupled immersed-boundary-finite-element solver for large-scale flow-induced deformation, AIAA J., 50, 7, 1638-1642 (2012)
[9] Tian, F.-B., Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems, J. Comput. Phys., 258, 451-469 (2014) · Zbl 1349.76274
[10] Schafer, M.; Heck, M.; Yigit, S., An implicit partitioned method for the numerical simulation of fluid-structure interaction, (Bungartz, H.-J.; Schaefer, M., Lecture Notes in Computational Science and Engineering (2006), Springer Verlag) · Zbl 1323.74093
[11] Förster, C.; Wall, W.; Ramm, E., Artificial mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows, Comput. Methods Appl. Mech. Eng., 196, 1278-1293 (2007) · Zbl 1173.74418
[12] Heil, M.; Hazel, A. L.; Boyle, J., Solvers for large-displacement fluid-structure interaction problems: segregated versus monolithic approaches, Comput. Mech., 43, 91-101 (2008) · Zbl 1309.76126
[13] Hron, J.; Turek, S., A monolithic FEM/multigrid solver for an ALE formulation of fluid-structure interaction with applications in biomechanics, (Bungartz, H.-J.; Schaefer, M., Lecture Notes in Computational Science and Engineering (2006), Springer Verlag) · Zbl 1323.74086
[14] Sahin, M.; Mohseni, K., An arbitrary Lagrangian-Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa Aequorea victoria, J. Comput. Phys., 228, 4588 (2009) · Zbl 1395.76062
[15] Tezduyar, T. E.; Sathe, S.; Stein, K.; Aureli, L., Modeling of fluid-structure interactions with the space-time techniques, (Bungartz, H.-J.; Schaefer, M., Lecture Notes in Computational Science and Engineering (2006), Springer Verlag) · Zbl 1323.74096
[16] Souli, M.; Ouahsine, A.; Lewin, L., ALE formulation for fluid-structure interaction problems, Comput. Methods Appl. Mech. Eng., 190, 659-675 (2000) · Zbl 1012.76051
[17] Peskin, C. S., Numerical analysis of blood flow in the heart, J. Comput. Phys., 25, 220-252 (1977) · Zbl 0403.76100
[18] Mittal, R.; Iaccarino, G., Immersed boundary methods, Ann. Rev. Fluid Mech., 37, 239-261 (2005), 2005 · Zbl 1117.76049
[19] Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F. M.; Vargas, A.; vonLoebbeck, A., A versatile immersed boundary methods for incompressible flows with complex boundaries, J. Comput. Phys., 227, 10 (2008) · Zbl 1388.76263
[20] Mittal, R.; Zheng, X.; Bhardwaj, R.; Seo, J. H.; Xue, Q.; Bielamowicz, S., Toward a simulation-based tool for the treatment of vocal fold paralysis, Front. Comput. Physiol. Med., 2, 1-15 (2011)
[21] De, A. K., A diffuse interface immersed boundary method for convective heat and fluid flow, Int. J. Heat Mass Transf., 92, 957-969 (2016)
[22] Ghias, R.; Mittal, R.; Dong, H., A sharp interface immersed boundary method for compressible viscous flows, J. Comput. Phys., 225, 528-553 (2007) · Zbl 1343.76043
[23] Seo, J. H.; Mittal, R., A high-order immersed boundary method for acoustic wave scattering and low-Mach number flow-induced sound in complex geometries, J. Comput. Phys., 230, 1000-1019 (2011) · Zbl 1391.76698
[24] Seo, J. H.; Moon, Y. J., Linearized perturbed compressible equations for low Mach number aeroacoustics, J. Comput. Phys., 218, 702-719 (2006) · Zbl 1161.76546
[25] Chaudhuri, A.; Hadjadj, A.; Chinnayya, A., On the use of immersed boundary methods for shock/obstacle interactions, J. Comput. Phys., 230, 1731-1748 (2011) · Zbl 1391.76531
[26] Eldredge, J. D.; Pisani, D., Passive locomotion of a simple articulated fish-like system in the wake of an obstacle, J. Fluid Mech., 607, 279-288 (2008) · Zbl 1145.76478
[27] Tahoe is an open source C++ finite element solver, which was developed at Sandia National Labs, CA, <http://sourceforge.net/projects/tahoe/; Tahoe is an open source C++ finite element solver, which was developed at Sandia National Labs, CA, <http://sourceforge.net/projects/tahoe/
[28] Lele, S., Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103, 16-42 (1992), 1992 · Zbl 0759.65006
[29] Gaitonde, D.; Shang, J. S.; Young, J. L., Practical aspects of higher-order accurate finite volume schemes for wave propagation phenomena, Int. J. Numer. Methods Eng., 45, 1849-1869 (1999) · Zbl 0959.65103
[30] Kawai, S.; Lele, S. K., Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes, J. Comput. Phys., 227, 22 (2008), 2008 · Zbl 1359.76223
[31] Cook, A. W.; Cabot, W. H., Hyperviscosity for shock-turbulence interactions, J. Comput. Phys., 203, 2, 379-385 (2005) · Zbl 1143.76477
[32] Luo, H.; Mittal, R.; Zheng, X.; Bielamowicz, S. A.; Walsh, R. J.; Hahn, J. K., An immersed-boundary method for flow-structure interaction in biological systems with application to phonation, J. Comput. Phys., 227, 22, 9303-9332 (2008) · Zbl 1148.74048
[33] Li, Z., A fast iterative algorithm for elliptic interface problems, SIAM J. Numer. Anal., 35, 1, 230-254 (1998) · Zbl 0915.65121
[34] Hughes, T. J.R., The Finite Element Method (1987), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0634.73056
[35] Negrut, D.; Rampalli, R.; Ottarsson, G.; Sajdak, A., On an implementation of the Hilber-Hughes-Taylor method in the context of index 3 differential-algebraic equations of multibody dynamics (DETC2005-85096), J. Comput. Nonlinear Dyn., 2, 73 (2007)
[36] Hilber, H. M.; Hughes, T. J.R.; Taylor, R. L., Improved numerical dissipation for time integration algorithms in structural dynamics, Earthq. Eng. Struct. Dyn., 5, 283-292 (1977)
[37] (Tam, C. K.W.; Hardin, J. C., Proceedings of the Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems (1997)), NASA-CP-3352
[38] Liu, Q.; Vasilyev, O. V., A Brinkman penalization method for compressible flows in complex geometries, J. Comput. Phys., 227, 946-966 (2007), (2007) · Zbl 1388.76259
[39] Edgar, N. B.; Visbal, M. R., A general buffer zone type non-reflecting boundary condition for computational aeroacoustics, (Proceeding of the AIAA (2003)), AIAA Paper 2003 - 3300
[40] Henderson, R. D., Details of the drag curve near the onset of vortex shedding, Phys. Fluids, 7, 9, 2102-2104 (1995)
[41] Williamson, C. H.K.; Roshko, A., Measurement of base pressure in the wake of a cylinder at low Reynolds numbers, Z. Flugwiss. Weltraumforsch., 14, 38-46 (1990)
[42] Fung, Y. C., Foundation of Solid Mechanics (1965), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[43] Giordano, J.; Jourdan, G.; Burtschell, Y.; Medale, M.; Zeitoun, D. E.; Houas, L., Shock wave impacts on deforming panel, an application of fluid-structure interaction, Shock Waves, 14, 1-2, 103-110 (2005), (2005) · Zbl 1178.74054
[44] Sanches, R. A.K.; Coda, H. B., On fluid-shell coupling using an arbitrary Lagrangian-Eulerian fluid solver coupled to a positional Lagrangian shell solver, Appl. Math. Model., 38, 3401-3418 (2014) · Zbl 1449.76018
[45] Deiterding, R.; Wood, S., Parallel adaptive fluid-structure interaction simulation of explosions impacting on building structures, Comput. Fluids, 88, 719-729 (2013)
[46] Deiterding, R., An adaptive level set method for shock-driven fluid-structure interaction, Proc. Appl. Math. Mech., 7, 1, 2100037-2100038 (2007)
[47] Deiterding, R.; Cirak, F.; Mauch, S. P., Efficient fluid-structure interaction simulation of viscoplastic and fracturing thin-shells subjected to underwater shock loading, (Proceedings of the International Workshop on Fluid-Structure Interaction: Theory, Numerics and Applications (2009), Kassel University Press GmbH), 65-80
[48] Li, Q.; Liu, P.; He, G., Fluid-solid coupled simulation of the ignition transient of solid rocket motor, Acta Astron., 110, 180-190 (2015)
[49] Thomson, W. T.; Dahleh, M. D., Theory of Vibration with Application (1997), Prentice Hall: Prentice Hall Upper Saddle River, New Jersey
[50] Kundu, A. K.; Soti, A. K.; Bhardwaj, R.; Thompson, M., The response of an elastic splitter plate attached to a cylinder to laminar pulsatile flow, J. Fluids Struct., 68, 423-443 (2017)
[51] Bentz, V.; Grimm, G., Joint Live Fire (JLF) Final Report for Assessment of Ocular Pressure as a Result of Blast for Protected and Unprotected Eyes, Report number JLF-TR-13-01) (2013), U.S. Army Aberdeen Test Center
[52] Shi, Y.; Hao, H.; Li, Z.-X., Numerical simulation of blast wave interaction with structure columns, Shock Waves, 17, 113-133 (2007)
[53] Anderson, J. D., Modern Compressible Flow (1990), McGraw Hill: McGraw Hill New York
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