Session: 12-04-02: Drucker Medal Symposium

Paper Number: 150206

150206 - Fluid--Structure Interaction Modeling for Underwater Explosions: Methods and Computations 

In [1], the authors developed a formulation for air–water free-surface flows focusing on ship hydrodynamics applications [2]. The formulation was based on solving the Navier–Stokes equations of incompressible flows where the interface between the air and water phases was captured using a level-set technique [3]. In this approach, the boundary between the two fluids was described implicitly as a zero level-set of a scalar function defined in the problem domain. The subdomains corresponding to negative and positive values of this function were prescribed the material properties of air and water, respectively. The level-set function was forced to satisfy a signed-distance property and was dynamically corrected by a global constant to satisfy the water mass balance. An important aspect of the formulation in [1] was the discretization of the Navier–Stokes and level-set equations using Isogeometric Analysis (IGA) [4] based on Non-Uniform Rational B-Splines (NURBS). As shown in [1], the use of higher-order and higher-continuity functions such as NURBS significantly improves the quality of the level-set solution compared to a low-order Finite Elements Method (FEM). The IGA-based multiphase flow approach was further extended in [5] to simulate dynamics of bubbles including surface tension. Surface tension models rely on an accurate computation of the bubble surface curvature, which again benefits from the use of smooth IGA discretizations.

In the present work, we develop a level-set approach for multiphase compressible flows. Here, the application of interest is the modeling of underwater explosion (UNDEX) scenarios, which involve the interaction of saltwater and explosive gas products. Both fluid phases are assumed to be compressible and are thus modeled using the Navier–Stokes equations of compressible flows complemented with an equation of state (EOS) for each phase. In fact, explosive gas bubbles undergo significant expansion and contraction during an UNDEX event. As a result, the ability to capture interfaces between saltwater and explosive products for this highly compressible flow is essential for the overall accuracy of the modeling and simulation of UNDEX phenomena. Because level-set methods in [1,5,6] were developed in the setting of incompressible flows, they require suitable modifications for the compressible-flow regime, which is one of the key contribution of the present paper. Inspired by the developments in [7], we augment the Navier–Stokes equations of compressible flows with the additional set of species mass conservation partial differential equations written in terms of the species volume fractions. The level-set signed-distance function is then introduced for each species. With the aid of an invertible mapping between the level-set and volume fraction functions, the level-set is reconstructed around the interface, sharpened (i.e., we ensure that the signed distance property is maintained), and mass-corrected for each species. We present several computations that show favorable comparisons with experimental data.

References

[1]  I. Akkerman, Y. Bazilevs, C. Kees, M. Farthing, Isogeometric analysis of free-surface flow, J. Comput. Phys. 230 (11) (2011) 4137–4152, Special issue High Order Methods for CFD Problems.

[2]  I. Akkerman, Y. Bazilevs, D.J. Benson, M.W. Farthing, C.E. Kees, Free-surface flow and fluid-object interaction modeling with emphasis on ship hydrodynamics, J. Appl. Mech. 79 (2012).

[3]  W. Mulder, S. Osher, J.A. Sethian, Computing interface motion in compressible gas dynamics, J. Comput. Phys. 100 (2) (1992) 209–228.

[4]  T.J. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng. 194 (39–41) (2005) 4135–4195.

[5]  J. Yan, S. Lin, Y. Bazilevs, G. Wagner, Isogeometric analysis of multi-phase flows with surface tension and with application to dynamics of rising bubbles, Comput. & Fluids 179 (2019) 777–789.

[6]  C. Kees, I. Akkerman, M. Farthing, Y. Bazilevs, A conservative level set method suitable for variable-order approximations and unstructured meshes, J. Comput. Phys. 230 (12) (2011) 4536–4558.

[7]  M.P. Kinzel, J.W. Lindau, R.F. Kunz, A multiphase level-set approach for all-Mach numbers, Comput. & Fluids 167 (2018) 1–16.

Presenting Author: Yuri Bazilevs Brown University

Presenting Author Biography: Yuri Bazilevs is the E. Paul Sorensen Professor in the School of Engineering at Brown University. His research interests are in computational science and engineering, with emphasis on the modeling and simulation in solids and structures, fluids, and their coupling in High-Performance Computing environments. For his research contributions Yuri received many awards and honors, including the 2018 Walter E. Huber Research Prize from the ASCE, the 2020 Gustus L. Larson Award from the ASME, and the Computational Mechanics Award from the International Association for Computational Mechanics (IACM). He is included in the lists of Highly Cited Researchers, both in the Engineering (2015-2018) and Computer Science (2014-2019) categories. Yuri recently completed his service as the President of the US Association for Computational Mechanics (USACM) and as the Chairman of the Applied Mechanics Division of the ASME. He currently serves on the US National Committee for Theoretical and Applied Mechanics (USNCTAM) and on the Executive Council of the IACM.

Authors:

Yuri Bazilevs Brown University