skip to main content

This content will become publicly available on September 28, 2023

Title: Self-similar diffuse boundary method for phase boundary driven flow
Interactions between an evolving solid and inviscid flow can result insubstantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such interactions include melting, sublimation, and deflagration, all of which exhibit bidirectional coupling, mass/heat transfer, and topological change of the solid-fluid interface. The diffuse interface method is a powerful technique that has been used to describe a wide range of solid-phase interface-driven phenomena. The implicit treatment of the interface eliminates the need for cumbersome interface tracking, and advances in adaptive mesh refinement have provided a way to sufficiently resolve diffuse interfaces without excessive computational cost. However, the general scale-invariant coupling of these techniques to flow solvers has been relatively unexplored. In this work, a robust method is presented for treating diffuse solid-fluid interfaces with arbitrary boundary conditions. Source terms defined over the diffuse region mimic boundary conditions at the solid-fluid interface, and it is demonstrated that the diffuse length scale has no adverse effects. To show the efficacy of the method, a one-dimensional implementation is introduced and tested for three types of boundaries: mass flux through the boundary, a moving boundary, and passive interaction of the boundary with an incident acoustic wave. more » These demonstrate expected behavior in all cases. Convergence analysis is also performed and compared against the sharp-interface solution, and linear convergence is observed. This method lays the groundwork for the extension to viscous flow, and the solution of problems involving time-varying mass-flux boundaries. « less
; ;
Award ID(s):
Publication Date:
Journal Name:
Physics of Fluids
Sponsoring Org:
National Science Foundation
More Like this
  1. Underwater explosion poses a significant threat to the structural integrity of ocean vehicles and platforms. Accurate prediction of the dynamic loads from an explosion and the resulting structural response is crucial to ensuring safety without overconservative design. When the distance between the explosive charge and the structure is relatively small (i.e., near-field explosion), the dynamics of the gaseous explosion product, i.e., the “bubble”, comes into play, rendering a multiphysics problem that features the interaction of the bubble, the surrounding liquid water, and the solid structure. The problem is highly nonlinear, as it involves shock waves, large deformation, yielding, contact, and possibly fracture. This paper investigates the two-way interaction between the cyclic expansion and collapse of an explosion bubble and the deformation of a thin-walled elastoplastic cylindrical shell in its vicinity. Intuitively, when a shock wave impinges on a thin cylindrical shell, the shell would collapse in the direction of shock propagation. However, some recent laboratory experiments have shown that under certain conditions the shell collapsed in a counter-intuitive mode in which the direction of collapse is perpendicular to that of shock propagation. In other words, the nearest point on the structural surface moved towards the explosion charge, despite being impactedmore »by a compressive shock. This paper focuses on replicating this phenomenon through numerical simulation and elucidating the underlying mechanisms. A recently developed computational framework (“FIVER”) coupling a nonlinear finite element structural dynamics solver and a finite volume compressible fluid dynamics solver is used to complete this study. The solver utilizes an embedded boundary method to track the wetted surface of the structure (i.e. the fluid-structure interface), which is capable of handling large structural deformation and topological changes (e.g., fracture). The solver also adopts the level set method for tracking the bubble surface (i.e. the liquid-gas interface). The fluid-structure and liquid-gas interface conditions are enforced by constructing and solving one-dimensional multi-material Riemann problems, which naturally accommodates the propagation of shock waves across the interfaces. In this paper, mesh refinement study is made to examine the sensitivity of the results to various meshing parameters. The results show that the intermediate level of refinement is appropriate in terms of both the accuracy and the computation costs. Next, the deformation history of both the bubble and the structure are presented and analyzed to provide a detailed view of the counter-intuitive collapse mode mentioned above. We show that timewise, the structural collapse spans multiple cycles of bubble oscillation. Additional details about the time-histories of fluid pressure, structure displacement, and bubble size are presented to elucidate this dynamic bubble-structure interaction and the resulting structural failure.« less
  2. Abstract. We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The fluid flow is modeled by the time-dependent Navier- Stokes equations in a three-dimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the two-dimensional linearly elastic Koiter shell equations coupled to a one-dimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many ap- plications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary Lagrangian-Eulerian approach, and a non-trivial extension of the Aubin-Lions-Simon compactness result to problems on moving domains.
  3. We present a quasi-incompressible Navier–Stokes–Cahn–Hilliard (q-NSCH) diffuse interface model for two-phase fluid flows with variable physical properties that maintains thermodynamic consistency. Then, we couple the diffuse domain method with this two-phase fluid model – yielding a new q-NSCH-DD model – to simulate the two-phase flows with moving contact lines in complex geometries. The original complex domain is extended to a larger regular domain, usually a cuboid, and the complex domain boundary is replaced by an interfacial region with finite thickness. A phase-field function is introduced to approximate the characteristic function of the original domain of interest. The original fluid model, q-NSCH, is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the solid surface. We show that the q-NSCH-DD system converges to the q-NSCH system asymptotically as the thickness of the diffuse domain interface introduced by the phase-field function shrinks to zero ( $\epsilon \rightarrow 0$ ) with $\mathcal {O}(\epsilon )$ . Our analytic results are confirmed numerically by measuring the errors in both $L^{2}$ and $L^{\infty }$ norms. In addition, we show that the q-NSCH-DD system not only allows the contact line to move on curved boundaries, but also makes the fluid–fluid interfacemore »intersect the solid object at an angle that is consistent with the prescribed contact angle.« less
  4. We derive expressions for the leading-order far-field flows generated by externally driven and active (swimming) colloids at planar fluid–fluid interfaces. We consider colloids adjacent to the interface or adhered to the interface with a pinned contact line. The Reynolds and capillary numbers are assumed much less than unity, in line with typical micron-scale colloids involving air– or alkane–aqueous interfaces. For driven colloids, the leading-order flow is given by the point-force (and/or torque) response of this system. For active colloids, the force-dipole (stresslet) response occurs at leading order. At clean (surfactant-free) interfaces, these hydrodynamic modes are essentially a restricted set of the usual Stokes multipoles in a bulk fluid. To leading order, driven colloids exert Stokeslets parallel to the interface, while active colloids drive differently oriented stresslets depending on the colloid's orientation. We then consider how these modes are altered by the presence of an incompressible interface, a typical circumstance for colloidal systems at small capillary numbers in the presence of surfactant. The leading-order modes for driven and active colloids are restructured dramatically. For driven colloids, interfacial incompressibility substantially weakens the far-field flow normal to the interface; the point-force response drives flow only parallel to the interface. However, Marangoni stresses inducemore »a new dipolar mode, which lacks an analogue on a clean interface. Surface-viscous stresses, if present, potentially generate very long-ranged flow on the interface and the surrounding fluids. Our results have important implications for colloid assembly and advective mass transport enhancement near fluid boundaries.« less
  5. Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimensionD7/3, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension ofD=2.36±0.03over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertainingmore »to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.

    « less