This content will become publicly available on September 28, 2023

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 »
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Publication Date:
NSF-PAR ID:
10373838
Journal Name:
Physics of Fluids
ISSN:
1070-6631
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 »
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 dimension$D≈7/3$, 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 of$D=2.36±0.03$over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertainingmore »