The interaction between a fluid and a solid surface in relative motion represents a dynamical process that is central to the problem of laminar-to-turbulent transition (and consequent drag increase) for air, sea and land vehicles, as well as long-range pipelines. This problem may in principle be alleviated via a control stimulus designed to impede the generation and growth of instabilities inherent in the flow. Here, we show that phonon motion underneath a surface may be tuned to passively generate a spatio-temporal elastic deformation profile at the surface that counters these instabilities. We theoretically demonstrate this phenomenon and the underlying mechanism of frequency-dependent destructive interference of the unstable flow waves. The converse process of flow destabilization is illustrated as well. This approach provides a condensed-matter physics treatment to fluid-structure interaction and a new paradigm for flow control.
A direct numerical simulation is performed on the full time-dependent three-dimensional Navier–Stokes equations in a spatially developing plane-channel flow at a Reynolds number of 10 000. Two-dimensional eigenfunctions based on the solution of the Orr–Sommerfeld equation are introduced at the inflow with random noise added to simulate a vibrating ribbon transition experiment. The flow is allowed to choose a natural path to secondary instability, either K-type (after Klebanoff) or H-type (after Herbert), depending on the amplitude of the two-dimensional disturbance. For low-amplitude two-dimensional disturbances (1 % of the centreline velocity), H-type modes are found to dominate, while a doubling of the amplitude (2 % of the centreline velocity) produces a mixed H-type/K-type disturbance field with explosive growth of the secondary modes. In addition, the use of a suction/blowing slot that is phase lagged with respect to a fixed wall pressure signal is demonstrated to significantly reduce the energy in the primary mode owing to the destruction of phase between the streamwise and wall-normal velocity components. The use of forward finite-time Lyapunov exponents to generate Lagrangian coherent structures as a means of flow visualization is also presented, showing qualitative agreement with previous experimental visualizations, and represents a viable means of identifying characteristic vortical flow structures.
The migration and trapping of supercritical CO2 (scCO2) in geologic carbon storage is strongly dependent on the geometry and wettability of the pore network in the reservoir rock. During displacement, resident fluids may become trapped in the pits of a rough pore surface forming an immiscible two‐phase fluid interface with the invading fluid, allowing apparent slip flow at this interface. We present a two‐phase fluid dynamics model, including interfacial tension, to characterize the impact of mineral surface roughness on this slip flow. We show that the slip flow can be cast in more familiar terms as a contact‐angle (wettability)‐dependent effective permeability to the invading fluid, a nondimensional measurement which relates the interfacial slip to the pore geometry. The analysis shows the surface roughness‐induced slip flow can effectively increase or decrease this effective permeability, depending on the wettability and roughness of the mineral surfaces. Configurations of the pore geometry where interfacial slip has a tangible influence on permeability have been identified. The results suggest that for large roughness features, permeability to CO2 may be enhanced by approximately 30% during drainage, while the permeability to brine during reimbibition may be enhanced or diminished by 60%, depending on the contact angle with the mineral surfaces and degrees of roughness. For smaller roughness features, the changes in permeability through interfacial slip are small. A much larger range of effective permeabilities are suggested for general fluid pairs and contact angles, including occlusion of the pore by the trapped phase.
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