Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

Effect of boundary layer on the transmission and attenuation of sound in an acoustically treated circular duct

Abstract: The transmission of sound in an acoustically treated circular duct containing sheared flow is treated by reduction of the governing equations to a two‐point boundary‐value problem. The pressure modes and transmission wavenumbers are obtained by an iterative procedure for a wide range of driving frequencies, duct‐flow Mach numbers, and boundary‐layer thicknesses with a given lining impedance model. Computations are made for both inlet and exhaust flows. For inlet flows, the direction of sound propagation is opposite to the flow direction, while in the exhaust flow the sound is propagated in the same direction as the flow. The numerical results show a major reduction of achievable attenuation of the least attenuated mode in the inlet flow, owing to the presence of the boundary layer, particularly at the higher Mach numbers. The attenuation in the exhaust flow shows only minor effects due to the presence of a boundary layer. The reduction in attenuation in the inlet flow indicates that the design of acoustic linings for inlet applications must include careful consideration of boundary‐layer effects.

On the instability of pipe Poiseuille flow

Abstract: Stability of the flow of incompressible viscous fluid in a circular pipe is studied numerically. A perturbation consisting of finite‐amplitude two‐dimensional and infinitesimal three‐dimensional parts is imposed on the basic flow. The temporal evolution of the perturbation is analyzed by direct numerical calculation of the Navier–Stokes equations. The two‐dimensional disturbances are independent of the streamwise coordinate and initially take the form of streamwise rolls. It is shown that the nonlinear development of two‐dimensional perturbations results in substantial spanwise modulation of the streamwise velocity component manifesting itself as a formation of streaks and the occurrence of inflection points. The modulated mean flow is found to be highly unstable to the three‐dimensional perturbations which are localized spatially near these points. An instability mechanism that includes the modulation of the flow by growing two‐dimensional disturbances and the inflectional instability of the modulated flow to three‐dimensional perturbations is proposed.

Viscous incompressible flow between concentric rotating spheres. Part 3. Linear stability and experiments

Abstract: The stability of flow of a viscous incompressible fluid contained between a stationary outer sphere and rotating inner sphere is studied theoretically and experimentally. Previous theoretical results concerning the basic laminar flow (part 1) are compared with experimental results. Small and large Reynolds number results are compared with Stokes-flow and boundary-layer solutions. The effect of the radius ratio of the two spheres is demonstrated. A linearized theory of stability for the laminar flow is formulated in terms of toroidal and poloidal potentials; the differential equations governing these potentials are integrated numerically. It is found that the flow is subcritically unstable and that the observed instability occurs at a Reynolds number close to the critical value of the energy stability theory. Observations of other flow transitions, at higher values of the Reynolds number, are also described. The character of the stability of the spherical annulus flow is found to be strongly dependent on the radius ratio.

Multiplicity of Steady Two-Dimensional Flows in Two-Sided Lid-Driven Cavities

Abstract: The two-dimensional steady incompressible flow in rectangular cavities is calculated numerically by a finite volume method. The flow is driven by two opposing cavity side walls which move with constant velocities tangentially to themselves. Depending on the cavity aspect ratio and the two side-wall Reynolds numbers different flow states exist. Their range of existence and the bifurcations between different states are investigated by a continuation method accurately locating the bifurcation points. When both side walls move in opposite directions up to seven solutions are found to exist for the same set of parameters. Three of these are point-symmetric and four are asymmetric with respect to the center of the cavity, if the side-wall Reynolds numbers have the same magnitude. When the walls move in the same direction, up to five different flow states are found. In this case only a single mirror symmetric solution exists for equal Reynolds numbers.