The dynamics of a perturbed incompressible, inviscid, axisymmetric, near-critical swirling flow in a long, finite-length, straight, circular pipe is studied through a weakly nonlinear analysis. The flow is subjected to non-periodic inlet and outlet conditions. The long-wave approach involves a rescaling of the axial distance and time. It results in a separation of the perturbation's structure into a critical standing wave in the radial direction and an evolving wave in the axial direction, that is described by a nonlinear model problem. The approach is first validated by establishing the bifurcation of non-columnar states from the critical swirl and the linear stability modes of these states. Examples of the flow dynamics at various near-critical swirl levels in response to different initial perturbations demonstrate the important role of the nonlinear steepening terms in perturbation dynamics. The computed dynamics shows quantitative agreement with results from numerical simulations that are based on the axisymmetric Euler equations for various swirl levels and as long as perturbations are small, thereby verifying the accuracy of each computation and capturing the essence of flow dynamics. Results demonstrate the various stages of the flow dynamics, specifically during the transition to vortex breakdown states. They reveal the evolution of faster-than-exponential and shape-changing modes as perturbations grow into the vortex breakdown process. These explosive modes provide the sudden and abrupt nature of the vortex breakdown phenomenon. Further analysis of the model problem shows the important role of the nonlinear evolution of perturbations and its relevance to the transfer of the perturbation's kinetic energy between the boundaries and flow bulk, the evolution of perturbations in practical concentrated vortex flows, and the design of control methods of vortex flows. A robust feedback control method to stabilize a solid-body rotation flow in a pipe at a wide range of swirl levels above critical is developed. The applicability of this method to stabilizing medium and small core-size vortices is also discussed.
When load is applied to bone, it deforms and causes fluid pressure to build up in bone. The pressure gradient between different portions of the bone microcnannels drives fluid flow through them. This kind of bone fluid flow can induces the streaming potentials which are considered to play a role for bone remodeling. Aimed to determine the impact of ribbed rough inner surfaces of the microchannels on the streaming potentials, streaming potentials were measured as bone fluid flowed through the mcrospaces of thin cylinder bone samples under different pressure loading rates. The results show that the streaming potentials decrease with the increase of the pressure loading rates. A digital simulation calculation was performed and the results demonstrated that there were turbulent flows near the inner wall surfaces, which making the streaming potentials smaller in bone microchannels.bone, streaming potentials, pressure rising rate, turbulent flow Citation:
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