Abstract
A numerical method is derived to take account of full flowwall interaction in la large deformation domain. To this end, a simplified Lagrangian and nonlinear model is derived to describe the wall motion. the flow is described by two dimensional Naiver stokes equation. The projection method is used to solve for the flow and fourth Rung-Kutta method is used to solve wall equation. The formulation of the problem allows full flow and wall interaction via the boundary conditions at the interface flow-wall. Some numerical simulation will be presented with periodic inlet flow. The method is applied to study the dynamics of aneurysms in arteries and veins. The flow inside the aneurysm is examined under the effects of a steady inlet flow as well as a pulsatile inlet flow for different aneurysm sizes. The wall model is analyzed when the wall is subjected to a constant transmural pressure and a quasi uniform inviscid flow. For a steady constant transmural pressure, a formal solution of the non linear integral-partial differential equation governing the wall motion is derived. For a steady and a quasi uniform inviscid flow, a first integral of the wall equation is obtained, then the solution is found to satisfy an integral non linear equation which is solved by numerical iteration
Highlights
The flow-wall interaction occurs in large number of practical applications, where the coupling between the flow and the moving machine components promotes the development and the creation of a coupled vibration
In Aeronautic, elastic flexible panels are used as a control tool, B
The boundary elements method is used to reduce the initially two dimensional problem to one dimensional problem using the displacement of the panel as unknown variable
Summary
The flow-wall interaction occurs in large number of practical applications, where the coupling between the flow and the moving machine components promotes the development and the creation of a coupled vibration. In energy domain these coupled vibrations arises in drill string, pipeline, compressor and turbine rotor-stator of natural gas compression installation for gas liquidization, valves of oil well and in offshore oil plate-form, the mentioned vibrations occur often in the small deformation domain but can reach large deformations domain and cause serious risk for the installation. It is shown that the system becomes unstable if the speed of the flow exceeded some critical prescribed value. It is shown that increasing the stiffness of the spring beyond some critical value does not effect on the instability of the system
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