Engineering topics
Publications and source records attributed to Menne, Stefan.
The breakdown of a vortex flow in a tube is studied for a slightly diverging tube by means of a numerical solution of the Navier-Stokes equations for a quasi-stationary, incompressible, laminar flow. Numerical results are compared to experiments of Faler and Leibovich. The numerical data display features similar to the experimental results concerning breakdown conditions, location, and structure.
The breakdown for both an isolated vortex and a vortex flow in a tube is studied by means of a numerical solution of the axisymmetric Navier-Stokes equations for an unsteady, incompressible, and laminar flow. Results are compared to those of other authors and to experiments. Various numerical solution methods and various physical boundary conditions are used in order to explain the existence of different solutions. The computational results reveal that the existence of different solutions is due to slightly different inflow conditions. The numerical problem for the isolated vortex becomes ill-posed at a certain time for the inflow condition of zero axial gradient of the radial velocity component. Different inflow conditions yield breakdown flowfields containing different features of the experimentally observed breakdown structure.
The slender vortex approximation was investigated using the Navier-Stokes equations written in cylindrical coordinates. It is shown that, for free vortices without external pressure gradient, the breakdown length is proportional to the Reynolds number. For free vortices with adverse pressure gradients, the breakdown length is inversely proportional to the value of its gradient. For low Reynolds numbers, the predictions of the simplified system agreed well with the ones obtained from solutions of the full Navier-Stokes equations, whereas for high Reynolds numbers, the flow became quite sensitive to pressure fluctuations; it was found that the failure of the slender vortex equations corresponded to the critical condition as identified by Benjamin (1962) for inviscid flows. The predictions obtained from the approximating system were compared with available experimental results. For low swirl, a good agreement was obtained; for high swirl, on the other hand, upstream effects on the pressure gradient produced by the breakdown bubble caused poor agreement.
The breakdown of a vortex flow in a tube is studied for a slightly diverging tube by means of a numerical solution of the Navier-Stokes equations for a quasi-stationary, incompressible, laminar flow. Numerical results are compared to experiments of Faler and Leibovich. The numerical data display features similar to the experimental results concerning breakdown conditions, location, and structure.