Rotating and non-rotating flows through gaps by the
Doctoral thesis, UCL (University College London).
Steady, two-dimensional flows of a single layer of inviscid fluid discharging through an aperture are treated in the hodograph or velocity plane on a rectangular grid. The following problems are considered individually: irrotational planar and axisymmetric flow of air through a nozzle, incompressible flow through an aperture with bottom topography and lastly rotating flow of a uniform potential vorticity fluid issuing from a passage on the wall. The rotating case differs from other cases in that three parameters are required to describe the solutions instead of two. In all cases the problems are formulated so that flows range from subcritical to supercritical including choked flow. The rectangular domain for the supercritical problems results from the way the information travels in the hodograph plane in the region that is image of the flow that occurs around the lip of the nozzle wall. Supercritical jets are solved up to a short distance away from the aperture, hence shocks that occur further downstream are avoided although limiting lines develop in the vicinity of the exit plane depending on the strength of the topography. The equations governing irrotational flows are expressed in terms of the Legendre potential and those for the rotating flow are expressed in terms of the streamfunction. Solutions of these equations are computed using standard finite-differences approximations. Knowledge of the characteristics directions and the corresponding compatibility equations in the supercritical region of the domain is not required which demonstrates the robustness of solving in the hodograph plane. All that is necessary is that the general direction in which information propagates is perceived so that explicit or implicit finite-differences can be employed.
|Title:||Rotating and non-rotating flows through gaps by the hodograph method|
|Additional information:||Permission for digitisation not received|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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