APPROXIMATION FOR SWIRL FLOWS IN THE VICINITY OF THE THROAT OF A LAVAL NOZZLE.
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO
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In order to obtain approximate solution for the flow in vicinity of the throat of a Laval nozzle assumptions of some kind must be made, but it is desirable to keep the arbitrariness introduced to a minimum. The flows considered in the report have swirl, besides the approximation should be applicable for nozzles which have rather large curvature. The report begins with some general observations regarding the choices that can be made. For the actual computations the flow equations are represented in natural coordinates i.e., they are expressed in terms of derivatives in the direction of the streamlines and in the direction normal to it. It is then assumed that within a narrow strip extending across the nozzle the flow angle and the enthalpy can be represented along each streamline by a polynomial of the second degree. The derivatives in the streamwise direction are replaced by finite differences while the derivatives normal to the streamline direction are retained in their original form. The flow equations then reduce to a system of ordinary differential equations. At the nozzle axis one has obvious symmetry conditions, at the nozzle wall the streamline curvature and its derivative in the streamwise direction can be prescribed. This two point boundary value problem is solved numerically. In the computation the strip has the sonic line as its upstream boundary, the other boundary is chosen and a nearly constant distance downstream. The report contains a number of tables and graphs for swirl flows computed by this method. Author
- Fluid Mechanics