Abstract
Simplified Navier-Stokes equations, of the elliptic and hyperbolic type in the subsonic and supersonic flow regions, respectively, are derived for viscous flows in channels and nozzles with curved walls whose local radii of longitudinal curvature are comparable with the transverse channel dimensions. A new numerical method is developed for the system of equations obtained. This method is of the evolution type along the longitudinal coordinate and includes global iterations of the streamline direction field and the longitudinal pressure gradient field. The effectiveness of the method is illustrated with reference to the solution of the direct Laval nozzle problem for an air flow at Reynolds numbers Re≈104 and 106 in conical nozzles with throat curvatures Kw=1.0 and 1.6 (Kw is the curvature divided by the inverse radius of the nozzle throat). Two iterations are sufficient to calculate the nozzle flow rate and power correct to 0.01%.
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