On the Importance of Contraction Design for SupersonicWind Tunnel Nozzles

摘要

CFD solutions were computed to decide whether the contraction contour has significant effect on the flow uniformity in the test section of an axisymmetric supersonic wind tunnel nozzle. The supersonic portion of a nozzle contour is usually designed with an aerodynamically rigorous method of characteristics, whereas the contraction contour is typically a convenient smooth mathematical function that has not been rigorously derived from aerodynamics theory. The design procedure for the supersonic contour must assume some flow profile in the throat as a boundary condition, but whether standard contraction contours deliver the assumed flow profile is not documented. A set of rules for good contraction design seems to have accumulated over the years, but it is unclear whether the rules are either necessary or sufficient. It is known from method of characteristics (MOC) analysis that the throat flow profile has an observable effect on flow quality. A question then is whether it would be useful to develop an aerodynamically rigorous contraction design procedure. In the present analysis, inviscid flow solutions were computed for axisymmetric nozzles with various contraction contours that selectively violate rules on maximum inflection angle and avoidance of any curvature discontinuities. The inviscid choice was made specifically for consistency with the standard inviscid MOC design procedure. Solutions were computed for the Arnold Engineering Development Center (AEDC) Tunnel C Mach 4 nozzle contour minus the boundary-layer correction. The contractions examined were (1) the original cylinder-quartic-cone-quartic as developed by James C. Sivells at AEDC, (2) a model based on sin~nx, and (3) a double ellipse model. Large excursions in inflection angle and curvature discontinuity were examined. Flow profiles were computed at the nozzle throat and at the nozzle exit. Results were compared to a baseline contraction, specifically the Tunnel C contraction contour as originally designed by Sivells. The primary finding was that large inflection angles and curvature discontinuities upstream of the throat do not significantly degrade test section flow uniformity if the curvature at the throat is continuous. Sivells' contraction model does deliver the throat flow profile assumed by his MOC design code. The results to date do not support the need to develop an aerodynamically rigorous contraction contour design procedure. However, the issue should be revisited if a nozzle design procedure is developed that relaxes some of the constraints in the current MOC procedure.