MINIMUM ENERGY HYPERSONIC NOSE AND LEADING EDGE SHAPES,
Abstract
A system of first-order differential equations governing the heat transfer (convection and shock layer radiation) and pressure drag of an axisymmetric or two-dimensional body in hypersonic flow is developed. The Pontryagin maximum principle is applied to this system, through the gradient method, and a series of optimum hypersonic nose and two-dimensional shapes of given fineness ratio is found. The axisymmetric minimum drag shape is similar to the familiar 3/4 power law profile while the two-dimensional result is wedge shaped. The minimum heat transfer profiles are found to be flat faced when considering convection alone and conical, with a cusped tip, when considering radiation alone. Minimum energy shapes are found wherein the various energy terms being minimized include the sum of convection plus drag work, convection plus radiation plus drag work and convection plus radiation. The axisymmetric results show reasonable accomodation for the various energy forms considered in each of the minimum energy nose shapes. The two-dimensional minimum energy shapes are found to be dominated by the drag work with the results being, for all practical purposes, wedge shaped. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1969
- Accession Number
- AD0697951
Entities
People
- Roger J. Furey