The solution of sharp-cone boundary-layer equations in the plane of symmetry

Abstract

A detailed study has been made of the solutions to cone boundary-layer equations in the symmetry plane in order to increase understanding of the mathematical nature and physical meaning of these solutions. A typical set of symmetry-plane solutions is presented. Included in this set are various solution branches not previously published. A double-valued solution curve is found which has not been studied prior to this time except at one trivial point. The extension of an existing solution branch through a removable singular point has also been accomplished. The solutions presented are categorized according to whether they are dependent on or independent of the boundary layer outside the symmetry plane. The region in which no solutions to the usual symmetry-plane equations exist is examined. Solutions in which the usual boundary-layer model predicts that conservation of mass is not satisfied at the symmetry plane are discussed. Non-analytical behaviour at the symmetry plane is also investigated. In both of these cases a boundary region exists at the symmetry plane.