A Study of the Asymmetric Transonic Flow Past a Sharp Leading Edge

An experimental and theoretical study has been made of the two-dimensional transonic flow past a 12° wedge airfoil with lower surface inclined 13° to the air stream. The experimental portion of the study consists of surveys of the flow field about the leading edge in a closed throat tunnel near choking Mach number by means of an X-ray densitometer. From these surveys various features have been determined; namely, the location of the stagnation point, the location of the sonic line, the size of the separation bubble on the upper surface, and the value of the Mach number at the bubble edge. These features were relatively insensitive to changes in Reynolds number in the range from 1X106 to 3X106 based on chord. The theoretical portion of the study consists of the calculation by relaxation methods of an unbounded, inviscid, two-dimensional flow about a portion of the same body at a free-stream Mach number of exactly unity. The calculations yield a separation bubble on the upper surface which has a shape shown to be compatible with known theoretical conditions for viscous attachment to the upper surface of the body. Agreement between theoretically calculated and the experimentally determined features of the flow was good in regions where the local Mach number was 2 or less. In regions of higher local Mach number the agreement was fair. The theoretically determined Mach number on the bubble edge was 2.80 whereas the experimentally determined value was 2.30. The theoretically determined length of the separation bubble was 1.54-percent chord whereas the experimentally determined length was about 5-percent chord. The theoretically determined location of the stagnation point was 0.16-percent chord from the leading edge whereas the experimentally determined location was at 0.56-percent chord. The experience gained in studying the flow suggests the possibility that the solution obtained is not unique and that another solution in better agreement with experiment might exist.