Linearized Theory of Two-Dimensional Nozzle Wakes and Applications to Laser Cavity Flow

摘要

This report's objective is to assemble, in compact form, the equations describing the development of wakes trailing from gas-dynamic-laser nozzle cusps. A particular family of appropriately short, geometrically similar DeLaval nozzles are considered. The exit flow is assumed parallel and the trailing edge thickness is taken to be sharp. Fully laminar and turbulent wakes are considered for arbitrary exit Mach and Reynolds numbers specific heat ratio and nozzle-to-stagnation temperature ratio. The total viscous drag and heat exchanged with the nozzle cusp are calculated (for such conditions) for both laminar and turbulent nozzle boundary layer. To calculate the laminar wake, Kubota's linearized similarity theory is then utilized; for the turbulent wake an analogous similarity theory is used, with key information on turbulent transport drawn from recent two-dimensional supersonic wake experiments. The results are given in nondimensional form by expressing distances in terms of the nozzle exit height. Most wake parameters are found insensitive to Reynolds number but strongly dependent upon the other design parameters. Procedures are indicated and charts and tables are supplied by which the reader can apply the formulas to any set of design parameters, and a specific example at Mach 4 is computed in detail. Assumptions and approximations are pointed out for future test by experiment. (Author)