Analysis of a propeller in compressible, steady flow

THIS Synoptic describes an analytical method for solving the equation governing the inviscid, irrotational, compressible, potential flow about a propeller. The equation and boundary conditions are transferred to a noninertial system of coordinates rotating with the propeller, in which the basic problem becomes a steady one. The solution method takes advantage of the linearity of the model by superposing a “compressible”THIS Synoptic describes an analytical method for solving the equation governing the inviscid, irrotational, compressible, potential flow about a propeller. The equation and boundary conditions are transferred to a noninertial system of coordinates rotating with the propeller, in which the basic problem becomes a steady one. The solution method takes advantage of the linearity of the model by superposing a “compressible” solution to the potential equation on an “incompressible” wake solution. In addition, the boundary conditions are satisfied by dividing the flowfield at the propeller plane, solving the equations separately ahead of and behind this plane, and enforcing continuity matching conditions. Applying the final boundary condition yields an infinite-series integral equation for the unknown circulation distribution. A lifting-line method is used to produce numerical results. Presented results establish the effect of compressibility on the induced field solution to the potential equation on an “incompressible” wake solution. In addition, the boundary conditions are satisfied by dividing the flowfield at the propeller plane, solving the equations separately ahead of and behind this plane, and enforcing continuity matching conditions. Applying the final boundary condition yields an infinite-series integral equation for the unknown circulation distribution. A lifting-line method is used to produce numerical results. Presented results establish the effect of compressibility on the induced field.