Power Balance in Aerodynamic Flows
A control volume analysis of the compressible viscous flow about an aircraft is performed, including integrated propulsors and flow-control systems. In contrast to most past analyses that have focused on forces and momentum flow, in particular thrust and drag, the present analysis focuses on mechanical power and kinetic energy flow. The result is a clear identification and quantification of all the power sources, power sinks, and their interactions, which are present in any aerodynamic flow. The formulation does not require any separate definitions of thrust and drag, and hence it is especially useful for analysis and optimization of aerodynamic configurations that have tightly integrated propulsion and boundary-layer control systems. Nomenclature b, c = wingspan and chord CD = dissipation coefficient Cf = skin friction coefficient Di = induced drag Dp = profile drag Dw = wave drag dS = surface element of control volume dV = volume element of control volume _ Ea = axial kinetic energy deposition rate _ Ep = pressure-work deposition rate _ Ev = transverse (vortex) kinetic energy deposition rate _ Ew = lateral wave-outflow energy deposition rate Fn = streamwise force from lateral outflow velocity Vn Fu = streamwise force from axial velocity u Fv = streamwise force from transverse velocities v, w Fx, Fz = total streamwise, normal aerodynamic forces