The problem of acoustic radiation from turbofan engine inlets in flow has not lent itself fully to analysis by numerical means because of the large domains and high frequencies involved. The current work has extended the use of finite elements and wave envelope elements, elements that simulate decay and wavelike behavior in their interpolation functions, from the no-flow case in which they have proven, to cases incorporating mean flow. By employing an irrotational mean flow assumption, the acoustics problem has been posed in an axisymmetric formulation in terms of acoustic velocity potential, thus minimizing computer solution storage requirements. The results obtained from the numerical procedures agree well with known analytical solutions, static experimental jet engine inflow data, and flight test results.
Nomenclaturea£aj~ = incident and reflected modal amplitudes, respectively c = nondimensional speed of sound in flow e£ef = positive and negative uniform duct eigenfunctions, respectively m = spinning mode number TV,-= interpolation function p = pressure t = time u = axial component of local Mach number U = Mach number v = radial component of local Mach number v = acoustic velocity V -velocity x = axial coordinate 7= ratio of specific heats e = penalty parameter TJ, £ = local finite element coordinates K,A = local and axial wave numbers, respectively IJL = uniform duct eigenvalue p = density > = velocity potential, trial function $(Q) = trial function space $ = full nondimensional velocity potential \l/ =test function ¥ (fi) = test function space co = harmonic frequency Superscripts ( )' = nondimensional quantity, derivative (see text) e = quantity defined inside a finite element