Computerized Study of Finite-Amplitude Standing Waves in a Duct Article Swipe
YOU?
·
· 1971
· Open Access
·
· DOI: https://doi.org/10.1121/1.1977558
· OA: W2041809511
A one-dimensional model of a finite-amplitude standing wave confined to a duct (wherein boundary-layer effects at the walls produce energy losses greater than those arising from viscous and thermal effects in the body of the fluid) has been established. The resultant set of coupled nonlinear equations can be solved either by a perturbation technique or by assuming a Fourier superposition of standing waves. The perturbation solution has been performed through sixth order and reveals the poor convergence properties of this approach. The Fourier superposition results in an infinite set of coupled nonlinear algebraic equations which can be solved by successive approximations with the help of a digital computer. Results have been obtained for Mb/δ1 below 0.75 and −1.0⩽2Δω/ωrδ1⩽2.0, where M is a Mach number, b = (γ+1)/2, γ is the ratio of specific heats of the gas, α1 = δ1ω/2c0, α1 is the absorption coefficient for the fundamental component of the standing wave in the infinitesimal amplitude limit, ω is the angular frequency of the fundamental, Δω is the difference ω − ωr (where ωr is the classically predicted resonance frequency), and c0 is the speed of sound in the limit b = δ1 = 0. Results show clearly that, for given Mach number, the strongest nonlinear distortions in wave-form are to be observed at frequencies above the classical resonance.
