Investigation of thermoacoustic oscillation attenuation by modified Helmholtz dampers with dual frequency bands

Case studies on aeroacoustics damping performances of Coupled Helmholtz Resonators over low frequency ranges

“…where, A þ and A À indicate the same wave propagating in different directions, [84][85][86][87][88] and k þ and k À represents the wave numbers in terms of Mach number, given as:…”

“…Overview of the noise damping mechanism and resonant frequency of Helmholtz resonators Review of noise damping mechanism of conventional Helmholtz resonators. The acoustic damping mechanism [86][87][88] of Helmholtz resonators consists of the conversion of acoustical energy into vortical energy. They are also known as linear and nonlinear damping mechanism.…”

“…The acoustic damping mechanism 86–88 of Helmholtz resonators consists of the conversion of acoustical energy into vortical energy. They are also known as linear and nonlinear damping mechanism.…”

“…The wavelength, λ is given by λ=2πc/ω. Hence, the equation can be expressed in terms of the wave number, where the wave number is defined as k=ω/c=2π/λ.Since harmonic plane waves are concerned, equation (47) can be further expressed by removing the aspect of time aswhere, A+ and A− indicate the same wave propagating in different directions, 84-88 and k+ and k− represents the wave numbers in terms of Mach number, given as: k+=ωc+ν=k1+M and k−=ωc−ν=k1−M To further simply equation (48), we introduce a modified wave number, K : K=k1−M2It brings the equation toEquation (49) is the 1-D equation for a harmonic wave propagating in a duct.…”

“…Since harmonic plane waves are concerned, equation (47) can be further expressed by removing the aspect of time aswhere, A+ and A− indicate the same wave propagating in different directions, 84-88 and k+ and k− represents the wave numbers in terms of Mach number, given as: k+=ωc+ν=k1+M and k−=ωc−ν=k1−M To further simply equation (48), we introduce a modified wave number, K : K=k1−M2…”