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...he neck of the Helmholtz resonator is p3 and is assumed to be equal to the upstream pressure at the junction. At the junction, according to Equation (2) the sound pressure can be expressed as follows: i i i1 e Re eI Rk x k x tp I (3) i i 2 e e Tk x tp T (4) , , 1 1 1I R T c c k k k c M M M (5) p2 p1 p1 U0 Figure 1. A side branch Helmholtz resonator in a grazing flow duct. The fluid particle velocities satisfy the following equation: 1 1 2 0 1 , Du p Du p Dt x Dt x 21 (6) The propagation of the wave can be characterized by the following equations [13]: 2 0 1 0 1 0 1 2 0 2 0 2 0 2 P p A U u A P p A U u A (7) 0 1 1 0 2 2 0 3 n U u A U u A S u 3 (8) where P0 is the equilibrium pressure, U0 is the mean flow velocity and 0 is the equilibrium density. Equation (7) and Equation (8) respectively indicates conservation of momentum and flow mass at the junction. Substituting Equations (1)-(5) into Equations (7) and (8) 2 2 21 1 1M I M R M T (9) 1 1 1 HR M C I M C R M T C c AZ (10) R is eliminated from the Equat...

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...g to the exciting frequency of source. Changes in exciting frequency and temperature result in the inconsistent between the noise source and HRs and hence decrease the effectiveness of the HRs. In order to adapt to the changes, a solution is integrating the Helmholtz resonator with active control system. Such system is referred to as a semi active Helmholtz resonator. Semi active control method utilizes active noise control strategy to tune the resonance frequency of passive HRs. Many studies were focused on tuning the resonance frequency via changing the volume of the cavity or the neck area [1, 2, 3, 4, 5]. Although the resonance frequency can be changed through the semi-active control, the adaptive resonators still work effectively over the natural resonance frequency and the effective frequency range is still narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the ac...

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...determined by the reactance. The acoustic reactance reaches minimum when resonance occurs. A lot of studies have been conducted on the acoustics impedance of a HR in a grazing flow duct. Although there is no unified model to indicate the flow effect on Copyright © 2013 SciRes. OJA X. F. SHI ET AL. 27 acoustic impedance of the HR, it is agreed that the flow mainly influence the resistance and the effective length of Helmholtz resonator. Many experimental work shows that acoustic resistance increases linearly and the effective length of the neck decrease as the flow velocity increased. Cummings [14] proposed an empirical impedance model: 0.32 0 12.52 2.44 3.2f R c ut fd d fd (13) 0 1, u d ft t (14) 0 0.12 1 0.6 exp 0.6 , 0.25 u d t ft t td d d u d ft t t (15) d and f are respectively diameter and the length of the Helmholtz resonator. Rf denotes resistance introduced by flow. is the end correction of the neck with grazing mean flow, 0 is the end correction without flow. u* is friction velocity at the boundary surface. With Cummings’ model, the effect of various flo...

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...ol it with positive real impedance to make the active HR more reliable and robust. Flow generated produced by the ventilation fans influences acoustic impedance of the Helmholtz resonator when flow passes through the orifice. The sound absorption performance of the resonator decreases as a result of the affected impedance. Meyer et al. [9] studied the flow effect on acoustic impedance and their experiments showed that the resonance frequency shifted to a higher frequency with the rising flow speed and a minimum attenuation even a negative value occurred above the resonance frequency. Anderson [10] measured the acoustic impedance of a single side branch HR in a circular flow duct and found that fundamental frequency increased with increasing flow while neck end correction decreased. Hersch and walker [11] derived a semi emCopyright © 2013 SciRes. OJA X. F. SHI ET AL. 26 pirical model for a HR mounted in a grazing flow duct. Their result showed that the resistance increased linearly as the flow velocity increased. Previous work on the semi active control with Helmholtz resonator did not take into account the effect of the mean flow. This paper aims at studying the effect of flow on the s...

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...h the orifice. The sound absorption performance of the resonator decreases as a result of the affected impedance. Meyer et al. [9] studied the flow effect on acoustic impedance and their experiments showed that the resonance frequency shifted to a higher frequency with the rising flow speed and a minimum attenuation even a negative value occurred above the resonance frequency. Anderson [10] measured the acoustic impedance of a single side branch HR in a circular flow duct and found that fundamental frequency increased with increasing flow while neck end correction decreased. Hersch and walker [11] derived a semi emCopyright © 2013 SciRes. OJA X. F. SHI ET AL. 26 pirical model for a HR mounted in a grazing flow duct. Their result showed that the resistance increased linearly as the flow velocity increased. Previous work on the semi active control with Helmholtz resonator did not take into account the effect of the mean flow. This paper aims at studying the effect of flow on the semi active Helmholtz resonator for duct noise control. Firstly, the plane wave propagation in a flow duct is introduced and the discontinuity condition is analytically derived. Then, the control controller trans...

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...g to the exciting frequency of source. Changes in exciting frequency and temperature result in the inconsistent between the noise source and HRs and hence decrease the effectiveness of the HRs. In order to adapt to the changes, a solution is integrating the Helmholtz resonator with active control system. Such system is referred to as a semi active Helmholtz resonator. Semi active control method utilizes active noise control strategy to tune the resonance frequency of passive HRs. Many studies were focused on tuning the resonance frequency via changing the volume of the cavity or the neck area [1, 2, 3, 4, 5]. Although the resonance frequency can be changed through the semi-active control, the adaptive resonators still work effectively over the natural resonance frequency and the effective frequency range is still narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the ac...

Citation Context

...g to the exciting frequency of source. Changes in exciting frequency and temperature result in the inconsistent between the noise source and HRs and hence decrease the effectiveness of the HRs. In order to adapt to the changes, a solution is integrating the Helmholtz resonator with active control system. Such system is referred to as a semi active Helmholtz resonator. Semi active control method utilizes active noise control strategy to tune the resonance frequency of passive HRs. Many studies were focused on tuning the resonance frequency via changing the volume of the cavity or the neck area [1, 2, 3, 4, 5]. Although the resonance frequency can be changed through the semi-active control, the adaptive resonators still work effectively over the natural resonance frequency and the effective frequency range is still narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the ac...

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...ill narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the acoustic impedance of the resonator through mounting a loudspeaker at the end of the HR. The control source was stimulated by a closed-loop adaptive control strategy to change the resonance frequency. Utsumi [7] also investigated a side branch Helmholtz resonator with active termination impedance. He explored the possibility of broad band noise control through varying the termination impedance. Based on the derived controller transfer function, he demonstrated the efficiency of the method by computer simulation. Yuan [8] proposed to control it with positive real impedance to make the active HR more reliable and robust. Flow generated produced by the ventilation fans influences acoustic impedance of the Helmholtz resonator when flow passes through the orifice. The sound absorption performance of the r...

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...ation impedance. He explored the possibility of broad band noise control through varying the termination impedance. Based on the derived controller transfer function, he demonstrated the efficiency of the method by computer simulation. Yuan [8] proposed to control it with positive real impedance to make the active HR more reliable and robust. Flow generated produced by the ventilation fans influences acoustic impedance of the Helmholtz resonator when flow passes through the orifice. The sound absorption performance of the resonator decreases as a result of the affected impedance. Meyer et al. [9] studied the flow effect on acoustic impedance and their experiments showed that the resonance frequency shifted to a higher frequency with the rising flow speed and a minimum attenuation even a negative value occurred above the resonance frequency. Anderson [10] measured the acoustic impedance of a single side branch HR in a circular flow duct and found that fundamental frequency increased with increasing flow while neck end correction decreased. Hersch and walker [11] derived a semi emCopyright © 2013 SciRes. OJA X. F. SHI ET AL. 26 pirical model for a HR mounted in a grazing flow duct. Thei...

Citation Context

...g to the exciting frequency of source. Changes in exciting frequency and temperature result in the inconsistent between the noise source and HRs and hence decrease the effectiveness of the HRs. In order to adapt to the changes, a solution is integrating the Helmholtz resonator with active control system. Such system is referred to as a semi active Helmholtz resonator. Semi active control method utilizes active noise control strategy to tune the resonance frequency of passive HRs. Many studies were focused on tuning the resonance frequency via changing the volume of the cavity or the neck area [1, 2, 3, 4, 5]. Although the resonance frequency can be changed through the semi-active control, the adaptive resonators still work effectively over the natural resonance frequency and the effective frequency range is still narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the ac...

Citation Context

...g to the exciting frequency of source. Changes in exciting frequency and temperature result in the inconsistent between the noise source and HRs and hence decrease the effectiveness of the HRs. In order to adapt to the changes, a solution is integrating the Helmholtz resonator with active control system. Such system is referred to as a semi active Helmholtz resonator. Semi active control method utilizes active noise control strategy to tune the resonance frequency of passive HRs. Many studies were focused on tuning the resonance frequency via changing the volume of the cavity or the neck area [1, 2, 3, 4, 5]. Although the resonance frequency can be changed through the semi-active control, the adaptive resonators still work effectively over the natural resonance frequency and the effective frequency range is still narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the ac...

Citation Context

...e resonance frequency via changing the volume of the cavity or the neck area [1, 2, 3, 4, 5]. Although the resonance frequency can be changed through the semi-active control, the adaptive resonators still work effectively over the natural resonance frequency and the effective frequency range is still narrow. If it is necessary to control relative low frequency noise, the tunable mechanical structure needs to be significantly complex and bulky. Later, some researchers started to extend the efficient frequency range of the resonator with the termination impedance control. Radcliffe and Birdsong [6] proposed an electronically tuned semi-active Helmholtz resonator. They controlled the acoustic impedance of the resonator through mounting a loudspeaker at the end of the HR. The control source was stimulated by a closed-loop adaptive control strategy to change the resonance frequency. Utsumi [7] also investigated a side branch Helmholtz resonator with active termination impedance. He explored the possibility of broad band noise control through varying the termination impedance. Based on the derived controller transfer function, he demonstrated the efficiency of the method by computer simulat...

Citation Context

...an electronically tuned semi-active Helmholtz resonator. They controlled the acoustic impedance of the resonator through mounting a loudspeaker at the end of the HR. The control source was stimulated by a closed-loop adaptive control strategy to change the resonance frequency. Utsumi [7] also investigated a side branch Helmholtz resonator with active termination impedance. He explored the possibility of broad band noise control through varying the termination impedance. Based on the derived controller transfer function, he demonstrated the efficiency of the method by computer simulation. Yuan [8] proposed to control it with positive real impedance to make the active HR more reliable and robust. Flow generated produced by the ventilation fans influences acoustic impedance of the Helmholtz resonator when flow passes through the orifice. The sound absorption performance of the resonator decreases as a result of the affected impedance. Meyer et al. [9] studied the flow effect on acoustic impedance and their experiments showed that the resonance frequency shifted to a higher frequency with the rising flow speed and a minimum attenuation even a negative value occurred above the resonance fr...