Helmholtz Resonance Frequency Research Articles

Derivation of analytic formulae for several resonance frequencies of the SparkJet actuator

Building on previous research that emphasized the importance of focusing on resonance frequencies for a fundamental understanding of the thrust and complex internal flow phenomena of the SparkJet actuators, this study theoretically derives analytic formulae for several important resonance frequencies. The research addresses the typical configuration of the SparkJet actuators, which consists of a cylindrical cavity and orifice connected by a conical converging nozzle. While the resonance frequencies of the SparkJet actuators can be obtained by solving the eigenvalue problem presented in previous studies, this eigenvalue problem, despite being a typical boundary value problem in the form of an elliptic partial differential equation, is challenging to solve using conventional numerical methods such as iterative methods, because the eigenvalue is included as an unknown in the operator. Consequently, Boundary Element Method (BEM) or methods using the Green functions have been proposed to obtain numerical solutions, but these still require handling large matrix data, resulting in significant computational costs and memory consumption. To overcome this, the current study first simplifies the eigenvalue problem using the conformal mapping presented in previous research. Then, referencing prior studies that claim that three types of resonance frequencies (Helmholtz resonance frequency and resonance frequencies representing streamwise or radial directional oscillation) significantly affect the thrust of the SparkJet actuators, characteristics of these frequencies are mathematically defined. Using these mathematical characteristics, the study derives the asymptotic and approximate solutions of the simplified eigenvalue problem, from which the resonance frequencies are obtained. The analytic formulae proposed in this study theoretically explain the already known geometric tendencies of the resonance frequencies and reveal new geometric factors influencing resonance frequencies, which were previously unknown. This approach is expected to facilitate obtaining several important resonance frequencies of the SparkJet actuator more promptly and accurately and to provide a deeper understanding of the nature of the complex oscillation phenomena inside the actuator.

Experiment research on the characteristics and mechanism of noise caused by a car door sealing cavity at wind excitation

Due to the various geometric shapes of cavities within car door sealing systems, the resulting cavity noise induced by wind excitation exhibits complex characteristics, leading to unclear noise mechanisms. To address this, a study was conducted to examine the acoustic properties of door sealing cavities located in the B-pillar, C-pillar, and backdoor of an SUV within a full-scale aeroacoustic wind tunnel. The main objective was to explore the relationship between cavity noise and interior noise. The results showed that peak components in the sound pressure level spectrum of the cavities significantly contribute to interior noise, particularly for cavities located close to the car’s interior. To gain further insight, the geometric characteristics of the cavities were extracted and transformed into equivalent regular cavities. These equivalent cavities were subsequently tested for their noise performance in a small-scale aeroacoustic wind tunnel, and the occurrence mechanisms were thoroughly investigated. The results demonstrated that the noise spectra of different cavities, whether they had sealing strips or leakage gaps, exhibited typical multipeak characteristics, with some cases even leading to whistling (e.g. backdoor cavity). The reason for the whistling was a resonance when the self-sustained oscillation frequencies of the cavities coincided with or approached the Helmholtz resonance frequencies or modal frequencies of the cavities. Interestingly, the self-sustained oscillation frequency and cavity modal resonance still persisted even when the two frequencies were somewhat separated, albeit with peaks of lower magnitude in the sound pressure spectrum (e.g. in the sealed cavities of the B-pillar and C-pillar).

Theoretical study on resonance frequencies of vibration modes of Janus-Helmholtz transducer

Janus-Helmholtz transducer has the characteristics of high-power and broadband transmission due to the coupling between the longitudinal resonance of the driver and the liquid cavity resonance of Helmholtz resonator. Traditional view holds that the low frequency resonance peak in the transmitting voltage response curve in water is fluid cavity mode of Helmholtz resonator while the high frequency resonance is the longitudinal mode of Janus transducer. However, in the past few decades, a large number of experimental studies have found that this conclusion is questionable. This work is to distinguish the two resonances in the response curve and the two vibration modes of Janus-Helmholtz transducer. Based on the Janus-Helmholtz transducer prototype reported in the literature, the resonance frequencies of the vibration modes of Janus-Helmholtz transducer are studied theoretically. The structure dimensions and material parameters of the prototype are listed in detail. The test results and simulation results of conductivity are also presented. The longitudinal resonance of the driver is determined by using the equivalent circuit method and finite element analysis. Radiation masses of both Janus transducer and typical longitudinal vibration transducer are also calculated to analyze the phenomenon of the sharp decrease of longitudinal resonance frequency in water. Acoustic modal analysis by using ANSYS software is performed to investigate the resonance frequency of complex Helmholtz resonator in Janus-Helmholtz transducer. Correction length on the vent introduced by external fluid sound radiation is used to obtain the accurate Helmholtz resonance frequency. The sound pressure distribution of Helmholtz resonator obtained through finite element method is investigated, and the correct equivalent formula for solving the Helmholtz resonance frequency is obtained. The results reveal that the first resonance in the response curve is driver resonance while the second one is Helmholtz resonance, which is contrary to the traditional view. The considerable reduction of driver resonance frequency in water is mainly due to the large radiation mass on the four large radiation surfaces of the Janus transducer, which also causes the sharp response of driver resonance. In Janus-Helmholtz transducer, there are two Helmholtz resonators with the same size, instead of only one resonator in the traditional view. The two resonance frequencies solved by the method proposed in this work are in good agreement with the test and simulation results. These conclusions play an important role in correctly understanding the structure and characteristics of Janus-Helmholtz transducer at source, as well as provide technical support for structural optimization and innovation, thus improving the acoustic emission properties of the transducer.

Aeroacoustic analysis of a bass-reflex loudspeaker using LES: Validation of 2D and 3D numerical model with experiment

A bass-reflex loudspeaker has a port that amplifies low frequencies through Helmholtz resonance. However, high sound pressure levels can cause fluid flow near the port tip, leading to noise and distortion. Two-dimensional axisymmetric aeroacoustic analysis is commonly used to predict these non-linear phenomena; however, it has been reported to overestimate harmonic distortion. Presently, its accuracy has not been adequately verified through three-dimensional simulations or comparison with experimental results. This study validates the numerical model by comparing results from three- and two-dimensional analyses with experimental measurements on a straight tube port axisymmetric speaker model. In aeroacoustic analysis, large-eddy simulations are adopted, and the speaker model is acoustically driven at the Helmholtz resonance frequency. The results show that while the two-dimensional axisymmetric model overestimates the harmonic distortion and noise in the frequency response of far-field sound pressure, the three-dimensional model agrees well with the experiment up to the band where the harmonic distortion and port noise appear. This indicates that three-dimensional aeroacoustic analysis is necessary to accurately reproduce the fluid-induced distortion and noise of a bass-reflex port speaker.

Design of coupled Helmholtz resonator with rectangular enclosure to mitigate low frequency noise in recording booths

This study summarizes theoretical and experimental findings for low frequency noise mitigation in small recording booths using coupled Helmholtz resonators. The room acoustical resonance modes were identified using ANSYS simulation software for the recording booth. An experimental setup validated the existence of the different low frequency modes and variation from theoretical results due to the enclosure wall's surface material. Microphone and speaker system were used to measure the room frequency response at the resonant frequencies. Piezoelectric sensors were placed at different positions within the room to determine the location of resonance peaks and the optimized position for the coupled Helmholtz resonator. The effects of damping on the Helmholtz resonator frequency response and deviation from theoretical design formulae were explored. The resonator apparatus proved to attenuate noise to half as loud in the selected low frequency range within the recording booth.

Optimal design for a perforated panel absorber combined with Helmholtz-resonance and plate vibration

This study proposes a perforated panel sound absorber combined with Helmholtz-resonance and plate vibration and its optimal design method to broaden the sound absorption characteristics. The proposed perforated absorber has a simple structure consisting of a flexible panel with a hole and an air cavity. The conventional optimal design theory of the dynamic vibration absorber is applied to the perforated absorber. The proposed absorber is designed so that the acoustic impedance density will be equalized and almost minimized at two points independently of the damping of the panel. Optimal parameters are related to the Helmholtz-resonance frequency, the natural frequency of the panel, and the loss factor of the panel. The absorber with the optimal parameters was fabricated, and the sound absorption coefficient was measured using an acoustic impedance tube. The experimental results shows that the proposed method can effectively design the perforated panel absorber with the broadband sound absorption characteristics.

Mechanical-acoustical analogy: From laboratory to home during the COVID-19 pandemic.

A clear comprehension of the oscillatory nature of sound for acoustics undergraduate students is of paramount importance. In this paper, two online experiments were implemented to aid teaching of the oscillatory nature of sound through the analogy between a mechanical mass-spring model and a Helmholtz resonator. The study was conducted among undergraduate students taking a science course in the Electronic and Electrical Engineering career curriculum. These in-class experiments were conducted during the COVID-19 pandemic via the Zoom platform. Students measured the Helmholtz resonant frequency of a plastic bottle with a smartphone application and compared its oscillatory behavior with that of a conventional harmonic oscillator under a professor-student collaborative environment. The results of this study suggest that, with careful experiment design, students can effectively benefit from the use of common technology tools, which, in turn, poses these methodologies as a rather satisfactory alternative to face-to-face laboratory sessions.

Enhancing Jet Velocity and Power Conversion Efficiency of Piezoelectric Synthetic Jet Actuators

The present work discusses an experimental investigation into the effect of piezoceramic employed to drive a synthetic jet actuator into a quiescent flow. The electromechanical coupling ratio of polycrystalline piezoceramics, lead zirconate–titanate 5A/5H (PZT-5A/5H), conventionally used in synthetic jet actuators, is inherently low. Therefore, this study aims to investigate using more electromechanically efficient piezoceramics, such as single-crystal, lead magnesium niobate–lead titanate (PMN-PT). In addition, two different orifice-diaphragm configurations of synthetic jet actuators, opposite and adjacent, are tested. It is identified that PMN-PT piezoceramic promotes three times higher transverse diaphragm displacement and two times more peak jet velocity compared to the PZT-5A piezoelectric actuator for the same input diaphragm voltage. A peak exit jet velocity of was obtained at 40 V of peak supply voltage, which can be classified as a low voltage supply compared to other studies in the literature that obtained similar exit jet velocity. Also, a power conversion efficiency of 72% was achieved, corresponding to the Helmholtz resonance frequency. A new figure-of-merit, momentum coefficient per power consumption, is defined to evaluate the potential impact for full-scale implementation. A state-of-the-art value of is achieved.

Hybrid Lumped-Element and Finite Element Model for Novel Synthetic Jet Actuator Shapes

A modeling approach was developed that combines lumped-element and finite element methods for analysis of synthetic jet actuator (SJA) geometries that deviate significantly from an ideal Helmholtz resonator. The diaphragm was modeled using the finite element method (FEM) coupled to lumped-element equations that govern the fluid flow. The loss coefficient was estimated based on the geometry of the cavity and orifice. A pressure acoustic FEM model of the cavity and orifice was used to determine a characteristic resonance frequency to use in place of the Helmholtz resonance frequency that appeared in the lumped element equations. The results were validated using experimental data for SJAs with geometries that deviate significantly from the Helmholtz resonator idealization. The combination of replacing the Helmholtz frequency with a more accurate characteristic frequency and using a computed value for the loss coefficient was shown to provide more accurate performance predictions for low-profile SJA designs.

A low-frequency wideband ventilation muffler based on an embedded rough-necked Helmholtz resonator

Aiming at the unsatisfactory low-frequency sound absorption effect of Helmholtz resonator, a novel broadband low-frequency ventilation absorber with rough neck is proposed. The roughness is introduced into the neck of Helmholtz resonator to change the shape of the neck and achieve the structure of rough neck Helmholtz resonator. The proposed absorber can effectively provide the acoustic impedance required for low-frequency sound absorption without changing the overall size, thereby reducing the resonant frequency. The finite element method is used to simulate the structure, and the impedance tube sound absorption test is carried out to verify it. The experimental and simulation results show high consistency with each other. The results also indicate that the rough neck Helmholtz resonator absorber with roughness introduced in the neck achieves an absorption peak at 58 Hz, with an absorption coefficient of about 0.63. Comparing with the absorber without roughness introduced, the resonant peak frequency becomes low, from 70 Hz to 58 Hz, reducing 17.1%. Therefore, adjusting the neck roughness can serve as a method of tuning the acoustic performance, and the absorption peak frequency can be adjusted by appropriately increasing the neck roughness so as to move it in the low frequency direction. Based on the verification that the roughness of the neck can effectively reduce the absorption peak frequency of Helmholtz resonator, a broadband low-frequency ventilation absorber with a rough neck, which is composed of eight absorption units, is designed. Through simulation calculation and experimental exploration, the absorption coefficient can achieve more than 0.8 in a target working frequency band of 500－1100 Hz. On this basis, the acoustic impedance of the structure can be adjusted by introducing roughness into the neck of Helmholtz resonator, so as to obtain the optimized broadband low-frequency ventilation absorber with a rough neck, which achieves a broadband sound absorption coefficient higher than 0.8 in a frequency range of 400–1200 Hz. The optimized structure also has 8 consecutive absorption peaks with amplitudes above 0.95. The proposed low-frequency broadband ventilation absorber provides a reference for designing and optimizing efficient low-frequency subwavelength acoustic absorbers. It has a wide range of applications in pipeline noise control.

Jet Velocity and Acoustic Excitation Characteristics of a Synthetic Jet Actuator

The effect of the excitation frequency of synthetic jet actuators on the mean jet velocity issuing from an array of circular orifices is investigated experimentally, focusing on the acoustic excitation characteristics of the actuator’s cavity. Two cavity configurations are considered. In the first configuration, synthetic jets are generated by exciting a single, large cavity having an array of sixteen orifices via sixteen piezoelectric elements. In the second configuration, the cavity volume of the first configuration is divided into eight isolated compartments, each with two orifices and two piezoelectric elements. Several distinct resonant peaks were observed in the frequency response of the synthetic jet actuator built with a single large-aspect-ratio cavity, whereas the case of compartmentalised cavities exhibited a single resonant peak. Acoustic simulations of the large-aspect-ratio-cavity volume showed that the multiple peaks in its frequency response correspond to the acoustic standing-wave mode shapes of the cavity. Due to its large aspect ratio, several acoustic mode shapes coexist in the excitation frequency range aside from the Helmholtz resonance frequency. When the actuator’s cavity volume is compartmentalised, only the Helmholtz resonance frequency is observed within the excitation frequency range.

Asymptotics of the meta-atom: plane wave scattering by a single Helmholtz resonator.

Using a combination of multipole methods and the method of matched asymptotic expansions, we present a solution procedure for acoustic plane wave scattering by a single Helmholtz resonator in two dimensions. Closed-form representations for the multipole scattering coefficients of the resonator are derived, valid at low frequencies, with three fundamental configurations examined in detail: the thin-walled, moderately thick-walled and extremely thick-walled limits. Additionally, we examine the impact of dissipation for extremely thick-walled resonators, and also numerically evaluate the scattering, absorption and extinction cross-sections (efficiencies) for representative resonators in all three wall thickness regimes. In general, we observe strong enhancement in both the scattered fields and cross-sections at the Helmholtz resonance frequencies. As expected, dissipation is shown to shift the resonance frequency, reduce the amplitude of the field, and reduce the extinction efficiency at the fundamental Helmholtz resonance. Finally, we confirm results in the literature on Willis-like coupling effects for this resonator design, and connect these findings to earlier works by several of the authors on two-dimensional arrays of resonators, deducing that depolarizability effects (off-diagonal terms) for a single resonator do not ensure the existence of Willis coupling effects (bianisotropy) in bulk.This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)’.

MEASUREMENT OF THE REGRESSION RATE IN A HYBRID ROCKET MOTOR BY ACQUIRING THE HELMHOLTZ FREQUENCY IN THE COMBUSTION CHAMBER

Low thrust values obtained with a hybrid rocket motor (HRM) are a consequence of the difficulty in quickly mixing the fuel and oxidizer, which is characterized by a low regression rate of the fuel grain. Therefore, the measurement of this parameter is of great importance in studies that aim at solutions for this deficiency in HRM. Several studies calculate a reliable value of the average regression rate over time by measuring the total mass of fuel before and after each burn. A method to measure instantaneous regression rate is by acquiring the Helmholtz resonance frequency in the combustion chamber. This work uses a piezoelectric pressure transducer to obtain the Helmholtz frequency mode of the combustion chamber in a laboratory scale test bench with high-density polyethylene (HDPE) and gaseous oxygen, and is based on the principle that this frequency is inversely proportional to the square-root of the chamber volume. With the chamber volume variation, the port diameter of the grain variation is obtained. In conclusion, the calculated variation of port diameter agreed well with the correlation for average regression rate, determined from mass loss during operation.

Waveguide demultiplexer based on Helmholtz-resonator mediated extraordinary acoustic transmission

The design of an acoustic demultiplexer based on in-line Helmholtz resonators is demonstrated analytically via a modified transfer matrix method and computationally through finite element simulations. The modeled system consists of a single input waveguide that splits in a Y-configuration into two output waveguides. Each output arm has a single tuned Helmholtz resonator embedded in-line along the length of the guide. The Helmholtz resonators in each arm consist of a single cavity with two necks—one directed towards the input and output sides of the guide. The phenomenon of extraordinary acoustic transmission results in near perfect transmission of sound along each output arm in a small frequency interval about the Helmholtz resonant frequency. The demultiplexed frequencies are determined by the physical dimensions of the Helmholtz resonator. Using a single Helmholtz resonator in each output arm means that the system is more compact compared to other proposed schemes using either side-loaded Helmholtz resonators or stubs.

Effects of Orifice Diameter of Pre-Chamber Jet Ignition on the Combustion Characteristics and Pressure Oscillations in a Kerosene-Fueled Engine

Abstract Jet orifice diameter directly impacts the combustion process of the pre-chamber jet ignition (PJI) engine and the optimized diameter is varied with the fuel properties. However, research on the optimization of the jet orifice diameter based on aviation kerosene fuel has not been reported. So, this paper investigates the effect of orifice diameter on combustion, pressure oscillation, and performance based on a kerosene-fueled single-cylinder test engine. Two pressure sensors are respectively fitted in the main combustion chamber and the pre-chamber, which can capture the pressure change process and pressure oscillations phenomenon at the two positions, respectively. The result demonstrates that the throttling of the jet orifice leads to a significant three-stage pressure imbalance between the combustion chambers. With the reduction of the orifice diameter, the combustion acceleration of PJI is enhanced, resulting in an advanced combustion phase, improved combustion stability, and enhanced knock. The time-frequency analysis proves that the pressure oscillation propagation to the pre-chamber is frequency-selective and related to the orifice diameter. By matching the pre-chamber Helmholtz resonance frequency with the main chamber resonance frequency, strong pressure oscillations can be excited in the pre-chamber. Meanwhile, the pressure oscillation energy can be absorbed by the pre-chamber, which may help reduce the engine's combustion noise. Moreover, the PJI with an orifice diameter between 2 mm and 4 mm can improve the combustion stability with the ISFC reduced by 4.7–5.6%, and the IMEP increased by 1.2–2.6%.

Effects of loudspeaker-driven synthetic jet actuator parameters on the characteristics of the synthetic jet

In this study, a method for calculating synthetic jet actuator (SJA) parameters by combining diaphragm boundary conditions based on the laws of particle vibration and geometric parameters of the cavity is proposed to obtain accurate rules of variation in which the characteristics of a synthetic jet (SJ) are affected by actuator parameters. Based on the calculating method,an aeroacoustics simulation model of loudspeaker-driven SJA is established with COMSOL software. Simulation results show that the influence of cavity geometry parameters on the velocity characteristics of SJ is greater than that of exciter parameters under the excitation of Helmholtz resonance frequency. Moreover, changing the cavity parameters can increase the jet velocity and reduce the sound pressure level. The velocity characteristics of SJ are consistent with the experimental results.On the basis of the simulation results, the relationship between the aperture length, the cavity length and the modulus of mechanical impedance is established to achieve the maximum jet velocity. It solves various complicated problems of the cavity geometry parameters caused by excitation frequency.

Semi-analytical estimation of Helmholtz resonators’ tuning frequency for scalable neck-cavity geometric couplings

Innovative meta-materials offer great flexibility for manipulating sound waves and assure unprecedented functionality in the context of acoustic applications. Indeed, they can exhibit extraordinary properties, such as broadband low-frequency absorption, excellent sound insulation, or enhanced sound transmission. These amazing properties have drawn the eye of the transport industry, especially for aeronautic applications where objects like these can be combined and coupled with primary structures aiming to reduce exterior and interior noise without increasing weight. However, the design of acoustic meta-materials with exciting functionality still represents a challenge, therefore there is a huge interest about the conceptualization and design of innovative acoustic solutions making use of meta-material resonance effects. The main target of the present research work is to obtain an accurate prediction of the tuning frequency of a Helmholtz-resonating device, whose resonance properties are exploited in a wide part of acoustic meta-material design. In this context, an investigation on a correction factor for the classical formulation used to estimate the Helmholtz resonance frequency starting from its geometric characteristics, accounting for different-shaped resonators with varying neck/cavity ratios, is performed. More specifically, a set of numerical simulations for several geometric configuration is considered in order to demonstrate the limits of pre-existing formulas, and a new correction factor formula is developed after theoretical considerations where it is possible. In the end, results in terms of correction factors are provided in both graphical and semi-analytical form, compared with Finite Element data.

Study on the Behavior of Helmholtz Resonance in Different Size Bottles

The resonance is the specific response of system which is capable to vibrate with certain frequency to an external force acting with the same frequency. When air is blown across the open mouth of different bottles then air vibrate in a neck at resonant frequency. In this study we consider 5-5 bottles of different five types bottles having different of length of neck, radius of port, cross-sectional area of port and same volume (250ml). Resonance in different bottles was studied to determine how the volume of air cavity of different bottle affects the resonance. From calculated and experimental data, we found that the Helmholtz resonance frequency decreases with increase in volume and vice versa in each case of different bottles. From graph we also found that the calculated and experimental model are about 100% and 99% variability of the response data around its mean. The practical range for these different bottles is from about 256 to 512 Hz. This is about an octave plus a musical fifth near the middle of the musical instrument, so most simple musical tunes can be produced with such bottles.

Causally-guided acoustic optimization of single-layer rigidly-backed micro-perforated partitions: Theory

This theoretical study adapts results obtained in electromagnetism on the optimal performance of radar slab absorbers to the field of acoustics to enhance the broadband dissipation of single-layer rigidly-backed micro-perforated absorbers (MPAs) under normal incidence. Based on the causality principle, an integral identity is derived. It shows that the MPA ultimate wideband performance, that integrates contributions of the intensity reflection coefficient over all the positive wavelengths, is upper bounded by the absorber cavity depth. A sensitivity analysis led to the proposal of a causal-based optimization criterion in order to find optimal MPAs that achieve maximum wideband performance while reaching perfect absorption at their Helmholtz resonance frequency. This simple criterion maximizes the sensitivity of the total reflected intensity with respect to the micro-perforated panel constitutive parameters. It can be readily implemented using numerical quadrature and optimization solvers. It is shown to be a suitable alternative to maximization of the total absorption and inverse-frequency weighted absorption for single-layer MPA broadband optimization.

Helmholtz Resonance Frequency of the Synthetic Jet Actuator

This paper presents the results of experimental investigations of 108 geometrical configurations of a loudspeaker-driven synthetic jet (SJ) actuator. The considered cases of the SJ actuator were characterized by a high coupling ratio. The experiment was performed to determine the impact of geometry on the Helmholtz resonance frequency. Geometrical parameters of the orifice diameter, orifice length, and cavity volume were changed within a wide range. The dependences of electrical and flow parameters that characterized the synthetic jet actuators as a function of the excitation frequency were also identified. The main goal of the research was to identify the optimal mathematical formula of the model to calculate the Helmholtz resonance frequency in the case of synthetic jet actuators. To determine the model that was characterized by the best fit of the experimental results, an additional geometrical dimensionless parameter, representing the ratio of the orifice cross-section area to the cross-section area of the cavity, was introduced. A significant impact of this parameter on the effective orifice length was noted. Based on the research findings, a model was obtained for which the results of the experiment were in the error range of ±6% for 95% of the measurement data. The obtained model is an improved version of the classical model used in the description of the resonance frequency in the case of a synthetic jet actuator. The model enables highly accurate determination of the Helmholtz resonance frequency at which the maximum synthetic jet actuator parameters occur.