Kundt's Tube Research Articles

Impedance Boundary Condition for Lattice Boltzmann Model

AbstractA surface based lattice Boltzmann impedance boundary condition (BC) using Ozyoruk’s model [J. Comput. Phys., 146 (1998), pp. 29-57] is proposed and implemented in PowerFLOW. In Ozyoruk’s model, pressure fluctuation is directly linked to normal velocity on an impedance surface. In the present study, the relation between pressure and normal velocity is realized precisely by imposing a mass flux on the surface. This impedance BC is generalized and can handle complex geometry. Combined with the turbulence model in the lattice Boltzmann solver PowerFLOW, this BC can be used to model the effect of a liner in presence of a complex 3D turbulent flow. Preliminary simulations of the NASA Langley grazing flow tube and Kundt tube show satisfying agreement with experimental results.

Micro-perforated elements in complex vibro-acoustic environment: Modelling and applications

Micro-perforated structures/panels (MPP) are widely used in various architectural, industrial and environmental applications for providing efficient sound absorptions. More recently, they found their use in compact mechanical systems, in which the property of the MPP is shown to be strongly influenced by the surrounding vibro-acoustic environment, which is drastically different from the one dimensional Kundt tube configuration, usually used in existing works. Unfortunately, very little has been done in this regard, due to the fact that modeling such a vibro-coustic system with MPPs as integrative elements is a very challenging task, not even to mention the optimization. Recently, a vibro-acoustic formulation based on the Patch Transfer Function (PTF) approach was proposed to model micro-perforated structures in a complex vibro-acoustic environment. As a sub-structuring approach, PTF allows assembling different vibro-acoustic subsystems, including micro-perforations and the flexibility of a MPP, through coupled surfaces. The proposed formulation provides explicit representation of the coupling among subsystems, with enhanced capability of handling system complexities and facilitating system optimization. In this talk, the overall approach will be reviewed and applied to a number of typical examples. The versatility and efficiency of the method as well as the underlying physics are demonstrated.

Implementation of acoustic materials to the VLS-1 Fairing - a sensitivity analysis using SEA

Satellite launchers are submitted to severe acoustic loads mainly during lift-off where SPL achieve, at the upper parts, values within the range of 140-160 dB. Such an excitation can damage embedded elements, if energy attenuation measures are not adopted. In view of managing the PLF vibro-acoustic environment, numerical techniques are applied to predict elasto-acoustic behavior. This manuscript presents a numerical study on the design of acoustic insulation for the VLS-1 fairing compartment. An excitation profile based on the literature is applied on a SEA coupled model of this structural-acoustic system and absorbing materials are added to the model. Two parameters of the absorbing material layer are analyzed: thickness and covered area. Two NCT modeling approaches are used to simulate the effect of blanketing the VLS-1 fairing: acoustic materials Biot's parameters, given by the manufacturer, and material samples absorption coefficient, measured in a Kundt Tube. Results show that an increase in the blanket thickness from 7.62 to 12.7 cm results in a TL of 1.7 dB OSPL, while variations of up to 3.0 dB OSPL are calculated if the fairing cavity blanketed area varies from 30% to 100%.

Modeling of micro-perforated panels in a complex vibro-acoustic environment using patch transfer function approach

A micro-perforated panel (MPP) with a backing cavity is a well known device for efficient noise absorption. This configuration has been thoroughly studied in the experimental conditions of an acoustic tube (Kundt tube), in which the MPP is excited by a normal incident plane wave in one dimension. In a more practical situation, the efficiency of MPP may be influenced by the vibro-acoustic behavior of the surrounding systems as well as excitation. To deal with this problem, a vibro-acoustic formulation based on the patch transfer functions (PTF) approach is proposed to model the behavior of a micro-perforated structure in a complex vibro-acoustic environment. PTF is a substructuring approach, which allows assembling different vibro-acoustic subsystems through coupled surfaces. Upon casting micro-perforations and the flexibility of the MPP under transfer function framework, the proposed PTF formulation provides explicit representation of the coupling between subsystems and facilitates physical interpretation. As an illustration example, application to a MPP with a backing cavity located in an infinite baffle is demonstrated. The proposed PTF formulation is finally validated through comparison with experimental measurements available in the literature.

Kundt’s Tube: An Acoustic Gas Analyzer

A Kundt tube is normally used to measure the speed of sound in gases. Therefore, from known speeds of sound, a Kundt tube can be used to identify gases and their fractions in mixtures. In these experiments, the speed of sound is determined by measuring the frequency of a standing sound wave at a fixed tube length, temperature, and pressure. This resonant frequency is dependent only on the properties of the gas, namely, its heat capacity ratio (adiabatic index) and molar mass. We discuss the capabilities of a Kundt tube for use as an instructional device to identify gases on the basis of their acoustic spectra and to use these spectra to determine the fractions of components of a binary mixture or to study the kinetics of gas-generating or gas-depleting reactions.

Synthesis of porous–acoustic absorbing systems by an evolutionary optimization method

Topology optimization is frequently used to design structures and acoustic systems in a large range of engineering applications. In this work, a method is proposed for maximizing the absorbing performance of acoustic panels by using a coupled finite element model and evolutionary strategies. The goal is to find the best distribution of porous material for sound absorbing panels. The absorbing performance of the porous material samples in a Kundt tube is simulated using a coupled porous–acoustic finite element model. The equivalent fluid model is used to represent the foam material. The porous material model is coupled to a wave guide using a modal superposition technique. A sensitivity number indicating the optimum locations for porous material to be removed is derived and used in a numerical hard kill scheme. The sensitivity number is used to form an evolutionary porous material optimization algorithm which is verified through examples.

Tests of sound absorption of seats of the Colon Theatre in Buenos Aires.

Having passed 100 years after its inauguration, the Colon Theatre located in Buenos Aires City is one of the most outstanding opera and symphonic music theatre of the world, and being one of the main architectural monuments of the Argentine Republic, it has needed a conservative restoration and a technological update. This has given place to the realization of a series of projects that guarantee its value with the premise to keep its acoustic quality. The methodology employed to select the textile material replacement and objects that have influence in the acoustics of the room consist in subjecting to laboratory tests the original samples together with their replacements in order to objectively characterize them and to verify that they had similar properties of sound absorption. This work presents the laboratory procedure which allowed the selection of textile material of seats replacement from reverberant chamber and Kundt tube tests.

Acoustic and mechanical properties of expanded clay granulates consolidated by epoxy resin

Porous materials were prepared by agglomerating the expanded clay with an epoxy resin with the aim to produce sound absorbers which combine good noise damping performances, excellent mechanical strength and low costs. The use of a polymeric binder, instead of the concrete typically employed in present commercial products, allows obtaining light sound-absorbing panels. In our research the acoustic and mechanical properties of samples of consolidated expanded clay with different thicknesses were experimentally tested. Particularly, the sound absorption properties were measured in a vertical Kundt tube by applying the standing wave ratio method. SEM (scanning electron microscope) observations and porosity measurements were also performed. Experimental results showed a good behaviour with respect to the flexure and compression tests, together with selective sound-absorbing performances and suggest further research opportunities and possible applications of these porous materials as sound absorbers.

On the use of porous inclusions to improve the acoustical response of porous materials: Analytical model and experimental verification

Acoustical composite materials obtained through a set of porous inclusions are studied. A theoretical model based on the homogenization hypotheses introduced by Boutin et al. [1] is presented; the inclusions are supposed periodic and the frame rigid. The idea behind the inclusion of a second acoustical porous material into the original single porosity material, is to obtain the pressure diffusion effect already observed in the double porosity case. At the same time, the main disadvantages of double porosity are faced, especially the absorption behavior at very low frequency and the loss of performances in transmission. Experimental data are obtained in Kundt Tubes of different dimensions in terms of absorption curves and compared to analytical results for representative configurations, thus validating the theoretical model.

Behavior of cylindrical liquid jets evolving in a transverse acoustic field

This paper presents a theoretical and an experimental investigation of low-velocity cylindrical liquid jets submitted to transverse planar acoustic waves. For this purpose, the behavior of a liquid jet traversing the section of a Kundt tube was examined. Experiments reported that the liquid jet could be either deviated from its trajectory or deformed as a succession of lobes oriented in space and whose length and width depend on the jet acoustic environment. Furthermore, for a sufficient acoustic velocity, the jet deformation increases in such proportion that a premature and vivid atomization mechanism disintegrates the liquid flow. Theoretical models are proposed to understand these behaviors. The first one calls out for acoustic radiation pressure to explain the jet deviation. The second one consists in a modal analysis of the vibrations of a jet when submitted to a transverse stationary acoustic field. As a first approach, a simplified two-dimensional model is proposed. This model reports that a sudden exposition of the jet to an acoustic field triggers two jet eigenmodes. One of them induces jet deformations that were not experimentally observed. This part of the solution emerges due to theoretical deficiencies. However, the second mode reproduces the lobe formation and leads to atomization criteria in good agreement with the experimental results. The paper ends with an extension of the mathematical development in three dimensions in order to provide a basis to a more consistent model.

Modal probabilistic analysis

In this paper, we first recall a method for estimating the numerical Probability Density Function (PDF) with Parzen-Rosenblatt estimators of experimental data (like the sound absorption coefficient with the Kundt's tube). Then we focus on the model of Mikki which is used as a predictive tool. We are interested then in inversing the model and in identifying the 3 parameters (q,σ,φ) of Mikki's model. But we want to go further and to identify from the estimated PDF directly the PDF of the 3 parameters. We explain first when it is possible, then we give some examples to illustrate the method. This work allows for evaluating the robustness of a model from experimental data.

An Evolutionary Optimization Method applied to Absorbing Poroelastic Systems

Poroelastic materials can be used in engineering applications such as: noise control of automobiles, acoustical insulation systems for aircrafts, industrial, environmental and domestic sound quality control, etc. The insulating systems must be as light as possible and the acoustic absorption in the low frequency domain must be maximized for certain gaps. Topology Optimization is frequently used to design structures and acoustic systems in a large range of engineering applications. In this work, we propose one method to maximize the absorbing performance of insulation poroelastic systems using a coupled finite element model and Evolutionary strategies. The goal is find the best distribution of poroelastic material on insulating systems. The absorbing performance of the poroelastic material samples in a Kundt tube is simulated using a coupled poroelastic and acoustic finite element model. The Biot-Allard Coupled Model is used to represent the foam material. The porous material model is coupled to a waveguide using a modal superposition technique. A sensitivity number indicating the optimum locations for porous material removing is derived and used in a numerical hard kill scheme. The sensitivity number is used to form an evolutionary poroelastic optimization (EPO) algorithm which is verified though numerical examples.

Measurement of acoustic and mechanical parameters of poroelastic materials by mean of active control and wave‐based methods

Poroelastic materials are used in sound barriers for sound insulation and absorption. At low frequencies, the medium is modeled using the Biot theory. This homogenised model needs to be feed by at least eight parameters using the Johnson‐Allard approach. The presented characterisation method relies on two specific test facilities. First, acoustic parameters are obtained thanks to a modified Kundt tube. The porosity and resistivity are obtained by direct measurements of the surface impedance with hard wall and zero pressure boundary conditions on the rear face of the sample, respectively. This last boundary conditions is achieved thanks to active control procedure. Finally, the remaining acoustic parameters are obtained in a least mean square sense. Mechanical parameters are then measured on a second test bench. A beam made of the poroelastic sample is subjected to mechanical broadband forcing. The transverse displacement is measured along the beam thanks to a laser vibrometre. Dispersion curves are then obtained by calculating the Inhomogeneous Wave Correlation (IWC) ratio. The Young modulus and loss factor of the sample are estimated thanks to an optimisation procedure applied to the finite element model of the test. Results are compared to those obtained using more classical quasi‐static methods.

A new impedance tube for large frequency band measurement of absorbing materials

The standard two microphones technique does not allow the measurement of absorbing materials characteristics at low frequency. Moreover, to cover a range from 100 to 6000 Hz two experiments have to be done with two different sample diameters. By using a sensor with a known volume velocity source developed by the LAUM together with the CTTM, it is demonstrated that the impedance can be obtained from 10 to 6000 Hz by performing only one measurement with a single material sample. Results showing the behaviour of some materials at low frequency are presented. On the other hand a comparison is done with classical Kundt tube results.

LabWorks and the Kundt's Tube: A New Way To Determine the Heat Capacities of Gases

Computer-controlled data acquisition is rapidly becoming the rule rather than the exception in chemistry laboratories. The LabWorks learning system is one of many computer-controlled data acquisition interfaces that allows students to quickly obtain and analyze chemistry data. This project involved adapting a classic physical chemistry experiment to using this modern data acquisition and analysis system. Heat capacities were measured for argon, nitrogen, and carbon dioxide gases using a fixed-length Kundt's tube. Measured heat capacities were determined to be within 4% of accepted values.

Supresión de modos de vibración acústicos con un resonador Helmholtz

La inserción de un Resonador Helmholtz (RH) en las paredes laterales de un tubo, con ondas estacionarias en su interior, logra suprimir uno o más de sus modos resonantes si se elige adecuadamente la frecuencia del resonador. El RH puede actuar también como filtro de ondas propagantes.' En este caso, el RH atenua las ondas en un rango de frecuencia muy selectivo. En la mayoría de los textos de acústica, solamente se desarrolla la teoría que explica el filtrado de ondas propagantes. Sin embargo, en los laboratorios de física basica, donde se dispone solamente de tubos de Kundt de pequeña longitud, no es simple realizar un arreglo experimental que asegure la presencia de ondas propagantes puras en su interior. La falta de una teoría para ondas estacionarias y las dificultades experimentales que señalamos han producido algunas confusiones en trabajos que tratan sobre el tema. En este artículo se presenta un modelo teórico que describe satisfactoriamente el comportamiento del RH cuando funciona como filtro de ondas estacionarias y se marcan las diferencias con la situación en que opera como filtro de ondas propagantes.

Induced Current Measurement of Rod Vibrations

The longitudinal1 normal modes of vibration of rods are similar to the modes seen in pipes open at both ends. A maximum of particle displacement exists at both ends and an integral number (n) of half wavelengths fit into the rod length. The frequencies fn of the normal modes is given by Eq. (1), where L is the rod length and V is the wave velocity: fn = nV2L. Many methods have been used to measure the velocity of these waves. The Kundt's tube method commonly used in student labs will not be discussed here. A simpler related method has been described by Nicklin.2 Kluk3 measured velocities in a wide range of materials using a frequency counter and microphone to study sounds produced by impacts. Several earlier methods4,5 used phonograph cartridges complete with needles to detect vibrations in excited rods. A recent interesting experiment6 used wave-induced changes in magnetization produced in an iron rod by striking one end. The travel time, measured as the impulsive wave reflects back and forth, gave the wave velocity for the iron rod. In the method described here, a small magnet is attached to the rod with epoxy, and vibrations are detected using the current induced in a few loops of wire. The experiment is simple and yields very accurate velocity values.

A New Technique for the Measurement of Characteristic Acoustic Impedance in Kundt Tubes Based on a Finite Difference Algorithm

In this paper we present a new technique for the measurement of specific impedance of acoustic materials based on the method of finite differences using acoustic pressure measurements with a single microphone in a Kundt tube. This method permits prediction of the acoustic pressure in all the points of the tube. We show here the algorithm and its modifications for the evaluation of acoustic impedance. Some comparisons with other methods are also considered.

An Alternative Method for the Characterisation of Fibrous Materials from Measurements of Absorption Using Techniques Based on the Allard and Champoux Model

In this work we present a method for characterising fibrous materials from absorption measurements in the Kundt tube. Specific Flow Resistance may be calculated, using techniques based on the Allard & Champoux model. Using this model and taking measurements of absorption as a starting point, the method presented here enables one to achieve a complete characterisation of a fibrous material.

The Characterisation of Fibrous Materials from Measurements of Absorption Using Techniques Based on Miki's Model

In this work the authors present a method for characterizing fibrous materials from absorption measurements in the Kundt tube. Specific Flow Resistance may be calculated, using techniques based on the Miki's model. Using this model and taking measurements of absorption as a starting point, the method presented here enables one to achieve a complete characterisation of a fibrous material, with the added advantage that no special equipment is needed.