The flow-reversal elliptical cylindrical end chamber mufflers of short length are used often in the modern day automotive exhaust systems. The conventional 1-D axial plane wave theory is not able to predict their acoustical attenuation performance in view of the fact that the chamber length is not enough for the evanescent 3-D modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large area expansion ratio at the inlet, the first few higher order modes get cut on even in the low frequency regime. This necessitates a 3-D FEM or 3-D BEM analysis, which is cumbersome and time consuming. Therefore, an ingenious 1-D transverse plane wave theory is developed by considering plane wave propagation along the major-axis of the elliptical section, whereby a 2-port axially short elliptical and circular chamber muffler is characterized by means of the transfer matrix [T] or impedance matrix [Z]. Two different approaches are followed: (1) a numerical scheme such as the Matrizant approach, and (2) an analytical approach based upon the Frobenius series solution of the Webster’s equation governing the transverse plane wave propagation. The convective effects of mean flow are neglected; however the dissipative effects at the ports are taken into account. The TL predicted by this 1-D transverse plane wave analysis is compared with that obtained by means of the 3-D analytical approach and numerical (FEM/BEM) methods. An excellent agreement is observed between this simplified 1-D approach and the 3-D approaches at least up to the cut-on frequency of the (1, 1) even mode in the case of elliptical cylindrical chambers, or the (1, 0) mode in the case of circular cylindrical chambers, thereby validating this 1-D transverse plane wave theory. The acoustical attenuation characteristics of such short chamber mufflers for various configurations are discussed, qualitatively as well as quantitatively. Moreover, the Frobenius series solution enables one to obtain non-dimensional frequencies for determining the resonance peak and trough in the TL graph. The use of this theory is, however, limited to configurations in which both the ports are located along the major axis in the case of elliptical chambers and along the same diameter for circular chambers. The method of cascading the [T] matrices of the 2-port elements cannot be used to analyze a network arrangement of 2-port elements owing to the non-unique direction of wave propagation in such a network of acoustic elements. Although, a few papers are found in the literature reporting the analysis of a network of 2-port acoustic elements, no work is seen on the analysis of a network of multi-port elements having more than two external ports. Therefore, a generalized algorithm is proposed for analyzing a general network arrangement of linear multi-port acoustic elements having N inlet ports and M outlet ports. Each of these multi-port elements constituting the network may be interconnected to each other in an arbitrary manner. By appropriate book-keeping of the equations obtained by the [Z] matrix characterizing each of the multi-port and 2-port elements along with the junction laws (which imply the equality of acoustic pressure and conservativeness of mass velocity at a multi-port junction), an overall connectivity matrix is obtained, whereupon a global [Z] matrix is obtained which characterizes the entire network. Generalized expressions are derived for the evaluation of acoustic performance evaluation parameters such as transmission loss (TL) and insertion loss (IL) for a multiple inlet and multiple outlet (MIMO) system. Some of the characteristic properties of a general multi-port element are also studied in this chapter. The 1-D axial and transverse plane wave analysis is used to characterize axially long and short chambers, respectively, in terms of the [Z] matrix. Different network arrangements of multi-port elements are constructed, wherein the TL performance of such MIMO networks obtained on the basis of either the 1-D axial or 1-D transverse plane wave theory are compared with 3-D FEA carried on a commercial software. The versatility of this algorithm is that it can deal with more than two external or terminal ports, i.e., one can have multiple inlets and outlets in a complicated acoustic network. A generalized approach/algorithm is presented to characterize rigid wall reactive multi-port chamber mufflers of different geometries by means of a 3-D analytical formulation based upon the modal expansion and the uniform piston-driven model. The geometries analyzed here are rectangular plenum chambers, circular cylindrical chamber mufflers with and without a pass tube, elliptical cylindrical chamber mufflers, spherical and hemispherical chambers, conical chamber mufflers with and without a co-axial pass tube and sectoral cylindrical chamber mufflers of circular and elliptical cross-section as well as sectoral conical chamber mufflers. Computer codes or subroutines have been developed wherein by choosing appropriate mode functions in the generalized pressure response function, one can characterize a multi-port chamber muffler of any of the aforementioned separable geometrical shapes in terms of the [Z] matrix, subsequent to which the TL performance of these chambers is evaluated in terms of the scattering matrix [S] parameters by making use of the relations between [Z] and [S] matrices derived earlier. Interestingly, the [Z] matrix approach combined with the uniform piston-driven model is indeed ideally suited for the 3-D analytical formulation inasmuch as regardless of the number of ports, one deals with only one area discontinuity at a time, thereby making the analysis convenient for a multi-port muffler configuration with arbitrary location of ports. The TL characteristics of SISO chambers corresponding to each of the aforementioned geometries (especially the elliptical cylindrical chamber) are analyzed in detail with respect to the effect of chamber dimensions (chamber length and transverse dimensions), and relative angular and axial location of ports. Furthermore, the analysis of SIDO (i.e., single inlet and double outlet) chamber mufflers is given special consideration. In particular, we examine (1) the effect of additional outlet port (second outlet port), (2) variation in the relative angular or axial location of the additional or second outlet port (keeping the location of the inlet port and the outlet ports of the original SISO chamber to be constant) and (3) the effect of interchanging the location of the inlet and outlet ports on the TL performance of these mufflers. Thus, design guidelines are developed for the optimal location of the inlet and outlet ports keeping in mind the broadband attenuation characteristics for a single inlet and multiple outlet (SIMO) system. The non-dimensional limits up to which a flow-reversal elliptical (or circular) cylindrical end chamber having an end-inlet and end-outlet configuration is acoustically short (so that the 1-D transverse plane wave theory is applicable) and the limits beyond which it is acoustically long (so that the 1-D axial plane wave theory is applicable) is determined in terms of the ratio or equivalently, in terms of the ratio. Towards this end, two different configurations of the elliptical cylindrical chamber are considered, namely, (1) End-Offset Inlet (located along the major-axis of the ellipse) and End-Centered Outlet (2) End-Offset Inlet and End-Offset Outlet (both the ports located on the major-axis of the ellipse and at equal offset distance from the center). The former configuration is analyzed using 3-D FEA simulations (on SYSNOISE) while the 3-D analytical uniform piston-driven model is used to analyze the latter configuration. The existence of the higher order evanescent modes in the axially long reversal chamber at low frequency (before the cut-on frequency of the (1, 1) even mode or (1, 0) mode) causes a shift in the resonance peak predicted by the 1-D axial plane wave theory and 3-D analytical approach. Thus, the 1-D axial plane wave analysis is corrected by introducing appropriate end correction due to the modified or effective length of the elliptical cylindrical chamber. An empirical formulae has been developed to obtain the average non-dimensional end correction for the aforementioned configurations as functions of the expansion ratio, (i.e., ), minor-axis to major-axis ratio, (i.e., ) and the center-offset distance ratio, (i.e., ). The intermediate limits between which the chamber is neither short nor long (acoustically) has also been obtained. Furthermore, an ingenious method (Quasi 1-D approach) of combining the 1-D transverse plane wave model with the 1-D axial plane wave model using the [Z] matrix is also proposed for the end-offset inlet and end-centered outlet configuration. A 3-D analytical procedure has also been developed which also enables one to determine the end-correction in axially long 2-port flow-reversal end chamber mufflers for different geometries such as rectangular, circular and elliptical cylindrical as well as conical chambers, a priori to the computation of TL. Using this novel analytical technique, we determine the end correction for arbitrary locations on the two end ports on the end face of an axially long flow-reversal end chamber. The applicability of this method is also demonstrated for determination of the end corrections for the 2-port circular cylindrical chamber configuration without and with a pass tube, elliptical cylindrical chambers as well as rectangular and conical chambers.

A theoretical study has been carried out on different methods available to analyze complex mufflers. Segmentation methods have been discussed in detail. The latest two port segmentation method has been discussed and employed for a few common muffler configurations, describing its implications and limitations. A new transfer matrix based method has been developed in view of the lacunae of the available approaches. This Integrated Transfer Matrix (ITM) method has been developed particularly to analyze complex mufflers. An Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The method presents a 1-D approach, using transfer matrices of simple acoustic elements which are available in the literature. Results from the present approach have been validated through comparisons with the available experimental and three dimensional FEM based results. The total pressure drop across perforated muffler elements has been measured experimentally and generalized expressions have been developed for the pressure loss across cross-flow expansion, cross-flow contraction elements, etc. These have then been used to derive empirical expressions for flow-acoustic resistance for use in the Integrated Transfer Matrix Method in order to predict the flow-acoustic performance of commercial mufflers. A flow resistance model has been developed to analytically determine the flow distribution and thereby pressure drop of mufflers. Generalized expressions for resistance across the perforated elements have been derived by means of flow experiments as mentioned above. The derived expressions have been implemented in a flow resistance network that has been developed to determine the pressure drop across any given complex muffler. The results have been validated with experimental data.

No description available.

No description available.

The flow-reversal elliptical cylindrical end chamber mufflers of short length are used often in the modern day automotive exhaust systems. The conventional 1-D axial plane wave theory is not able to predict their acoustical attenuation performance in view of the fact that the chamber length is not enough for the evanescent 3-D modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large area expansion ratio at the inlet, the first few higher order modes get cut on even in the low frequency regime. This necessitates a 3-D FEM or 3-D BEM analysis, which is cumbersome and time consuming. Therefore, an ingenious 1-D transverse plane wave theory is developed by considering plane wave propagation along the major-axis of the elliptical section, whereby a 2-port axially short elliptical and circular chamber muffler is characterized by means of the transfer matrix [T] or impedance matrix [Z]. Two different approaches are followed: (1) a numerical scheme such as the Matrizant approach, and (2) an analytical approach based upon the Frobenius series solution of the Webster’s equation governing the transverse plane wave propagation. The convective effects of mean flow are neglected; however the dissipative effects at the ports are taken into account. The TL predicted by this 1-D transverse plane wave analysis is compared with that obtained by means of the 3-D analytical approach and numerical (FEM/BEM) methods. An excellent agreement is observed between this simplified 1-D approach and the 3-D approaches at least up to the cut-on frequency of the (1, 1) even mode in the case of elliptical cylindrical chambers, or the (1, 0) mode in the case of circular cylindrical chambers, thereby validating this 1-D transverse plane wave theory. The acoustical attenuation characteristics of such short chamber mufflers for various configurations are discussed, qualitatively as well as quantitatively. Moreover, the Frobenius series solution enables one to obtain non-dimensional frequencies for determining the resonance peak and trough in the TL graph. The use of this theory is, however, limited to configurations in which both the ports are located along the major axis in the case of elliptical chambers and along the same diameter for circular chambers. The method of cascading the [T] matrices of the 2-port elements cannot be used to analyze a network arrangement of 2-port elements owing to the non-unique direction of wave propagation in such a network of acoustic elements. Although, a few papers are found in the literature reporting the analysis of a network of 2-port acoustic elements, no work is seen on the analysis of a network of multi-port elements having more than two external ports. Therefore, a generalized algorithm is proposed for analyzing a general network arrangement of linear multi-port acoustic elements having N inlet ports and M outlet ports. Each of these multi-port elements constituting the network may be interconnected to each other in an arbitrary manner. By appropriate book-keeping of the equations obtained by the [Z] matrix characterizing each of the multi-port and 2-port elements along with the junction laws (which imply the equality of acoustic pressure and conservativeness of mass velocity at a multi-port junction), an overall connectivity matrix is obtained, whereupon a global [Z] matrix is obtained which characterizes the entire network. Generalized expressions are derived for the evaluation of acoustic performance evaluation parameters such as transmission loss (TL) and insertion loss (IL) for a multiple inlet and multiple outlet (MIMO) system. Some of the characteristic properties of a general multi-port element are also studied in this chapter. The 1-D axial and transverse plane wave analysis is used to characterize axially long and short chambers, respectively, in terms of the [Z] matrix. Different network arrangements of multi-port elements are constructed, wherein the TL performance of such MIMO networks obtained on the basis of either the 1-D axial or 1-D transverse plane wave theory are compared with 3-D FEA carried on a commercial software. The versatility of this algorithm is that it can deal with more than two external or terminal ports, i.e., one can have multiple inlets and outlets in a complicated acoustic network. A generalized approach/algorithm is presented to characterize rigid wall reactive multi-port chamber mufflers of different geometries by means of a 3-D analytical formulation based upon the modal expansion and the uniform piston-driven model. The geometries analyzed here are rectangular plenum chambers, circular cylindrical chamber mufflers with and without a pass tube, elliptical cylindrical chamber mufflers, spherical and hemispherical chambers, conical chamber mufflers with and without a co-axial pass tube and sectoral cylindrical chamber mufflers of circular and elliptical cross-section as well as sectoral conical chamber mufflers. Computer codes or subroutines have been developed wherein by choosing appropriate mode functions in the generalized pressure response function, one can characterize a multi-port chamber muffler of any of the aforementioned separable geometrical shapes in terms of the [Z] matrix, subsequent to which the TL performance of these chambers is evaluated in terms of the scattering matrix [S] parameters by making use of the relations between [Z] and [S] matrices derived earlier. Interestingly, the [Z] matrix approach combined with the uniform piston-driven model is indeed ideally suited for the 3-D analytical formulation inasmuch as regardless of the number of ports, one deals with only one area discontinuity at a time, thereby making the analysis convenient for a multi-port muffler configuration with arbitrary location of ports. The TL characteristics of SISO chambers corresponding to each of the aforementioned geometries (especially the elliptical cylindrical chamber) are analyzed in detail with respect to the effect of chamber dimensions (chamber length and transverse dimensions), and relative angular and axial location of ports. Furthermore, the analysis of SIDO (i.e., single inlet and double outlet) chamber mufflers is given special consideration. In particular, we examine (1) the effect of additional outlet port (second outlet port), (2) variation in the relative angular or axial location of the additional or second outlet port (keeping the location of the inlet port and the outlet ports of the original SISO chamber to be constant) and (3) the effect of interchanging the location of the inlet and outlet ports on the TL performance of these mufflers. Thus, design guidelines are developed for the optimal location of the inlet and outlet ports keeping in mind the broadband attenuation characteristics for a single inlet and multiple outlet (SIMO) system. The non-dimensional limits up to which a flow-reversal elliptical (or circular) cylindrical end chamber having an end-inlet and end-outlet configuration is acoustically short (so that the 1-D transverse plane wave theory is applicable) and the limits beyond which it is acoustically long (so that the 1-D axial plane wave theory is applicable) is determined in terms of the ratio or equivalently, in terms of the ratio. Towards this end, two different configurations of the elliptical cylindrical chamber are considered, namely, (1) End-Offset Inlet (located along the major-axis of the ellipse) and End-Centered Outlet (2) End-Offset Inlet and End-Offset Outlet (both the ports located on the major-axis of the ellipse and at equal offset distance from the center). The former configuration is analyzed using 3-D FEA simulations (on SYSNOISE) while the 3-D analytical uniform piston-driven model is used to analyze the latter configuration. The existence of the higher order evanescent modes in the axially long reversal chamber at low frequency (before the cut-on frequency of the (1, 1) even mode or (1, 0) mode) causes a shift in the resonance peak predicted by the 1-D axial plane wave theory and 3-D analytical approach. Thus, the 1-D axial plane wave analysis is corrected by introducing appropriate end correction due to the modified or effective length of the elliptical cylindrical chamber. An empirical formulae has been developed to obtain the average non-dimensional end correction for the aforementioned configurations as functions of the expansion ratio, (i.e., ), minor-axis to major-axis ratio, (i.e., ) and the center-offset distance ratio, (i.e., ). The intermediate limits between which the chamber is neither short nor long (acoustically) has also been obtained. Furthermore, an ingenious method (Quasi 1-D approach) of combining the 1-D transverse plane wave model with the 1-D axial plane wave model using the [Z] matrix is also proposed for the end-offset inlet and end-centered outlet configuration. A 3-D analytical procedure has also been developed which also enables one to determine the end-correction in axially long 2-port flow-reversal end chamber mufflers for different geometries such as rectangular, circular and elliptical cylindrical as well as conical chambers, a priori to the computation of TL. Using this novel analytical technique, we determine the end correction for arbitrary locations on the two end ports on the end face of an axially long flow-reversal end chamber. The applicability of this method is also demonstrated for determination of the end corrections for the 2-port circular cylindrical chamber configuration without and with a pass tube, elliptical cylindrical chambers as well as rectangular and conical chambers.

This thesis endeavors towards developing various concepts employed in analysis and design of acoustic filters for varied applications ranging from combination mufflers for automobiles to complex networks of gas carrying ducts to multiply connected complex automotive silencing devices to the noise control coatings for underwater applications. A two-dimensional wave modeling approach has been proposed to evaluate sound attenuation characteristics of dissipative mufflers of finite length with/without extended inlet and outlet tubes including very large mufflers. The correctness of the method has been validated through comparison with experimental results from literature. Two other frequently used approximate schemes have been discussed briefly with reference to the available literature. These three approaches have then been weighed against each other to show the effectiveness and limitations of each one. A thorough comparison study has been performed to investigate each one’s extent of applicability. A parametric study with different parameters suggests some useful design guidelines that can be put to use while designing such mufflers. Benefits and drawbacks of reactive and dissipative mufflers have been discussed with an intention of striking a compromise between them to achieve a better transmission quality over a broad frequency range. This has been accomplished by combining these two types of mufflers/filters explicitly. These combination mufflers are analyzed using a transfer matrix based approach by extending the aforesaid concept of two-dimensional wave modeling for finite dissipative ducts. The present approach has been used to analyze axi-symmetric circular lined plenum chambers also. The effectiveness of the bulk reaction assumption to model absorptive lining is illustrated. A parametric study has been carried out to investigate the effects of different thicknesses and placements of the absorptive lining. The contributions of reflective and absorptive portion of the combination mufflerto overall attenuation performance have been investigated from the designer’s point of view A generalized algorithm has been developed for studying the plane sound wave propa- gation in a system of interconnected rigid-walled acoustic filter elements. Interconnection between various elements is represented by a connectivity matrix. Equations of volume velocity continuity and pressure equilibrium at the interconnections are generated using this connectivity matrix and are solved using the Gauss-Jordan elimination scheme to get the overall transfer matrix of the system. The algorithm used for generalized labeling of the network and computation of Transmission Loss has also been discussed. The algorithm has been applied to investigate a multiply connected automobile mufflers as a network of acoustic elements which guides the way to a specialized application discussed next. Results for some configurations have been compared with those from the FEM analysis and experiments. A parametric study with respect to some geometric variables is carried out. The acoustical similarity between apparently different networks is discussed. The approach is flexible to incorporate any other acoustic elements, provided the acoustic variables at the junctions of the element can be related by a transfer matrix a priori. Commercial automotive mufflers are often too complex to be broken into a cascade of one dimensional elements with predetermined transfer matrices. The one dimensional (1-D) scheme presented here is based on an algorithm that uses user friendly visual volume elements to generate the system equations which are then solved using a Gauss-Jordan elimination scheme to derive the overall transfer matrix of the muffler. This work attempts and succeeds to a great extent in exploiting the speed of the one dimensional analysis with the flexibility, generality and user friendliness of three dimensional analysis using geometric modeling. A code based on the developed algorithm has been employed to demonstrate the generality of the proposed method in analyzing commercial muffers by considering three very diverse classes of mufflers with different kinds of combinations of reactive, perforated and absorptive elements. Though the examples presented in the thesis are not very complex for they are meant to be just representative cases of certain classes of mufflers, yet the algorithm can handle a large domain of commercial mufflers of high degree of complexity. Results from the present algorithm have been validated through comparisons with both the analytical and the more general, three-dimensional FEM based results. The forte of the proposed method is its power to construct the system matrix consistent with the boundary conditions from the geometrical model to evaluate the four pole parameters of the entire muffer and thence its transmission loss,etc. Thus, the algorithm can be used in conjunction with the transfer matrix based muffler programs to analyze the entire exhaust system of an automobile. A different kind of acoustic filter than the above mentioned cases is then taken up for investigation. These refer to the specialized underwater acoustic filters laid as linings on submerged bodies. These kind of underwater noise control linings have three different types of objectives, namely, Echo Reduction, Transmission Reduction (TL maximization) and a combination thereof. These coatings have been shown to be behaving very differently with different shape, size and number of air channels present in the layer. In this regard, a finite element model based methodology has been followed. An hybrid type finite element based on the Pian and Tong formulation has been modified and used so as to make the computational efforts less demanding as compared to the original one. The developed finite element has been shown to be immune to the difficulties that arise due to the near incompressible characteristics of the viscoelastic materials used and the high distortion of the elements of the FE mesh. The adequacy of this formulation has been shown by comparing its results with the analytical, FE based, and experimental results. Then, this methodology has been used to analyze and generate design curves to control various geometrical parameters for proper designing of these linings. Different unit cell representations for different types of distributions of air cavities on the linings have been discussed. Four different types of layers have been introduced and analyzed to address different objectives mentioned above. They have been termed as the Anechoic layer, Insulation layer and Combination Layer of coupled and decoupled type in this thesis. The first two layers have been designed to achieve very dissimilar characteristics and the next two layers have been designed to balance their disparities. A thorough parametric study has been carried out on the geometrical parameters of all the layers to come up with the design guidelines. For anechoic and the insulation layers, different distributions have been analyzed with different unit cell geometries and their usability in specific situations has been outlined. Effect of static pressure has also been studied by using an approximate finite element method. This method can be used to simulate deep-sea testing environment.

Increased national and international travel over the lastdecades has caused an increase in the global number ofpassengers using different means of transportation. Greateffort is being directed to improving the noisy environment inthe residential community. This is to face the growing strictnoise requirements which are implemented by international noiseregulatory authorities, governments, and local airports. Thereis also a strong competition between different manufacturers tomake their products quieter. The propulsion system in anaircraft is the major source of noise during relevant flightconditions. The engine noise in a vehicle dominates the totalradiated noise at low speeds especially inside cities. Manyrecent studies on noise reduction involve the use of perforatedplates in the air and gas flow ducting connected to the engine.This thesis deals with the modelling of perforates as anabsorbent. There are many difficulties in using liners in theseapplications. The most important is that there is no largesurface area to which the linings may be applied. Equally, theenvironment in which linings have to survive is hostile.Therefore, liners have to be carefully tailored in order toachieve the most efficient attenuation. The full-scalesimulation testing, which is usually necessary to define thenoise attenuation produced by a liner installation, is bothtime-consuming and expensive. Therefore, a need for accuratemodels is a must. This thesis fills some gaps in the impedancemodelling of perforated liners. It also concentrates on thosecomplicated situations of sound propagation in ducts that weresolved earlier using Finite Element Methods. Alternateanalytical solutions to these problems are developed here,which gives more physical insight into the results. The key design parameter of perforates is the acousticimpedance. The impedance is what determines their efficiency toabsorb sound waves. A semi empirical impedance model wasdeveloped to be capable of accurately predicting the linerimpedance as a function of its physical properties and thesurrounding conditions. It was compared to all previous modelsin the literature. Nothing in the literature has been reportedon the effect of temperature on the perforate impedance,therefore a complete study was performed. A new inverseanalytical impedance measurement technique was proposed. It isbased on educing the impedance value based on the measurementof the attenuation across a lined duct section. Twoapplications were further considered: The effect of hard stripsin lined ducts on there attenuation properties; and themodelling of perforations in a complicated automotive mufflersystem. Keywords:Perforates–Liners–Acousticimpedance–Hot stream liners–Hard splices–Mufflers–Lined ducts–Collocation–Flowduct.

<p>Increased national and international travel over the lastdecades has caused an increase in the global number ofpassengers using different means of transportation. Greateffort is being directed to improving the noisy environment inthe residential community. This is to face the growing strictnoise requirements which are implemented by international noiseregulatory authorities, governments, and local airports. Thereis also a strong competition between different manufacturers tomake their products quieter. The propulsion system in anaircraft is the major source of noise during relevant flightconditions. The engine noise in a vehicle dominates the totalradiated noise at low speeds especially inside cities. Manyrecent studies on noise reduction involve the use of perforatedplates in the air and gas flow ducting connected to the engine.This thesis deals with the modelling of perforates as anabsorbent.</p><p>There are many difficulties in using liners in theseapplications. The most important is that there is no largesurface area to which the linings may be applied. Equally, theenvironment in which linings have to survive is hostile.Therefore, liners have to be carefully tailored in order toachieve the most efficient attenuation. The full-scalesimulation testing, which is usually necessary to define thenoise attenuation produced by a liner installation, is bothtime-consuming and expensive. Therefore, a need for accuratemodels is a must. This thesis fills some gaps in the impedancemodelling of perforated liners. It also concentrates on thosecomplicated situations of sound propagation in ducts that weresolved earlier using Finite Element Methods. Alternateanalytical solutions to these problems are developed here,which gives more physical insight into the results.</p><p>The key design parameter of perforates is the acousticimpedance. The impedance is what determines their efficiency toabsorb sound waves. A semi empirical impedance model wasdeveloped to be capable of accurately predicting the linerimpedance as a function of its physical properties and thesurrounding conditions. It was compared to all previous modelsin the literature. Nothing in the literature has been reportedon the effect of temperature on the perforate impedance,therefore a complete study was performed. A new inverseanalytical impedance measurement technique was proposed. It isbased on educing the impedance value based on the measurementof the attenuation across a lined duct section. Twoapplications were further considered: The effect of hard stripsin lined ducts on there attenuation properties; and themodelling of perforations in a complicated automotive mufflersystem.</p><p><b>Keywords:</b>Perforates–Liners–Acousticimpedance–Hot stream liners–Hard splices–Mufflers–Lined ducts–Collocation–Flowduct.</p>

For an engine running at a constant speed, both exhaust and intake processes are periodic in nature. This inspires the muffler designer to go for the much easier and faster frequency domain modeling. But analogous to electrical filter, as per Thevenin’s theorem, the acoustic filter or muffler requires prior knowledge of the load-independent source characteristics (acoustic pressure and internal impedance), corresponding to the open circuit voltage and internal impedance of an electrical source. Studies have shown that it is not feasible to evaluate these source characteristics making use of either the direct measurement method or the indirect evaluation method. Hence, prediction of the radiated exhaust or intake noise has been subject to trial and error. Making use of the fact that pressure perturbation in a duct is a superposition of the forward moving wave and the reflected wave, a simple hybrid approach has been proposed making use of an interrelationship between progressive wave variables of the linear acoustic theory and Riemann variables of the method of characteristics. Neglecting the effect of nonlinearities, reflection of the forward moving wave has been duly incorporated at the exhaust valve. The reflection co-efficient of the system downstream of the exhaust valve has been calculated by means of the transfer matrix method at each of the several harmonics of the engine firing frequency. This simplified approach can predict exhaust noise with or without muffler for a naturally aspirated, single cylinder engine. However, this proves to be inadequate in predicting the exhaust noise of multi-cylinder engines. Thus, estimation of radiated noise has met only limited success in this approach. Strictly speaking, unique source characteristics do not exist for an IC engine because of the associated non-linearity of the time-varying source. Yet, a designer would like to know the un-muffled noise level in order to assess the required insertion loss of a suitable muffler. As far as the analysis and design of a muffler is concerned, the linear frequency-domain analysis by means of the transfer matrix approach is most convenient and time saving. Therefore, from a practical point of view, it is very desirable to be able to evaluate source characteristics, even if grossly approximate. If somehow it were possible to parameterize the source characteristics of an engine in terms of basic engine parameters, then it would be possible to evaluate the un-muffled noise before a design is taken up as a first approximation. This aspect has been investigated in detail in this work. A finite-volume CFD (one dimensional) model has been used in conjunction with the two-load or multi-load method to evaluate the source characteristics at a point just downstream of the exhaust manifold for the exhaust system, and upstream of the air filter (dirty side) in the case of the intake system. These source characteristics have been extracted from the pressure time history calculated at that point using the electro-acoustic analogy. Systematic parametric studies have yielded approximate empirical expressions for the source characteristics of an engine in terms of the basic engine parameters like engine RPM, capacity (swept volume or displacement), air-fuel ratio, and the number of cylinders. The effect of other parameters has been found to be relatively insignificant. Unlike exhaust noise, the intake system noise of an automobile cannot be measured because of the proximity of the engine at the point of measurement. Besides, the intake side is associated with turbocharger (booster), intercooler, cooling fan, etc., which will make the measurement of the intake noise erroneous. From the noise radiation point of view, intake noise used to be considered to be a minor source of noise as compared to the exhaust noise. Therefore, very little has been done or reported on prediction of the intake noise as compared to the exhaust noise. But nowadays, with efficient exhaust mufflers, the un-muffled intake noise has become a contributing factor to the passenger compartment noise level as a luxury decisive factor. Therefore, in this investigation both the intake and the exhaust side source characteristics have been found out for the compression ignition as well as the spark ignition engines. Besides, in the case of compression ignition engines, typical turbocharged as well as naturally aspirated engines have been considered. One of the inputs to the time-domain simulation is the intake valve and exhaust valve lift histories as functions of crank angle. It is very cumbersome and time-consuming to measure and feed these data into the program. Sometimes, this data is not available or cannot be determined easily. So, a generalized formula for the valve lift has been developed by observing the valve lift curves of various engines. The maximum exhaust valve lift has been expressed as a function of the swept volume of the cylinder. This formulation is not intended for designing a cam profile; it is for the purpose of determining approximate thermodynamic quantities to help a muffler designer for an initial estimation. It has also been observed during the investigation that from the acoustic point of view, sometimes it is better to open the exhaust valve a little earlier, but very slowly and smoothly, and keep it open for a longer time. Although the exact source characteristics for an automobile engine cannot be determined precisely, yet the values of source characteristics calculated using this methodology have been shown to be reasonably good for approximate prediction of the un-muffled noise as well as insertion loss of a given muffler. The resultant empirical expressions for the source characteristics enable the potential user to make use of the frequency-domain cum-transfer matrix approach throughout; the time consuming time-domain simulation of the engine exhaust source is no longer necessary. Predictions of the un-muffled sound pressure level of automotive engines have been corroborated against measured values as the well as the full scale time-domain predictions making use of a finite-volume software.

No description available.