Division of Mechanical Scienceshttp://etd.iisc.ac.in/handle/2005/332021-01-18T04:58:16Z2021-01-18T04:58:16Z1-D And 3-D Analysis Of Multi-Port Muffler Configurations With Emphasis On Elliptical Cylindrical ChamberMimani, Akhileshhttp://etd.iisc.ac.in/handle/2005/22182020-05-11T10:11:21Z2013-08-28T00:00:00Z1-D And 3-D Analysis Of Multi-Port Muffler Configurations With Emphasis On Elliptical Cylindrical Chamber
Mimani, Akhilesh
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.
2013-08-28T00:00:00Z2D Compressible Viscous Flow Computations Using Acoustic Flux Vector Splitting (AFVS) SchemeRavikumar, Devakihttp://etd.iisc.ac.in/handle/2005/2772020-10-13T10:57:23Z2007-05-07T09:56:12Z2D Compressible Viscous Flow Computations Using Acoustic Flux Vector Splitting (AFVS) Scheme
Ravikumar, Devaki
The present work deals with the extension of Acoustic Flux Vector Splitting (AFVS) scheme for the Compressible Viscous flow computations. Accurate viscous flow computations require much finer grids with adequate clustering of grid points in certain regions. Viscous flow computations are performed on unstructured triangulated grids. Solving Navier-Stokes equations involves the inviscid Euler part and the viscous part. The inviscid part of the fluxes are computed using the Acoustic Flux Vector Splitting scheme and the viscous part which is diffusive in nature does not require upwinding and is taken care using a central difference type of scheme. For these computations both the cell centered and the cell vertex finite volume methods are used. Higher order accuracy on unstructured meshes is achieved using the reconstruction procedure. Test cases are chosen in such a way that the performance of the scheme can be evaluated for different range of mach numbers. We demonstrate that higher order AFVS scheme in conjunction with a suitable grid adaptation strategy produce results that compare well with other well known schemes and the experimental data. An assessment of the relative performance of the AFVS scheme with the Roe scheme is also presented.
2007-05-07T09:56:12ZA 3D High Resolution Unstructured Viscous Flow SolverMishra, Asitavhttp://etd.iisc.ac.in/handle/2005/14712020-10-09T10:01:31Z2011-10-11T00:00:00ZA 3D High Resolution Unstructured Viscous Flow Solver
Mishra, Asitav
2011-10-11T00:00:00ZA 3D Lattice Model For Fracture Of Concrete : A Multiscale ApproachMungule, Mahesh Parshuramhttp://etd.iisc.ac.in/handle/2005/22362020-05-21T05:23:15Z2013-09-10T00:00:00ZA 3D Lattice Model For Fracture Of Concrete : A Multiscale Approach
Mungule, Mahesh Parshuram
It is quite well known that fracture behavior of concrete is complex and is influenced by several factors. Apart from material properties, geometric parameters influence fracture behavior and one notable phenomenon is size effect. The existence of the size effect in concrete is well known and various attempts to model the behavior is
well documented in literature. However the approach by Bazant to describe the size
effect behavior in concrete has received considerable attention. The major advantage
of developing the size effect law for concrete is the ability to describe the fracture behavior (namely failure strength) of large size structures inaccessible to laboratory testing. The prediction of size effect is done on the basis of laboratory testing of small size geometrically similar structures. In all the models developed earlier heterogeneity of concrete has not been quantitatively simulated. Hence, the complete description considering heterogeneity in concrete is attempted using the lattice model to understand size effect behavior in concrete.
In the present study, a detailed description of the heterogeneity in concrete is at-
tempted by 3D lattice structure. Analytical treatment to gain insights to fracture
behavior is difficult and hence a numerical approach capable of handling the het-
erogeneous nature of the material is adopted. A parametric study is performed to
understand the influence of various model parameters like mesh size, failure criterion,
softening model. The conventional size effect studies for 2D geometrically similar
structures are performed and a comparison is done with experimentally observed
behavior. The variation of fracture process zone with respect to structure size is
observed as the reason for size effect. The influence of variation in properties of ag-
gregate, matrix and interface are studied to explain the deviation in pre-peak and
post-peak response. A statistical study is performed to establish the size dependence
of linear regression parameters (Bf ‘t and D0) which are used in Bazant size effect law.
An analytical framework is also proposed to substantiate the above results. Size effect
in concrete is generally attributed to the effect of depth viz. the dimension in the
plane of loads. However although the effect of thickness viz. a dimension in a plane
perpendicular to that of the loads is not considered in concrete. The same is quite
well known in fracture of metals. Therefore the variation in grading of aggregates
along with the influence of thickness on fracture behavior is analysed. To understand
the thickness effect a comparison of 2D and 3D geometrically similar structures is
performed to understand the effect of thickness on fracture parameters.
Heterogeneity is a matter of scale. A material may be homogeneous at a coarser scale while at a finer scale it is heterogeneous. Hence only way to capture the effect of the behavior at micro level on the behavior at meso level particularly in a heterogeneous material like concrete is by a multi-scale modelling. The best numerical tool for multiscale model of a heterogeneous material is lattice model. The heterogeneous
nature of concrete is not just due to the presence of aggregates but is evident right
from the granular characteristics of cement. The hydration of cement grain leads to
the development of products with varying mechanical and chemical properties. As
the micro-crack initiation and development of thermal cracking is observed at the
micron level, understanding of hydration behavior in concrete can be thought of as
a pre-requisite for complete understanding of fracture behavior. The properties of
matrix and interface observed during hydration modelling can also be used as an
input for fracture predictions at upper scale models (eg. mesoscale). This can also be used to study the coupling of scales to understand the multi-scale fracture behavior in concrete. A numerical model is hence developed to study the hydration of concrete.
Due to the existence of complex mechanisms governing the hydration behavior in con-
crete and the large number of parameters affecting its rate, the hydration of a grain
is assumed to proceed in isolation. A single particle hydration model is developed to
study the hydration of isolated grain. A shrinking core model usually used to describe
the burning of coal is adopted as a base model for analytically describing the hydra-
tion behavior. The shrinkage core model in literature is modified to be applicable to
hydration of cement matrix. The effect of particle diameter as well as changing water
concentration is incorporated into the model whereas the influence of reduction in
pore sizes as well as the effect due to embedding of particles and the constraint due
to hydration of neighbouring particles is accounted using correction factor. The effect
of temperature on rate of hydration is considered to be independent of the physical
and chemical aspects of grain. Hence a temperature function developed using Arrhe-
nius equation and activation energy is incorporated separately. The porous nature of
reaction products affects the diffusivity leading to the development of tortuous path
for flow of water through the hydrated portion. Knowing the tortuosity it is possible to obtain the diffusivity which in turn can be used as an input to the lattice model.
An algorithm is developed to determine the tortuosity in diffusion of water through
the reaction products. The tortuosity depends on the distribution of pores in the
hydrated system. This requires the use of simulation technique to generate the initial
position of voids. A simulation technique is also required to generate the initial con-
figuration of hydrating cement system. In order to generate the initial configurations
of such systems a numerical technique to generate a large scale assembly of particles
is proposed.
In the present work, parameters of Bazant's size effect law Bf’t and D0 are shown
to depend on structure size and heterogeneity. The span to thickness ratio of the structure increases fracture energy and also substantially influences the response of structure. The variation in failure load occurring due to the heterogeneous nature of the material is shown to follow a normal distribution. The fracture behavior of a material is seen to be influenced strongly by the variation in the strength of matrix and interface. The model proposed to describe the hydration process of cement can be used to determine the properties of matrix and interface. The degree of hydration as well as the embedded centre plane area can be adopted as a measure of strength of matrix and interface. The understanding of the hydration process and the wall effect around the aggregate surface can possibly improve our ability to predict the strength of interface. The material strength of the interface is certainly a necessary input to the lattice model. Infact experimental determination of interface strength is a lot more complicated than the present numerical approach. The only weakness of the present numerical approach is the assumption regarding certain empirical constants which of course may be improved further. Understanding of material behavior can be further improved if a molecular dynamics approach is adopted to describe the hydration behavior of cement. The approach via molecular dynamics is suggested as a problem for future research.
2013-09-10T00:00:00Z