Mechanical Engineering (ME)
https://etd.iisc.ac.in/handle/2005/43
2023-01-28T05:49:54Z1-D And 3-D Analysis Of Multi-Port Muffler Configurations With Emphasis On Elliptical Cylindrical Chamber
https://etd.iisc.ac.in/handle/2005/2218
1-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.
2013-08-28T00:00:00ZAcoustic Source Characterization Of The Exhaust And Intake Systems Of I.C. Engines
https://etd.iisc.ac.in/handle/2005/757
Acoustic Source Characterization Of The Exhaust And Intake Systems Of I.C. Engines
Hota, Rabindra Nath
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.
2010-07-15T00:00:00ZAdaptive Mesh Redistribution for Hyperbolic Conservation Laws
https://etd.iisc.ac.in/handle/2005/3281
Adaptive Mesh Redistribution for Hyperbolic Conservation Laws
Pathak, Harshavardhana Sunil
An adaptive mesh redistribution method for efficient and accurate simulation of multi dimensional hyperbolic conservation laws is developed. The algorithm consists of two coupled steps; evolution of the governing PDE followed by a redistribution of the computational nodes. The second step, i.e. mesh redistribution is carried out at each time step iteratively with the primary aim of adapting the grid to the computed solution in order to maximize accuracy while minimizing the computational overheads. The governing hyperbolic conservation laws, originally defined on the physical domain, are transformed on to a simplified computational domain where the position of the nodes remains independent of time. The transformed governing hyperbolic equations are recast in a strong conservative form and are solved directly on the computational domain without the need for interpolation that is typically associated with standard mesh redistribution algorithms. Several standard test cases involving numerical solution of scalar and system of hyperbolic conservation laws in one and two dimensions are presented in order to demonstrate the accuracy and computational efficiency of the proposed technique.
2018-03-19T00:00:00ZAir-Assited Atomization Strategies For High Viscosity Fuels
https://etd.iisc.ac.in/handle/2005/2506
Air-Assited Atomization Strategies For High Viscosity Fuels
Mohan, Avulapati Madan
Atomization of fuel is an important pre-requisite for efficient combustion in devices such as gas turbines, liquid propellant rocket engines, internal combustion engines and incinerators. The overall objective of the present work is to explore air-assisted atomization strategies for high viscosity fuels and liquids. Air-assisted atomization is a twin-fluid atomization method in which energy of the gas is used to assist the atomization of liquids. Broadly, three categories of air-assisted injection, i.e., effervescent, impinging jet and pre-filming air-blast are studied. Laser-based diagnostics are used to characterize the spray structure in terms of cone angle, penetration and drop size distribution. A backlit direct imaging method is used to study the macroscopic spray characteristics such as spray structure and spray cone angle while the microscopic characteristics are measured using the Particle/droplet imaging analysis (PDIA) technique.
Effervescent atomization is a technique in which a small amount of gas is injected into the liquid at high pressure in the form of bubbles. Upon injection, the two-phase mixture expands rapidly and shatters the liquid into droplets and ligaments. Effervescent spray characteristics of viscous fuels such as Jatropha and Pongamia pure plant oils and diesel are studied. Measurements are made at various gas-to-liquid ratios (GLRs) and injection pressures. A Sauter Mean Diameter (SMD) of the order of 20 µm is achieved at an injection pressure of 10 bar and GLR of 0.2 with viscous fuels. An image-based method is proposed and applied to evaluate the unsteadiness in the spray. A map indicating steady/unsteady regime of operation has been generated. An optically accessible injector tip is developed which has enabled visualization of the two-phase flow structure inside the exit orifice of the atomizer. An important contribution of the present work is the correlation of the two-phase flow regime in the orifice with the external spray structure. For viscous fuels, the spray is observed to be steady only in the annular two-phase flow regime. Unexpanded gas bubbles observed in the liquid core even at an injection pressure of 10 bar indicate that the bubbly flow regime may not be beneficial for high viscosity oils.
A novel method of external mixing twin-fluid atomization is developed. In this method, two identical liquid jets impinging at an angle are atomized using a gas jet. The effect of liquid viscosity (1 cP to 39 cP) and surface tension (22 mN/m to 72 mN/m) on this mode of atomization is studied by using water-glycerol and water-ethanol mixtures, respectively. An SMD of the order of 40 µm is achieved for a viscosity of 39 cP at a GLR of 0.13 at a liquid pressure of 8 bar and gas pressure of 5 bar. It is observed that the effect of liquid properties is minimal at high GLRs where the liquid jets are broken before the impingement as in the prompt atomization mode. Finally, a pre-filming air-blast technique is explored for transient spray applications. An SMD of 22 µm is obtained with diesel at liquid and gas pressures as low as 10 bar and 8.5 bar, respectively. With this technique, an SMD of 44 µm is achieved for Jatropha oil having a viscosity 10 times higher than that of diesel.
2016-02-25T00:00:00Z