Noise reduction with perforated three-duct muffler components

This paper describes the authors’ distributed parameter approach for derivation of closed-form expressions for the four-pole parameters of the perforated three-duct muffler components. In this method, three simultaneous second-order partial differential equations are first reduced to a set of six first-order ordinary differential equations. These equations are then uncoupled by means of a modal matrix. The resulting 6 × 6 matrix is reduced to the 2 × 2 transfer matrix using the relevant boundary conditions. This is combined with transfer matrices of other elements (upstream and downstream of this perforated element) to predict muffler performance like noise reduction, which is also measured. The correlation between experimental and theoretical values of noise reduction is shown to be satisfactory.

Homogenization of eigenvalue problems in perforated domains

In this paper, we treat some eigenvalue problems in periodically perforated domains and study the asymptotic behaviour of the eigenvalues and the eigenvectors when the number of holes in the domain increases to infinity Using the method of asymptotic expansion, we give explicit formula for the homogenized coefficients and expansion for eigenvalues and eigenvectors. If we denote by ε the size of each hole in the domain, then we obtain the following aysmptotic expansion for the eigenvalues: Dirichlet: λε = ε−2 λ + λ0 +O (ε), Stekloff: λε = ελ1 +O (ε2), Neumann: λε = λ0 + ελ1 +O (ε2).Using the method of energy, we prove a theorem of convergence in each case considered here. We briefly study correctors in the case of Neumann eigenvalue problem.

Rack Level Modeling of Air Flow Through Perforated Tile in a Data Center

Effective air flow distribution through perforated tiles is required to efficiently cool servers in a raised floor data center. We present detailed computational fluid dynamics (CFD) modeling of air flow through a perforated tile and its entrance to the adjacent server rack. The realistic geometrical details of the perforated tile, as well as of the rack are included in the model. Generally, models for air flow through perforated tiles specify a step pressure loss across the tile surface, or porous jump model based on the tile porosity. An improvement to this includes a momentum source specification above the tile to simulate the acceleration of the air flow through the pores, or body force model. In both of these models, geometrical details of tile such as pore locations and shapes are not included. More details increase the grid size as well as the computational time. However, the grid refinement can be controlled to achieve balance between the accuracy and computational time. We compared the results from CFD using geometrical resolution with the porous jump and body force model solution as well as with the measured flow field using particle image velocimetry (PIV) experiments. We observe that including tile geometrical details gives better results as compared to elimination of tile geometrical details and specifying physical models across and above the tile surface. A modification to the body force model is also suggested and improved results were achieved.

Detonation-driven-shock wave interactions with perforated plates

The study of detonations and their interactions is vital for the understanding of the high-speed flow physics involved and the ultimate goal of controlling their detrimental effects. However, producing safe and repeatable detonations within the laboratory can be quite challenging, leading to the use of computational studies which ultimately require experimental data for their validation. The objective of this study is to examine the induced flow field from the interaction of a shock front and accompanying products of combustion, produced from the detonation taking place within a non-electrical tube lined with explosive material, with porous plates with varying porosities, 0.7-9.7%. State of the art high-speed schlieren photography alongside high-resolution pressure measurements is used to visualise the induced flow field and examine the attenuation effects which occur at different porosities. The detonation tube is placed at different distances from the plates' surface, 0-30 mm, and the pressure at the rear of the plate is recorded and compared. The results indicate that depending on the level of porosity and the Mach number of the precursor shock front secondary reflected and transmitted shock waves are formed through the coalescence of compression waves. With reduced porosity, the plates act almost as a solid surface, therefore the shock propagates faster along its surface.

Sound radiation from a perforated panel set in a baffle with a different perforation ratio

A finite flexible perforated panel set in a differently perforated rigid baffle is considered. The radiation efficiency from such a panel is derived using a 2-D wavenumber domain formulation. This generalization is later used to represent a more practical case of a perforated panel fixed in an unperforated baffle. The perforations are in the form of an array of uniformly distributed circular holes. A complex impedance model for the holes available in the literature is used. An averaged fluid particle velocity is derived using the continuity equation and the surface pressure is derived using an appropriate momentum equation. The discontinuity in the perforate impedance (due to different hole dimensions or perforation ratio) at the panel-baffle interface is carefully taken into account. It is found that there exists a `coupling' of different wavenumbers of the spatially mean fluid particle velocity field. The change in the resonance frequencies and the modeshapes of the panel due to the perforations is taken into account using the Receptance method. Analytical expressions for the radiated power and radiation efficiency are derived in an integral form and numerical results are presented. Several comparisons are made to understand the radiation efficiency curves. Since both the resistive and reactive components of the hole impedance are taken into account, the model is directly applicable to micro-perforated panels also. (C) 2016 Elsevier Ltd. All rights reserved.

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples.

Bismuth tungsten-oxide bronzes - a study of intergrowth phases and related aspects

Reaction of bismuth metal with WO$_3$ in the absence of oxygen yields interesting bronze-like phases. From analytical electron microscopy and X-ray photoelectron spectroscopy, the product phases are found to have the general composition Bi$_x$ WO$_3$ with bismuth in the 3+ state. Structural investigations made with high resolution electron micrscopy and cognate techniques reveal that when x < 0.02, a perovskite bronze is formed. When x $\geqslant$ 0.02, however, intergrowth tungsten bronzes (i.t.b.) containing varying widths of the WO$_3$ slab are formed, the lattice periodicity being in the range 2.3-5.1 nm in a direction perpendicular to the WO$_3$ slabs. Image-matching studies indicate that the bismuth atoms are in the tunnels of the hexagonal tungsten bronze (h.t.b.) strips and the h.t.b. strips always remain one-tunnel wide. Annealed samples show a satellite structure around the superlattice spots in the electron diffraction patterns, possibly owing to ordering of the bismuth atoms in the tunnels. The i.t.b. phases show recurrent intergrowths extending up to 100 nm in several crystals. The periodicity varies considerably within the same crystal wherever there is disordered intergrowth, but unit cell dimensions can be assigned from X-ray and electron diffraction patterns. The maximum value of x in the i.t.b. phases is ca. 0.07 and there is no evidence for the i.t.b. phase progressively giving way to the h.t.b. phase with increase in x. Hexagonal tungsten bronzes that contain bismuth with x up to 0.02 can be formed by starting from hexagonal WO$_3$, but the h.t.b. phase seems to be metastable. Optical, magnetic and electron transport properties of the i.t.b. phases have been measured and it appears that the electrons become itinerant when x > 0.05.

A study on bullock carts. Part 2. Experimental study of forces in a bullock cart

A strain gauge load cell with separate bridges for measurement of the pull and the bending moment in the plane containing the net neck load and pull was developed and fixed in the longitudinal member of an experimental cart. A cart fitted first with pneumatic wheels and then with steel-rimmed wooden wheels was tested on three terrains—tar road, mud road and grassy terrain. Pull vs time and moment vs time records were obtained in each test and analysed. It is found that the bullocks pull the cart rather discontinuously at the low velocities at which these carts normally operate. On the tar road and the grassy terrain, the mean static coefficient of friction is significantly higher for the cart with steelrimmed wooden wheels. The dynamic frictional resistance of the terrain for the cart with steel-rimmed wooden wheels is lower than for the cart with pneumatic wheels so long as the wheels do not dig or sink into the terrain. The fluctuation in the neck load is lower in the cart fitted with pneumatic wheels. Also, the ground-induced low-amplitude high-frequency vibratory load content in the neck load is lower in the cart with pneumatic wheels.

Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.

Note on the stability of parallel magnetic fields

The stability characteristics of parallel magnetic fields when fluid motions are present along the lines of force is studied. The stability criterion for both symmetric (m=0) and asymmetric (m=1) modes are discussed and the results obtained by Trehan and Singh (1978) are amended in the present study. The results obtained for the cylindrical geometry are shown to play an important role forka<4, wherek is the wave number,a is the radius of the cylinder, compared to the results obtained by Geronicolas (1977) for the slab geometry.

Intergrowth tungsten bronzes of bismuth

High resolution electron microscopic studies show that bismuth forms intergrowth tungsten bronzes containing varying widths of the WO3 slab and one-tunnel wide HTB strips.

Flexural Strength of Modified Square Footings

The ultimate flexural strength behavior of isolated square tapered and beam-slab reinforced footings are presented. Yield line solutions are developed for generalized contact pressure distributions and the influence of taper, beam size, fillet size, negative moment capacity, and contact pressure distribution on the collapse load is brought out. In beam-slab footings the optimum relative beam capacity required to make the beam rigid is indicated. Results of experimental investigations on footings resting on sand reveal that tapered (with isotropic as well as with alternative reinforcement patterns) and beam-slab footings exhibit superior structural behavior in terms of normalized first crack load, collapse load, relative rigidity, relative efficiency, and failure mechanism.

Melting of an Anchored Bilayer: Phase Transitions in the Organic-Inorganic Hybrid Pervoskite (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 (n=11, 13, 15, 17)

The conformation, organization, and phase transitions of alkyl chains in organic-inorganic hybrids based on the double pervoskite-slab lead iodides, (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 (n = 11, 13, 15, 17) have been investigated by X-ray diffraction, calorimetry, and infrared vibrational spectroscopy. In these hybrid solids, double pervoskite (CH3NH3)Pb2I7 slabs are interleaved with alkyl ammonium chains with the anchored alkyl chains arranged as tilted bilayers and adopting a planar all-trans conformation at room temperature. The (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 compounds exhibit a single reversible phase transition above room temperature with the associated enthalpy change varying linearly with alkyl chain length. This transition corresponds to the melting in two-dimensions of the alkyl chains of the anchored bilayer and is characterized by increased conformational disorder of the methylene units of the chain and loss of tilt angle coherence leading to an increase in the interslab spacing. By monitoring features in the infrared spectra that are characteristic of the global conformation of the alkyl chains, a quantitative relation between conformational disorder and melting of the anchored bilayer is established. It is found that, irrespective of the alkyl chain length, melting occurs when at least 60% of the chains in the anchored bilayer of (CH3NH3)(CH3(CH2)(n)NH3)(2)Pb2I7 have one or more gauche defects. This concentration is determined by the underlying lattice to which the alkyl chains are anchored.

Limit analysis of rectangular R.C. slabs on ground

A method is presented for obtaining lower bound on the carrying capacity of reinforced concrete foundation slab-structures subject to non-uniform contact pressure distributions. Functional approach suggested by Vallance for simply supported square slabs subject to uniform pressure distribution has been extended to simply supported rectangular slabs subject to symmetrical non-uniform pressure distributions. Radial solutions, ideally suited for rotationally symmetric problems, are shown to be adoptable for regular polygonal slabs subject to contact pressure paraboloids with constant edge pressures. The functional approach has been shown to be well suited even when the pressure is varying along the edges.