A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

1987 ◽  
Vol 116 (1) ◽  
pp. 71-88 ◽  
Author(s):  
M.L. Munjal
Keyword(s):  
Numerical Method ◽  
Dimensional Analysis ◽  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Expansion Chamber ◽  
Stationary Medium ◽  
Simple Expansion

scholarly journals Reduction of Discrete-Frequency Fan Noise Using Slitlike Expansion Chambers

2003 ◽  
Vol 9 (4) ◽  
pp. 239-246 ◽  
Author(s):  
Akira Sadamoto ◽  
Yoshinori Murakami
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Side Branch ◽  
Rotor Blades ◽  
Expansion Chamber ◽  
Fan Noise ◽  
Circular Duct ◽  
Discrete Frequency ◽  
Rotor Stator Interaction ◽  
Simple Expansion

As is generally known, discrete-frequency noises are radiated from fans due to rotor-stator interaction. Their fundamental frequency is the blade-passage frequency, which is determined by the number of rotor blades and their rotating speeds. To reduce such noises, several types of silencers have been designed. Among them, the authors noted a slitlike expansion chamber (hereafter referred to asslit, for simplicity) and have studied its performance. A slit is a simple expansion chamber with a very short axial length that is placed in a duct. A slit with a circular cross-section that is concentric with a circular duct may be studied using the same interpretation as is used for a side-branch resonator muffler (closed-end tube connected to a duct); that is, the resonant frequency of a slit depends on its depth (with an open-end correction). It is expected, hence, that a slit might be applicable as a simple and axially compact silencer that is effective on discrete-frequency noises. In this article, the properties of a slit are introduced, and the applicability of a slit to actual rotating machinery is described using experimental data.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

scholarly journals Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Daniel Omondi Onyango ◽  
Robert Kinyua ◽  
Abel Nyakundi Mayaka
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Plane Wave ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
The Other ◽  
Expansion Chamber ◽  
Central Tube ◽  
Simple Expansion ◽  
Plane Wave Propagation

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

scholarly journals Numerical simulation of minor losses coefficient on the example of elbows

2018 ◽  
Vol 180 ◽  
pp. 02093
Author(s):  
Smyk Emil ◽  
Mrozik Dariusz ◽  
Olszewski Łukasz ◽  
Peszyński Kazimierz
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Numerical Method ◽  
Cross Section ◽  
Analytical Methods ◽  
Circular Cross Section ◽  
Experimental Methods ◽  
Loss Coefficient ◽  
Complicated Problem ◽  
Minor Losses

Determining of minor losses coefficient is very complicated problem. Analytical methods are often very difficult and experimental methods are very expensive and time-consuming. Consequently, the use of numerical methods seems to be a good solution, but there are no publications describing this issue. Therefore, the paper is describing the numerical method of determining the minor loss coefficient ξ on the example of elbows with circular cross-section.

Geometry Effects in Eulerian/Granular Simulation of a Turbulent FCC Riser with a (kg-?g)-KTGF Model

2010 ◽  
Vol 8 (1) ◽  
Author(s):  
Hamid Reza Nazif ◽  
Hassan Basirat Tabrizi ◽  
Farhad A Farhadpour
Keyword(s):  
Cross Section ◽  
Large Scale ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Good Prediction ◽  
Model Predictions ◽  
Secondary Circulations ◽  
Sharp Corners ◽  
Granular Simulation

Three-dimensional, transient turbulent particulate flow in an FCC riser is modeled using an Eulerian/Granular approach. The turbulence in the gas phase is described by a modified realizable (kg-?g) closure model and the kinetic theory of granular flow (KTGF) is employed for the particulate phase. Separate simulations are conducted for a rectangular and a cylindrical riser with similar dimensions. The model predictions are validated against experimental data of Sommerfeld et al (2002) and also compared with the previously reported LES-KTGF simulations of Hansen et al (2003) for the rectangular riser. The (kg-?g)-KTGF model does not perform as well as the LES-KTGF model for the riser with a rectangular cross section. This is because, unlike the more elaborate LES-KTGF model, the simpler (kg-?g)-KTGF model cannot capture the large scale secondary circulations induced by anisotropic turbulence at the corners of the rectangular riser. In the cylindrical geometry, however, the (kg-?g)-KTGF model gives good prediction of the data and is a viable alternative to the more complex LES-KTGF model. This is not surprising as the circulations in the riser with a circular cross section are due to the curvature of the walls and not due to the presence of sharp corners.

scholarly journals Computational Study of Zigzag Spacer Design with Elliptical Cross-Section Filaments

2020 ◽  
Vol 307 ◽  
pp. 01047
Author(s):  
Gohar Shoukat ◽  
Farhan Ellahi ◽  
Muhammad Sajid ◽  
Emad Uddin
Keyword(s):  
Mass Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Computational Study ◽  
Flow Direction ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Two Dimensional ◽  
Permeate Flux ◽  
Elliptical Cross

The large energy consumption of membrane desalination process has encouraged researchers to explore different spacer designs using Computational Fluid Dynamics (CFD) for maximizing permeate per unit of energy consumed. In previous studies of zigzag spacer designs, the filaments are modeled as circular cross sections in a two-dimensional geometry under the assumption that the flow is oriented normal to the filaments. In this work, we consider the 45° orientation of the flow towards the three-dimensional zigzag spacer unit, which projects the circular cross section of the filament as elliptical in a simplified two-dimensional domain. OpenFOAM was used to simulate the mass transfer enhancement in a reverse-osmosis desalination unit employing spiral wound membranes lined with zigzag spacer filaments. Properties that impact the concentration polarization and hence permeate flux were analyzed in the domain with elliptical filaments as well as a domain with circular filaments to draw suitable comparisons. The range of variation in characteristic parameters across the domain between the two different configurations is determined. It was concluded that ignoring the elliptical projection of circular filaments to the flow direction, can introduce significant margin of error in the estimation of mass transfer coefficient.

Axially Symmetric Waves in Elastic Rods

1960 ◽  
Vol 27 (1) ◽  
pp. 145-151 ◽  
Author(s):  
R. D. Mindlin ◽  
H. D. McNiven
Keyword(s):  
Cross Section ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Rods ◽  
Axially Symmetric ◽  
Elastic Rod ◽  
One Dimensional ◽  
Axial Shear ◽  
Wave Numbers ◽  
Complex Wave

A system of approximate, one-dimensional equations is derived for axially symmetric motions of an elastic rod of circular cross section. The equations take into account the coupling between longitudinal, axial shear, and radial modes. The spectrum of frequencies for real, imaginary, and complex wave numbers in an infinite rod is explored in detail and compared with the analogous solution of the three-dimensional equations.

scholarly journals Numerical simulation of cavitating two-phase gas-liquid three-dimensional flow in a duct of varying cross-section based on homogenous mixture model

2006 ◽  
Vol 28 (3) ◽  
pp. 134-144
Author(s):  
Nguyen The Duc
Keyword(s):  
Numerical Simulation ◽  
Numerical Method ◽  
Cross Section ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Curvilinear Grid

The paper presents a numerical method to simulate two-phase turbulent cavitating flows in ducts of varying cross-section usually faced in engineering. The method is based on solution of two-phase Reynolds-averaged Navier-Stokes equations of two-phase mixture. The numerical method uses artificial compressibility algorithm extended to unsteady flows with dual-time technique. The discreted method employs an implicit, characteristic-based upwind differencing scheme in the curvilinear grid systems. Numerical simulation of an unsteady three-dimensional two-phase cavitating flow in a duct of varying cross-section with available experiment was performed. The unsteady important characteristics of the unsteady flow can be observed in results of numerical simulation. Comparison of predicted results with experimental data for time-averaged velocity and phase fraction are provided.

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