Axisymmetric waves in compressible Newtonian liquids contained in rigid tubes: steady-periodic mode shapes and dispersion by the method of eigenvalleys

A major purpose of the Technical Information Center is to provide the broadest dissemination possible of information contained in DOE's Research and Development Reports to business, industry, the academic community, and federal, state and local governments.Although a small portion of this report is not reproducible, it is being made available to expedite the availability of information on the research discussed herein. ANL-85-51 ------------------------------ 11-6References--Sec. Current DOE funding for this work is from the Office of Reactor Systems, Development and Technology within the Office of Nuclear Energy.A significant amount of material presented in this report is taken from the results of various program activities sponsored by AEC, ERDA, and DOE at ANL.The author is indebted to those who supported the program at ANL throughout the years, in particular, Messrs. Nicholas Grossman and Chet Bigelow for their interest and recognition of this important and challenging subject.The author is grateful for the support received from his colleagues of the Vibration Analysis Section of the Components Technology Division of ANL, which provides the resources necessary to perform this work.The Section Manager, Dr. M. W. Wambsganss, with his unfaltering faith in me, gave me encouragement and confidence to complete this report.Grateful appreciation is expressed to Miss Joyce Stephens for her superb typing and word-processing and to Mrs. S. K. Zussman for her expert editing of the manuscript. 28 CREDITSThe author and Argonne National Laboratory gratefully acknowledge the courtesy of the organizations aLid individuals who granted permission to use illustrations and. other information in this report.The sources of this information are listed below. Figs. 6.3, 6.4 This report summarizes the flow-induced vibration of circular cylinders in quiescent fluid, axial flow, and crossf low, and applications of the analytical methods and experimental data in design evaluation of various system components consisting of circular cylinders.

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“…Given the parameters w, v, v', the dispersion relation can be solved for all the eigenvalues (Scarton and Rouleau 1973).…”

Section: -39mentioning

confidence: 99%

Flow-Induced Vibration of Circular Cylindrical Structures

Chen

1985

159

203

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“…Nayfeh (1973) recently extended Cremer's equivalent impedance concept to situations where the medium is inhomogeneous and nonuniformly moving. Paradoxically, the full problem has not yet been solved numerically, although the case of waves in a viscous fluid contained in a cylindrical tube was treated by Gerlach and Parker (1967) and very recently by Scarton and Rouleau (1973). Scarton and Rouleau, in particular, used the method of eigen-valleys to show the existence of a previously unknown family of vorticity-dominated modes.…”

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confidence: 99%

Effects of friction and heat conduction on sound propagation in ducts

Huerre

Karamcheti

1975

2nd Aeroacoustics Conference

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“…The points where this function has a minimum are indicated by black spots. A detailed description of the location of the propagation constant of different modes in the complex plane, and the dependency of these locations on different parameters (such as viscosity coefficient and frequency) is given by Scarton [41,42]. He named this approach the method of eigenvalleys, and applied it to isothermal viscous wave propagation in cylindrical prismatic tubes.…”

Section: The Methods Of Eigenvalleysmentioning

confidence: 99%

“…Building on this concept, Scarton [41] and Scarton and Rouleau [42] used numerical techniques to find the roots of Kirchhoff's dispersion equation. They obtained 'exact' solutions to the linearized Navier-Stokes equations for higher order acoustic modes, excluding thermal boundary effects.…”

Section: Numerical Solutions To Kirchhoff's Dispersion Equationmentioning

confidence: 99%

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Viscothermal wave propagation

Nijhof¹

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SummaryIn engineering practice, the simplest, most efficient model that yields the desired level of accuracy is usually the model of choice. This is particulary true if an optimization process is involved, in which case the choice of the underlying models is often a trade-off between efficiency and accuracy. It is therefore important to know not only how efficient a model is, but also how accurate.In this work, the accuracy, efficiency and range of applicability of various (approximate) models for viscothermal wave propagation are investigated in a general setting. Models for viscothermal wave propagation describe the wave behavior of fluids including viscous and thermal effects. Cases where viscothermal effects are significant generally involve small fluid domains, low frequencies, or fluid systems near resonance. Examples of practical applications of these models are, for instance, describing the behavior of in-ear hearing aids, MEMS devices, microphones, inkjet printheads and muffler systems involving acoustic resonators.Amongst the various models for viscothermal wave propagation that are considered, a prominent role is taken by the family of approximate models known as Low Reduced Frequency (or LRF) models. These are the most efficient approximate models available and they have been used extensively to model a wide variety of problems involving viscothermal wave propagation. Nevertheless, LRF models are only available for a limited number of geometries and can become inaccurate under certain conditions. A second family of models that is considered consists of exact solutions to the equations describing viscothermal wave propagation. These models, which are less efficient than the LRF models, provide reference solutions which can be used to determine the accuracy of the LRF models. A drawback of the exact models is that they are only available for a small number of geometries. Therefore a third family of models is considered, which is based on a newly developed Finite Element (or FE) approximation of the equations for viscothermal wave propagation. The main attraction of these FE models is that they can be used to model arbitrary geometries and boundary conditions. A drawback is that obtaining a solution requires much more computing power than needed for the LRF or exact models. The vi numerical stability and convergence properties of the developed FE methods are investigated to ensure that they can yield reference solutions of a desired accuracy for cases where an exact solution is not available.Using these three families of models, a number of parameter studies are carried out that yield detailed information on accuracy of the highly efficient LRF models for a range of geometries and boundary conditions. The gathered data provides a means of estimating the accuracy of simple coupled LRF models a priori.Besides the investigation into the accuracy of LRF models, two engineering applications where viscothermal wave propagation takes a prominent role are described. The first application involves the passive si...

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Axisymmetric waves in compressible Newtonian liquids contained in rigid tubes: steady-periodic mode shapes and dispersion by the method of eigenvalleys

Cited by 31 publications

References 17 publications

Flow-Induced Vibration of Circular Cylindrical Structures

Flow-Induced Vibration of Circular Cylindrical Structures

Effects of friction and heat conduction on sound propagation in ducts

Viscothermal wave propagation

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