A quasi-one-dimensional theory of sound propagation in lined ducts with mean flow

2018 ◽  
Vol 419 ◽  
pp. 1-17
Author(s):  
Erkan Dokumaci
1998 ◽  
Vol 120 (4) ◽  
pp. 965-969 ◽  
Author(s):  
B. Manoj Kumar ◽  
R. I. Sujith

The purpose of this paper is to present closed form expressions for sound propagation in ducts with polynomial mean temperature profiles. It is shown that using appropriate transformations, the one-dimensional wave equation for ducts with an axial mean temperature gradient can be reduced to a standard differential equation whose form depends upon the specific mean temperature profile in the duct. The solutions are obtained in terms of Bessel and Neumann functions. The analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0.1. The developed solution is used to investigate the sound propagation in a quarter wave tube with an axial mean temperature gradient. The expressions for the four pole parameters are also presented.


1981 ◽  
Vol 104 ◽  
pp. 81-92 ◽  
Author(s):  
R. Mani

A systematic low-frequency theory is developed for the propagation of one-dimensional sound waves in a variable-area duct. The mean flow in the duct is assumed to be isentropic, compressible, and one-dimensional. Two applications are made of the theory. One concerns the reflexion coefficient from a pipe-nozzle combination, in which case comparisons are also made with some experimental data. In the second application, we consider the case of a sonic throat separating subsonic and supersonic flow. In this case, if the mean Mach number distribution in addition to being unity at the throat is also stationary at the throat, there is an axial ‘boundary-layer’ region in which the impedance of the sound wave changes from a fundamentally unsteady (reflexion-free) value at the sonic throat to the quasi-steady value away from the throat.


AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 768-773 ◽  
Author(s):  
Yusuf Ozyoruk ◽  
Lyle N. Long

1969 ◽  
Vol 24 (10) ◽  
pp. 1449-1457
Author(s):  
H. Klingenberg ◽  
F. Sardei ◽  
W. Zimmermann

Abstract In continuation of the work on interaction between shock waves and magnetic fields 1,2 the experiments reported here measured the atomic and electron densities in the interaction region by means of an interferometric and a spectroscopic method. The transient atomic density was also calculated using a one-dimensional theory based on the work of Johnson3 , but modified to give an improved physical model. The experimental results were compared with the theoretical predictions.


2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.


Author(s):  
R. H. Kim

Abstract An investigation of air flow along a 90 degree elbow-like tube is conducted to determine the velocity and temperature distributions of the flow. The tube has a sharp 90 degree turn with a radius of curvature of almost zero. The flow is assumed to be a steady two-dimensional turbulent flow satisfying the ideal gas relation. The flow will be analyzed using a finite difference technique with the K-ε turbulence model, and the algebraic stress model (ASM). The FLUENT code was used to determine the parameter distributions in the passage. There are certain conditions for which the K-ε model does not describe the fluid phenomenon properly. For these conditions, an alternative turbulence model, the ASM with or without QUICK was employed. FLUENT has these models among its features. The results are compared with the result computed by using elementary one-dimensional theory including the kinetic energy loss along the passage of the sharp 90 degree curved tube.


2021 ◽  
Vol 933 ◽  
Author(s):  
Yu Liang ◽  
Xisheng Luo

Shock-induced light-fluid-layer evolution is firstly investigated experimentally and theoretically. Specifically, three quasi-one-dimensional helium gas layers with different layer thicknesses are generated to study the wave patterns and interface motions. Six quasi-two-dimensional helium gas layers with diverse layer thicknesses and amplitude combinations are created to explore the Richtmyer–Meshkov instability of a light-fluid layer. Due to the multiple reflected shocks reverberating inside a light-fluid layer, the speeds of the two interfaces gradually converge, and the layer thickness saturates eventually. A general one-dimensional theory is adopted to describe the two interfaces’ motions and the layer thickness variations. It is found that, for the first interface, the end time of its phase reversal determines the influence of the reflected shocks on it. However, the reverberated shocks indeed lead to the second interface being more unstable. When the two interfaces are initially in phase, and the initial fluid layer is very thin, the two interfaces’ spike heads collide and stabilise the two interfaces. Linear and nonlinear models are successfully adopted by considering the interface-coupling effect and the reverberated shocks to predict the two interfaces’ perturbation growths in all regimes. The interfacial instability of a light-fluid layer is quantitatively compared with that of a heavy-fluid layer. It is concluded that the kind of waves reverberating inside a fluid layer significantly affects the fluid-layer evolution.


2000 ◽  
Author(s):  
Alex Povitsky

Abstract In this study we consider one method of parallelization of implicit numerical schemes on multiprocessor systems. Then, the parallel high-order compact numerical algorithm is applied to physics of amplification of sound waves in a non-uniform mean flow. Due to the pipelined nature of this algorithm, its efficient parallelization is based on scheduling of processors for other computational tasks while otherwise the processors stay idle. In turn, the proposed scheduling algorithm is taken as a special case of the general shop scheduling problem and possible extentions and generalizations of the proposed scheduling methodology are discussed. Numerical results are discussed in terms of baroclinic generation of wave-associated vorticity that appear to be a key process in energy transfer between a non-uniform mean flow and a propagating disturbance. The discovered phenomenon leads to significant amplification of sound waves and controls the direction of sound propagation.


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