Commentary on manuscript “Comment on ‘The one-dimensional acoustic field with arbitrary mean axial temperature gradient and mean flow’ (J. Li and A. S. Morgans, Journal of Sound and Vibration 400 (2017) 248–269)”

2017 ◽  
Vol 410 ◽  
pp. 488-494 ◽  
Author(s):  
Jingxuan Li ◽  
Aimee S. Morgans
Keyword(s):  
Temperature Gradient ◽  
Acoustic Field ◽  
Mean Flow ◽  
Axial Temperature Gradient ◽  
One Dimensional ◽  
Axial Temperature ◽  
The One

Exact Solution for One-Dimensional Acoustic Fields in Ducts With Polynomial Mean Temperature Profiles

1998 ◽  
Vol 120 (4) ◽  
pp. 965-969 ◽  
Author(s):  
B. Manoj Kumar ◽  
R. I. Sujith
Keyword(s):  
Temperature Gradient ◽  
Sound Propagation ◽  
Temperature Profiles ◽  
Mean Flow ◽  
Wave Tube ◽  
One Dimensional ◽  
Mean Temperature ◽  
Quarter Wave ◽  
The One ◽  
Dimensional Wave

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.

Controlling the axial temperature gradient in inductively heated Czochralski systems

2003 ◽  
Vol 38 (1) ◽  
pp. 42-46 ◽  
Author(s):  
S. Ganschow ◽  
P. Reiche ◽  
M. Ziem ◽  
R. Uecker
Keyword(s):  
Temperature Gradient ◽  
Axial Temperature Gradient ◽  
Axial Temperature

Amplification of energy flux of nonlinear acoustic waves in a gas-filled tube under an axial temperature gradient

2002 ◽  
Vol 456 ◽  
pp. 377-409 ◽  
Author(s):  
N. SUGIMOTO ◽  
K. TSUJIMOTO
Keyword(s):  
Boundary Layer ◽  
Temperature Gradient ◽  
Energy Flux ◽  
Acoustic Waves ◽  
Wave Equations ◽  
Main Flow ◽  
Nonlinear Wave Equations ◽  
Axial Temperature Gradient ◽  
Axial Temperature ◽  
Nonlinear Acoustic

This paper considers nonlinear acoustic waves propagating unidirectionally in a gas-filled tube under an axial temperature gradient, and examines whether the energy flux of the waves can be amplified by thermoacoustic effects. An array of Helmholtz resonators is connected to the tube axially to avoid shock formation which would otherwise give rise to nonlinear damping of the energy flux. The amplification is expected to be caused by action of the boundary layer doing reverse work, in the presence of the temperature gradient, on the acoustic main flow outside the boundary layer. By the linear theory, the velocity at the edge of the boundary layer is given in terms of the fractional derivatives of the axial velocity of the gas in the acoustic main flow. It is clearly seen how the temperature gradient controls the velocity at the edge. The velocity is almost in phase with the heat flux into the boundary layer from the wall. With effects of both the boundary layer and the array of resonators taken into account, nonlinear wave equations for unidirectional propagation in the tube are derived. Assuming a constant temperature gradient along the tube, the evolution of compression pulses is solved numerically by imposing the initial profiles of both an acoustic solitary wave and of a square pulse. It is revealed that when a positive gradient is imposed, the excess pressure decreases while the particle velocity increases and that the total energy flux can indeed be amplified if the gradient is suitable.

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