Ultrasonic wave propagation in thermoviscous moving fluid confined by heating pipeline and flow measurement performance.

Ultrasonic wave propagation in thermoviscous fluid with pipeline shear mean flow in the presence of a temperature gradient is investigated. On the assumption of irrotational and axisymmetric wave propagation, a mathematical formulation of the convected wave equation is proposed without simplification in the manner of Zwikker and Kosten. A method based on the Fourier-Bessel theory, which is complete and orthogonal in Lebesgue space, is introduced to convert the wave equations into homogeneous algebraic equations. Then numerical calculation of the axial wavenumber is presented. In the end, wave attenuation in laminar and turbulent flow is numerically studied. Meanwhile measurement performance of an ultrasonic flow meter is parametrically analyzed.

[1]  Mats Åbom,et al.  The effect of turbulence damping on acoustic wave propagation in tubes , 2010 .

[2]  W. Beltman,et al.  Viscothermal wave propagation including acousto-elastic interaction, part I: theory , 1999 .

[3]  K. S. Peat,et al.  A First Aproximation To The Effects Of Mean Flow On Sound Propagation Through Cylindrical Capillary Tubes , 1992 .

[4]  E. Dokumaci.  AN APPROXIMATE DISPERSION EQUATION FOR SOUND WAVES IN A NARROW PIPE WITH AMBIENT GRADIENTS , 2001 .

[5]  D. Blokhintzev,et al.  The Propagation of Sound in an Inhomogeneous and Moving Medium I , 1946 .

[6]  Temperature gradients and flow-meter performance , 2001 .

[7]  Xiaoqian Chen,et al.  Thermal-Mechanical Wave Propagation in Inviscid Non-Uniform Flow Confined by Heating Pipeline and Implications for Transit-Time Flow Meter , 2013 .

[8]  M. Bruneau,et al.  Coupled equations for particle velocity and temperature variation as the fundamental formulation of linear acoustics in thermo-viscous fluids at rest , 2006 .

[9]  M Willatzen.  Ultrasonic flowmeters: temperature gradients and transducer geometry effects. , 2003, Ultrasonics.

[10]  E. Dokumaci.  Sound transmission in narrow pipes with superimposed uniform mean flow and acoustic modelling of automobile catalytic converters , 1995 .

[11]  Henry A. Scarton,et al.  ATTENUATION OF HIGHER ORDER CIRCUMFERENTIAL THERMOACOUSTIC WAVES IN VISCOUS FLUID LINES , 1996 .

[12]  Liguo Tang,et al.  Data transfer using the low frequency longitudinal guided wave in a liquid-filled pipe , 2012 .

[13]  E. Dokumaci.  ON TRANSMISSION OF SOUND IN CIRCULAR AND RECTANGULAR NARROW PIPES WITH SUPERIMPOSED MEAN FLOW , 1998 .

[14]  M. L. Sanderson,et al.  A novel ultrasonic/thermal clamp-on flowmeter for low liquid flowrates in small diameter pipes , 1996 .

[15]  On the transient solutions of three acoustic wave equations: van Wijngaarden's equation, Stokes' equation and the time-dependent diffusion equation. , 2008, The Journal of the Acoustical Society of America.

[16]  P. Nagy,et al.  Viscosity‐induced attenuation of longitudinal guided waves in fluid‐loaded rods , 1996 .

[17]  L. Elvira-Segura.  Acoustic wave dispersion in a cylindrical elastic tube filled with a viscous liquid. , 2000, Ultrasonics.

[18]  H. Tijdeman.  On the propagation of sound waves in cylindrical tubes , 1974 .

[19]  M. Willatzen.  Phase shift and attenuation characteristics of acoustic waves in a flowing gas confined by cylindrical walls , 2003 .

[20]  R. C. Weast.  CRC Handbook of Chemistry and Physics , 1973 .

[21]  Yong Zhao,et al.  Bessel-fourier theory for acoustic propagation in inviscid fluid flow confined by rigid cylindrical waveguide , 2013, 2013 American Control Conference.

[22]  H. Kwun,et al.  Dispersion of longitudinal waves propagating in liquid-filled cylindrical shells , 1999 .

[23]  M. Daniels,et al.  Ultrasound simulation of real-time temperature estimation during radiofrequency ablation using finite element models. , 2008, Ultrasonics.

[24]  Willem Martinus Beltman.  Viscothermal wave propagation, including acousto‐elastic interaction , 2004 .

[25]  K. Peat.  CONVECTED ACOUSTIC WAVE MOTION ALONG A CAPILLARY DUCT WITH AN AXIAL TEMPERATURE GRADIENT , 1997 .

[26]  Jeong-Guon Ih,et al.  A NUMERICAL STUDY ON THE PROPAGATION OF SOUND THROUGH CAPILLARY TUBES WITH MEAN FLOW , 1996 .

[27]  M. Anderson,et al.  Thermo-viscous effects on finite amplitude sound propagation in a rectangular waveguide , 1991 .

[28]  Lu Wang,et al.  Effect of temperature gradient on ultrasonic Doppler velocimetry measurement during pipe flow , 2004 .

[29]  Yong Chen,et al.  Fourier-Bessel theory on flow acoustics in inviscid shear pipeline fluid flow , 2013, Commun. Nonlinear Sci. Numer. Simul..

[30]  M. R. Stinson.  The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross- sectional shape , 1991 .

[31]  Louis Rosenhead,et al.  The Second Coefficient of Viscosity of Liquids and Gases , 1952 .

[32]  Choon-Su Park,et al.  A MODEL FOR SOUND PROPAGATION IN CAPILLARY DUCTS WITH MEAN FLOW , 1996 .

[33]  Chafik Karra,et al.  An integral equation formulation for boundary element analysis of propagation in viscothermal fluids , 1997 .

[34]  Xiaoqian Chen,et al.  Acoustic propagation in viscous fluid with uniform flow and a novel design methodology for ultrasonic flow meter. , 2013, Ultrasonics.

[35]  G. A. Watson.  A treatise on the theory of Bessel functions , 1944 .

[36]  R. J. Astley,et al.  WAVE PROPAGATION IN CATALYTIC CONVERTERS: FORMULATION OF THE PROBLEM AND FINITE ELEMENT TO SOLUTION SCHEME , 1995 .

[37]  L. N. Liebermann,et al.  The Second Viscosity of Liquids , 1949 .