Acoustic Wave Propagation in Water Filled Buried Plastic Pipes
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1 Acoustic Wave Popagation in Wate Filled Buied Plastic Pipes T. Gaf School of Engineeing and Achitectue Lucene Univesity Technikumstasse 1 CH-6048 How (Lucene), Switzeland
2 Motivation System Lono: Detecting leak noise leak noise spectum vs. time db Hz 18/11/014 COMSOL Confeence, Cambidge 014
3 Application Example 1: How (Switzeland) GD-FZM-150 (ed) GU-00 (blue), c = 180 m/s. Leak was pinpointed and found at X on Example : Hegiswil (Switzeland) PE 140, c = 370 m/s 18/11/014 COMSOL Confeence, Cambidge 014 3
4 Model Geomety wate, pessue acoustics soil, pessue acoustics cylindical PML pipe, linea elastic otational symmety Mapped and tiangula mesh = 0 soil nomal acceleation = 0 18/11/014 COMSOL Confeence, Cambidge 014 4
5 Govening Equations isotopic, elastic wave equation: u c 1 u c u 0 t c 1 L Lamé constants: L L L c L E 1 1 G E 1 Helmholtz equation: 1 1 p p 0 c t x 1 p p c t j t p pˆ pˆ pˆ 0 c pˆ k pˆ 0 coupling, BC at inteface: n p n and n pn 1 t u stess tenso 0 18/11/014 COMSOL Confeence, Cambidge 014 5
6 Mateial popeties Wate (0 C) Soil Ai (0 C) Polyethylene (PE100) Ductile Ion Density 1000 kg/m 3 Speed of sound c 1481 m/s Density 500 kg/m 3 Speed of sound c 1000 m/s Density 1.19 kg/m 3 Speed of sound c 343 m/s Density 950 kg/m 3 Elastic modulus E Pa Poisson s atio 0.33 Density 7050 kg/m 3 Elastic modulus E Pa Poisson s atio 0.5 Standad Dimension Ratio SDR = D = 11 o 17 T 18/11/014 COMSOL Confeence, Cambidge 014 6
7 Acoustic Wave in Wate-Pipe-Soil 50 Hz soil Plane wave in wate PML PML PML 400 Hz 400 Hz PE100 pipe, 160 SDR 11 E = 1.1 GPa, OD 160 mm S mm Acoustic wave in soil, coupled to wate wave via pipe laye. No significant adiation loss 87 m s Acoustic wave in soil adjacent to pipe 00 Hz Maximum amplitude (wate, soil) adhees to pipe laye 18/11/014 COMSOL Confeence, Cambidge 014 7
8 1 mode: v vs. f pase velocity of sound v (ms -1 ) v f, D D 40 D 90 D 160 D 50 D 400 D fequency f (Hz) v v SD R17 SD R phase velocity of sound in wate v (ms -1 ) E elative fequency f el f c d nom w-p-ai SDR 17 w-p-soil SDR 11 w w-p-ai SDR 11 univesal cuves f el f f d f c nom w 18/11/014 COMSOL Confeence, Cambidge 014 8
9 1 mode: v( f, E ) phase velocity of sound in wate column v (ms -1 ) E 0 E 0 10 E 0 5 E 0 3 E 0 E0 0.5 E E 0 10 E 0 5 E 0 3 E 0 E 0 v f, E 5 SDR 17 phase velocities in wate v (ms -1 ) f min (Hz) w-p-ai 160 SDR 11 v E w-p-ai 160 SDR 11 fm in E v 0 v v NDLN N D LN v min m in c w B d w 1 E T B w.5 GPa >. GPa 0.5 E SDR fequency f (Hz) elastic modulus of pipe wall E (GPa) 18/11/014 COMSOL Confeence, Cambidge 014 9
10 phase velocity v (m/s) FEM vs. Expeiment 600 v f, E 500 E 3.3 G Pa 400 E. G Pa Exp. E 1.1 G Pa Manufactue E = 1.1 GPa = E fequency f (Hz) 18/11/014 COMSOL Confeence, Cambidge
11 Expeimental Setup audio DAC and peamplifie Matlab high accuacy: Hz polyethylene test pipe, 11 m hydants hydo 8 ba wate pessue -phone signal souce 18/11/014 COMSOL Confeence, Cambidge
12 Eigenfequency, cut-off / cut-on nomalized eigenfequency f eig d /c w 10 1 anti cossing fel : E Bessel adial displacement Zeos: SDR 11 SDR 11 w-p-vac 160 SDR 17 & 11 and 5 SDR 17 1E elastic modulus of pipe wall E (GPa) 18/11/014 COMSOL Confeence, Cambidge û
13 Eigenmodes, Had Walls adial displacement amplitude u µ a. u. 18/11/014 COMSOL Confeence, Cambidge
14 Modes, Radial Displacement nomalized eigenfequency f eig d /c w f el 10 1 SDR 11 PE SDR 11 Fe w-p-vac 160 SDR 17 & 11 and 5 SDR E E (GPa) elastic modulus of pipe wall E (GPa) Amplitude û of adial displacement of ai o pipe paticles as a function of adius Elastic pipe wall û 18/11/014 COMSOL Confeence, Cambidge
15 Highe Wave Modes pase velocity of wate in pipe v (ms -1 ) GPa 0.5 GPa 110 GPa GPa 5.5 GPa 3.3 GPa ET1 ET1 ET 1 ET 0 1 ET 0 Lafleu et al, khz 100 1E fel f ET0 coesponds to 3.3 GPa cuve f el 18/11/014 COMSOL Confeence, Cambidge
16 Summay The popagation of leak noise in polyethylene pipes was investigated. The axisymmetic 1 mode is the majo component of the leak noise. Univesal dispesion elations of the 1 mode wee obtained. Thee exists little dispesion at low fequency. The D eigenfequencies incease in steps as a function of wall elasticity. Hydophone Hinni hydants ae equipped with hydophones. A monitoing algoithm shall locate the leak in the pipe netwok. 18/11/014 COMSOL Confeence, Cambidge
17 Thank you fo you attention! 18/11/014 COMSOL Confeence, Cambidge
18 Eigenfequency, cut-off / cut-on fel : E Bessel Zeos: nomalized eigenfequency f eig d /c w 10 1 anti cossing SDR 11 SDR 11 w-p-vac 160 SDR 17 & 11 and 5 SDR E elastic modulus of pipe wall E (GPa) 18/11/014 COMSOL Confeence, Cambidge
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