" .. -.. • • -- ---- ... --. .; -. • .r • -./ . • , ' . PULSATING FLOW OF NON-NEWTONIAN FLUIDS IN PIPES . . • ..,. \ - bi ..... _.' @ .. E.I'..SA YEO, B.Sc.(Eng.), M.Sc. (Eng.) .... '. (0 the ScQ.ool of Graduate Studies \' in Partial Fulfillment of the Req!1irements fop the I§egree • • '. -, A Thesis Doctor of Philosophy (0 \ " ' . .' • J - • McMdSte'r - Februaryl984 • , .
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Pulsating Flow of Non-Newtonian Fluids in Pipes · PDF filePULSATING. FLOW OF NON-NEWTONIANFLUIDS IN PIPES. ... 4.4.2 DeterminationofFlow Patterns ... LIST OF FIGC-RES
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PULSATING FLOW OF NON-NEWTONIAN FLUIDS IN PIPES. .•
2.11 Increase in flowrte at different pulsing frequencies for visco-elastic fluid. From Walters and Townsend [21. 31
2.12 Pressure grad'ient vs. now velocity for heterogeneous slurries. 36•
2.13 E"ormation of particle-free laye,' in pulsating llow ofheterogeneous slurrie.s. 36
2.1-1 Ratio of hydraulic energy of pulsating flow to that of steady llowas a function of pulsing frequency for sand-water ;lurries.E"rom Round [51: 38
", ,..... '.~
U toy relation for a generalized Bingham fluid. ·-13
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4.2
4.3
4.4
4.5
5.1
5.2
5.3
5.4
Flow ofa Bingham fluid in a circular pipe.
Solution ofequation (4.12) - for n =0..5, 1.0, 1.5 and 2.0.
Comparison ofexperimental data for laminar flow with equation,(4.12). Top bracketed data from ref. [91; botto/" bracketed datafrom ~ef. [861. , •
Finite difference network.
Schematic diagram ofexperimental pipe loop.· .
Schematic dia"gram of pulse generating mechanism.
Shear stress vs. shear rate for bentonite clay·water suspensiortsat different solids weight concentrations (obtained by Haakeviscometer).
· Coal particle size distribution.
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47
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62
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5.5
5.6
5.7
Photomicrograph ofa 'coal sample.\ ..
Pressure transducer calibration curve.
•Flowmeter caiibration curve.
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79..80
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6.1
6.1cont.
6.2
)6.3
Theoretical predictions ofv~locity profiles for p'llsating !Jows of(a) Newtonian,(b) power law n =0.7,(c) i<jeal Bingham tJtw = 0.32.Results at <= 5.0 and. = I.
(d) generalized Bingham n = 0.7 and tJtw =0.32,(e) ideal Bingham tJtw = 0.44,(0 generalized Bingham n =0.7 and tJtw =0.44.Results at <= 5.0 and. = I.
· Theoretical predictionS';;f'velocity profiles for pulsating flo.wsofan ideal Bingham fluid at different frequencies.
. .,:{a) <=. 4.0, '-,(b) <=7.0,(c) <=; 10Results at tJtw =0.44 and,. = I.
•Theoretical predictions of velocity profiles for pulsating flowsof a generalized Bingham fluid at different frequencies.(a) l; =4.0,· ((b) l; = 7.0,(c) l; = 10Results at n = 0.7, toltw = 0.44 and·. = I.
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89
>.....90
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6.4 Theoretical predictions of velocity profiles for pulsating flowsofa generalized Bingham fluid at difTerent amplitudes.
______ (a) c = 0.5,(b) c = L,(c) c = 1.5,(t» c = 2.Results at n = 0.7, tohw = 0.32 and ~ = 7.
Theoretical predictions ofdimensionless pulsating flowrates S vs.dimensionless frequency ~ (c = 1).
Theoretical predictions.ofdimensionless pulsating hydraulicpower requirements E vs. dimensionless frequency ~ (c = 1).
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94
96
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6.9
6.10
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6.11
7.1
7.2
7.3
7.4
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Theoretical predictions of phase angle 4> vs. dimensionlessfrequency ~ (c ~ 1). f
The~etical predictions of velocity profiles for start-up flowfor a~ewtonian (middle) and two-power law fluids n = 0.7(bottom) and 1:4 (top). .
.Theoreticalf:rdictions of velocity profiles for start-up flowfor an ideal ngham (top) and a generalized Bingham fluid(bottom), to t'w = 0.32, n.= 0.7.
Theoretical predictions of velocity profiles for start-UIl11owfor an ideal Bingham ltop) and a generalized Bingham fluid(bottom), tohw = 0.44, n =0.7.
Velocity development as a function ofdimensi"nless time Tob' the pipe centerline for start-up flcw..".[,Newtonianand non-Newtonian fluids. .~
Output signals from the pressure transducer at difTerentpulsing frequencies (A = 52.1 mm)
•~ H'ydraulic power ratio of pulsating to steady flow vs. pulsingfrequency. Experimental results for bentonite c1'l,Y-water _suspension lCw =2.97%).
Hydraulic power ratio of pulsatil)g to steady flow vs.dimensionless velocity amplitude. Experimentall'esults for bentoniteclay-water suspension lCw = 2.97%1.
Hydraulic power ratio of pulsating to stcady flow vs. pulsingfrequency. Experimental results for bentonite clay-watersuspension lC w = 4.47%).
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100
101
102
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104
106
109
110
111
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7.5 Hydraulic power ratio of pulsating to steady flow Ys.dimensionless velocity amplitude. Experimental results forbentonite clay-water suspension (Cw = 4.47%). '112
7.6 Hydraulic power ratio ofpulsating to steady flow vs. pulsingfrequency. Experimental results for bentonite clay-watersuspension (Cw = 7.63%). 113
7.7 Hydraulic power ratio of pulsating to steady flow vs.dimensionless velocity amplitude. Experimental re""lts forbentonite clay-water suspens~on(Cw = 7.63%). 114
7.8 Hydraulic power ratio of pulsating to steady flow vs. pulsingfrequency. Experimental results for bentonite clay-watersuspension (C w = 11.2%). 115
./ 7.9 Hydraulic power ratio of pulsating to steady flow vs.dimensionless velocity amplitude. Experimental results forbentonite clay-water suspension (Cw = 11:2%). 116
I • : ':" oJ'
7.10 Hydraulic power ratio of pulsating·to steady. flow vs. pulsingfrequency. Experimental results for coal-water slurry(Cw = 5.34%). 124
7:-1.1 Hydraulic power ratio of pulsating to steady flow vs. pulsingfre.quency. Experimental results for coal-water sl urry(Cw = 8.9%). 125
7.12 Hydraulic power ratio of pulsating to steady flow vs. pulsingfrequency. Experimental results for coa!-water slurry(Cw = 14.25%). 1~6
7.13 . Hydraulic power ratio of pulsating to steady flow vs. pulsing..frequency.,Experimental results for coal-water slurry •(Cw = 19.59%). • ·127
'~4 Hydraulic power ratio of pulsating to steady flow vs. pulsingfrequency. E"perimental results for coal-water slurry(Cw = 24.93%). 128
7.15 Hydraulic power ratio ~fpulsatingto steady flow vs. pulsing
7.16 Hydraulic power ratio of pulsating to steady flo\~ vs. pulsingfrequency. Experimental results forcoal'water slurry ,.,(C w = 37.5%). 130
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7.17
7.18
·7.19
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Hydraulic power ratio ofpuf'jating to steady flow vs. pulsingfrequency, Experimental results for coal-water slurry(Cw =44.64%).
Hydraulic power ratio of pulsating to steady fl~w vs. pulsingfrequency. Experimental results for coal-water slurry(C w = 53.7%). . \.
Hydraulic power ratio of pulsating to steady flow vs. solidsweight concentration. Experimental results for coal-water slurry.Experimenpalesults at pulsing a'!lplitude A =34.6 mm, averageflow velocit = 1.63 mls and pulsing frequency A = 0.3 Hz.,