EGG 199 acting Flows Spring 006 Lecture a Blending of Viscous, ewtonian Fluids Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche All rights reserved.
-Cap Blend time is rarely used as design criterion: Often short compared to other time-scales (e.g. filling tank). Used as measure of mixing efficiency for various impellers. 95 5.40 1/ 3 T 1/ 3 5.40 Fo 1 1/ 3 T 1/ 3 T / 3 EGG 199 Lecture a Slide Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Implications for Scale-Up Scaling-up at equal power input per unit mass and same geometry - blend time increases by X /3. Comparing impellers of equal diameter, operating with same power in same vessels - same blend time. Hydrofoil must run faster than PBT to achieve same power input - lower torque - lower capital cost. A large diameter impeller will be more energy efficient than a small one. What happens as viscosity increases and decreases? EGG 199 Lecture a Slide 3 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Transitional gime imensionless Blend Time: Constant of proportionality dependent on, / T. 1 wer umber: K Three dimensionless groups in transitional regime: 1/ 3 186 Fo 95 186 / 3 T EGG 199 Lecture a Slide 4 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Expand imensionless Groups 95 186 / 3 T Blend time is proportional to fluid viscosity. -arrange to express in terms of power input, etc. 1 / 3 T / 3 T / 3 Blend time reduces on scale-up? Implications for researchers working in lab? EGG 199 Lecture a Slide 5 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
EGG 199 Lecture a Slide 6 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved. Blend Time reduces on Scale-Up For scale-up at constant power per mass and geometry: Blend time will decrease on scale-up. 3 / 3 4 / 3 / 3 L S S L L S S L L L S S S L L S S L
Solve two correlations: Boundary between gimes 1/ 3 5 1/ 3.40 Fo 186 Fo At boundary of two regimes: 1 1/ 3 Fo 1186 6404 Values are independent of impeller type. What does this mean? EGG 199 Lecture a Slide 7 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Eddy ynolds o. efine Eddy ynolds o. EY u l EY u ( l) 1/ 3 P M T 3 3 5 3 for fixed geometry. l u 1/ 3 u l 1/ 3 1/ 3 EY IMP EGG 199 Lecture a Slide 8 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Turbulence ynolds o. alone does not account for change in mixing regime. At boundary: Hydrofoil: = 10000 At boundary: Rushton: = 3000 At equal ynolds o. (i.e. equal speed and diameter) a Rushton inputs 15 x the power of a hydrofoil. Generates more intense turbulence. Equal power input - equal turbulence - equal blend time. EGG 199 Lecture a Slide 9 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Experimental set-up: Blend Time versus sition Three probes in regions of different mixing intensity: 1 - Under Impeller - Between Shaft and Wall 3 - Behind Baffle EGG 199 Lecture a Slide 10 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
sults for Pitched Blade Turbine - Individual EGG 199 Lecture a Slide 11 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
sults for Pitched Blade Turbine - RMS EGG 199 Lecture a Slide 1 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Conclusions In Turbulent gime: 1 3 In Transitional gime: 1 3 egree of deviation increases as ynolds number decreases. Blend Time for whole vessel is weighted by longest individual time. Impeller region is turbulent (Blend time and wer o.). Viscosity damps intensity of turbulence away from impeller. EGG 199 Lecture a Slide 13 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Laminar gime Boundary between transitional and laminar regimes: 00 : -1 50 : Blending performance becomes laminar before wer o. starts to rise. Blend time for vessel governed by slowest mixing region. Slow near wall, behind baffles, at surface. Turbulence still being generated near impeller. -1 May be possible to use turbine at lower ynolds os: epends on process requirements (e.g. cycle time). EGG 199 Lecture a Slide 14 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Impeller Selection for Laminar Blending Blending vessel contents relies on convection of fluid from impeller zone to wall and back again. As viscosity rises, pumping capability of turbines reduces. eed positive-displacement impeller. Close-clearance - 0.90 < / T < 0.98. Anchors and Helical Ribbons. Use Helical Ribbons. EGG 199 Lecture a Slide 15 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
wer Consumption Equation for predicting power consumption: P 3 5 In the laminar regime: K P K P Combining: P K P 3 For turbine impellers: 50 < K P < 70. For Anchors: K P = 5. For Helical Ribbons: K P = 350. EGG 199 Lecture a Slide 16 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Single or ual Flight. Helical Ribbons May have Central Auger. Ribbon width - 8-10 % of diameter. Pitch = Height of one turn. Clearance = Gap between impeller and vessel wall. EGG 199 Lecture a Slide 17 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Anchors versus Ribbons Helical Ribbon: Produce 3- flow pattern. Good mixing. Higher power. Anchors: Produce strong tangential flow. Little axial flow. or overall mixing. EGG 199 Lecture a Slide 18 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Construction For turbine impellers, maximum diameter may be 70 % of vessel diameter: Large clearance between tip of blade and baffle (or wall). For anchors / ribbons, maximum diameter may be 98 % of vessel diameter: Small clearance between tip of blade and wall. Engineered equipment is specified with tolerances : i.e. diameter +/- allowance for workmanship. Includes roundness of vessel. Take care than maximum O of impeller is less than minimum I of vessel!! EGG 199 Lecture a Slide 19 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Prediction of wer Consumption From Shamlou & Edwards (1985): id their own experiments and searched literature for more data. Correlated all data with: K P 150 h p n b c w / 3 h is impeller height; is impeller diameter; n b is number of blades; p is impeller pitch; c is clearance from wall; w is ribbon width. EGG 199 Lecture a Slide 0 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.
Problem Correlations for blend time and power consumption exist for ewtonian fluids. Transitional regime: Laminar regime: Blend time proportional to viscosity. wer proportional to viscosity. All(?) viscous fluids used in industry are non-ewtonian. How should rules relating to ewtonian fluids be modified for non-ewtonian ones? EGG 199 Lecture a Slide 1 Copyright 000, A.W. Etchells, R.K.Grenville & R.. LaRoche. All rights reserved.