AGITATION/GAS-LIQUID DISPERSION. CHEM-E Fluid Flow in Process Units

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1 AGITATION/GAS-LIQUID DISPERSION CHEM-E Fluid Flow in Process Units

2 1. INTRODUCTION Agitation: Mixing: Blending: Suspension: Dispersion: Induced motion of a material in a specific way, usually in a circulatory pattern inside some sort of container. Mixing is random distribution, into and through one another, of two or more initially separate phases. Agitation of two miscible liquid phase Suspending solid particles into liquid. Dispersing a gas through the liquid in the form of small bubbles. Purpose of this work is to measure and calculate power consumption with and without aeration of a six-blade turbine and compare measurements to values from literature.. VISCOSITY Concept of viscosity and its definitions are not straightforward. In this case, only basic ideas will be described. Viscosity depicts ability of fluid to resist shear-stress (Figure 1.). flow F, u u > u 1 y Figure 1. Newtonian fluid between two plates. u 1 Velocity gradient In Figure 1, top plate has a velocity u. Because of friction, a force is needed to keep the top plate in motion. This force causes a velocity gradient (= shear stress) which is equal to force F divided by area of the plate A. F (1) A Thus fluid can not resist fully it begins to flow. Change of velocity function of distance of plates (y) is velocity gradient: du velocity gradient () dy. DEFINING THE VISCOSITY In a Newtonian fluid, the viscosity is constant in constant state. The viscosity of a Newtonian fluid although depends on temperature and pressure. For Newtonian fluid F F / A (3) A u / y

3 is constant in specific condition. So, only one (F/A) / (u/y) determination is needed to define viscosity of a Newtonian fluid. 3. POWER CONSUMPTION 3.1 DEFINING POWER CONSUMPTION Purpose of this work is to study how rotational speed, impeller type and viscosity of fluid affect to power consumption. In this work, torque caused by agitation and rotational speed of impeller are measured. The power of agitation a.k.a. power input, PB, can be obtained following: P B M F l m gl nmgl (4) where is angular velocity, M is torque, F is power, l is torque arm and g is gravitional acceleration. The power input is the power transformed to the fluid; the power which increases mechanical energy of the fluid. The power of electric motor, PE, is greater than power input and can be obtained following: E P B PE (5) MEK 3. DIMENSIONLESS NUMBERS Power number Po, agitator Reynolds number Re and Froude number Fr are needed when researching power consumption. Those dimensionless number are defined to impeller, which takes the power P and which diameter is Da and which rotational speed is n in fluid, which density and viscosity are and, by following equations: nd Re a (6) P Po (7) 3 5 n D a n Da Fr (8) g Agitator Reynolds number Re describes the type of flow near the impeller. Power number Po describes ability of impeller (Da) transport mechanical power (P) with specific rotational speed (n) to fluid (). The greater the Power number is more power ca be transport to the fluid and agitation is more efficient. Froude number Fr is significant, when surface of the fluid is not even that will say when waves occur (ships) or when there is a vortex in the agitator Reynolds number, Newtonian

4 If diameter of impeller used is around 0.1 m and if agitated fluid is water (= 1000 kg/m 3, = 1 mpas), rotational speed is: kg/ms 1 n Re (9) m kg/m 3 s D a in laminar case and kg/ms 1 n Re (10) m kg/m 3 s D a in turbulent case. Power number is not depended to agitator Reynolds number when Reynolds number is greater than 1000 (or even 100). This can be assumed as a limit for turbulent flow Power Number With larger Reynolds number (Re > or Re > 1000 or even Re > 100) the power number is independent to Reynolds number, and it is specific parameter KT to each impeller type, McCabe et al. (1993, s. 53): Po K T (3) from Eq. (17): P K T n 3 D 5 a (4)

5 3.3 EFFECT OF GAS FLOW ON POWER CONSUMPTION The following is according to McCabe, Smith, Harriot, Uinit Operations of Chemical Engineering, 001. The power consumed by a turbine impeller dispersing a gas is less than for agitating liquids only. The ratio of the power required when a gas is present to that for liquid alone depends mainly on superficial gas velocity and to some extent the impeller speed, tank size, impeller design and diameter and the properties of the liquid. The relative power Pg/P0 drops rapidly to about 0.5 or 0.6 at a superficial velocity of 10 mm/s and then decreases slowly to less than 0.3 at a velocity of 90 mm/s. The results of some earlier studies for a six-blade turbine are correlated in the figure below Power consumption in aerated turbine-agitated vessels, Pg power with gas dispersion W, P0 powerconsumption in ungassed liquid, Vs superfiscial velocity mm/s The relative power consumption can be represented as a function of a dimensionless aeration number qg N Ae 3 n D, a where qg volumetric flow of the gas, m 3 /s n rotational speed, rounds per s, 1/s Da diameter of impeller, m

6 Relative power consumption in agitated vessels versus aeration number, Pg power with gas dispersion W, P0 power consumption in ungassed liquid, NAe, aeration number 3.4 RISE OF TEMPERATURE In steady state, when flow velocities in the vessel are constant, all mechanical energy delivered changes to heat energy. P B Kuva. tasealue The power loss of mechanical energy is equal to the generation power of heat energy. Because, the total power loss of mechanical energy is equal to the input power of agitator, it can be obtained that: P P H, GEN B (5) When the fluid volume of the system is V, the rate of temperature rise is following: dt dt P H, GEN (6) V c p 4. EQUIPMENT USED IN THE LABORATORY 4.1 MIXING EQUIPMENT

7 Mixing equipment consist of mixing vessels, shaft, different impellers, and bearing-mounted and torque shaft equipped electric motor. Water is used as liquid, air as gas. 4. MEASURING APPARATUS Torque measuring apparatus is closely installed to the mixing equipment. Thermometer in needed to measure temperatures of liquids. Tacometer to measure rotational speed Frequency transformer to adjust rotational speed 5. OPERATING THE MIXER 5.1 STARTING THE WORK Fill (or drain) the mixing vessels so that height of the fluid is equal to diameter of the vessel. Measure the temperature of the water to determine viscosity and density. 5. MEASUREMENTS WITH WATER One six blade standard impeller is used in measurements. Use six (6) different rotational speeds with only water (,3 7 1/s). Then with aeration use three different aeration speeds (4,5,6 m 3 /h) and the three of the same rotational speeds as above (5,6,7 1/s). Install the impeller to the mixer. Adjust the rotational speed with the tacometer and frequency transformer. Set weights to the cage so that measuring scales are parallel. Write down length of shaft and weight (cage + weights). Repeat with every rotational speed and aeration flow. 6. REPORT 1. Introduction. Materials and methods 3. Results Including Power consumption Power number to water Power number aka parameters KT for the impeller and compared to literature data Effect of gas flow on power consumption Power consumption versus superficial velocity Relative power consumption in agitated vessels versus aeration number Rise of temperature for agitation without aeration 4. Discussion You can use excel sheet CHEM-E7160.XLS as your help. (You have to do something more than just fill the yellow cells :-D

8 7. REFERENCES Astarita, G. and Marrucci, G., Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, 1974 Keskinen, K.I., Kemian laitetekniikan taulukoita ja piirroksia, Otakustantamo, 1989 McCabe, W.L., Smith, J.C. and Harriot, P., Unit Operations of Chemical Engineering, 5th ed., McGraw-Hill, Streeter, V.L., ed., Handbook of Fluid Dynamics, McGraw-Hill, 1961

9 . APPENDICES 1. Measuring viscosity with Brookfield - viscometer 9. NOMENCLATURE A area, m Da diameter of impeller, m Dt tank diameter, m E height of impeller above vessel floor, m F force, N Fr Froude number, dimensionless g gravitational acceleration, m/s H depth of liquid in vessel, m J width of baffles, m K viscosity parameter, Pas KT parameter, dimensionless L length of impeller blades, m l shaft, m m mass, kg M torque = Fl, Nm n rotational speed, rounds per s, 1/s n viscosity parameter, dimensionless PB input power, W Pg power with gas dispersion, W Po power number witout aeration, dimensionless PE power, power of electric motor, W Re agitator Reynolds number, dimensionless rpm rotational speed, rounds per minute, 1/min S1 - S6 shape factors, dimensionless u velocity, m/s W impeller width, m y distance, m Greek letters (w) radian velocity, rad/s (tau) shear stress = F/A, N 0 boundary shear stress, Pas (eta) viscosity, Pas apparent viscosity, Pas (roo) density, kg/m 3 E efficiency of electric motor, dimensionless mechanical efficiency, dimensionless MEK

ENGG 199 Reacting Flows Spring Lecture 2b Blending of Viscous, Non-Newtonian Fluids

ENGG 199 Reacting Flows Spring 2006 Lecture 2b Blending of Viscous, Non-Newtonian Fluids Copyright 2000, A.. Etchells, R..Grenville & R.D. LaRoche All rights reserved. Re-Cap In turbulent regime, viscosity