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Separationsteknik/ Separation technology 424105

9. Mixning, omrörning och blandning/ Mixing, stirring and blending

Ron ZevenhovenÅbo Akademi University

Thermal and Flow Engineering Laboratory/ Värme- och strömningsteknik

tel. 3223 ; ron.zevenhoven@abo.fi

9.1 Overview, Flow types

oktober 2017

Mixing, stirring & blending /1

The purpose of equipment for mixing, stirring or blending is to remove or reduce non-uniformities and gradients in composition, temperature, particle size, ...

The result is – (Better) dispersion of other phases in a bulk phase,

homogenising miscible (fluid) mixtures; for example L/L, L/S, S/S, G/L, G/L/S

– Improved heat transfer to walls or heat exchangesurfaces

– Improved mass transfer, especially for immiscibleliquids, G/L and L/S dispersions, and to support chemical reaction

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oktober 2017

Mixing, stirring & blending /2 A mixture can be considered homogeneous if at each point

the concentration is equal to an average value Inhomogeneities are characterised by 1) scale = size of

unmixed fluid elements and 2) intensity = concentration differences between unmixed regions. With chemistry, this leads to side-reactions (→ by-products).

Miscible liquids mixing can be achieved in turbulent pipe flow after ~ 50 diameters (plus valves etc.)

Most mixtures will show tendency for segregation and an energy input is needed is to get the correct balance between mixing and segregation.

Liquid mixing is usually done in a vessel with a rotating impeller.

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oktober 2017

Impellers for mixed vessels Impellers have the task

to create turbulent flow in axial, radial and tangential directions.

Most important types, giving different types of flow patterns:– a. Flat-blade paddle – b. Pitch-blade paddle– c. Flat-blade turbine– d. Marine-type propeller– e. Spiral mixer– f. Anchor mixer

Picture: Z875/16Åbo Akademi - Värme- och strömningsteknik Biskopsgatan 8, 20500 Åbo

Flow: tangential, radial

Tangential flow may rotate the entire fluid mass without much mixing

Is created with blade- and turbine-type impellers, especially with smooth vessel walls

The centrifugal effect may create a vortex at the surface

Baffles at the wall put a limit to tangential flow

Meeting the vessel wall makes the fluid flow return towards the impeller, creating radial flow

Created by blade- and turbine-type impellers

Picture: Z876Åbo Akademi - Värme- och strömningsteknik Biskopsgatan 8, 20500 Åbo

Flow: axial, baffled

Axial flow arises with propeller-type and pitched impellers

A guidance tube can enhance the axial flow circulation

A cruciform baffle at the vessel bottom can further improve mixing and dispersion

Baffles at walls and bottom considerably increase power input requirements

As a rule, baffle width × number of baffles≈ 0.4 × vessel diameter (for example 4 baffles á 0.1 diameters)Pictures: Z87, CRBH83

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Off-setting; Liquid level Using the impeller in a off-set

position can improve mixing by minimising vortex formation

Liquid filling level with respect to the position of the impeller affects mixing as well

Too low level Correct level

Too high levelPictures: Z87

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9.2 Power requirements, Design

see e.g. BMH99 for mixing (energy) needed to keep dispersed particles in dispersion

oktober 2017

Power requirements /1 Power requirements depend on fluid

properties, process parameters, sizes and size-ratio’s

Dimensional analysis gives a relation between power P (W) and Reynolds number Re, Froude number Fr, power number Poand size ratio’s D/T, D/Z etc., where

with rotation rate n (1/s), density ρ, dynamic viscosity η, impeller diameter D and gravity g

Dnρ

PPo;gDnFr;

ηρnDRe

Picture: Z87

Note: product n·D (m/s) is thetip-speed of the impeller

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oktober 2017

Power requirements /2 For geometrically similar stirred vessels, Po = f(Re,Fr) If vortexing is not occuring, Po = f(Re) For Re < 10 (laminar), Po ~ 1/Re → P = Po· η· n2· D3

For Re > 104 (turbulent) Po ~ constant → P = Po· ρ· n3· D5

Lower without bafflesbecause some some gas is sucked in which reduces fluid density

Power consumption curve for a turbine-type impeller

Picture: BMH99

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Power requirements /3

Power number for various impeller types

Po

Re

transition

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Mixture properties For non-homogeneous mixtures, average values for

density (ρ) and viscosity (η) may be used (gives goodresults for turbulent mixing).

With dispersed phase ”d” dispersed at volume faction ε(m3/m3) in a continous phase ”c”:mixture density

mixture viscosity

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A typical design

An example for a well- performingL/L mixing vessel:

6-blade turbine impeller, circular vessel with 4 baffles, Z/T = 1, D/T = 1/3, B/T = 1/12, C/Z = 1/2 This set-up with 4 baffles with

B ≥ 0.1·T is referred to as ”fully baffled” Typically, for a vessel with volume V

(m3) and flow throughput Φv (m3/s), good (turbulent) mixing is obtained in time tmix = 4· V/Φv = 4· tresidence, average

Picture: Z87

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Heat transfer

For heat exchange (primarily for temperature control) a mantle volume can be put around the whole vessel (left), or spirals can be put inside the vessel (centre, right). If necessary, condensers or evaporators are used.

For the various types of impeller, the heat transfer to/from wall or spirals is given by heat transfer coefficients from Nusselt number, such as Nu = f(Re, Pr, D/T, T/D, T/C, w/D, ηwall/η,....) Picture: Z87

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Sources

BMH99 Beek, W.J., Muttzall, K.M.K., van Heuven, J.W. ”Transport phenomena” Wiley, 2nd edition (1999)

CRBH83 J.M. Coulson, J.F. Richardson , J.R. Blackhurst, J.H. Harker”Chemical engineering”, vol. 2, 3rd ed. Pergamon Press (1983) Ch. 13.2

SH06 J.D. Seader, E.J Henley ”Separation process principles” John Wiley, 2nd edition (2006) 8.1 **

Z97 F. Zuiderweg ”Physical separation methods” (in Dutch: FysischeScheidingsmethoden) TU Delft 1987 (vol. 2)

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* * See ÅA course library