Mixing of Miscible Liquids

GBH Enterprises, Ltd.

Process Engineering Guide:
GBHE-PEG-MIX-701

Mixing of Miscible Liquids

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Process Engineering Guide:

Mixing of Miscible Liquids

CONTENTS

SECTION

0

INTRODUCTION/PURPOSE

4

1

SCOPE

4

2

FIELD OF APPLICATION

4

3

DEFINITIONS

4

4

SELECTION OF EQUIPMENT

4

4.1
4.2
4.3

Mechanically Agitated Vessels
Jet Mixed Vessels
Tubular ('Flow') Mixers

4
4
5

5

AGITATED VESSELS

5

5.1
5.2
5.3

6
9

5.4
5.5

Mixing Time for Liquids in Stirred Tanks
Power Requirements
Vortex Formation and Surface Entrainment in
Unbaffled and Baffled Vessels
Heat-Transfer in Stirred Vessels
Flow and Circulation

34
39
44

6

JET MIXED TANKS

45

6.1
6.2
6.3
6.4

Introduction
Recommended Configuration
Design Procedure
Design for Continuous Mixing

45
45
46
51


7

TUBULAR JET FLOW MIXERS FOR MISCIBLE LIQUIDS

51

7.1
7.2
7.3

Recommended Configurations
Mixer Design
Additional Considerations

55
55
60

8

MOTIONLESS MIXERS

63

8.1
8.2

Recommended Types
Correlations

63
63

TABLES

1

TYPICAL CONSTANTS FOR EQUATION (1)

7

2

POWER CURVES FIGURES AND CORRECTION
FACTORS

10

VORTEX PARAMETERS, TURBINE, PROPELLER
AND SAWTOOTH

35

4

CHARGING A HOT VESSEL WITH A COLD PRODUCT

43

5

INJECTING A HOT FLUID INTO THE JACKET OF
A COLD VESSEL

44

6

TYPICAL DISCHARGE COEFFICIENTS

45

7

CONSTRAINTS FOR LAMINAR FLOW MOTIONLESS
MIXERS

64

CONSTANTS FOR TURBULENT FLOW MOTIONLESS
MIXERS

65

LENGTH FACTORS FOR HIGH VISCOSITY RATIOS

65

3

8

9


FIGURES

1

POWER NUMBERS FOR 45° ANGLED-BLADE TURBINES

12

2

CORRECTION FACTORS FOR DIAMETER RATIOS

13

3

BLADE ANGLE AND THICKNESS CORRECTION FACTORS

13

4

POWER NUMBERS FOR SINGLE 60° ANGLED-BLADE
TURBINES

14

POWER NUMBERS FOR TWIN 60° ANGLED-BLADE
TURBINES

15

POWER NUMBERS FOR TRIPLE 60° ANGLED-BLADE
TURBINES

16

BAFFLE WIDTH AND NUMBER CORRECTION FACTORS
FOR DIFFERENT DIAMETER RATIOS

19

8

CORRECTION FACTORS FOR SUBMERGENCE

19

9

CORRECTION FACTORS FOR SEPARATION

19

10

POWER NUMBERS FOR DISC-TURBINES

20

11

CORRECTION FACTORS FOR BAFFLES

22

12

CORRECTION FACTORS FOR BASE CLEARANCE

22

13


23

14

POWER NUMBERS FOR RETREAT-CURVE IMPELLERS

24

15

CORRECTION FACTORS FOR PARTIAL BAFFLES

26

16

POWER NUMBERS CORRECTION FACTORS FOR RETREATCURVE AND IMPELLERS H/T RATIOS OF 2.0

26

17

POWER NUMBERS FOR FLAT-BLADED TURBINES

27

18

BOTTOM CLEARANCE CORRECTION FACTOR

29

5

6

7


19

POWER NUMBERS FOR ANCHOR AND GATE AGITATORS

30

20

POWER NUMBERS FOR PROPELLERS

32

21

IMPELLER SPACING CORRECTION FACTORS

33

22

STANDARD NOTATION FOR VORTEX CALCULATIONS

37

23

VORTEX DATA FOR 2 - BLADED PADDLES
(W/D = 0.33, T/D = 2)

37

24

VORTEX CORRECTION FACTORS FOR PADDLES

38

25

JET DIRECTION

47

26

SINGLE JET MIXERS

52

27

MULTIJET MIXERS

53

28

SERIES ARRANGEMENT OF MIXERS

54

29

BATCH MIXERS

54

30

DESIGN PROCEDURE

56

31

EMPIRICAL FACTORS

60

32

RECIRCULATION ZONES

62

33

FRICTION FACTOR DATA FOR KENICS AND SULZER MIXERS 66

DOCUMENTS REFERRED TO IN THIS PROCESS
ENGINEERING GUIDE

67


0

INTRODUCTION

This Guide is one in a series of Mixing Guides and has been produced for GBH
Enterprises.

1

SCOPE

This Guide caters for the majority of mixing duties for miscible liquids, but does
not cover the more specialized cases for which reference should be made to
mixing experts.
The Guide is divided into 4 main sections dealing with the mixing devices most
commonly employed for miscible liquid systems, namely Stirred Vessels, Jetmixed Vessels, Jet Flow Mixers and Static (or Motionless) Mixers.

2

FIELD OF APPLICATION

This Guide applies to Process Engineers in GBH Enterprises worldwide.

3

DEFINITIONS

No specific definitions apply to this Guide.

4

SELECTION OF EQUIPMENT

All considerations refer to macro-mixing, i.e. blending and uniformity throughout
the vessel. Mixing on smaller, local scales (micro-mixing) is not covered at
present, and will follow different trends and rules.
The operating costs, as measured by the energy required per unit throughput, for
the mixers are likely to be similar.


4.1

Mechanically Agitated Vessels

Mechanically agitated vessels are very versatile. They can be operated in either
a batch or continuous mode. They are suitable for use where long mixing times
(10 - 10000 secs or longer) can be tolerated and where long residence times are
desirable. The mixing time is generally independent of throughput, in contrast to
'flow' mixers. With the appropriate choice of agitator they can handle the entire
range of liquid viscosities.
Power input per unit volume is usually low. The capital cost of the tank and
agitator system is high.
Heat transfer area per unit volume is not large, especially for large vessels. It can
be extended either by the use of internal coils, or by an external recycle pumped
through a heat exchanger. Exotherms can also be handled by boiling and
condensation and, since the vessel is backmixed, some of the heat of reaction
can be absorbed by feeding in ”cold” inlet streams.

4.2

Jet Mixed Vessels

Jet mixed tanks are usually used only to blend low viscosity liquids (so that Re j
1000) with a jet to bulk density difference of less than about 30%. They can be
operated in either a batch or continuous mode. Mixing times are of the same
order of magnitude as stirred tanks. For the same mixing duty, a jet mixed tank
has a lower energy efficiency than a mechanically agitated tank.
For a given duty the capital cost of a jet mixed tank will be lower than that of a
mechanically agitated vessel.
Jet mixing can be particularly attractive in terms of capital cost for very large,
irregularly shaped
vessels such as lagoons and reservoirs.
4.3

Tubular ('Flow') Mixers

Tubular mixers e.g. jet mixers, motionless mixers, orifice plates, venturis, etc are
essentially continuous flow devices although they can be used in batch loop
recycle systems. Their principal uses are:


(a)

the continuous blending of miscible liquids over the whole
range of liquid viscosity;

(b)

the rapid (0.01 - 5 seconds) contacting of low viscosity reactants for a
`”fast” reaction especially when the product spectrum is affected by the
mixing rate;

(c)

the processing of hazardous liquids where the amount being processed at
any instant must necessarily be small.

High heat transfer rates are possible with these devices because of the intense
turbulence and the high surface area to volume ratio.
The capital costs of this type of mixer are very low compared with jet mixed and
mechanically agitated tanks. However, the continuous, plug flow short residence
time characteristics of these devices may mean that instrumentation costs are
higher.
When used in 'single pass' configurations the mixing performance depends upon
the throughput. The requirement of mixing intensity determines the diameter and
residence time fixes the length for a given process flowrate. This means that the
tube gets narrower and longer with scale-down.

5

AGITATED VESSELS

The main parameters in the design of agitated (or stirred) vessels for mixing
miscible liquids are:
(a)

Mixing time;

(b)

Power requirements;

(c)

Vortex formation;

(d)

Heat transfer;

(e)

Flow and circulation.


5.1

Mixing Time for Liquids in Stirred Tanks

In many processes it is important to mix reactants quickly and thoroughly. This
can be assessed for any system by the overall 'mixing time', which is the time
taken to reduce the root mean square concentration variations by a factor,
frequently 20. This is the 95% mixing time, tm95%.
Prediction of mixing time from the literature is not easy and values should not be
relied on to better than ± 50%. In practice the designer usually only wants to
know if a vessel is "adequately mixed" so this degree of precision is normally
sufficient. If more precise values are required, specific experiments carefully
related to the particular problem are recommended.
If scale model measurements can be done easily, they are more reliable than
prediction from the correlations given below. Mixing time depends strongly on
circulation flows through the vessel, especially for low viscosity systems, so
results in the turbulent region (Re > 104) scale up well with the relation "mixing
time × agitator speed = constant". The constant is called 'the dimensionless
mixing time'.
5.1.1 Low Viscosity Newtonian Liquids
For low viscosity Newtonian liquids mixing is usually best performed with a
turbine or propeller type agitator.
The best configuration is with:

(See Figure 1 for definition of symbols. Pitch is the liquid progression distance
per revolution; a is the angle of the blade to the horizontal. Down-pumping
turbines have a!< 90°.)


Baffles increase the vertical circulation and thus are an effective means of
shortening mixing time (but at the cost of increase power) and also reduce the
complicating factors of vortex formation on prediction. Data on mixing times in
unbaffled vessels is sparse but for a crude estimate the mixing time for the same
vessel with baffles, at the same power, can be used.
Fluid density differences can significantly increase mixing time.
Mixing times (95%) for these systems can be predicted from correlations
involving the power number (Po). These can be calculated by the methods given
in 5.2.
For low viscosity liquids;

The density and viscosity is that of the mixed liquid.
First calculate Po1/3 × Re. If the value is greater than or equal to 6400 then use
the appropriate constant as listed in Table 1.
For values less than 6400 use equation (3) developed for high viscosity
Newtonian liquids.


TABLE 1

TYPICAL CONSTANTS FOR EQUATION (1)

5.1.2 High Viscosity Liquids
For high viscosity liquids the best agitators are either stacked pitched blade
turbines, helical screws, straight anchors or bent anchors (see GBHE-PEG-MIX700). As fluid motion decays more rapidly with distance from the agitator than
with low viscosity fluids, relatively larger agitators are needed which sweep a
greater volume of liquid.
To estimate mixing times (and power) with Newtonian liquids use:

For turbine-type agitators with Newtonian liquids the formula developed by FMP
can be used.

If the liquid is known or suspected to be non-Newtonian a rheogram of shear
stress versus shear rate should be obtained (see GBHE-PEG-FLO-302). If the
data is not available it should be measured. If the shear stress is low at low shear
rates, then the mixing time should be calculated as if the liquid were Newtonian.
(If in doubt calculate Ns as described below and check it is an order of magnitude
smaller than the working speed.)
For determination of the appropriate "apparent" viscosity use the Metzner and
Otto relation:

Values of k s for typical configurations are:

If there is a significant shear stress at zero shear rate (a "yield stress") and a
turbine-type agitator is being used then a cavern of well mixed material may form
round the agitator while the material near the walls and surface of the vessel
remains unmixed. In this case rather than try to estimate mixing times it is better
to use a correlation from the work of Solomon (1981) and Elson (1985) to
estimate the minimum agitator speed for the cavern size to equal the vessel
size (equation 5). Under this condition the vessel can be considered well mixed.


It is assumed that the agitator is half way up the vessel. If this is not so, for a safe
design, replace H by twice the distance from the agitator to the surface or twice
the distance from the agitator to the bottom, whichever is the greater.
Etchells (1987) suggests that this approach should apply to materials where the
"yield stress" is at least (5 × the viscosity at infinite shear × the shear rate). This
is the case for many slurries.

5.2

Power Requirements
5.2.1 Levels of Power Input
Power inputs from agitators to low-viscosity Newtonian liquids are usually
in the range 100 to 2000 W/m3; though for some applications, inputs of
4000 to 10000 W/m3 are used. Power inputs above this level are rare in
stirred tanks and are difficult to achieve using conventional agitators. They
tend to be restricted to tanks of 2 m3 capacity or smaller, where very short
mixing times are required, as in polythene reactors which run at 100 to
200 W/m3.


5.2.2 Factors Affecting Power Dissipation
Power dissipation is a function of agitator geometry, speed of rotation,
fluid properties, vessel fittings, vessel geometry and fluid aspect ratio.
Fluid properties are characterized by Reynolds and/or Froude Numbers:
up to Re of the order of 10 to 30 the flow is mainly viscous and power
dissipation is proportional to viscosity and independent of density. As Re
increases above about 1000, the flow is essentially turbulent and the
power is much more dependent on density than viscosity. Geometries,
fittings and speed are usually interdependent in complex ways and their
effects vary between systems.

5.2.3 Power Correlation
It has been shown that the power supplied by an agitator can be
expressed by:

P/(ρ N3 D5) = fn ((N D2 u/µ).(N2 D/g). R1....RI)
where R1....Ri represent the various geometric ratios describing the
agitator and vessel. For a given agitator-vessel system this gives:

P/(ρ N3 D5) = Po = K (N D2 ρ/µ)m. (N2 D/g)n
where Po is the Power Number of the agitator-vessel system and is
comparable to the drag coefficient in a flowing fluid system. At Re < 10, m
tends to -1 and at high Re it tends to zero, especially in baffled vessels. In
fully baffled vessels and systems with no free liquid surface, n becomes
zero. K depends upon the geometry.
The correlation of Po with Re is universally recognized as a reliable
means of predicting power requirements at widely differing scales of
operation for geometrically similar vessels. The correlation must be
established experimentally for each geometric system, which has a unique
Po-Re relationship. Graphs of Po vs Re data for a number of basic
impeller designs are presented here: deviations from the "standard"
designs have to be allowed for by using a series of correction factors.


5.2.4 Calculation of Power
(a)

Calculate the agitator Reynolds Number (ND ρ/µ).

(b)

Select appropriate power curve for the type and geometry of
agitator (see Table 2), and read the value of Po for Re obtained
under (a).

(c)

Tabulate the variations between the actual agitator and the
"standard" design, as illustrated in the same Figure as the power
curve.

(d)

Use appropriate Figure for the agitator (as listed in Table 2).

(e)

Determine the relevant correction factors for each variation from the
"standard".

(f)

Multiply the value of Po by these correction factors.

(g)

Calculate the power (P = Po ρ N D ).

2

3

5

Note: that commercially available programs are available to calculate the
power.


TABLE 2

POWER CURVES FIGURES AND CORRECTION FACTORS

Power numbers for 'hydrofoils' can be found in the GBHE Mixing and Agitation
Manual.
5.2.5 Correction Factors for Power Numbers of 45° Angled-Blade
Turbines
For impellers and vessel configurations different from the standard system
shown in Figure 1, multiply the standard power number by each correction
factor described below:
(a)

Vessel diameter (T )
No correction factor recommended.

(b)

Baffle-width (W b )

T/10 flat baffles, Cb =
T/12 flat baffles, Cb =

1.10
1.0

no wall gap
no wall gap.


(c)

Non-standard internals: assume an otherwise unbaffled vessel
except for the helical coil:

Single finger baffle,
Twin finger baffles,
Beavertail baffle,
Triangular wall
baffle,
Single dip-pipe,
Ringlet coil (a),

C i = 0.71
C i = 0.81
C i = 0.74
C i = 0.97 ... projected W b = T/9
C i = 0.56 ... diameter = T/23
C i = 0.73 ... tube od = T/55
pitch!= T/34
coil pitch = T/8


(j)

Blade angle and thickness (a and X)
The correction factor Ca is plotted in Figure 3, note that Po is a very
strong function of angle and errors of 2.5 will alter Po by 10%. All
the data refers to downward pumping impellers; for upward
pumping impellers use an additional correction factor of 0.9. Data
from 3 bladed turbines will probably be within 10% of that for 4
blades.

FIGURE 1

POWER NUMBERS FOR 45° ANGLED-BLADE TURBINES


FIGURE 2

CORRECTION FACTORS FOR DIAMETER RATIOS

FIGURE 3

BLADE ANGLE AND THICKNESS CORRECTION FACTORS


FIGURE 4

POWER NUMBERS FOR SINGLE 60° ANGLED-BLADE
TURBINES


FIGURE 5 POWER NUMBERS FOR TWIN 60° ANGLED-BLADE TURBINES


FIGURE 6

POWER NUMBERS FOR TRIPLE 60° ANGLED-BLADE
TURBINES


5.2.6 Correction Factors for Power Numbers of 60° Angled-Blade Turbines
For impellers and vessel configurations different from the standard system shown
in Figure 4, multiply the standard power number by each correction factor
described below. Note that these correction factors, where relevant, also apply to
dual and triple 60° angled-blade impellers.
(a)


C t = (T/0.304) -0.08
(b)

range 0.2 T 3.0 m

Baffle width (W b )
Use Figure 7.

(c)

Non-standard internals: assume an otherwise unbaffled vessel, except for
the helical coil:
4 × T/12 flat wall baffles + T/40 wall-gap
4 × T/10 flat wall baffles + no wall-gap
4 × T/10 profiled (triangular) wall baffles
4 × T/12 + wall gap.....half vessel height
1 × finger baffle
2 × finger baffles
1 × beavertail baffle
2 × beavertail baffles
1 × ringlet coil
1 × dip-pipe or tubular thermopocket
2 × dip-pipes or tubular thermopockets
Helical coil (coil pitch > tube diameter)
Helical coil....treat supports as baffles.

(d)

Ci = 1.00
Ci = 1.10
Ci = 0.97
Ci = 0 92
Ci = 0.70
Ci = 0.80
Ci = 0.84
Ci = 1.10
Ci = 0.73
Ci = 0.40
Ci = 0.50
Ci = 1.00

Diameter ratio (D/T )
See Figure 2, also for 45° impellers.

(e)

Bottom clearance (Z/D)

Cc = (Z/0.537D) -0.20

range 0.33 Z/D 1.10


(f)

Submergence (S/T )
See Figure 8.

(g)

Number of blades (n)

n
Cn

=2
= 0.60

(h)

Blade width (Wp)

3
0.87

4
1.00

5
1.17

6
1.28

C w = (Wp/0.336D)1.17
(j)

0.34

Blade angle (a to the horizontal)
range 55° a 75°

Blade thickness (X )

C x = 1.0
(l)

8
1.41

range 0.2 Wp/D

Ca = ( [sin a ] /0.866)2.10
(k)

7
1.31

range 0.04

X/W

0.10

Blade roundness

Cr = 0.95

r/W = 0.2
X/W = 0.05 to 0.08

Cr = 0.56

(m)

corner radius,
blade thickness,
corner radius,
blade thickness,

r/W = 0.5
X/W = 0.30

Pumping direction
Pumping down Cp = 1.00;

Pumping up Cp = 0.91


(n)

Vessel base shape
Dished base C v = 1.00;

(p)

Flat base C v = 0.98

Multiple impellers
For multiple impellers of the same geometry, use Figures!5 and 6. For
multiple impellers of mixed geometries, use Figure 21 or the sum of the
individual power numbers, which would give high (safe) values.

(q)

Impeller separation

Use Figure 9.
FIGURE 7

BAFFLE WIDTH AND NUMBER CORRECTION FACTORS FOR
DIFFERENT DIAMETER RATIOS


FIGURE 8


FIGURE 9

CORRECTION FACTORS FOR SEPARATION


FIGURE 10

POWER NUMBERS FOR DISC-TURBINES


5.2.7 Correction Factors for Flat-Bladed "RUSHTON" Disc-Turbines
For impellers and vessel configurations different from the standard shown
in Figure 10, multiply the standard power number by each correction factor
described below:
(a)


Ct = T0.065.
(b)

Baffle width (W b)
Use Figure 11.

(c)

Non-standard internal fittings
No information.


(d)


Cd = 1.0 (at Z/T = 0.30)
(e)

range 0.14 D/T 0.70

Bottom clearance (Z/T )
Use Figure 12.

(f)

Submergence (S)
Use Figure 13.

(g) Number of blades (n)


(n)

Multiple impellers
Use Figure 21 or the sum of individual impellers, where multiple impeller
power number data is not available: this gives high (safe) values.

FIGURE 11 CORRECTION FACTORS FOR BAFFLES

FIGURE 12 CORRECTION FACTORS FOR BASE CLEARANCE


FIGURE 13 CORRECTION FACTORS FOR SUBMERGENCE

FIGURE 14 POWER NUMBERS FOR RETREAT-CURVE IMPELLERS


5.2.8 Correction Factors for Power Numbers of Retreat-Curve Impellers
shown in Figure 14, multiply the standard power number by each
correction factor described below.
(a)

No information available.

(b)

Baffle-width (W b)
T/10 flat baffles, C b = 1.0 no wall gap
T/12 flat baffles, C b = 1.0 T/40 wall gap


(c)
Non-standard internals: 4x flat wall-baffles taken as the reference
power number

Also see Figure 15.
(d)


C d = (0.8T/D)0.58
(e)

Bottom clearance (Z/D)
No information available

(f)

range, 0.5 D/T 0.80

normally, 0.061 Z/D 0.1

Submergence (S/T )
No information available.

(g)

Batch height (H/T )
See Figure 16.

(h)

Blade width (W/D)

C w = (W/0.125D)0.6
(i)

range, 0.1 W/D 0.194

Blade angle and thickness (a and X )
No information available normally, a is 10° or 15°.


FIGURE 15 CORRECTION FACTORS FOR PARTIAL BAFFLES

FIGURE 16 POWER NUMBERS CORRECTION FACTORS FOR RETREATCURVE AND IMPELLERS H/T RATIOS OF 2.0


FIGURE 17 POWER NUMBERS FOR FLAT-BLADED TURBINES


5.2.9 Correction Factors for Power Numbers of Flat-Bladed Turbines
For impeller and vessel configurations different from the standard system
correction factor described below:
(a)


(b)

Baffle width (W b)
Use Figure 7.

(c)

Non-standard internals: assume an otherwise unbaffled vessel
apart from the helical-coil, which is located on a 4x flat wall-baffle
cage:

(d)

Use Figure 7.

(e)

Bottom clearance (Z/T )
Use Figure 18.

(f)

Submergence (S/T )
Use Figure 13.


(g)

See the relationships for Blade width (h) below.

(h)

Blade width (W )

(j)

Blade thickness (X )
Po varies by less than 5% in the range, 0.01 X/D 0.0332

(k)

Vessel shape (V )
Flat bottom
Dished bottom

C v = 1.11
Cv = 1.00


FIGURE 18 BOTTOM CLEARANCE CORRECTION FACTOR

FIGURE 19 POWER NUMBERS FOR ANCHOR AND GATE AGITATORS


5.2.10

Correction Factors for Power Numbers of Anchor and Gate
Agitators
correction factor described below:
(a)


(b)

Blade height (L/D)

C l = 0.86L/D + 0.11.


(c)

Agitator shape

Cf = 0.89L/D + 0.11n
Cf ' = C f (1 + (D i /D)5)
(d)

n = number of cross-bars
for gates > 2 vertical bars

See (e) below.

(e)

Side & bottom clearance (e/T )

(f)

No correction factors recommended.

(g)

Blade width (W/D)

C w = 1.0

W/D = 0.083 to 0.125


FIGURE 20 POWER NUMBERS FOR PROPELLERS


5.2.11

Correction Factors for Power Numbers of Propellers
(a)


(b)

Baffle width (W b)

FIGURE 21 IMPELLER SPACING CORRECTION FACTORS

1
2

Disc turbines
Angled-blade turbines & propellers
(pumping in the same direction)


5.2.12 Power Numbers for Multiple Impellers
Notation
Po(c) =
Po(1) =
Po(2) =
Po(n) =

combination power number
bottom impeller power number
2nd impeller power number
nth. Impeller power number

(a) Twin impellers - Po(1) + Po(2) × (Po(n)/Po).
(b) Triple impellers - Po(1) + [Po(2) + Po(3)] × [Po(n)/Po].
MIXED IMPELLERS, use Po(n)/Po = 1.0 until data becomes available.

5.3

Vortex Formation and Surface Entrainment in Unbaffled and Baffled
Vessels

Unbaffled vessels were formerly preferred for liquid blending and solid
suspension duties. The impeller is usually mounted centrally and except in the
case of a sawtooth disc, the designer must check that the vortex does not reach
it. The rise of the vortex is obviously critical in open vessels and could be critical
in closed vessels where instrument probes or vent lines need to be kept clear of
liquid. The general configuration of vessel, impeller and vortex is shown in
Figure!22.
Off-centre mounting of the agitator can give a flow regime closer to that of a
baffled vessel but causes large fluctuating forces on the agitator shaft. Little
design information is available and this option is not recommended. A major
vortex is not normally generated in fully baffled vessels. In both baffled and
unbaffled systems, it may be necessary to avoid gas entrainment into the liquid
or to specify conditions under which a light solid may be rapidly incorporated into
a liquid surface.
(a)

Agitator types
Data are given for disc-turbines, flat bladed paddles, sawtooth, propeller
and anchor agitators. Extensive information is available in the GBHE
Mixing and Agitation Manual on paddle mixers, covering a wide range of
geometries. Table 3 gives vortex parameters for modern mixers and
Figure 22 shows h1 and h2: the displacement of the vortex below and
above the original liquid level.


(b)

Parameters covered
Vortex depths are related to impeller Reynolds Number (ND2ρ/µ) and
Froude Number!(N2D/g). Experimental checks at GBHE have shown that
separate equations are not needed for Froude Numbers less than 0.1.

5.3.1 Recommendations
Vortex configuration in unbaffled vessels
(a)

Turbine, propeller and sawtooth relevant k values are in Table 3.
(1) For all T/D ratios and Re below 2000:

(2) At Reynolds Numbers greater than 5000:


TABLE 3

VORTEX PARAMETERS, TURBINE, PROPELLER AND
SAWTOOTH


where:
Vortex Parameter is shown in Figure 23, and generally f = f1
gives correction factors for h1 and f = f 2 for h2 from the respective
graphs in Figure 24.
This work performed for GBHE, is the most comprehensive range of
correction factors available for paddles.

5.3.2

Avoidance of Gas Entrainment in Standard Baffled Vessels

It may be necessary to avoid gas entrainment from the surface in a
standard baffled vessel, in which case a maximum impeller speed, above
which entrainment could occur, is given below for agitator/vessel diameter ratios
in the range 0.33 to 0.47.


FIGURE 22 STANDARD NOTATION FOR VORTEX CALCULATIONS


FIGURE 23 VORTEX DATA FOR 2 - BLADED PADDLES
(W/D = 0.33, T/D = 2)

FIGURE 24 VORTEX CORRECTION FACTORS FOR PADDLES


5.4

Heat-Transfer in Stirred Vessels
It is seldom that heat-transfer is the only operation to be promoted by
agitation and the choice is often a compromise between conflicting
requirements. In those cases where heat-transfer considerations are a
prime factor in the design, the aim should be to select an impeller design
which gives high bulk flowrates of the fluid with good general mixing and
high fluid velocities close to the heat-transfer surfaces.


For low viscosity fluids (up to 1 N.s/m2) flat paddles, angled blade turbines,
disc turbines or propellers with D/T ratios of 1/3 to 1/2 can meet these
requirements and give broadly similar rates of heat-transfer. The choice
between them can be based on other mixing criteria for the process, e.g.
suspension of solids, gas dispersion. Note however that relatively small
changes of viscosity can influence heat-transfer performance quite
markedly. As viscosity increases further to about 3 N.s/m2 the impeller
diameter should be increased to give D/T = 2/3 or more, whilst at the
same time reducing the blade width to conserve power. At higher
viscosities (> 3 N.s/m2) anchor stirrers and dual or triple wide-diameter
impellers are used whilst at very high viscosities (> 25 N.s/m2) screw and
helix impellers are preferred.
Jackets and limpet coils are used extensively on carbon steel, stainless
steel and glassed steel vessels. Limpet coils show advantages over
jackets in cost, pressure rating and heat-transfer performance. However
there can be fatigue problems on limpet coils subjected to thermal cycling.
Typical pressure ratings of jackets and limpet coils are 6 bar and 14 bar
respectively. Jackets and limpet coils are preferred to internal coils when
processing viscous liquids. Jacket heat-transfer performance can be
influenced markedly by the use of aids such as jetted feed, tangential
inlets, baffles, and multiple outlets.
Internal coils are used primarily to supplement heat-transfer area in
jacketed vessels and in cases where heat-transfer through the wall is very
poor or impracticable, e.g. rubber lined tanks, GRP tanks. Coils are
suitable for higher pressure service fluids and in cases where a large
corrosion allowance must be provided. Large helical coils are used in twopiece vessels when a long service life is expected. Hairpin and ringlet coils
are used in one-piece vessels and often act as baffles in the agitation
system. They have the advantage of being easily removed if the
process duty changes or in the event of failure. Broadly speaking, jackets,
helical coils and ringlet coils of reasonable proportions in a given vessel,
are capable of meeting similar heat transfer duties.


5.4.1 Correlations and Design Guides
Heat-transfer in stirred vessels is brought about primarily through
conduction and forced convection. The process is assumed to be
governed by the combined resistance of:
(a)

the wall separating the service and process fluids;

(b)

the dirt films on each side of the wall and

(c)

laminar films of process and service fluids adjacent to the
wall.
Correlations for local coefficients of heat-transfer are of the
form:

ᵞ

= bulk liquid viscosity/viscosity at the wall.

(1)

Use any Standards which apply, e.g. vessels, jackets, limpet coils,
helical coils, ringlet coils, impellers, service pumps, etc.

(2)

Check that the batch depth lies between about 0.8 and 1.0 vessel
diameters. If below this range consider using a smaller vessel; if
above the range consider putting additional impellers on the shaft.

(3)

With low viscosity fluids (< 1 N.s/m2) use an impeller which meets
other process duties. A simple, cheap design should be chosen
giving high circulation rates and moderate power inputs, e.g. 0.5 to
0.7 kW/m3 in baffled vessels, 0.2 to 0.5 kW/m 3 in unbaffled
vessels.


(4)

In viscous fluids, impeller blades should reach close to the fluid
surface, even if this means adding additional impellers or crossmembers. Blade widths and wall clearances should be about 1/10
of the vessel diameter.

(5)

In non-jacketed vessels, helical coil diameters are close to the tank
diameter: the coil often being supported by the tank wall about 50
to 150 mm away from it. In jacketed vessels where the coil is
supplementing the jacket, the coil diameter should be about
90% of the vessel diameter.

(6)

When multiple concentric helical coils are used, care must be taken
to stagger and increase the pitch to ensure they do not shield each
other.

(7)

Tube diameters for coils vary between 25 and 100 mm; by far the
most common sizes being 37 to 50 mm.


5.4.2 Correlations
(a)

Service-Side Heat Transfer Coefficients
(1)

(2)

Conventional Jackets with low flows [ velocity < 0.03 m/s, no
phase change ] (enhanced natural convection)

Conventional jackets with high flows
(sensible heating/cooling)


All physical properties, except µw, are evaluated at bulk temperature.
Two cases arise:
(i)

Radial fluid inlet

(ii)

Tangential fluid inlet:

(3)

Conventional jackets with condensing heating medium

(ii)

[Re i > 9000] (ie no swirl)

[Re i > 20000]

Turbulent condensate film, see HTFS Design Report


(4)

Limpet coils (sensible heating/cooling)

(5)

Limpet coils (condensing service fluid)
See HTFS Design Report

(6)

Spiral jackets (sensible heating/cooling)
Use the same correlation as the limpet coils.

(7)

Immersed coils (sensible heating/cooling)

where:
di
Dc

=
=

pipe inside diameter
coil diameter


(8)

Immersed coils (condensing service fluid)
As for limpet coils.

(b)

Process-Side Heat Transfer Coefficients
(1)

Vessel Wall Surface

5.4.3 Thermal Shock in Glass-Lined Steel (GLS) Vessels
When using a GLS vessel for heating or cooling duties, it is important to prevent
thermal shock from damaging the glass lining.
Table 4 shows the maximum allowable temperature difference when charging
into a heated vessel.

TABLE 4

CHARGING A HOT VESSEL WITH A COLD PRODUCT

* use this ΔT for vessel temperatures up to 121°C.
Table 5 shows the maximum allowable temperature difference when charging
into a cooled vessel.
TABLE 5

INJECTING A HOT FLUID INTO THE JACKET OF A COLD
VESSEL

* use this ΔT for vessel temperatures up to 121°C.


5.5

Flow and Circulation

Details of flow patterns, velocities and local concentrations may be obtained from
the CFD computer program.
The following other measurements are sometimes used in mixing vessels:
(a)

Agitator discharge volumetric flowrate, Q p

Where Flρ is a discharge coefficient for the agitator (because of
entrainment the actual circulation flow will usually be much greater than,
Qp). Values of Flp are given in Table 6.

(b)

Circulation time, tc

tc is the average time interval for successive passages of a fluid element
through the agitator. For a 6 bladed disc turbine (D/T = 0.3 to 0.5; Z/T =
0.3 to 0.5; H/D = 0.2; L/D = 0.25):

As this is not dimensionless, V must be in m 3.
For turbulent, baffled stirred vessels the following rule of thumb is
frequently used:


TABLE 6

TYPICAL DISCHARGE COEFFICIENTS

6

JET MIXED TANKS

6.1

Introduction

Jet mixing in tanks can be used for the batch or continuous mixing of miscible
low viscosity (µj < 0.1 Ns/m2) liquid systems.
In tank jet mixing, a fast moving stream of liquid, the 'jet' liquid, is injected into a
very slow moving, almost stationary liquid, the 'bulk' or 'tank' or 'secondary' liquid.
The velocity gradient between the jet and bulk liquids creates a mixing layer at
the jet bulk boundary. This mixing layer entrains bulk liquid into the jet flow.
Turbulence within the jet flow then mixes the jet and bulk liquids.
Side entry jets (i.e. jets through the tank wall) or axial jets (i.e. jets directed along
the axis of the tank) are commonly used. Such jets are usually positioned either
near the tank floor pointing towards the liquid surface or near the liquid surface
pointing towards the tank floor. Swirl decreases the efficiency of mixing.


6.2

Recommended Configuration

The design objective should be to produce liquid motion throughout the whole
tank.
The tank should be cylindrical with a vertical axis, for other shapes consult the
GBHE Mixing and Agitation Manual. The liquid height, HL, to tank diameter, T,
ratio should preferably be in the range:

although other HL /T ratios are permissible.
Depending on the tank geometry and the mixing duty, a single jet through the
tank wall (a side entry jet) or a single jet on the axis of the tank (an axial jet) or
multiple jets may be used. The jet can be positioned either near the tank floor
pointing towards the liquid surface or near the liquid surface pointing towards the
tank floor. The jet nozzle should always be submerged during the mixing
operation.
The side entry jet should protrude no more than 5 nozzle diameters either from
the tank wall or from the tank base or liquid surface. The axial jet nozzle should
be as close to the tank floor or liquid surface as possible.
The side entry jet should be installed along a radius to the tank wall and the axial
jet on the tank axis perpendicular to the tank floor or liquid surface.
For the same mixing duty, the mixing rates achieved by axial and side entry jets
are essentially the same.


6.3

Design Procedure

The procedure for design for a given mixing time t99 for a given volume, V, of
liquid is as follows:
(a)

Choose a tank diameter such that:

This, of course, may not be possible if either T and/or HL are fixed by site or
mechanical considerations, or if the tank already exists.

The recommended tank/jet configuration, which depends on HL/T, is:

The design for side entry or axial jets is detailed below. For multiple jets
the tank should be considered as divided into separate volumes of H/T 1,
each with their own jet, see the GBHE Mixing and Agitation Manual for
more detail.
(b)

Jet direction
A jet can be positioned pointing either upwards or downwards, see Figure
25. If the jet is pointed upwards then it may break the surface and give rise
to spray. Aeration may occur. The spray may induce a build up of static
charge. These problems will not occur when the jet is pointed downwards
towards the base of the tank and is adequately submerged. The centre
line exit velocity should be 1 to 2 m/s.
When the mixing duty is merely to maintain homogeneity in a tank, the
density of the jet liquid is essentially the same as the density of the bulk
liquid, and stratification is not a problem. In this case the choice of jet
direction is arbitrary.


FIGURE 25 JET DIRECTION


FIGURE 25 JET DIRECTION (Continued)


(c)

Position of recycle suction
For an upward pointing side entry jet in a flat base tank the recycle suction
should be positioned either as near as possible to the tank floor on the
opposite side of the tank to the jet, or as near as possible to the liquid
surface on the same side of the tank as the jet. For a dished base tank the
recycle suction must be placed at, or very near, the lowest point of the
base.
For a downward pointing side entry jet in a flat base tank the recycle
suction should be positioned either as near as possible to the liquid
surface, on the opposite side of the jet, or as near to the tank floor on the
same side as the jet. Again, for this type of jet in a dished base tank, the
recycle suction must be placed at, or very near, the lowest point of
the base.
For an upward pointing axial jet in a flat base tank the recycle suction
should be positioned either as near as possible to the tank floor, or as
near as possible to the liquid surface in a tank with a dished base. Jet
protrusion should be as small as possible in a dished base tank.
For a downward pointing axial jet in a flat base tank the recycle suction
should be placed either as near as possible to the liquid surface or as near
as possible to the tank floor. For this type of jet in a dished base tank, the
recycle suction should be placed near the liquid surface.

(d)

Mixing time
(1)

Upward pointing jets
The mixing time, t99, for upward pointing jets is given by:


where for both side entry and axial jets:

This correlation is based on experimental work on small tanks, (T up to
about 1 m) for low viscosity liquid mixing,

The correlation is for flat based tanks. It applies to side entry jets with nozzles
which are no more than 5 nozzle diameters either from the nearest tank wall or
from the tank base and axial jets with nozzles which are close to the tank base.
(2)

Downward pointing jets
For downward pointing jets in tanks where


(3)

Hemispherical based tanks
The mixing time in hemispherical based tanks is less than that in flat
bottomed tanks:

(e)

Jet diameter
The jet diameter, Dj, should be chosen such that:

Here, X is the jet path length, for both upward and downward side entry jets
placed as recommended above:

Initially choose the smallest Dj.
The choice of jet velocity, vj, depends on the mixing duty being
undertaken. If one liquid is being mixed with a second liquid of different
density there is a danger of stratification (see GBHE Mixing and Agitation
Manual) if the jet velocity is too low.


(f)

Number of jets
As stated in (a), multiple jets should only be used for HL /T > 3.0. There is
no advantage in mixing from multiple jets for the same overall flowrate in
other cases.

6.4

Design for Continuous Mixing

If the tank is run at a constant level, HL, and the fresh feed fed through a nozzle
near the recycle line nozzle, then the tank will be well mixed if:

VT is the volume of liquid in the tank and Qf is the fresh liquid feed rate. t99 is the
batch mixing time calculated by the method given in 6.3.
7

TUBULAR JET FLOW MIXERS FOR MISCIBLE LIQUIDS
Jet flow mixers are recommended for mixing low viscosity liquid phase
systems i.e. systems where turbulent pipe flow can be achieved (Re >
5000). Mixing times from a few milliseconds on the small scale to several
seconds on the large scale are possible with this type of device.
In jet flow mixers a stream of liquid, the primary liquid is injected into
another liquid, the secondary liquid. The velocity gradient between the jet
and secondary liquids creates a turbulent mixing layer at the jet boundary.
The mixing layer grows in the direction of the jet flow entraining and
mixing the jet with the secondary liquid. Pressure drop at and along the
pipe after the mixing point provides the energy required for mixing the two
streams.


There are three basic types of jet flow mixer geometries, the coaxial jet
mixer, the side entry jet mixer and the impinging jet mixer, see Figure 26.
In the coaxial jet mixer the jet liquid is introduced through a small diameter
pipe running coaxially inside a large diameter pipe. In the side entry jet
mixer the jet liquid is introduced at an angle (usually 90 degrees) into the
secondary liquid stream. In the impinging jet mixer the two feed streams
are fed through directly opposing branches of a tee-piece. Multiple jet flow
mixers, see Figure 27, are also sometimes used.
A series arrangement of mixers, Figure 28, can be used to mix more than
two streams. This arrangement can also be used either when the flowrate
ratio of the feed streams is very high or when the mix temperature rise due
to mixing would be unacceptably high if the mixing were to be carried out
in one stage. Interstage cooling can then be used.
A series arrangement of mixers, Figure 28, can be used to mix more than
two streams. This arrangement can also be used either when the flowrate
ratio of the feed streams is very high or when the mix temperature rise due
to mixing would be unacceptably high if the mixing were to be carried out
in one stage. Interstage cooling can then be used.


FIGURE 26 SINGLE JET MIXERS


FIGURE 27 MULTIJET MIXERS


FIGURE 28 SERIES ARRANGEMENT OF MIXERS


Mixing of Miscible Liquids

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