Selecting Tube Inserts for Shelland-Tube Heat Exchangers
Group 4:
Daniel Ehlers
David Ehlig
Erik Maki
Darren Finney
Tasnim Mohamed
http://brandguide.tamu.edu/downloads/logos/TAMU-logos-rgb/TAM-Logo/TAM-Logo.png
http://www.jscengineers.com/wp-content/uploads/2011/10/DayRefinery.jpg
Nomenclature
A = correlation constant for static mixer heattransfer
equation (Eq. 3)
B = exponent for static mixer heat-transfer equation
(Eq. 3)
Cp = specific heat, J/kg-K
D = inside tube diameter, m
De = equivalent inside tube diameter for turbulent
flow
heat transfer, m
Dh = inside hydraulic tube diameter, m
Dh1 = inside hydraulic tube diameter with Insert 1, m
Dh2 = inside hydraulic tube diameter with Insert 2, m
G = mass velocity of fluid, kg/s-m2
Gz = Graetz number (Eq. 1)
hcore = heat-transfer coefficient with core insert,
W/m2-K
htube = heat-transfer coefficient without insert,
W/m2-K
h1 = heat-transfer coefficient with Insert 1, W/m2-K
h2 = heat-transfer coefficient with Insert 2, W/m2-K
k = thermal conductivity, W/m-K
L = fluid flow length inside tube from entrance to
first
boundary layer interruption, m
L1 = interrupted flow length with Insert 1, m
L2 = interrupted flow length with Insert 2, m
Nfa = net free area inside tube with or without insert,
m2
Nu = Nusselt number (Eqs. 2 and 3)
Pr = Prandtl number = Cpμ/k
Re = Reynolds number = ρvDh/μ
v = velocity of the fluid, m/s
Greek Letters
μ = fluid viscosity, N-s/m2
μw = fluid viscosity at the inside tube wall
temperature, N-s/m2
ρ = fluid density, kg/m3
http://cnx.org/content/m42205/latest/Figure_13_01_01a.jpg
2
Introduction/Methodology
•
Shell-and-tube heat exchangers are a class of heat exchanger designs.
•
They are the most common type of heat exchangers in oil refineries and other large
chemical processes.
•
Steps to specifying a shell-and-tube heat exchanger:
•
Select a shell design
•
Determine most effective baffle arrangement
•
Focus on tube-side design
Figure 1: Cross-sectional diagram
of a U-tube Heat Exchanger.
Arrows show fluid flow pathways
on both shell and tube sides.
3
http://en.wikipedia.org/wiki/Shell_and_tube_heat_exchanger
Laminar Tubeside Flow Patterns
Velocity Profile
Temperature profile
Figure 2
Figure 3
Velocity Flow Pattern
• Velocity is lowest at the walls and greatest at the center
• An inviscid region forms in the center of the pipe
Temperature Flow Pattern
• An isothermal region forms at the center of the pipe
• Fluids with high thermal conductivity form short thermal entry lengths
• Fluids with low thermal conductivity form long thermal entry lengths
R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012.
4
Single-phase Heat Transfer Inserts
Isothermal
Separation
Thermal
Mixing
Figure 4
Heat transfer inserts improve heat exchanger efficiency by:
• Disturbing the inviscid, isothermal separation region which increases
thermal energy transfer inside the tube
• Increasing heat exchanger life-span and dependability
• Reducing energy usage and maintenance expenditures
• Reducing general emissions
5
Student generated figure
Types of Single-Phase Heat Transfer Inserts
Static Mixers
Boundary Layer Interrupters
Figure 5
Figure 6
Swirl-Flow Insert
Displaced-Flow Insert
Figure 7
Figure 8
[1] http://www.stamixco-usa.com/products/extrusion-melt-blender-static-mixer/default.html
[2] R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012.
6
Determining Optimal Tube Inserts
function chooseinsert(Re,Pr,Dh,L)
if Graetz<=200 & Graetz>20
%function determines which tube insert is
optimal
'Laminarization Present - USE STATIC MIXER
INSERT'
%Re = Reynolds number
end
%Pr = Prandtl number
if Re <= 200 & Graetz>200
%Dh = tube's hydraulic diameter (m)
'USE BOUNDARY LAYER INTERRUPTION INSERT'
%L = fluid flow length from the tube's
entrance to the first boundary layer
elseif (Re > 200) & (Re <= 1000)
& Graetz>200
%interruption (m)
'USE EITHER BOUNDARY LAYER OR SWIRL FLOW
INSERTS'
Graetz=Re*Pr*(Dh/L)
elseif (Re>1000) & (Re <= 2300) & Graetz>200
if Graetz<=20
'USE SWIRL FLOW INSERT'
'insufficient energy in the flow for
augmentation'
End
elseif Graetz>200 & Re>2300
'USE DISPLACED FLOW INSERT'
end
Examples
>> chooseinsert(500,12,10,.5)
>> chooseinsert(2500,12,6,5)
>> chooseinsert(500,.1,1,1)
Graetz =
120000
Graetz =
36000
Graetz =
50
ans =
USE EITHER BOUNDARY LAYER OR SWIRL
FLOW INSERTS
ans =
USE DISPLACED FLOW
INSERT
ans =
Laminarization Present - USE STATIC
MIXER INSERT
7
Laminarized Flow
Laminarized flow - occurs when the thickness of the laminar boundary
layer becomes equal to the dimension of the flow channel and there is
no free flow stream beyond the boundary layer
Graetz Number:
𝐷-ℎ
𝐺𝑧 = 𝑅𝑒 × 𝑃𝑟 × ( )
𝐿
• A useful dimensionless number used to estimate the onset of the
laminarized regime
• Laminarization occurs for viscous liquid flow at Graetz numbers less than
about 20-200
Sieder-Tate Equation for Laminar Flow:
𝐷ℎ 0.33 𝜇 0.14
𝑁𝑢 = 1.75 ( 𝑅𝑒 × 𝑃𝑟
) (
)
𝐿
𝜇𝑤
8
Numerical Differentiation of Gz
Problem statement
• Use centered finite-difference formulas and Richardson Extrapolation to find
at L=3.
𝑑(𝐺𝑧)
𝑑𝐿
• Given: Fluid: liquid water, 𝑚 = 0.1 kg/s, Pr = 2.0409 @ 180 oF, η = 10-3 kg/(m*s).
A) Function Derivation
𝑅𝑒×𝑃𝑟×𝐷ℎ
𝐿
2
𝐷ℎ 𝑣𝜌(𝑃𝑟)
η𝐿
1)
Given equation (3): 𝐺𝑧 =
2)
𝑅𝑒 =
3)
𝐴 = 4 𝜋𝐷ℎ2  𝑣 = 𝜌𝐴  𝐺𝑧 =
1
𝐷ℎ×𝑣×𝜌
η
 𝐺𝑧 =
𝑚
4𝑚(𝑃𝑟)
𝜋η𝐿
9
Numerical Differentiation of Gz
B) Centered finite-difference evaluation
ℎ1
2
1) Evaluate the function at ℎ1and ℎ2 where ℎ2 =
:
ℎ1 = 0.5
Figure 9
ℎ2 = 0.25
L
Gz
L
Gz
2
129.9277
2.5
103.9422
2.5
103.9422
2.75
94.49289
3
86.61849
3
86.61849
3.5
74.24442
3.25
79.95553
4
64.96386
3.5
74.24442
𝑑(𝐺𝑧)
= [-(64.96386)+8*(742.24442)𝑑𝐿
8*(103.9422)+(129.9277)]/[12*(0.5)]
𝑑(𝐺𝑧)
𝑑𝐿
= -28.7697
Figure 10
𝑑(𝐺𝑧)
= [-(74.24442)+8*(79.95553)8*(94.49289)+(103.9422)]/[12*(0.25)]
𝑑𝐿
𝑑(𝐺𝑧)
𝑑𝐿
= -28.8671
10
Numerical Differentiation of Gz
C) Richardson Extrapolation
where ℎ2 =
1)
ℎ1
2
Evaluate the function:
4
𝐷 = 3 (−28.8671) −
𝑑(𝐺𝑧)
𝑑𝐿
1
3
−28.7697
= 𝐷 = −28.8995
D) Error Analysis
1) Determine the analytical value:
𝑑(𝐺𝑧)
4𝑚(𝑃𝑟)
=−
𝑑𝐿
𝜋η𝐿2
𝑑 𝐺𝑧
𝑑𝐿
2)
(3) = -28.8728
Determine the true error:
𝜀𝑡 =
𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 −𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒
∗ 100 = 0.09241 %
11
Nusselt Number Plot for Laminar Flow
Scenario
Problem statement
• Write a function to create a plot of Nusselt Number, 𝑁𝑢 vs. Laminar Reynolds Numbers, 𝑅𝑒
(0 to 2400) for a given flow scenario.
• Given: Pr = 2.0409, 𝐷ℎ = 0.05 m, 𝐿 = 5 m, 𝜇 = 0.001 kg/(m*s), 𝜇𝑤 = 0.001 kg/(m*s)
A) MATLAB Function Creation (Nugraph.m):
function Nugraph(Pr,Dh,L,Visc,wVisc)
% Input:
% Pr = Prandtl number
% Dh = Hydraulic Diameter (m)
% L = Fluid flow length from tube’s
entrance to the first boundary layer
interruption (m)
% Visc = Fluid Viscocity (n=s/m^2)
% wVisc = Fluid viscocity at the inner
tube wall’s temperature (N-s/m^2)
% Output: Nusselt Number plot over
Laminar Reynolds Numbers
Re = linspace(0,2300,5000);
Nu =
1.75*(Re*Pr*Dh/L).^0.33.*(Visc/wVisc)^0.1
4;
plot(Re,Nu);
hold on
xlabel('Re - Laminar Reynolds Number
(0 to 2400)');
ylabel('Nu - Nusselt Number');
title('Nusselt Number Values vs.
Laminar Reynolds Numbers');
xlim([0 2400]);
grid on;
hold off
end
12
Nusselt Number Plot for Laminar Flow
Scenario
B) MATLAB Input:
>> Nugraph(2.0409,.05,5,.001,.001)
C) MATLAB Output:
Figure 10: Nusselt Number vs. Laminar Reynolds
Flow for a given flow scenario.
13
Static Mixing Insert
Figure 11: depicts
the fluid mixing
performed by a
static mixing insert
Laminar Region
•
•
•
•
•
Static Mixing Insert
Well Mixed Region
Static mixers are motionless inserts which accelerate the inline mixing by disturbing the flow
layers.
Commonly used for cooling highly viscous polymers
The only mixers which can operate in the laminarized flow region
Can increase heat transfer efficiency by six fold
There are various types and designs consisting of plates, baffles, helical elements all
positioned to direct flow and increase turbulence
14
http://www.sulzer.com/en/Products-and-Services/Agitators-Mixers-and-Dispensers/Static-Mixers/General-Purpose-Mixers
Boundary-Layer Interruption
Figure 12: Typical interruption
layers placed in a laminar flow
tube
• This insert is preferred for very high Graetz numbers (typically with Reynolds
numbers between 1-1,000).
• This allows the boundary-layer of the fluid to be easily reduced and thinned to its
minimum thickness.
• How effective the reduction/thinning is determined by how high the interrupts
are and the spacing between them.
• This method is usually used to augment the flow of oils that are laminar in nature.
R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012.
15
Boundary-Layer Interruption Cont.
•
The interrupt cannot allow the boundary
thicker than the interrupt can handle.
Figure 14: Heat flux redistribution for interrupts [2].
•
•
Figure 13: Symmetrical interruption panel and the
general flow patterns it creates [1].
The heating process will be
rendered ineffective if this
happens.
The more symmetrical an
interrupt is the more likely it will
be effective in transferring
heating to a fluid.
[1] Journal of Heat Transfer:
http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleid=1450593
16
[2] Journal of Heat Transfer:
http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleid=1737304
Heat Transfer Increase
•
The overall rate of heat transfer is measured by the inverse relationship
between the hydraulic diameter of the pipe and the length of the interrupt.
This relationship can be described as follows:
𝒉𝟏
𝑫𝒉𝟐 𝑳𝟐
=
𝒉𝟐
𝑫𝒉𝟏 𝑳𝟏
𝟏/𝟑
• The h is the heat-transfer coefficient, D is the hydraulic diameter of the tube,
L is the length of the interrupted flow, and 1 & 2 represent either two
separate inserts or an insert and the tube itself.
17
Taylor Series Expansion
Problem Statement:
Use Taylor Series Expansion, zero- to fourth-order, to predict the heat-transfer
coefficient ratio for insert length of 0.5 m and an initial value, L_0, of 0.2 for:
𝒉𝟏
𝑫𝒉𝟐 𝑳𝟐
=
𝒉𝟐
𝑫𝒉𝟏 𝑳𝟏
𝟏/𝟑
The tube length and diameter (L1 and D1 ) are 1.5 m and 0.5 m, respectively. The
diameter of the insert (D2) is 0.5 m.
True Value:
𝒉𝟏
𝒉𝟐
=
𝟎.𝟓∗𝟎.𝟓 𝟏/𝟑
𝟎.𝟓∗𝟏.𝟓
=0.693361
18
Zero- to Fourth Order
Zero Order:
First Order:
Second Order:
Third Order:
Fourth Order
19
Analysis
It seems that the value is oscillating between the value of about 0.75 and 0.63,
roughly, with its value slowly approaching the true value. It is probable with more
iterations the true value would have been found.
Relative & True Error
Order
Value
Ea
Et
35
0
0.510873
N/A
26.31933
30
1
0.766309
33.33329
10.52093
Error (%)
25
20
2
0.638591
19.99997
7.899204
3
0.745023
14.28573
7.450953
10
4
0.638591
16.66669
7.899204
5
Figure 15: Taylor Series value and
Relative and True Error values (student
generated).
TRUE
15
Relative
0
0
1
2
3
4
5
Iteration
Figure 16: Plots of the Relative and True Error
(student generated)
20
Swirl Flow
•
The swirl-flow augment is most effective with
the higher laminar flow rates, which typically
has a Reynolds number from 200-10,000.
•
The helical design produces a higher velocity
within the tubes. This velocity is related to the
flow angle of the insert.
•
Figure 17: Piping with uniform flow that
provides no “dead spots” for heating
As well, this design creates a rotational and
centripetal flow that further increases the
mixing and turbulence within.
–
Inducing turbulence at lower Reynolds
numbers is what causes successful and
effective heat transfer.
http://www.oxide.co.il/en/twisted-tube.html
Figure 18: Illustrated
flow through twisted
tapes (tubes)
21
Displaced Flow
Cylindrical Rod Insert
Displaced Flow inserts increase
heat transfer by lowering the
net fee area (Nfa) inside the
tube, which creates higher
velocities along the tube wall
heat transfer surface.
Figure 19
Inserts like the one shown above are the simplest types of
displaced flow inserts they are supported in the center of
the tube and extend the entire length of the tube.
22
R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012
Displaced Flow cont.
•
Equivalent Diameter, De
– The equivalent diameter is used to calculate the new heat transfer coefficient
by the equation
• hcore is the new heat transfer coefficient with the insert
• htube is the heat transfer coefficient with no insert
•
For fluids with similar viscosities to water, heat transfer can be increased by over
2.5 times
– The value increased is dependent on the pressure drop that occurs over the
tube
23
Displaced Flow Rate
Figure 20
•
The flow rate with a displacing insert as shown above
can be calculated using the Hagen-Poiseuille equation:
Figure 20
•
Where
24
Flow Regime Overlap
•
Flow Regime overlap: Usually more than one type of insert can be used to improve
heat transfer.
– The exception being static mixers
Wire wrapped core insert
Figure 21
•
Some inserts like the one above are designed to take advantage of more than one
kind of flow augmentation.
– The insert above utilizes both displaced and swirl flow thus further enhancing
the heat transfer beyond the value of either insert alone.
25
R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012
Two-Phase Flow Inserts
• What is two-phase flow?
–Flow in which two phases exist (i.e. gas and liquid flow)
• Types of two-phase flow regimes:
26
http://www.drbratland.com/PipeFlow2/chapter1.html
Figure 22
Two-Phase Flow Inserts
What are two-phase flow inserts?
Devices placed in a tube
containing two phases
Types of two-phase flow inserts:
• Static Mixers
• Boundary-Layer Interruption
Devices
• Displaced-Flow Mechanisms
How do these inserts help?
These inserts increase turbulence
and enhance mixing
Figure 23: Enhanced tubes for augmentation of heat transfer.
(a) Corrugated or spirally indented tube with internal protuberances.
(b) Integral external fins. (c) Integral internal fins. (d) Deep spirally
27
fluted tube. (e) Static mixer insert. (f) Wire-wound insert.
http://www.thermopedia.com/content/574/
Two-Phase Flow Inserts
Static Mixers and Boundary-Layer
Interruption Devices
• Improve heat transfer by a full
order of magnitude
• Improper design results in high
pressure drops
Figure 24: Simulation of flow division and radial mixing in a static
mixer http://en.wikipedia.org/wiki/Static_mixer
Figure 25: Luer Connection Flow Interrupter
This design can be used to automatically purge air from a
pressurized fluid delivery system where gravity cannot be used.
http://www.medrad.com/enus/resources/Documents/techpubs08-001.pdf
28
Two-Phase Flow Inserts
Displaced-Flow Mechanisms
–These inserts enhance heat transfer only as much as the resulting increase in
velocity
Figure 26
Flow disruption caused by a wire matrix turbulator
(A) Laminar flow conditions (B) Turbulence caused by tube inserts
http://farm2.static.flickr.com/1097/1339225054_4c6616613c.jpg
29
Practical Considerations when using Tube
Inserts
• Pressure drop
–Tube inserts can significantly increase pressure drop of plain-tube system
conditions
–Most inserts designed to produce same pressure drop as experienced by a
longer, plain tube
Figure 27: Pressure drop
evolution with vapor quality
for Gplain = 75 kg/m2 s
and Tsat = 5 °C.
30
http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.07.003
Practical Considerations when using Tube Inserts
Figure 28
Upset conditions
• Inserts are attached to faces
of tube sheets to allow for
maintenance
• Attachment can be designed
to withstand pressure drop if
upset conditions are known
• For example, inserts can be
found embedded in a
downstream pump if upset
conditions not accounted
for.
http://www.hcheattransfer.com/fouling1.html
Sedimentation occurs when particles (e.g. dirt, sand or
rust) in the solution settle and deposit on the heat transfer
surface. Like scale, these deposits may be difficult to
remove mechanically depending on their nature.
31
Practical Considerations when using Tube
Inserts
• Transient operation
–Flow stops and cools to ambient temperature
–Start-up pressure drop can reach 100 times normal operating conditions
–Heat tube-side fluid to operating temperature before reaching desired flow
rate to prevent problems.
Figure 29: Thermal and
temperature stress on heat
exchanger
32
http://crackedheatexchanger.com/what-is-a-thermalstress-point-or-temperature-stress-point/
Practical Considerations when using Tube
Inserts
Materials compatibility
• Insert material must be
compatible with tube material
and fluid
Carbon steel inserts in a water service
often “weld” themselves to the tube
wall.
Sometimes scrapping of the entire tube
bundle is required.
Stainless steel and other corrosionresistant metallurgies is often the best
way to avoid this problem
Figure 30: Stainless SteelThreaded tube inserts serve as
end plugs in tubing
33
http://www.directindustry.com/prod/ganter/threadedinserts-to-be-fitted-tube-end-15596-897461.html
Practical Considerations when using Tube
Inserts
• Fluid condition
–Be aware of tube-side fluid conditions
–For example, fluid in laminar flow should be relatively free of particulates to
prevent tube plugging
•An interrupter can act as a particulate dam in laminar flow
•Swirl flow may not produce enough turbulence to carry particulates
through each helical rotation
Figure 31: Particle Trajectories
in a Laminar Static Mixer
34
http://www.comsol.com/model/particle-trajectories-in-a-laminar-static-mixer-10644
Practical Considerations when using Tube
Inserts
Anticipated fouling
• Evaluate the extent and types
of fouling expected
• Determine if removing insert
for maintenance is possible
Figure 32: Heat exchanger in a steam
power plant, fouled by macro fouling
35
http://en.wikipedia.org/wiki/Fouling
Typical Application
• Process stream preheated
using waste heat
Figure 33
• Maximum energy recovery
involves a temperature cross
• Outlet temperature of
cold stream higher than
inlet temperature of hot
stream
• Heat exchanger must be either
a single counter-flow or
multiple shells in series
• Five alternate tube-side
designs were compared and
are summarized in Figure 35
on the next slide..
http://nptel.iitm.ac.in/courses/103103032/module8/lec34/3.html
Figure 34: Flow pattern and temperature profile
in
36
exchanger showing cross flow
Figure 35
Figure 35: Effects of tube inserts on heat transfer [1].
[1]
R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012.
37
Conclusions
• Through the use of many different numerical methods, such as Taylor series
expansion, centered finite differences, and Richardson extrapolation, we are able
to determine several parameters involving pipe flow which allow us to better
understand the nature of the flow as well as analyze and compare the
effectiveness of different heat transfer inserts.
• Further Research:
–Further research may be performed regarding Flow regime overlap in order
to determine a maximum effectiveness of different combinations of heat
transfer inserts with regards to heat exchange.
–Further research in static mixing may also be performed in order to maximize
the effectiveness of the mixing and minimizing the inhibition of the flow
through the tube.
–Both of these studies would involve using a variety of numerical methods such
as the ones used earlier in order to obtain the desired results from the data.
http://civil.engr.siu.edu/cheval/engr351/Images/ENGR351.jpg
38
Further Work Suggestions
• Fluid flow simulations of various inserts
• Graphical model depicting efficiency of insert
Figure 36: Geometries of peripherally-cut
twisted tapes (PTs) and typical twisted tape (TT)
Figure 37: A rendering of a set of fluid flow lines from
a simulation of a shell and tube heat exchanger.
39
http://dx.doi.org/10.1016/j.expthermflusci.2009.12.013
http://en.wikipedia.org/wiki/Shell_and_tube_heat_exchanger
Further Work Suggestions
• Algorithm to determine best design for each type of tube-insert
Figure 38: Fluid flow velocity profile over valve
connections
http://www.sureflowequipment.com/whatsnewimages/Fluid%20Flow.jpg
Figure 39: Fluid flow velocity profiles over insert
http://www.exolete.com/images/vtkexample.png
Figure 40: Velocity and temperature profiles
over tube-inserts
http://www.frontierlattices.ch/wpcontent/uploads/2011/06/temp_micro.png
40
References
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
http://www.mathworks.com/help/physmod/hydro/ref/annularorifice.html
R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP
Magazine, pp. 19-25, Sep, 2012.
http://en.wikipedia.org/wiki/Shell_and_tube_heat_exchanger
http://www.drbratland.com/PipeFlow2/chapter1.html
http://en.wikipedia.org/wiki/Static_mixer
http://www.medrad.com/en-us/resources/Documents/techpubs08-001.pdf
http://farm2.static.flickr.com/1097/1339225054_4c6616613c.jpg
http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.07.003
http://www.hcheattransfer.com/fouling1.html
http://crackedheatexchanger.com/what-is-a-thermal-stress-point-or-temperaturestress-point/
http://www.directindustry.com/prod/ganter/threaded-inserts-to-be-fitted-tube-end15596-897461.html
http://www.comsol.com/model/particle-trajectories-in-a-laminar-static-mixer-10644
http://en.wikipedia.org/wiki/Fouling
http://nptel.iitm.ac.in/courses/103103032/module8/lec34/3.html
http://dx.doi.org/10.1016/j.expthermflusci.2009.12.013
http://www.staticmixers.com/staticmixer_designs.pdf
http://www.heatexchanger-fouling.com/papers/papers2009/56_Krueger_F.pdf
41