Selecting Tube Inserts for Shell-and-Tube Heat ExchangersGroup 4:

Daniel EhlersDavid EhligErik Maki

Darren FinneyTasnim Mohamed

http://www.jscengineers.com/wp-content/uploads/2011/10/DayRefinery.jpg

http://brandguide.tamu.edu/downloads/logos/TAMU-logos-rgb/TAM-Logo/TAM-Logo.png

NomenclatureA = correlation constant for static mixer heat-transferequation (Eq. 3)B = exponent for static mixer heat-transfer equation(Eq. 3)Cp = specific heat, J/kg-K

D = inside tube diameter, mDe = equivalent inside tube diameter for turbulent flowheat transfer, mDh = 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-m2Gz = Graetz number (Eq. 1)

hcore = heat-transfer coefficient with core insert, W/m2-Khtube = 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-KL = fluid flow length inside tube from entrance to firstboundary layer interruption, mL1 = 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, m2Nu = Nusselt number (Eqs. 2 and 3)Pr = Prandtl number = Cpμ/kRe = Reynolds number = ρvDh/μv = velocity of the fluid, m/sGreek Lettersμ = fluid viscosity, N-s/m2μw = fluid viscosity at the inside tube wall temperature, N-s/m2ρ = fluid density, kg/m3

2http://cnx.org/content/m42205/latest/Figure_13_01_01a.jpg

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.

http://en.wikipedia.org/wiki/Shell_and_tube_heat_exchanger

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Laminar Tubeside Flow PatternsVelocity Profile Temperature profile

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.

Figure 2Figure 3

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Single-phase Heat Transfer Inserts

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

Student generated figure

TUB

E IN

SER

T

HEAT HEAT HEAT HEAT

HEAT HEAT HEAT HEAT

Isothermal Separation Thermal

Mixing

Figure 4

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Types of Single-Phase Heat Transfer Inserts

[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.

Static MixersBoundary Layer Interrupters

Displaced-Flow InsertSwirl-Flow Insert

Figure 5Figure 6

Figure 7 Figure 8

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Determining Optimal Tube Insertsfunction chooseinsert(Re,Pr,Dh,L)

%function determines which tube insert is optimal

%Re = Reynolds number

%Pr = Prandtl number

%Dh = tube's hydraulic diameter (m)

%L = fluid flow length from the tube's entrance to the first boundary layer

%interruption (m)

Graetz=Re*Pr*(Dh/L)

if Graetz<=20

'insufficient energy in the flow for augmentation'

End

if Graetz<=200 & Graetz>20

'Laminarization Present - USE STATIC MIXER INSERT'

end

if Re <= 200 & Graetz>200

'USE BOUNDARY LAYER INTERRUPTION INSERT'

elseif (Re > 200) & (Re <= 1000) & Graetz>200

'USE EITHER BOUNDARY LAYER OR SWIRL FLOW INSERTS'

elseif (Re>1000) & (Re <= 2300) & Graetz>200

'USE SWIRL FLOW INSERT'

elseif Graetz>200 & Re>2300

'USE DISPLACED FLOW INSERT'

end

>> chooseinsert(2500,12,6,5)

Graetz = 36000

ans =USE DISPLACED FLOW INSERT

>> chooseinsert(500,12,10,.5)

Graetz = 120000

ans =USE EITHER BOUNDARY LAYER OR SWIRL FLOW INSERTS

>> chooseinsert(500,.1,1,1)

Graetz = 50

ans =Laminarization Present - USE STATIC MIXER INSERT

Examples

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Laminarized Flow

𝑁𝑢 = 1.75 ( 𝑅𝑒 × 𝑃𝑟 𝐷ℎ𝐿 )0.33( 𝜇𝜇𝑤 )0.14

𝐺𝑧= 𝑅𝑒 × 𝑃𝑟 × (𝐷-ℎ𝐿) Graetz Number:

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

• 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:

8

Numerical Differentiation of Gz

Problem statement•Use centered finite-difference formulas and Richardson Extrapolation to find at

L=3.•Given: Fluid: liquid water, = 0.1 kg/s, Pr = 2.0409 @ 180 oF, η = 10-3 kg/(m*s).

A) Function Derivation1) Given equation (3): 2) 3)

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Numerical Differentiation of GzB) Centered finite-difference evaluation

1) Evaluate the function at and where :

L Gz

2 129.92772.5 103.94223 86.61849

3.5 74.244424 64.96386

= 0.5

= [-(64.96386)+8*(742.24442)-8*(103.9422)+(129.9277)]/[12*(0.5)]= -28.7697

L Gz

2.5 103.94222.75 94.49289

3 86.618493.25 79.955533.5 74.24442

= 0.25

= [-(74.24442)+8*(79.95553)-8*(94.49289)+(103.9422)]/[12*(0.25)]= -28.8671

Figure 9 Figure 10

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Numerical Differentiation of GzC) Richardson Extrapolation

1) Evaluate the function:

28.8995

D) Error Analysis2) Determine the analytical value:

-28.8728

2) Determine the true error:

= 0.09241 %

where

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Nusselt Number Plot for Laminar Flow Scenario

Problem statement• Write a function to create a plot of Nusselt Number, vs. Laminar Reynolds Numbers, (0 to

2400) for a given flow scenario.• Given: = 2.0409, = 0.05 m, = 5 m, = 0.001 kg/(m*s), = 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)^0.14; 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

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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

http://www.sulzer.com/en/Products-and-Services/Agitators-Mixers-and-Dispensers/Static-Mixers/General-Purpose-Mixers

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

Figure 11: depicts the fluid mixing performed by a static mixing insert

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Boundary-Layer Interruption

• 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.

Figure 12: Typical interruption layers placed in a laminar flow tube

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Boundary-Layer Interruption Cont.

• The interrupt cannot allow the boundary thicker than the interrupt can handle.

• 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[2] Journal of Heat Transfer: http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleid=1737304

Figure 13: Symmetrical interruption panel and the general flow patterns it creates [1].

Figure 14: Heat flux redistribution for interrupts [2].

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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:

• 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:

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:

0.693361

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Zero- to Fourth OrderZero Order:

First Order:

Second Order:

Third Order:

Fourth Order

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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.

Figure 15: Taylor Series value and Relative and True Error values (student generated).

Figure 16: Plots of the Relative and True Error (student generated)

Order Value Ea Et

0 0.510873 N/A 26.31933

1 0.766309 33.33329 10.52093

2 0.638591 19.99997 7.899204

3 0.745023 14.28573 7.450953

4 0.638591 16.66669 7.899204

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

30

35

Relative & True Error

TRUE

Relative

Iteration

Err

or

(%)

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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.

• 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.

Figure 18: Illustrated flow through twisted tapes (tubes)

Figure 17: Piping with uniform flow that provides no “dead spots” for heating

http://www.oxide.co.il/en/twisted-tube.html 21

Displaced Flow

Cylindrical Rod Insert

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.

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.

R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012

Figure 19

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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

• The flow rate with a displacing insert as shown abovecan be calculated using the Hagen-Poiseuille equation:

• Where

Figure 20

Figure 20

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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

• 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.

Wire wrapped core insert

R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp. 19-25, Sep, 2012

Figure 21

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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:

http://www.drbratland.com/PipeFlow2/chapter1.html Figure 2226

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 fluted tube. (e) Static mixer insert. (f) Wire-wound insert.http://www.thermopedia.com/content/574/

27

Two-Phase Flow InsertsStatic 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 InterrupterThis design can be used to automatically purge air from a pressurized fluid delivery system where gravity cannot be used.http://www.medrad.com/en-us/resources/Documents/techpubs08-001.pdf

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Two-Phase Flow InsertsDisplaced-Flow Mechanisms

–These inserts enhance heat transfer only as much as the resulting increase in velocity

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

Figure 26

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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.

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2012.07.00330

Practical Considerations when using Tube Inserts

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.

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.

http://www.hcheattransfer.com/fouling1.html

Figure 28

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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.

http://crackedheatexchanger.com/what-is-a-thermal-stress-point-or-temperature-stress-point/

Figure 29: Thermal and temperature stress on heat exchanger

32

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 corrosion-resistant metallurgies is often the best way to avoid this problem

Figure 30: Stainless Steel-Threaded tube inserts serve as end plugs in tubing

http://www.directindustry.com/prod/ganter/threaded-inserts-to-be-fitted-tube-end-15596-897461.html

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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

http://www.comsol.com/model/particle-trajectories-in-a-laminar-static-mixer-10644

34

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

http://en.wikipedia.org/wiki/Fouling35

Typical Application• Process stream preheated

using waste heat• 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..

Figure 34: Flow pattern and temperature profile in exchanger showing cross flowhttp://nptel.iitm.ac.in/courses/103103032/module8/lec34/3.html

Figure 33

36

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.

38http://civil.engr.siu.edu/cheval/engr351/Images/ENGR351.jpg

Further Work Suggestions• Fluid flow simulations of various inserts• Graphical model depicting efficiency of insert

Figure 37: A rendering of a set of fluid flow lines from a simulation of a shell and tube heat exchanger.

http://dx.doi.org/10.1016/j.expthermflusci.2009.12.013

Figure 36: Geometries of peripherally-cut twisted tapes (PTs) and typical twisted tape (TT)

http://en.wikipedia.org/wiki/Shell_and_tube_heat_exchanger39

Further Work Suggestions

http://www.exolete.com/images/vtkexample.pnghttp://www.sureflowequipment.com/whatsnewimages/Fluid%20Flow.jpg

http://www.frontierlattices.ch/wp-content/uploads/2011/06/temp_micro.png

• Algorithm to determine best design for each type of tube-insert

Figure 38: Fluid flow velocity profile over valve connections

Figure 39: Fluid flow velocity profiles over insert

Figure 40: Velocity and temperature profiles over tube-inserts

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-temperature-stress-point/• http://

www.directindustry.com/prod/ganter/threaded-inserts-to-be-fitted-tube-end-15596-897461.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