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**Selecting Tube Inserts for Shell-and-Tube Heat Exchangers**

Group 4: Daniel Ehlers David Ehlig Erik Maki Darren Finney Tasnim Mohamed

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**Nomenclature A = correlation constant for static mixer heat-transfer**

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

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**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.

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**Laminar Tubeside Flow Patterns**

Temperature profile Velocity 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 , Sep, 2012.

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**Single-phase Heat Transfer Inserts**

TUBE INSERT HEAT 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 Student generated figure

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**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] [2] R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012.

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**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 'USE EITHER BOUNDARY LAYER OR SWIRL FLOW INSERTS' %interruption (m) 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' elseif Graetz>200 & Re>2300 'USE DISPLACED FLOW INSERT' End Examples >> chooseinsert(500,12,10,.5) Graetz = 120000 ans = USE EITHER BOUNDARY LAYER OR SWIRL FLOW INSERTS >> chooseinsert(2500,12,6,5) Graetz = 36000 ans = USE DISPLACED FLOW INSERT >> chooseinsert(500,.1,1,1) Graetz = 50 ans = Laminarization Present - USE STATIC MIXER INSERT

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**Laminarized Flow 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 Graetz Number: 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 Sieder-Tate Equation for Laminar Flow:

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**Numerical Differentiation of Gz**

Problem statement Use centered finite-difference formulas and Richardson Extrapolation to find 𝑑(𝐺𝑧) 𝑑𝐿 at L=3. Given: Fluid: liquid water, 𝑚 = 0.1 kg/s, Pr = 180 oF, η = 10-3 kg/(m*s). A) Function Derivation Given equation (3): 𝐺𝑧= 𝑅𝑒×𝑃𝑟×𝐷ℎ 𝐿 𝑅𝑒= 𝐷ℎ×𝑣×𝜌 η 𝐺𝑧= 𝐷ℎ2𝑣𝜌(𝑃𝑟) η𝐿 𝐴= 1 4 𝜋𝐷ℎ2 𝑣= 𝑚 𝜌𝐴 𝐺𝑧= 4 𝑚 (𝑃𝑟) 𝜋η𝐿

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**Numerical Differentiation of Gz**

B) Centered finite-difference evaluation 1) Evaluate the function at ℎ1and ℎ2 where ℎ2= ℎ1 2 : ℎ1 = 0.5 ℎ2 = 0.25 L Gz 2 2.5 3 3.5 4 L Gz 2.5 2.75 3 3.25 3.5 Figure 9 Figure 10 𝑑(𝐺𝑧) 𝑑𝐿 = [-( )+8*( )-8*( )+( )]/[12*(0.5)] 𝑑(𝐺𝑧) 𝑑𝐿 = 𝑑(𝐺𝑧) 𝑑𝐿 = [-( )+8*( )-8*( )+( )]/[12*(0.25)] 𝑑(𝐺𝑧) 𝑑𝐿 =

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**Numerical Differentiation of Gz**

C) Richardson Extrapolation Evaluate the function: 𝐷= 4 3 (− ) − − 𝑑(𝐺𝑧) 𝑑𝐿 =𝐷= − D) Error Analysis Determine the analytical value: 𝑑(𝐺𝑧) 𝑑𝐿 =− 4 𝑚 (𝑃𝑟) 𝜋η𝐿2 𝑑 𝐺𝑧 𝑑𝐿 (3)= Determine the true error: 𝜀𝑡= 𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 −𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 ∗100 = % where ℎ2= ℎ1 2

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**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 = , 𝐷ℎ = 0.05 m, 𝐿 = 5 m, 𝜇 = kg/(m*s), 𝜇𝑤 = kg/(m*s) A) MATLAB Function Creation (Nugraph.m): function Nugraph(Pr,Dh,L,Visc,wVisc) % Input: % Pr = Prandtl number Nu = 1.75*(Re*Pr*Dh/L).^0.33.*(Visc/wVisc)^0.14; % Dh = Hydraulic Diameter (m) % L = Fluid flow length from tube’s entrance to the first boundary layer interruption (m) plot(Re,Nu); hold on % Visc = Fluid Viscocity (n=s/m^2) xlabel('Re - Laminar Reynolds Number (0 to 2400)'); % wVisc = Fluid viscocity at the inner tube wall’s temperature (N-s/m^2) ylabel('Nu - Nusselt Number'); % Output: Nusselt Number plot over Laminar Reynolds Numbers title('Nusselt Number Values vs. Laminar Reynolds Numbers'); Re = linspace(0,2300,5000); 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.

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Static Mixing Insert Laminar Region Static Mixing Insert Well Mixed Region Figure 11: depicts the fluid mixing performed by a static mixing insert 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

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**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 , Sep, 2012.

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**Boundary-Layer Interruption Cont.**

The interrupt cannot allow the boundary thicker than the interrupt can handle. Figure 14: Heat flux redistribution for interrupts [2]. 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. Figure 13: Symmetrical interruption panel and the general flow patterns it creates [1]. [1] Journal of Heat Transfer: [2] Journal of Heat Transfer:

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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: 𝒉 𝟏 𝒉 𝟐 = 𝑫 𝒉𝟐 𝑳 𝟐 𝑫 𝒉𝟏 𝑳 𝟏 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.

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**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: 𝒉 𝟏 𝒉 𝟐 = 𝑫 𝒉𝟐 𝑳 𝟐 𝑫 𝒉𝟏 𝑳 𝟏 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: 𝒉 𝟏 𝒉 𝟐 = 𝟎.𝟓∗𝟎.𝟓 𝟎.𝟓∗𝟏.𝟓 𝟏/𝟑 =

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**Zero- to Fourth Order Zero 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. Order Value Ea Et N/A 1 2 3 4 Figure 15: Taylor Series value and Relative and True Error values (student generated). Figure 16: Plots of the Relative and True Error (student generated)

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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 ,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 17: Piping with uniform flow that provides no “dead spots” for heating Figure 18: Illustrated flow through twisted tapes (tubes)

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

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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

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Displaced Flow Rate Figure 20 The flow rate with a displacing insert as shown above can be calculated using the Hagen-Poiseuille equation: Where 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 Figure 21 R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012

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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: In two-phase flow, the effects of swirl flow inside a tube are different than the effects generated in single-phase flow. Two-phase flow is usually very turbulent, and the relative densities of the liquid and vapor phases often exceed 100:1. Therefore, swirl flow acts as a centrifuge to concentrate the denser liquid phase at the tube wall and the lighter vapor phase near the tube center. Figure 22

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**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.

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**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 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.

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**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

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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.

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**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. 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.

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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. Figure 29: Thermal and temperature stress on heat exchanger

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**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

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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

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**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

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**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 33 Figure 34: Flow pattern and temperature profile in exchanger showing cross flow

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**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 , Sep, 2012.

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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.

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**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.

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**Further Work Suggestions**

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

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

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