Presentation on theme: "Selecting Tube Inserts for Shell-and-Tube Heat Exchangers"— Presentation transcript:
1 Selecting Tube Inserts for Shell-and-Tube Heat Exchangers Group 4:Daniel EhlersDavid EhligErik MakiDarren FinneyTasnim Mohamed
2 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-KD = inside tube diameter, mDe = equivalent inside tube diameter for turbulent flowheat transfer, mDh = inside hydraulic tube diameter, mDh1 = inside hydraulic tube diameter with Insert 1, mDh2 = inside hydraulic tube diameter with Insert 2, mG = 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-Kh1 = heat-transfer coefficient with Insert 1, W/m2-Kh2 = heat-transfer coefficient with Insert 2, W/m2-Kk = thermal conductivity, W/m-KL = fluid flow length inside tube from entrance to firstboundary layer interruption, mL1 = interrupted flow length with Insert 1, mL2 = interrupted flow length with Insert 2, mNfa = 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
3 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 designDetermine most effective baffle arrangementFocus on tube-side designFigure 1: Cross-sectional diagram of a U-tube Heat Exchanger. Arrows show fluid flow pathways on both shell and tube sides.
4 Laminar Tubeside Flow Patterns Temperature profileVelocity ProfileFigure 2Figure 3Velocity Flow PatternVelocity is lowest at the walls and greatest at the centerAn inviscid region forms in the center of the pipeTemperature Flow PatternAn isothermal region forms at the center of the pipeFluids with high thermal conductivity form short thermal entry lengthsFluids with low thermal conductivity form long thermal entry lengthsR. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012.
5 Single-phase Heat Transfer Inserts TUBE INSERTHEATIsothermal SeparationThermal MixingFigure 4Heat transfer inserts improve heat exchanger efficiency by:Disturbing the inviscid, isothermal separation region which increases thermal energy transfer inside the tubeIncreasing heat exchanger life-span and dependabilityReducing energy usage and maintenance expendituresReducing general emissionsStudent generated figure
6 Types of Single-Phase Heat Transfer Inserts Static MixersBoundary Layer InterruptersFigure 5Figure 6Swirl-Flow InsertDisplaced-Flow InsertFigure 7Figure 8 R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012.
7 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 numberend%Pr = Prandtl numberif 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 layerelseif (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>200if Graetz<=20'USE SWIRL FLOW INSERT''insufficient energy in the flow for augmentation'elseif Graetz>200 & Re>2300'USE DISPLACED FLOW INSERT'EndExamples>> chooseinsert(500,12,10,.5)Graetz =120000ans =USE EITHER BOUNDARY LAYER OR SWIRL FLOW INSERTS>> chooseinsert(2500,12,6,5)Graetz =36000ans =USE DISPLACED FLOW INSERT>> chooseinsert(500,.1,1,1)Graetz =50ans =Laminarization Present - USE STATIC MIXER INSERT
8 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 layerGraetz Number:A useful dimensionless number used to estimate the onset of the laminarized regimeLaminarization occurs for viscous liquid flow at Graetz numbers less than aboutSieder-Tate Equation for Laminar Flow:
9 Numerical Differentiation of Gz Problem statementUse 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 DerivationGiven equation (3): 𝐺𝑧= 𝑅𝑒×𝑃𝑟×𝐷ℎ 𝐿𝑅𝑒= 𝐷ℎ×𝑣×𝜌 η 𝐺𝑧= 𝐷ℎ2𝑣𝜌(𝑃𝑟) η𝐿𝐴= 1 4 𝜋𝐷ℎ2 𝑣= 𝑚 𝜌𝐴 𝐺𝑧= 4 𝑚 (𝑃𝑟) 𝜋η𝐿
10 Numerical Differentiation of Gz B) Centered finite-difference evaluation 1) Evaluate the function at ℎ1and ℎ2 where ℎ2= ℎ1 2 :ℎ1 = 0.5ℎ2 = 0.25LGz22.533.54LGz2.52.7533.253.5Figure 9Figure 10𝑑(𝐺𝑧) 𝑑𝐿 = [-( )+8*( )-8*( )+( )]/[12*(0.5)]𝑑(𝐺𝑧) 𝑑𝐿 =𝑑(𝐺𝑧) 𝑑𝐿 = [-( )+8*( )-8*( )+( )]/[12*(0.25)]𝑑(𝐺𝑧) 𝑑𝐿 =
11 Numerical Differentiation of Gz C) Richardson ExtrapolationEvaluate the function:𝐷= 4 3 (− ) − −𝑑(𝐺𝑧) 𝑑𝐿 =𝐷= −D) Error AnalysisDetermine the analytical value:𝑑(𝐺𝑧) 𝑑𝐿 =− 4 𝑚 (𝑃𝑟) 𝜋η𝐿2𝑑 𝐺𝑧 𝑑𝐿 (3)=Determine the true error:𝜀𝑡= 𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 −𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 ∗100 = %where ℎ2= ℎ1 2
12 Nusselt Number Plot for Laminar Flow Scenario Problem statementWrite 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 numberNu = 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 Numberstitle('Nusselt Number Values vs. Laminar Reynolds Numbers');Re = linspace(0,2300,5000);xlim([0 2400]);grid on;hold offend
13 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.
14 Static Mixing InsertLaminar RegionStatic Mixing InsertWell Mixed RegionFigure 11: depicts the fluid mixing performed by a static mixing insertStatic mixers are motionless inserts which accelerate the inline mixing by disturbing the flow layers.Commonly used for cooling highly viscous polymersThe only mixers which can operate in the laminarized flow regionCan increase heat transfer efficiency by six foldThere are various types and designs consisting of plates, baffles, helical elements all positioned to direct flow and increase turbulence
15 Boundary-Layer Interruption Figure 12: Typical interruption layers placed in a laminar flow tubeThis 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.
16 Boundary-Layer Interruption Cont. The interrupt cannot allow the boundary thicker than the interrupt can handle.Figure 14: Heat flux redistribution for interrupts .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 . Journal of Heat Transfer: Journal of Heat Transfer:
17 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 𝟏/𝟑The 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.
18 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 𝟏/𝟑The 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 =
19 Zero- to Fourth Order Zero Order: First Order: Second Order: Third Order:Fourth Order
20 AnalysisIt 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.OrderValueEaEtN/A1234Figure 15: Taylor Series value and Relative and True Error values (student generated).Figure 16: Plots of the Relative and True Error (student generated)
21 Swirl FlowThe 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 heatingFigure 18: Illustrated flow through twisted tapes (tubes)
22 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 19Inserts 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
23 Displaced Flow cont. Equivalent Diameter, De The equivalent diameter is used to calculate the new heat transfer coefficient by the equationhcore is the new heat transfer coefficient with the inserthtube is the heat transfer coefficient with no insertFor fluids with similar viscosities to water, heat transfer can be increased by over 2.5 timesThe value increased is dependent on the pressure drop that occurs over the tube
24 Displaced Flow RateFigure 20The flow rate with a displacing insert as shown abovecan be calculated using the Hagen-Poiseuille equation:WhereFigure 20
25 Flow Regime OverlapFlow Regime overlap: Usually more than one type of insert can be used to improve heat transfer.The exception being static mixersSome 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 insertFigure 21R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012
26 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
27 Two-Phase Flow Inserts What are two-phase flow inserts?Devices placed in a tube containing two phasesTypes of two-phase flow inserts:Static MixersBoundary-Layer Interruption DevicesDisplaced-Flow MechanismsHow do these inserts help?These inserts increase turbulence and enhance mixingFigure 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.
28 Two-Phase Flow Inserts Static Mixers and Boundary-Layer Interruption DevicesImprove heat transfer by a full order of magnitudeImproper design results in high pressure dropsFigure 24: Simulation of flow division and radial mixing in a static mixerFigure 25: Luer Connection Flow InterrupterThis design can be used to automatically purge air from a pressurized fluid delivery system where gravity cannot be used.
29 Two-Phase Flow Inserts Displaced-Flow MechanismsThese inserts enhance heat transfer only as much as the resulting increase in velocityFigure 26Flow disruption caused by a wire matrix turbulator(A) Laminar flow conditions (B) Turbulence caused by tube inserts
30 Practical Considerations when using Tube Inserts Pressure dropTube inserts can significantly increase pressure drop of plain-tube system conditionsMost inserts designed to produce same pressure drop as experienced by a longer, plain tubeFigure 27: Pressure drop evolution with vapor quality for Gplain = 75 kg/m2 s and Tsat = 5 °C.
31 Practical Considerations when using Tube Inserts Figure 28Upset conditionsInserts are attached to faces of tube sheets to allow for maintenanceAttachment can be designed to withstand pressure drop if upset conditions are knownFor 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.
32 Practical Considerations when using Tube Inserts Transient operationFlow stops and cools to ambient temperatureStart-up pressure drop can reach 100 times normal operating conditionsHeat tube-side fluid to operating temperature before reaching desired flow rate to prevent problems.Figure 29: Thermal and temperature stress on heat exchanger
33 Practical Considerations when using Tube Inserts Materials compatibilityInsert material must be compatible with tube material and fluidCarbon 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 problemFigure 30: Stainless Steel-Threaded tube inserts serve as end plugs in tubing
34 Practical Considerations when using Tube Inserts Fluid conditionBe aware of tube-side fluid conditionsFor example, fluid in laminar flow should be relatively free of particulates to prevent tube pluggingAn interrupter can act as a particulate dam in laminar flowSwirl flow may not produce enough turbulence to carry particulates through each helical rotationFigure 31: Particle Trajectories in a Laminar Static Mixer
35 Practical Considerations when using Tube Inserts Anticipated foulingEvaluate the extent and types of fouling expectedDetermine if removing insert for maintenance is possibleFigure 32: Heat exchanger in a steam power plant, fouled by macro fouling
36 Typical Application Process stream preheated using waste heat Maximum energy recovery involves a temperature crossOutlet temperature of cold stream higher than inlet temperature of hot streamHeat exchanger must be either a single counter-flow or multiple shells in seriesFive alternate tube-side designs were compared and are summarized in Figure 35 on the next slide..Figure 33Figure 34: Flow pattern and temperature profile in exchanger showing cross flow
37 Figure 35 Figure 35: Effects of tube inserts on heat transfer .  R. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012.
38 ConclusionsThrough 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.
39 Further Work Suggestions Fluid flow simulations of various insertsGraphical model depicting efficiency of insertFigure 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.
40 Further Work Suggestions Algorithm to determine best design for each type of tube-insertFigure 38: Fluid flow velocity profile over valve connectionsFigure 39: Fluid flow velocity profiles over insertFigure 40: Velocity and temperature profiles over tube-inserts
41 ReferencesR. L. Shilling, “Selecting Tube Inserts for Shell-and-Tube Heat Exchangers,” CEP Magazine, pp , Sep, 2012.