HP 5 HEAT PROCESSES Heat transfer in ducts

HP 5 HEAT PROCESSES Heat transfer in ducts, fouling Noncircular profiles and equivalent diameter of pipe. Compact and plate heat exchangers. Hydraulic and thermal analysis of chevron type heat exchanger (H. Martin). Heat transfer enhancement (static mixers, centrifugal forces, Deans vortices). Flow invertors. Performance criteria (PEC). Fouling (example: crude oil fouling - Polley model Rudolf Žitný, Ústav procesní a and diagrams). zpracovatelské techniky ČVUT FS 2010

HP 5 Noncircular ducts Eliptical, rectangular ducts, channels with longitudinal fins Multiply connected regions (annular, tube bundle in shell and tube exchanger)

HP 5 Noncircular ducts General cross section of a channel can be characterized by equivalent hydraulic diameter Dh, that is used in definition of Reynolds and Nusselt numbers. Cross section surface Perimeter of cross section Volume of channel Surface of wall At turbulent flows the same correlations for pressure drop (friction factor) and heat transfer (Nusselt number) can be used. Correlations for circular pipe are usually used, however the cross sections with sharp corners (triangles, cusped ducts) lead to error up to 35%. Equivalent diameter is used also in laminar flows, but different correlations for different cross sections must be used (from this point of view the laminar regime is more complicated). Modified definitions of equivalent diameter exist for specific classes of cross sections (e. g. average distance from the point of maximum velocity in triangles, or square root of the cross section area, see next slides).

HP 5 Noncircular ducts-examples Laminar flow – pressure drop and asymptotic Nusselt number (extremes) Increased Nu and f when compared with circular pipe b The value 96 corresponds to laminar flow and very thin gap. Compare with f. Re=64 for circular pipe a Decreased Nu and f when compared with circular pipe Asymptotic Nu. The value 7. 54 corresponds to a narrow flat channel with the constant wall temperature. Compare with the limiting value 3. 66 for circular pipe. Shah R. K. , London A. I. “Laminar flow forced convection in ducts”, Supplement 1 to Advances in Heat transfer eds. Irvine, Hartnett, Academic Press, N. Y. 1978, Referred by Rohsenow “Handbook of heat transfer”, Mc. Graw Hill, Boston, 1998

HP 5 Friction factor f = f/4 Warning: There exist two different friction factors for pressure drop calculation, be careful whether you are using the correct one f-Fanning friction factor

HP 5 Parallel plate heat exchangers Simultaneous development of temperature and velocity profiles (laminar). Both plates at constant temperature Tw Stephan K. Chem. Ing. Techn. 31 (1959), p 773 -787 Tw Wrong behaviour at WHAT IS CORRECT? ? ? There are two different correlations in two very respected books used by thousands profesionals Gz . Thermal boundary layer increases with Gz One plate is insulated You can found this correlation in VDI Warmeatlas Tw Mercer W. E. , et al: J. Heat Transfer 89 (1967), p. 251 -67 One plate is at constant temperature Similar but different correlation in Rohsenow’s book Shah R. K. , London A. I. “Laminar flow forced convection in ducts”, Supplement 1 to Advances in Heat transfer eds. Irvine, Hartnett, Academic Press, N. Y. 1978,

HP 5 Parallel plate heat exchangers Have you noticed the basic difference between correlations for circular tube and parallel channel? The difference is in the exponent of Gz (1/3 for tube, 1/2 for planar channel) x x

HP 5 Corrugated plates Heat exchangers How to calculate pressure drop and heat transfer coefficient in plate heat exchangers with corrugated heat transfer walls?

Corrugated plates paper Martin Holger HP 5 Applications of CFD is rather demanding and not very accurate. According to my opinion the best way how to calculate pressure drop and heat transfer in heat exchangers with corrugated plates is the semiempirical method described by Martin Holger in Chemical Engineering and Processing, 1996. Pay attention to the following features: ØHow to blend results for friction factors corresponding to different flow patterns (longitudinal and furrow flows) ØHow to apply analogy between momentum and heat transfer (how to predict heat transfer from friction factors). Quite unique feature is the Leveque analogy.

HP 5 Corrugated plates paper Martin Holger The first problem: how to define equivalent hydraulic diameter? D plate distance wavelength

HP 5 Corrugated plates paper Martin Holger Friction factor correlation Heat transfer (generalised Leveque) Brave idea to apply Leveque concept also at turbulent flows!

HP 5 Corrugated plates paper Martin Holger Few more details about Friction factor correlation Functions 0 1 are defined separately for laminar and turbulent regime Flow along walleys (like in a straight pipe) Flow in a wavy channel, characterized by separation of vortices at down and up-hills Few more details on Heat transfer (generalised Leveque) L is the distance between two crossings (and not the length of plate). This distance is quite small so that thermal boundary layer is thin enough to fulfill the Leveque’s assumption (it is assumed that the boundary layer is restored at each crossing) Is it really Leveque? Yes, because at laminar flow Re=constant Leveque analogy is discussed in paper Martin H. : The generalized Leveque equation and its practical use for the prediction of heat and mass transfer rates from pressure drop, Chem. Eng. Science, 57 (2002), pp. 3217 -3223

HP 5 HT enhancement Dalí

HP 5 HT enhancement How to increase heat transfer coefficient at internal channel flows (in pipes)? 1. Artificial wall roughness, porous wall 2. Fins, grooves, dimples 3. Inserts (static mixers, twisted tape, wire mesh, invertors) 4. Centrifugal forces (coiled tubes, bends) 5. Vibration, ultrasound, nanoparticles…

HP 5 HT enhancement Heat transfer augmentation (Nu increase – desirable effect) is usually accompanied by pressure drop increase (undesirable effect). There exist many different PEC (Performance Evaluation Criteria) characterising efficiency of considered modification (only those giving PEC>1 should be used). The most frequently used This PEC follows from comparison of the two identical pipes (the same diameter and length), one pipe is empty (Fanning friction factor f 0) the second one is modified by inserts, fins, … (higher f). So that the pumping power will be the same the flowrate in the augmented pipe (f>f 0) must be decreased Assuming the same temperature approach T in the both pipes, thermal power is proportional to the Nu and the PEC can be interpreted as Comparison of thermal powers for the same pumping power, the same flow rates but different lengths Proof!

HP 5 HT enhancement –wall Heat transfer can be increased by a modification of wall such that the heat transfer surface is extended (fins, dimples), and thermal boundary layer is disrupted (for example by vortices generated at protrusions or dimples). Only a little bit controversial enhancement by dimples will be presented in next slides.

HP 5 HT enhancement – dimpled wall H. Lienhart et al. / Int. J. Heat and Fluid Flow 29 (2008) 783– 791 Drag reduction by dimples? – A complementary experimental/numerical investigation

HP 5 HT enhancement – inserts Inserts (static mixers, twisted tape) extend heat transfer surface (as far as a good thermal contact with pipe wall is ensured) and generate secondary flows diminishing thermal boundary layer. Inserts are effective first of all in laminar flow regime (PEC is highest at low Re), but heat transfer enhancement in turbulent regime is also significant. Wire coils disrupt thermal boundary layer (suitable for laminar flows), wire mesh affects the main flow and is effective in turbulent flows. Advantage: Tiny wire at wall has only small effect upon pressure drop. What is surprising: inserts usually suppress fouling!

HP 5 HT enhancement SM Kenics Static mixers (Kenics, Sulzer, Helax, …) serve for mixing of liquids but also for the heat transfer intensification. Standard solution consists in filling the whole tube by SM elements (tight arrangement). For Kenics SM the heat transfer at laminar flows is increased as (see Joshi, Nigam, Cibulski) Compare with empty pipe (Leveque) On the other hand, the tube filled by SM elements exhibits higher pressure drop (friction factor) Question: f, f 0 represent Fanning or the Darcy Weissbach friction factor? Answer : Fanning (see empty tube)

HP 5 HT enhancement twisted tape International Communications in Heat and Mass Transfer 38 (2011) 348– 352

HP 5 HT twisted tape & wire coil Lieke Wang, Bengt Sundén Performance comparison of some tube inserts International Communications in Heat and Mass Transfer, Volume 29, Issue 1, January 2002, Pages 45 -56 Twisted tape (laminar/transition/turbulent) Wire coil (laminar/transition/turbulent) Swirl number

HP 5 HT– centrifugal forces Centrifugal forces in coiled pipes (spirals, helically coiled pipes) create secondary flows similar to vortices induced e. g. by a twisted tape. Local effect of centrifugal forces and secondary flow appear also in bends (for example U-tube acts as a partial flow inverter). Advantage: Increased Nu is not accompanied by too large pressure drop increase. Positive effect is significant reduction of fouling (spiral heat exchangers are suitable for dirty fluids, fibrous pulps, …). Residence time characteristics are improved (residence times of fluid particles moving at axis of pipe and in vicinity of wall are not so different as in a straight pipe). Disadvantage: Effect of centrifugal forces disappears at creeping flow, therefore this technique cannot be applied for highly viscous liquids (Re<10) Dean, W. R. , Note on the motion of fluid in a curved pipe, Phil. Mag. Ser. 7, vol. 4, no. 4, pp. 208, 1927.

HP 5 HT– centrifugal forces Some trivial facts: u Centrifugal force acting on particle of mass m Fc=2 mu 2/Dc Dc m Force acting on plate with cross section D x 1 Fi= ur 2 D ur D

HP 5 HT enhancement coiled pipe Centrifugal forces generate two counter-rotating vortices (secondary flow). Characteristic velocity of circulation ur (transversal velocity) can be estimated from balance of equilibrium force Fc and inertial force Fd Intertial force related to unit length of pipe (dynamic pressure acts on area D) From the force equilibrium follows the ratio between radial and axial velocity Thermal boundary layer and penetration depth Mori a Nakayama (1965) See also M. M. Mandal et al. / Chemical Engineering Science 65 (2010) 999– 1007 centrifugal force on unit length of pipe (acting on volume in the whole cross section) This is only brief derivation showing principles

HP 5 HT enhancement coiled pipe Have you noticed similarity between Dean’s and Swirl number?

HP 5 Flow inversion transfers overheated fluid from wall to axis Partial flow inversion in bends

HP 5 Flow inversion in a bend paper Zitny R, Luong TCT, Strasak P, et al. : Heat Transfer Enhancement and RTD in Pipes with Flow Inversion. Heat Transfer Engineering, Vol. 25 (2004), pp. 67 -79 R Centrifugal forces in a bend generate secondary flows and the flow inversion (counter-rotating vortices transfer fluid particles from pipe axis toward wall) L Rc L Secondary vortex Centrifugal force

HP 5 Flow inversion in a bend Optimum flow inversion causes half-rotation of the secondary vortex and this situation is achieved at about Re. =100 (laminar flow) R L R c L

HP 5 Flow inverter paper Zitny R, Thi C. T. L, Sestak J : Heat Transfer Enhancement in a Pipe Using a Flow Inverter. Heat Transfer Engineering, Vol. 30 (2009), pp. 952 -960 inverter Hot center, cold wall Incoming stream is mechanically subdivided into the central and the wall region and mutually

HP 5 Flow inverter In case of Re<10 centrifugal forces are not strong enough to generate secondary flows and flow inversion. “Mechanical” subdivision operates also at Re<<1.

HP 5 Flow inverter Performance Evaluation Criterion

HP 5 Extended surfaces Previous analysis was concentrated upon the heat transfer enhancement by increasing heat transfer coefficient. Inserts or modifications of pipe walls increases at the same time the heat transfer surface, however this additional surface can be fully accounted for only if thermal resistance of inserts or fins is negligible. Dalí

HP 5 Extended surfaces (fins) Compact heat exchanger Plate and fin T 2 T 1 Tw 1 T 2 H B Q 12 1 T 2 T 1 H/2 b T 1 Tw x b T 2 In the case that thermal resistance of walls is zero (infinitely large thermal conductivity of fins) the surface of fins can be added to the heat transfer surface and In the case that thermal resistance of fins cannot be neglected the heat transfer surface must be reduced Efficiency of fin can be calculated from temperature profile T(x) in a fin, determined by Fourier equation 2 -because the fin is heated from both sides completed by boundary conditions

HP 5 Extended surfaces (fins) Solution of previous equation yields temperature profile along the height of fin Efficiency of fin is calculated from temperature gradient at the heel of fin (the gradient determines heat flux at the heel) In a similar way the efficiency of circular fin can be derived where are dimensionless radii I 1, K 1 are modified Bessel functions

HP 5 Extended surfaces (fins) Example: Calculate efficiency of rectangular fin of constant thickness 1 mm, height H=20 mm made from stainless steel for heat transfer coefficient 3000 W/m 2/K Result =0. 16 If the same fin will be from aluminium, the efficiency increases to =0. 54

HP 5 Fouling Formation of deposits on heat transfer surface increases thermal resistance (and pressure drop) Photographs from paper Precipitation Corrosion Khalil Ranjbar: Effect of flow induced corrosion and erosion on failure of a tubular heat exchanger. Materials and Design 31 (2010) 613 – 619 Chemical deposits Biochemical deposits Solidification There are many ways how to mitigate fouling: addition of tiny particles (nano, pulps), sonication, pulsating electrical field, turbulisation of flow (e. g. wire mesh usually mitigates fouling): S. N. Kazi, G. G. Duffy, X. D. Chen: Fouling mitigation of heat exchangers with natural fibres. Applied Thermal Engineering 50 (2013) 1142 -1148 Y. I. Cho, B. G. Choi: Validation of an electronic anti-fouling technology in a single-tube HE. Int. J. Heat and Mass Transfer. 42 (1999), 1491 -1499

HP 5 Fouling evolution 1. Induction period 2. Negative fouling (e. g. promoted nucleate boiling, heat transfer increased) 3. Linear fouling (constant rate of deposits formation, thermal resistance increases) 4. Falling fouling (decreasing rate of fouling formation) 5. Asymptotic fouling (zero rate) Rf=h/ t

HP 5 Fouling fouling rate models Chemical fouling of oil products (Ebert Panchal model) Deposits as a product of chemical reaction with activation energy E Rate of deposits removal proportional to wall shear stress The production rate is proportional to the volume of reaction zone – overheated thermal boundary layer of thickness B. L. Yeap, D. I. Wilson, G. T. Polley, S. J. Pugh: Mitigation of Crude Oil Refinery Heat Exchanger Fouling Through Retrofits Based on Thermo-Hydraulic Fouling Models Chemical Engineering Research and Design, Volume 82, Issue 1, January 2004, Pages 53 -71 G. T. Polley, D. I. Wilson, B. L. Yeap, S. J. Pugh Evaluation of laboratory crude oil threshold fouling data for application to refinery pre-heat trains Applied Thermal Engineering, Volume 22, Issue 7, May 2002, Pages 777 -788 W. A. Ebert, C. B. Panchal, Analysis of Exxon crude slipstream coking data, in: C. B. Panchal, et al. (Eds. ), Fouling Mitigation of Industrial Heat-Exchange Equipment, Begell House, 1997, pp. 451– 460.

HP 5 Fouling fouling rate models Asymptotic fouling is characterized by and from the Ebert Panchal fouling model follows the value of critical wall shear stress ensuring zero fouling rate This criterion is used for heat exchanger design by Poddar diagrams. See next slide

HP 5 Fouling fouling rate models G. T. Polley et al. Use of crude oil fouling threshold data in heat exchanger design. Applied Thermal Engineering 22 (2002) 763– 776 T. K. Poddar, G. T. Polley, Optimising the design of shell-and-tube heat exchangers, Chemical Engineering Progress (September) (2000). Problem specification: Calculate number of tubes and length of S&T HE for given thermal duty (power), flowrates in shell and tubes, maximum pressure drops in shell and tubes. Poddar diagram Region of design parameters (L, n) satisfying constraints on duty and pressure drop (in this case is limiting the shell side) Optimum design: 600 tubes in bundle, length 3. 2 m Length Unpleasant situation-for the optimum design parameters a fouling in tubes can be expected

HP 5

HP 5 EXAM Noncircular channels Concept of equivalent diameter (Dh is used in definition Nu and Re)

HP 5 What is important (at least for exam) Heat transfer and thermal boundary layer grows faster at a plate than at the wall of pipe tube (Léveque) x x Parallel plate channel constant temperature of both plates x

HP 5 What is important (at least for exam) Corrugated plates (chevron HE) Fanning friction factor f (denoted as in original paper by H. Martin) is calculated from correlation as a function of chevron angle and Reynolds number. Generalised Léveque correlation is based upon analogy between momentum and heat transfer. Nu is calculated from friction factor (take into account that f. Re=const at laminar flow regime) This correlation holds at laminar and turbulent flow regime!

HP 5 What is important (at least for exam) Inserts in pipes and centrifugal forces (heat transfer enhancement) -static mixers (enhanced Leveque ) -twisted tape (Nu depends upon swirl number ) -helical coils (Nu depends upon Dean number ) Extended heat transfer surface (fins) The effective heat transfer surface of fins must be reduced by where H is height, b is thickness of fin and Biot number is b H

HP 5 What is important (at least for exam) Fouling in pipes (Ebert Panchal 3 parametric model , , E-activation energy, the model assumes that rate of deposits formation is proportional to the volume of overheated fluid inside turbulent thermal boundary layer, see Dittus Boelter correlation Nu~Re 0. 8 Pr 1/3)