# Provedení, principy činnosti a základy výpočtu pro výměníky ...

HP5 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 itn, stav procesn a and diagrams). zpracovatelsk techniky VUT FS 2010 HP5 Noncircular ducts Eliptical, rectangular ducts, channels with longitudinal fins Multiply connected regions (annular, tube bundle in shell and tube exchanger)

HP5 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 Volume of channel 4 A 4V Dh P S Perimeter of cross section 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). HP5 Noncircular ducts-examples Laminar flow pressure drop and asymptotic Nusselt number (extremes) Increased Nu and f when compared with circular pipe b 4ab 2b 2(a b) 1 b / a a a 2 a 3 f Re 96(1 1.355 1.9467( ) 1.701( ) ...) b b b Dh The value 96 corresponds to laminar flow and very thin gap. Compare with

fRe=64 for circular pipe a a Nu 7.541(1 2.61 ....) b Decreased Nu and f when compared with circular pipe f Re 28 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, McGraw Hill, Boston, 1998 HP5 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 1 L p f u 2 2 D 1 L p f u 2 8 D f-Fanning friction factor HP5 Parallel plate heat exchangers Simultaneous development of temperature and velocity profiles (laminar). Both plates at constant temperature 0.024Gz1.14 Nu 7.55 1 0.0358Gz 0.64 Pr 0.17

Tw Stephan K. Chem.Ing.Techn. 31 (1959),p773-787 Tw WHAT IS CORRECT??? One plate is insulated behaviour at There are two different correlations in two very respected books used Wrong by thousands profesionals You can found this correlation in VDI Warmeatlas Tw One plate is at constant temperature Similar but different correlation in Rohsenows book

Gz. Thermal boundary layer increases with Gz 0.061Gz1.2 Nu 4.86 1 0.091Gz 0.17 Mercer W.E., et al: J.Heat Transfer 89 (1967),p.251-67 0.061Gz1.2 Nu 4.86 1 0.091Gz 0.7 Pr 0.17 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, HP5 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) plate

ax ux ( x)tube ax 3 ux x x HP5 Corrugated plates Heat exchangers How to calculate pressure drop and heat transfer coefficient in plate heat exchangers with corrugated heat transfer walls? HP5 Corrugated plates paper Martin Holger 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: How to blend results for friction factors corresponding to different flow patterns (longitudinal and furrow flows) How to apply analogy between momentum and heat transfer (how to predict heat transfer from friction factors). Quite unique feature is the Leveque analogy. HP5 Corrugated plates paper Martin Holger The first problem: how to define equivalent hydraulic diameter? Dh 4V S D plate distance wavelength HP5

Corrugated plates paper Martin Holger Friction factor correlation Heat transfer (generalised Leveque) Brave idea to apply Leveque concept also at turbulent flows! HP5 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 the thermal boundary layer is thin enough to fulfill the

Leveques 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 HP5 HT enhancement Dal HP5 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

HP5 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 PEC Nu Nu0 3 f0 f This PEC follows from comparison of the two identical pipes (the same diameter and length), one pipe is empty (Fanning friction factor f0) 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, the 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 Q Nu f 0 PEC Q0 Nu0 f Proof! QV Nu Q 0V0 Nu0 3 f0 f f V 3 0 V0 f Proof!

HP5 HT enhancement wall Heat transfer can be increased by a modification of wall such that the heat transfer surface is extended (fins, dimples), and the 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. HP5 HT enhancement dimpled wall H. Lienhart et al. / Int. J. Heat and Fluid Flow 29 (2008) 783791 Drag reduction by dimples? A complementary experimental/numerical investigation HP5 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! HP5 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) Nuln 3.66 3.89Gz1/3 Compare with empty pipe (Leveque) Nuln 3.66 1.618Gz1/3 On the other hand, the tube filled by SM elements exhibits higher pressure drop (friction factor) f 110 / Re tube filled by Kenics SM

Question: f, f0 represent Fanning or the Darcy Weissbach friction factor? f 0 16 / Re empty tube Answer : Fanning (see empty tube) HP5 HT enhancement twisted tape International Communications in Heat and Mass Transfer 38 (2011) 348352 HP5 HT twisted tape & wire coil Lieke Wang, Bengt Sundn 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) Swirl number Sw Re D H

D Nu 0.1Sw0.677 Pr 0.265 ( ) 0.14 w 300 Re 30000 Wire coil (laminar/transition/turbulent) HP5 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. HP5 HT centrifugal forces Some trivial facts: u Centrifugal force acting on particle of mass m Fc=2mu2/Dc Dc m Force acting on plate with cross section D x 1 Fi=ur2D ur D HP5 HT enhancement coiled pipe Centrifugal forces generate two counter-rotating vortices (secondary flow). Characteristic velocity of circulation u r

(transversal velocity) can be estimated from balance of equilibrium force Fc and inertial force Fd 2 D ur2 D k u 2 Dc 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 D 2 at a ur ur

D k u Dc centrifugal force on unit length of pipe (acting on volume in the whole cross section) This is only brief derivation showing principles ur D D Du D D Nu D Pr Re Pr De aD a Dc Dc

Mori a Nakayama (1965) Nu 4.75 De 1 1 See also M.M. Mandal et al. / Chemical Engineering Science 65 (2010) 9991007 77 4 Pr 2 De Re D 12 Dc HP5 HT enhancement coiled pipe Have you noticed similarity between Deans and Swirl number? D

De Re Dc D Sw Re H HP5 Flow inversion Flow inversion transfers overheated fluid from wall to axis Partial flow inversion in bends HP5 Flow inversion in a bend paper Zitny 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 Flow inversion in a bend HP5 Optimum flow inversion causes half-rotation of the secondary vortex and this situation is achieved at about Re.F=100 (laminar flow) Gz=50 F /2 Rc/R=2 F /2 Rc/R=4 F /2 Rc/R=16 F /2 Rc/R=50 S F /4 Rc/R=50 S

F Rc/R=2 1.4 1.3 Nu/Nus 1+0.37[1-exp(-0.01ReF )] 1.2 R L R 1.1 c L 1 10 100

Re.F 1000 HP5 Flow inverter paper Zitny 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 HP5 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.

HP5 Flow inverter Performance Evaluation Criterion Nu PEC Nu0 3 f0 f 1.200 A Re=50 A Re=0.1 1.150 S Re=50 S Re=0.1 PEC 1.100

1.050 1.000 0.950 0.900 0.001 0.010 1/Gz 0.100 HP5 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 the thermal resistance of inserts or fins is negligible. Dal HP5

Extended surfaces (fins) Compact heat exchanger T2 T2 H T1 T2 Tw1 T1 Q12 1 B Plate and fin T2 T2 H/2 T1

T1 b Tw x b T2 In the case that the 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 Q12 1 (T1 Tw1 )( B H ) In the case that thermal resistance of fins cannot be neglected the heat transfer surface must be reduced Q (T T )( B H ) 12 1 1 w1 fin

Efficiency of fin fin can be calculated from temperature profile T(x) in a fin, determined by Fourier equation 2-because the fin is 2 d T 2 0 2 (T1 T ) dx b heated from both sides completed by boundary conditions T Tw at x 0 dT 0 dx at x H / 2 Extended surfaces (fins)

HP5 Solution of previous equation yields temperature profile along the height of fin T ( x) T1 (Tw T1 )( e x 1 e 2 b 2 H b e x 1 e

2 b ) 2 H b Efficiency of fin is calculated from temperature gradient at the heel of fin (the gradient determines heat flux at the heel) fin Q Q dT |x 0 2 2 b H dx

tanh 2 H (Tw T1 ) H 2b 1 tgh Bi Bi b 0.5 0 0 1 In a similar way the efficiency of circular fin can be derived K I I1 1 K1 0 2 circular 2 0 2 1 1 1 0 .

1 0 K1 1 I 0 0 I1 1 K 0 0 where are dimensionless radii 2 3 I1,K1 are modified Bessel functions r 2 Bi , b Bi b , 2 HP5 Extended surfaces (fins) Example: Calculate efficiency of rectangular fin of constant thickness 1mm, height H=20mm made from stainless steel for heat

transfer coefficient 3000 W/m2/K Result =0.16 If the same fin will be from aluminium, the efficiency increases to =0.54 HP5 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) 613619 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 HP5 Fouling 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 HP5 Fouling fouling rate models Chemical fouling of oil products (Ebert Panchal model) dR f E

0.8 1/3 exp( ) w dt Re Pr RT film 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 Nu c Re0.8 Pr1/3 dR f dt

c E exp( ) w RT film 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. 451460. HP5 Fouling fouling rate models Asymptotic fouling is characterized by dR f dt 0 and from the Ebert Panchal fouling model follows the value of critical wall shear stress ensuring zero fouling rate

w Re0.8 Pr exp( 1/3 E ) RT film This criterion is used for heat exchanger design by Poddar diagrams. See next slide HP5 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) 763776 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 HP5 HP5 EXAM

Noncircular channels Concept of equivalent diameter (Dh is used in definition Nu and Re) 4 Across sec tion Dh Pwetted perimeter HP5 What is important (at least for exam) Heat transfer and thermal boundary layer thermal boundary layer grows faster at a plate than at the wall of pipe fluid ( x)tube ( x) plate ax 3 ux ax

ux Parallel plate channel tube (Lveque) x x plate channel constant temperature of both plates x 0.024Gz1.14 Nu 7.55 0.67 Gz 0.64 0.17

1 0.0358Gz Pr for short plate HP5 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 Lveque correlation is based upon analogy between momentum and heat transfer. Nu is calculated from friction factor (take into account that fRe=const at laminar flow regime) Nu 0.4 3 f Re 2 Pr d L

This correlation holds at laminar and turbulent flow regime! HP5 What is important (at least for exam) Inserts in pipes and centrifugal forces (heat transfer enhancement) -static mixers (enhanced Leveque Nuln Gz1/3 ) -twisted tape (Nu depends upon swirl number Sw Re D H ) -helical coils (Nu depends upon Dean number D

De Re Dc ) H Bi b The effective heat transfer surface of fins must be reduced by fin H where H is height, b is thickness of fin and Biot number is Bi b b Bi 2 b Extended heat transfer surface (fins) tgh H HP5 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~Re0.8Pr1/3) dR f E 0.8 1/3 exp( ) w dt Re Pr RT film

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