Heat transfer in ducts, fouling Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 HEAT PROCESSES HP5 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 and diagrams).
Transcript
Heat transfer in ducts, fouling
Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010
HEAT PROCESSESHP5
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 and diagrams).
Noncircular ductsHP5
Eliptical, rectangular ducts, channels with longitudinal fins
Multiply connected regions (annular, tube bundle in shell and tube exchanger)
Noncircular ductsHP5
General cross section of a channel can be characterized by equivalent hydraulic diameter Dh, that is used in definition of Reynolds and Nusselt numbers.
4 4h
A VD
P S
Cross section surface
Volume of channel
Perimeter of cross section
Surface of wall
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).
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% .
Noncircular ducts-examplesHP5
a
b
2 3
4 2
2( ) 1 /
Re 96(1 1.355 1.9467( ) 1.701( ) ...)
h
f
ab bD
a b b a
a a a
b b b
The value 96 corresponds to laminar flow and very thin gap. Compare with
fRe=64 for circular pipe
7.541(1 2.61 ....)a
Nub
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.
Re 28f
Laminar flow – pressure drop and asymptotic Nusselt number (extremes)
Increased Nu and f when compared with circular pipe
Decreased Nu and f when compared with 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
Friction factor f = f/4HP5
Warning: There exist two different friction factors for pressure drop calculation, be careful whether you are using the correct one
2
2
1
21
8
f
Lp u
DL
p f uD
f-Fanning friction factor
Parallel plate heat exchangers HP5
Mercer W.E., et al: J.Heat Transfer 89 (1967),p.251-67
1.2
0.17
0.0614.86
1 0.091
GzNu
Gz
1.14
0.64 0.17
0.0247.55
1 0.0358 Pr
GzNu
Gz
Stephan K. Chem.Ing.Techn. 31 (1959),p773-787
1.2
0.7 0.17
0.0614.86
1 0.091 Pr
GzNu
Gz
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,
Tw
Tw
Tw
Simultaneous development of temperature and velocity profiles (laminar).
Both plates at constant temperature
One plate is insulatedYou can found this correlation in VDI
Warmeatlas
Similar but different
correlation in Rohsenow’s book
WHAT IS CORRECT??? There are two different correlations in two very respected books used by thousands profesionalsWrong behaviour at Gz. Thermal boundary layer
increases with Gz
One plate is at constant temperature
Parallel plate heat exchangers HP5
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)
3
( )
( )
platex
tubex
axx
u
axx
u
x
x
Corrugated plates Heat exchangers HP5
How to calculate pressure drop and heat transfer coefficient in plate heat exchangers with corrugated heat transfer walls?
Corrugated plates paper Martin Holger HP5
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.
Corrugated plates paper Martin Holger HP5
The first problem: how to define equivalent hydraulic diameter?
D plate distance
wavelength
4h
VD
S
HP5
Friction factor correlation
Heat transfer (generalised Leveque)
Corrugated plates paper Martin Holger
Brave idea to apply Leveque concept also at turbulent flows!
HP5
Few more details about Friction factor correlation
Few more details on Heat transfer (generalised Leveque)
Corrugated plates paper Martin Holger
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
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 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=constantLeveque 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
Dalí
HP5 HT enhancement
How to increase heat transfer coefficient at internal channel flows (in pipes)?
HP5 HT enhancementHeat 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 03
0
fNuPEC
Nu 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>f0) must be decreased
03
0
fV
V f
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
03
0 0 0
fQV Nu
Q V Nu f
Proof!
0
0 0
fQ NuPEC
Q Nu f
Comparison of thermal powers for the same pumping power, the same flow rates but different lengths
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 wallH. Lienhart et al. / Int. J. Heat and Fluid Flow 29 (2008) 783–791
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
1/3ln 3.66 3.89Nu Gz
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)1/3
ln 3.66 1.618Nu Gz On the other hand, the tube filled by SM elements exhibits higher pressure drop (friction factor)
0
110 / Re tube filled by Kenics SM
16 / Re empty tube
f
f
Question: f, f0 represent
Fanning or the Darcy Weissbach friction factor? Answer : Fanning (see empty tube)
HP5 HT enhancement twisted tapeInternational Communications in Heat and Mass Transfer 38 (2011) 348–352
HP5 HT twisted tape & wire coil
Swirl number ReD
SwH
0.677 0.265 0.140.1 Pr ( )
300 Re 30000w
DNu Sw
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
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
u
m
Dc
ur
Centrifugal force acting on particle of mass m
Fc=2mu2/Dc
Force acting on plate with cross section D x 1
Fi=ur2D
D
Some trivial facts:
HP5 HT enhancement coiled pipe
NuDe
4 75
1 177
4 2
.
Pr
Mori a Nakayama (1965) Re 12
c
DDe
D
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 2
2 2r
c
Du D k u
D
Intertial force related to unit length of pipe (dynamic pressure acts on area D) centrifugal force on unit length
of pipe (acting on volume in the whole cross section)From the force equilibrium follows the ratio between radial and axial velocity
r
c
u Dk
u D
Thermal boundary layer and penetration depth2
r
Dat a
u
Pr Re Prr
c c
uD D Du D DNu D De
aD a D D
This is only brief derivation showing
principles
See also M.M. Mandal et al. / Chemical Engineering Science 65 (2010) 999–1007
HP5 HT enhancement coiled pipe
Rec
DDe
D
Have you noticed similarity between Dean’s and Swirl number?
ReD
SwH
HP5 Flow inversion
Partial flow inversion in bends
Flow inversion transfers overheated fluid from wall to axis
HP5 Flow inversion in a bend paper Zitny
L
L
Rc
R
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
Centrifugal forces in a bend generate secondary flows and the
flow inversion (counter-rotating vortices transfer fluid particles
from pipe axis toward wall)
Centrifugal force
Secondary vortex
HP5 Flow inversion in a bend
Gz=50
1
1.1
1.2
1.3
1.4
10 100 1000Re.F
Nu/Nu s
F /2 Rc/R=2F /2 Rc/R=4F /2 Rc/R=16F /2 Rc/R=50 SF /4 Rc/R=50 SF Rc/R=2
1+0.37[1-exp(-0.01ReF )]
Optimum flow inversion causes half-rotation of the secondary vortex and this situation is achieved at about Re.F=100 (laminar flow)
L
LR
c
R
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
HP5 Flow inverterIn 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
0.900
0.950
1.000
1.050
1.100
1.150
1.200
0.001 0.010 0.100
1/Gz
PE
C
A Re=50
A Re=0.1
S Re=50
S Re=0.1
Flow inverter
Performance Evaluation Criterion
03
0
fNuPEC
Nu f
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.
Dalí
HP5 Extended surfaces (fins)
T1 T1T1
T2 T2T2
T2T2B
H
b
b
1Tw1
Q12 T2
H/2T1
Compact heat exchanger Plate and fin
12 1 1 1( )( )wQ T T B H
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
Tw
x
In the case that thermal resistance of fins cannot be neglected the heat transfer surface must be reduced
12 1 1 1( )( )w finQ T T B H
Efficiency of fin fin can be calculated from temperature profile T(x) in a fin, determined by Fourier equation
2
12
20 ( )
d TT T
dx b
completed by boundary conditions
at 0
0 at / 2
wT T x
dTx H
dx
2-because the fin is heated from both sides
HP5 Extended surfaces (fins)Solution of previous equation yields temperature profile along the height of fin
2 2
1 1 2 2( ) ( )( )
1 1
x xb b
wH H
b b
e eT x T T T
e e
Efficiency of fin is calculated from temperature gradient at the heel of fin (the gradient determines heat flux at the heel)
20
21
| 2tanh
( ) 2
x
finw
dTbQ b Hdx
Q H T T H b
1 1 1 0 1 1 1 002 21 0 1 1 0 0 1 1 0 0
2.circular
K I I K
K I I K
In a similar way the efficiency of circular fin can be derived
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)
Precipitation
Corrosion
Chemical deposits
Biochemical deposits
Solidification
Photographs from paper
Khalil Ranjbar:Effect of flow induced corrosion and erosion on failure of a tubular heat exchanger. Materials and Design 31 (2010) 613–619
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
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):
HP5 FoulingFouling 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)
t
Rf=h/
HP5 Fouling fouling rate models
Chemical fouling of oil products (Ebert Panchal model)
0.8 1/3exp( )
Re Prf
wfilm
dR E
dt RT
Deposits as a product of chemical reaction
with activation energy E
Rate of deposits removal proportional to wall shear stress
0.8 1/3Re PrNu c
exp( )fw
film
dR c E
dt RT
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.
HP5 Fouling fouling rate models
Asymptotic fouling is characterized by 0fdR
dt
0.8 1/3exp( )
Re Prwfilm
E
RT
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
HP5 Fouling fouling rate models
G.T. Polley et al. Use of crude oil fouling threshold data in heatexchanger 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).
Poddar diagram
Length
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
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.
Unpleasant situation-for the optimum design parameters a
fouling in tubes can be expected
HP5
EXAMHP5
Noncircular channels
Concept of equivalent diameter (Dh is used in definition Nu and Re)
sec
4 cross tionh
wetted perimeter
AD
P
What is important (at least for exam)HP5
Heat transfer and thermal boundary layer
3( )
( )
tubex
platex
axx
u
axx
u
x
x
fluid
thermal boundary layer grows faster at a plate than at the wall of pipe
1.14
0.64 0.17for short plate
0.0247.55 0.67
1 0.0358 Pr
GzNu Gz
Gz
Parallel plate channel
tube (Léveque)
x
plate channel
constant temperature of both plates
What is important (at least for exam)HP5
Corrugated plates (chevron HE)
3 2 PrRe40L
df .Nu
Generalised Léveque 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)
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.
This correlation holds at laminar and turbulent flow regime!
What is important (at least for exam)HP5
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 )
1/3lnNu Gz
ReD
SwH
Rec
DDe
D
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
fin
Htgh Bi
bH
Bib
2
bBi
b
H
What is important (at least for exam)HP5
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)
