Chemical Engineering Science 66 (2011) 499–509

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

w.augus

journal homepage: www.elsevier.com/locate/ces

Roughness and constriction effects on heat transfer in crystallization fouling

Florian Albert, Wolfgang Augustin n, Stephan Scholl

Institute for Chemical and Thermal Process Engineering, Technische Universitat Braunschweig, Langer Kamp 7, 38106 Braunschweig, Germany

a r t i c l e i n f o

Article history:

Received 19 August 2010

Received in revised form

18 October 2010

Accepted 11 November 2010Available online 18 November 2010

Keywords:

Crystallization fouling

Fouling resistance

Heat transfer

Roughness

Acceleration

Turbulence

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ces.2010.11.021

esponding author. Tel.: +49 0 531 391 2789;

ail addresses: f.albert@tu-bs.de (F. Albert),

tin@tu-bs.de (W. Augustin), s.scholl@tu-bs.d

a b s t r a c t

This contribution addresses apparent negative fouling resistances for crystallization fouling. Two effects

contribute to this phenomenon; surface roughness enhances heat transfer in the roughness controlled

phase. In the crystal growth phase, surface roughness as well as the constriction of flow cross section due

to the fouling layer build-up is taken into consideration. Fouling experiments were carried out in a double

pipe heat exchanger with a supersaturated aqueous CaSO4 solution at a Reynolds number of 17,500

corresponding to a flow velocity of 0.65 m s�1. The measured pressure drop between inlet and

outlet allowed the calculation of the integral friction factor for the current surface roughness. With

the given friction factor it was possible to estimate the actual heat transfer coefficient of the inner tube.

Accounting for the increase in heat transfer caused by surface roughness in the roughness controlled

phase, the fouling resistance was recalculated. In the subsequent growth phase flow acceleration due to

constriction effects is considered in addition to the roughness effect. Overall the integral fouling

resistance and consequently the deposit thickness are underestimated by a factor of up to 2.5 when

simply using heat balance. With the proposed approach apparent negative fouling resistances can be

eliminated quantitatively.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Fouling is generally defined as the unwanted deposition or growthof suspended, dissolved or chemically generated species from processfluids onto process equipment surfaces, such as distillation columntrays, membranes, crystallizers or fluidized bed walls. Owing totemperature differences being the driving force of many depositionprocesses fouling often occurs in heat exchangers. These layers canlead to a drastic increase of the thermal resistance and therefore to adecreased efficiency of the heat exchanger.

1.1. Crystallization fouling

In crystallization fouling typically three phases can be identified,namely the induction or delay period, the roughness controlled phaseand the crystal growth period. In the induction period, the mechan-ism of fouling starts with nucleation on the surface caused by localsupersaturation. The length of this period depends, among otherparameters, on the energetic characteristics and topography of theheat transfer surface and on the salt concentration. Fig. 1 showsvalues for the integral, area-averaged and heat transfer resistance 1/Uas determined in a double pipe heat exchanger. The induction periodis followed by the roughness controlled period in which the overall

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fax: +49 0 531 391 2792.

e (S. Scholl).

heat transfer coefficient increases rather than decreases. This is dueto the fact that the enhancement of turbulent convective heattransfer, caused by the roughening of the inside tube wall by thefirst perceptible scale, overrides the thermal resistance effect of thescale. For a limited time span the thickness of the fouling layer isnegligible relative to the inner tube diameter and surface roughnessalone exerts a significant influence on heat transfer. As foulingprogresses the constriction of the flow cross section due to the foulinglayer additionally becomes significant (Epstein, 1978; Crittenden andAlderman, 1988). For heat exchangers at constant flow rate condi-tions, the velocity will increase and therefore the heat transfercoefficient may also be increased. Hence, in the crystal growth periodroughness as well as constriction effects have to be considered. Thiscontribution aims at separating these two effects through indepen-dent measurements of fluid dynamic and thermal consequences.Based on this analysis apparent negative fouling resistances may becorrected and explained quantitatively for the first time.

1.2. Effect of surface roughness on heat transfer

The effect of surface roughness on heat transfer is wellestablished and is widely used to improve the performance ofmany kinds of heating equipment (Pohl, 1933; Sheriff and Gumley,1966; Feurstein and Rampf, 1969; Taylor et al., 1992; Bohnet andAugustin, 1993). The quantitative effect of roughness on heattransfer depends on the nature of the roughness, i.e., the size,shape, orientation and distribution of the roughness elements

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509500

(Mahato and Shemilt, 1968). Information about the roughness offouling deposits is rather limited in literature (Crittenden andAlderman, 1992). Generalized correlations for the roughnessstructure of fouling deposits are not available. Two effects maycontribute to heat transfer enhancement due to roughness: (i) anenlargement of the surface area relative to a smooth wall and (ii) anincrease in near wall turbulence. The effect of roughness on flowand consequently heat transfer is quantified by the relation for heattransfer and friction characteristics of smooth and rough tubes inmany empirical approaches:

eNu ¼Nu

Nu0pel ¼

ll0

ð1Þ

where l is the resistance due to friction of the rough surface and l0

consequently of the smooth surface. Original correlations for theheat transfer in smooth pipes were either of the form

Nu¼ C Ren Prm ð2Þ

Fig. 1. Different stages in crystallization fouling.

Table 1Heat transfer correlations accounting for surface roughness effects.

Author Geometry ks (mm)

Nunner (1956) 16.4

22.8

17.7

3.14

1.31

6.4

Burck (1969) 0.412

0.455

0.373

0.43

0.412

0.412

Hughmark (1975) Sand 0.135

Sand 0.023

Sand 0.24

0.5

0.326

1.0

1.7

Ceylan and Kelbaliyev (2003) Sand r8

or semi-empirical correlations, which are based on an approach ofPrandtl (Prandtl, 1949):

fl8¼ St¼

Nu

Pr Reð3Þ

where f is a correction term for Prandtl numbers other than one.As further experimental data became available the aboveapproaches were refined. Nunner (1956) conducted experimentswith gas flow on the heat transfer performance of rough surfaces.For this he introduced circlips, varied in shape and separation,inside tubes of different diameters. He proposed a correlation forthe Nusselt number in tubes with rough surfaces (see Table 1). Forliquid flow with Prandtl numbers different from one Nunner

introduced the following extension:

Nu

Nu0¼

ll0

� �1=m

;m¼ Pr

2 þ1:5; Pr41

m¼ Prþ1:1; Pro1ð4Þ

With his empirical approach for smooth pipes,

Nu0 ¼ðl0=8ÞRePr

1þ1:5Re�1=8 Pr�1=6ðPr�1Þð5Þ

it is possible to determine the effect of roughness on heat transfer.Revaluating Nunners work (Nunner, 1956), Burck (1969) assessedthat the circlips Nunner used were not in direct contact with theheat transfer surface. Thus, the roughness elements only act as aturbulence promoter but do not increase the heat transfer areanecessarily. In his experiment Burck (1969) used different types ofroughness, one being rectangular grooves in the tube wall, cut withdifferent shapes and distances. Furthermore he varied the Prandtlnumber in a range from 3 to 180. He found a relation between theeffect on heat transfer Nu/Nu0, the friction ratio l/l0, the Prandtlnumber Pr and the dimensionless roughness k+:

Nu

Nu0¼ f

ll0

, Pr, kþ� �

ð6Þ

For details see Table 1. k+ is the ratio of the equivalentsand roughness ks and the viscous sublayer dl. Nu0 is theNusselt number for smooth pipes, calculated by an approach of

Pr (dimensionless) Nusselt equations

0.72Nu¼

ðl=8ÞRePr

1þ1:5Re�1=8 Pr�1=6ðPrðl=l0Þ�1Þ

3Nu¼Nu0 log

Pr0:33

kþ0:243�0:32� 10�3kþ logPrþ1:25

� �ll0–

180

0.7

Nu¼ffiffil8

qRe

10:0303þ0:0615 Pr1=2 þ

10:625þ0:062 Pr1=3

þ 17:16ffiffiffiffiffiffiðl=8Þp

Reþ2

ffiffiffiffiffiffiffiffiðl=8Þp

Pr

264

375�1

–

14.3

0.7Nu¼ 1:15Nu0 Pr1=7ð1�0:106kþð1=4ÞÞ

ll0–

50

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509 501

Petukhov and Popov (1963):

Nu0 ¼ðl0=8ÞRePr

1:07þ12:7ffiffiffiffiffiffiffiffiffiffiffiffiffiffiðl0=8Þ

pðPr2=3�1Þ

ð7Þ

With this correlation for the heat transfer and friction char-acteristics of smooth and rough surfaces it is possible to calculatethe increase of heat transfer for rough pipes by means of pressuredrop measurements.

Another correlation for heat and mass transfer for turbulentpipe flow is given by Hughmark (1975). He proposed that the wallregion consists of a developing laminar layer at the wall and atransitional region. Both have different characteristics. Hence,considering the two distinct regions in the vicinity of the wall,he established a three-resistance model for turbulent pipe flowwith molecular and eddy diffusion properties.Hughmark (1975)used experimental data from Dipprey and Sabersky, (1963), Gowenand Smith (1968) and Kolar (1965) to verify his theoreticalapproach for rough surfaces. These data include a sand grainroughness and roughness formed by cutting triangular threadsin the tube wall, which all represent moderate roughness(k+ o100). The model is in good agreement with the experimentaldata. For high Reynolds numbers (Reb5�105) and extremeroughness (k+

b100) he found that the experimental coefficientsare much lower than calculated coefficients.

Ceylan and Kelbaliyev (2003) proposed a correlation to estimatethe Nusselt number in fully developed turbulent flow throughrough pipes based on experimental data from Eckert and Drake(1972). For Pro50 and 104oReo107, Ceylan and Kelbaliyev(2003) give an empirical equation, shown in Table 1, where Nu0

is the Nusselt number for smooth pipes according to Petukhov andPopov (1963) Eq. (7).

2. Experimental methods

An experimental setup was chosen, which represents industrialconditions. The investigated heat exchanger has technical dimensions;

Fig. 2. Experimental setup of the dou

heat flux density and fluid velocity are in the range of industrialprocesses. Calcium sulphate as a mineral causing the hardness of wateris typically found in cooling water systems.

2.1. Fouling test rig

The fouling experiments with an aqueous CaSO4 solution weremonitored by three different approaches: fluid dynamics based onpressure drop measurements, heat transfer performance as well asoptical inspection via an endoscope. While the first two approachesmonitor integral performance in-situ of the heat exchange surfacethe endoscopic inspection allows for local observations ex-situ. Thesetup of the fouling facility is shown schematically in Fig. 2.A supersaturated feed solution containing 0.027 mol l�1 CaSO4

was prepared by dissolving calcium nitrate tetrahydrate (Appli-Chem) and sodium sulphate (Merck) in deionised water. This highconcentration was chosen to receive results in a quite reasonabletime. The CaSO4 concentration in the resulting solution wasdetermined and adjusted by means of EDTA (ethylene diaminetetra-acetic acid; Merck) titration every 12 h. The bulk temperatureof the process fluid at the test section inlet was 42 1C. Theexperiments were conducted under turbulent flow conditions witha mean flow velocity in the test section of 0.65 m s�1 correspond-ing to an average Reynolds number of 17,500. Fully developed flowconditions were adjusted by providing 30 diameters of hydro-dynamic entrance length ahead of the actual test section.

The experimental setup consists of three parts: (i) the feed tanksinclude the product vessel B1 (50 l) and the heating water vessel B2(150 l). The product vessel contains the aqueous solution ofcalcium sulphate. A rotating stirrer (Ekato) prevents temperatureand concentration gradients. Hot water is provided in vessel B2 bytwo immersion heaters (Heinrich Industrietechnik) with an overallelectrical power of 14 kW. (ii) The supply unit consists of twocentrifugal pumps (KSB), a cartridge filter (Grunbeck) and a plateheat exchanger (GEA Ecoflex). The filter avoids sedimentation ofparticles and secondary nucleation in the test sections since seedparticles can influence nucleation behaviour considerably. The heat

ble pipe heat exchanger facility.

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509502

exchanger E1 guarantees a constant inlet temperature of theprocess fluid at the test sections. (iii) The test section containsthe two identical double pipe heat exchangers (self-construction),one of which may be used for reference measurements. The heatexchangers are heated by hot water on the shell side. The slightlysupersaturated solution is fed in counter current flow through theinner tubes, which have an internal diameter of 16 mm and a lengthof 2000 mm. In addition to the common drawn stainless steel tubes(SS 304), electro-polished stainless steel tubes (SS 304EP) wereused for the current experiments. All materials in contact with theprocess fluid were made of stainless steel. The flow rate of each testsection, on the shell side as well as on the tube side, is determinedby inductive flow meters (KROHNE). The flow sensors have beencalibrated against a piston-prover with an uncertainty of 0.02% bythe manufacturer. The calibration results of all flow meters showeda maximum deviation for the given flow rate of 0.2% (KROHNE,2007). All temperatures are measured by pre-calibrated type Kthermocouples (TMH). The calibrated thermocouples showed amaximum deviation from the master temperature (HP QuartzThermometer) of 0.266%. To eliminate heat losses the whole test rigis insulated by mineral wool. The pressure loss between the inletand outlet of each test section is measured by two capacitivepressure transducers (Honeywell) with an accuracy of 0.25%. Inaddition to that the absolute pressure is recorded at the inlet ofeach heat exchanger (Honeywell). Hence, friction coefficients weredetermined from fluid flow rate and pressure drop measurements.All measured data are recorded by a data scan unit (Agilent).

For the optical measurements an endoscope (Everest) with adiameter of 8 mm and a working length of 1420 mm was insertedin the dismantled tubes after the fouling experiment. The endo-scope was guided by a centered track with a scale for the accuratedetermination of the axial position. By turning the tube the wholelength could be observed. The observable section has a diameter of5 mm.

2.2. Determination of the heat flux

Neglecting heat losses the heat flow from the hot fluid iscompletely transferred to the cold fluid stream. Thus, the heat fluxcan be written as

_Q ¼ _mhcP,hðTh,i�Th,oÞ ¼ _mccP,cðTc,o�Tc,iÞ ð8Þ

The subscripts h and c denote the hot and cold process stream,whereas i and o indicate inlet and outlet. Independent energybalances on hot and cold side could be matched to a difference byless than 5% indicating a very good overall thermal efficiency of thetest rig. Deviations in the fluid properties of the aqueous solution

Fig. 3. Fouling built-up at different axial position

against water were approximated by 2%. Hence, the maximumcalculation error of Eq. (8) was determined by an error analysis to6.49%. The heat flux through the tube wall is given by

_Q ¼UADTm ð9Þ

U is the overall heat transfer coefficient, A the heat transfer areaand DTm the suitable log mean temperature difference (LMTD)across the heat exchanger. For constant mass flow rates andconstant inlet temperatures on the shell side as well as on thetube side of the heat exchanger, the decrease of the overall heattransfer caused by fouling can be measured by the change in eachoutlet temperature. Considering fouling only on the inside and nochange of the inner heat transfer coefficient the integral foulingresistance can be written as

Rf ¼1

Uf�

1

U0¼

xfiA

lfiAfi�

xfiA

lfiAið10Þ

The reference area A is the outer surface of the inner tube and thesurface of the fouling build-up Afi is set to the inner surface Ai asapproximation.

3. Results and discussion

3.1. Roughness effects in the initial fouling stages

In the following section, results of fouling experiments in anelectro-polished stainless steel tube (SS 304EP) are shown. Afterevery experimental run endoscopic photographs were taken atdifferent axial positions. Fig. 3 shows the fouling build-up along thelength of the heat exchanger tube. It may be seen that no compactfouling layer is formed on the inner tube surface and only singleclusters with a size between 0.5 and 2.5 mm (increasing with theaxial length in flow direction) can be detected, thus allowing anyconstriction effect for this initial phase to be neglected.

The overall size of the crystal clusters ranges from 0.5 to 2.5 mmin diameter. By using the force balance equation for fully developedisothermal and incompressible fluid flow, it is possible to calculatethe actual friction factor for the present roughness:

l¼Dpdi

L

2

rw2ð11Þ

where di is the inner diameter of the tube, L is the correspondingtube length and w is the flow velocity of the process stream. Itshould be noted that the extracted values for l are integral valuesfor the whole inner tube surface although Fig. 3 clearly reveals anaxial distribution of surface coverage with crystals.

s at time t¼110 h (visible section: |5 mm).

Fig. 4. Fouling resistance and friction coefficient versus time.

Fig. 5. Temperature profile through a cylindrical wall with fouling on the inside.

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509 503

Fig. 4 shows the fouling resistance calculated by Eq. (10) and thefriction factor determined by Eq. (11) versus time. The foulingresistance Rf shows a negative value over the whole time of theexperiment apart from the very beginning. The profile of thefriction factor is inverse to the fouling resistance, which indicatesthat both the heat balance and the fluid dynamics show indepen-dent but corresponding reproductions of the fouling process. Theincrease in heat transfer is caused by the disturbance of the viscoussublayer dl. The latter can be estimated by an approach ofSchlichting and Gersten (2006):

dl

di¼ 122

lnRe

ReGðlnReÞð12Þ

G(ln Re) is a function, which can be approximated to a value of 1.35for a turbulent flow regime between 2300oReo107. For a givenReynolds number of 17,500 the calculated thickness of the laminarsublayer is 0.8 mm. This is well within the range of the height of the

crystal clusters. Although Eq. (12) is only valid for smooth surfacesit is used here to estimate viscous sublayer thickness for the roughsurface.

The reason for a negative fouling resistance Rf during theinitial stages of fouling can be deduced by properly accountingfor the earlier findings. Fig. 5 shows a temperature gradientthrough the cylindrical wall of the heat exchanger with a foulinglayer on the inside only. The formation of crystal growth leadsto an increase in surface roughness and therefore to an improve-ment of the local heat transfer coefficient hi due to higherturbulence.

According to the heat balance in Eqs. (8)–(10) of the present heatexchanger, and in the case of a very thin fouling layer (AiEAfi), theoverall heat transfer coefficient Uf can be written as

1

Uf¼

A

hiAiþ

xA

kAmþ

A

haAa

� �þ

xfiA

kfiAi

� �ð13Þ

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509504

where Am is the corresponding average surface area. The firstbracket of Eq. (13) describes the overall heat transfer resistance ofthe clean surface 1/U0 at zero-time of the fouling process. If the filmheat transfer coefficient on the inner side of the tube wall is set toconstant for the whole fouling process, 1/U0 will also be a constant.As shown above, surface roughness causes an increase of the filmheat transfer coefficient during the fouling process. To consider theeffect of surface roughness on heat transfer during the initial stageof fouling, Eq. (13) may be expressed as follows:

1

Uf¼

A

hiðtÞAiþRf ðtÞþ

1

U�0with

1

U�0¼

xA

kAmþ

A

haAaa f ðtÞ ð14Þ

For the inner heat transfer coefficient hi(t) the effect of rough-ness on heat transfer may be quantified through the frictionfactor l:

hiðtÞplf ðtÞ

l0hi0, NuðtÞp

lf ðtÞ

l0Nu0 ð15Þ

According to the empirical approaches in Table 1, l0 is thefriction factor of the clean surface at zero-time and lf (t) the currentresistance due to friction of the fouling process.

Fig. 6. Heat transfer efficiency for different dimensionless roughness calculated

with approaches of Table 1.

Fig. 7. Recalculated fouling resistances

Fig. 6 shows the heat transfer efficiency c¼eNu/el as a functionof the roughness parameter k+ . The graphs show distinct differ-ences between the absolute values of the different empiricalmodels. While the equations of Nunner (1956) and Hughmark(1975) always result in efficiencies less than one, the empiricalmodels of Burck (1969) and Ceylan and Kelbaliyev (2003) predictvalues greater than one for low values of k+ . In his model Burck(1969) distinguished between integral and superimposed rough-ness. Integral roughness, like finned tubes, is in direct contact withthe heat transfer surface or may even be manufactured out of thetube wall material. Hence, two effects contribute to an increase inheat transfer: (i) increase in surface area and (ii) conduction inradial direction into the viscous sublayer adjacent to the surface.Superimposed roughness may have a similar shape as integralroughness, therefore, the resistance due to friction could beidentical, whereas the effect on heat transfer is different due tothe thermal contact resistance between heat transfer surface androughness element.

The relation between heat transfer and friction characteristicsfor the fouling process can be quantified by substitution of hi fromEq. (15) in Eq. (14). Thus, the corrected fouling resistance Rf (t) canbe written as

Rf ðtÞ ¼1

Uf�

A

ðhi,0eNu,lÞAi�

xA

lAmþ

A

haAa

� �ð16Þ

hi,0 is the inner heat transfer coefficient of the clean surfacecalculated from the heat balance and ha the average heat transfercoefficient of the annular ring determined by the Wilson-plotmethod (Wilson, 1915; Fernandez-Seara et al., 2007).

Fig. 7 shows the recalculated fouling resistances in comparisonto the fouling resistance calculated from Eq. (10). According to thedifferent characteristics, the highest amount of fouling is calculatedwith the approaches by Burck (1969) and Ceylan and Kelbaliyev(2003). Considering the amount of crystalline deposits in Fig. 3, theestimated thermal resistances seem unrealistically high for thesetwo models. Additionally, both models start with an offset which isphysically unacceptable. Low fouling resistances are calculated byusing the empirical equation of Nunner (1956) and slightly highervalues are obtained by using Hughmark’s equation (Hughmark,1975). Further experiments with electro-polished tubes (SS 304EP),shown in Fig. 8, have been conducted under the same processconditions and all of them show reproducible and comparableresults.

at Re¼1500 according to Eq. (6).

Fig. 8. Recalculated fouling resistances at Re¼17,500 according to Eq. (16), electro-polished tube (SS 304EP).

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509 505

3.2. Constriction effects in the crystal growth period

As fouling progresses the fouling layer increasingly constrictsthe tube cross section. The effect of roughness also persists for thecrystal growth period. Therefore, for a heat exchanger operating atconstant flow rate, the flow velocity will increase resulting in anincrease of the heat transfer coefficient. The total pressure drop

may be divided into two parts: friction and fluid acceleration(Nunner, 1956):

Dp¼DplþDpo ¼ lL

diþ2ln

wf

w0

� �rw2

2ð17Þ

Here w is the average flow velocity, wf is the flow velocity of theconstricted and w0 of the original tube diameter. One major difficulty

Fig. 9. Idealized deposit distribution along the heat exchanger tube.

Fig. 10. Tube inlet and outlet at the end of the fouling experiment.

Table 2Experimental results of the restricted flow cross section by using the volumetric method.

Experiment wf(z¼0 m) (m s�1) wf(z¼L) (m s�1) df(z¼L) (m) Dp (Pa) Dpo (Pa) Dpl (Pa) l (dimensionless)

SS 304 0.65 0.84 0.0139 47,012 148 46,864 1.296

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509506

in solving Eq. (17) is the exact definition of the starting point of theconstriction and consequently of the free flow cross section. For a firstassumption volumetric measurements of the deposits as well asmeasurements of the deposit height at the in- and outlet region of thetube were taken after every experimental run. Endoscopic photo-graphs and local temperature measurements during the foulingexperiments in conventional drawn stainless steel tubes (SS 304)reveal that a non-uniform deposit profile was formed due to thetemperature gradient along the heat exchanger tube.

Fig. 9 shows an idealized scale formation along the heatexchanger tube. At z¼L the product reaches its maximum bulktemperature plus experiences the highest wall temperature. Owingto the inverse solubility of CaSO4 this results in a maximum layerthickness. By using the equation of a truncated cone the reduceddiameter df at position L can be determined from

df ¼�d0

2þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12VC

pL�

3d20

4

sð18Þ

The volume VC of the truncated cone can be estimated experi-mentally by filling of the fouled tube with water after the foulingexperiment. The deposit height at the heat exchanger entrance(z¼0 m) is set to zero (df¼d0) as found from visual inspection,see Fig. 10.

Table 2 shows the current values of a fouling experiment in aconventional drawn stainless steel tube (SS 304) after a runtime of

280 h. During the fouling process a compact but not uniformlydistributed layer was formed. Calculating the tube diameter df

by using Eq. (18) the constriction due to the deposit thickness is15% of the original tube diameter. The calculated pressure drop Dpodue to the velocity increase is moderate (see Table 2). Therefore,the friction factor by using Eq. (17) gets unrealistically highcompared to literature data (Herwig, 2008) when the remainingamount of the measured pressure drop is attributed to roughnesseffects alone.

Fig. 9 implies a compact nonporous scale formation along thetube axis. Optical inspections via endoscope revealed a highlyporous structure of the fouling layer, see Fig. 10. At the tube exit atz¼L the free inner diameter could be estimated to 6.4 mm. In a firstestimation of the acceleration effect df (z¼L) was set to 6.4 mm andstagnant fluid was assumed in the porous fouling structure. Withthese assumptions and the experimental value for total pressuredrop the friction factor can be extracted applying Eq. (17), seeTable 3. A value of l¼0.081 is obtained which is in reasonableagreement with literature data (Nikuradse, 1933; Neddermann andShearer, 1964; Herwig, 2008). The average porosity of the foulinglayer can also be estimated to be F¼0.744.

Based on these findings the start of constriction effects isdefined as the moment that the friction factor reaches l¼0.081.From this time on friction and roughness effects are set constantand all further increase in pressure drop is attributed to constric-tion, see Fig. 11 top.

Fig. 11. Recalculated fouling resistances at Re¼17,500 accounting for roughness as well as constriction effects.

Fig. 12. Asymptotic fouling resistance and corresponding deposit thickness accord-

ing to five different approaches.

Table 3Experimental results of the restricted flow area by using the photographic method.

Experiment wf(z¼L) (m s�1) df(z¼L) (m) Dp (Pa) Dpo (Pa) Dpl (Pa) l (dimensionless) F (dimensionless)

SS 304 3.94 0.0064 47,012 9465 37,547 0.081 0.744

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509 507

Compared to the fouling resistance with constant heat transfercoefficient, all recalculated resistances take positive values imme-diately after the end of the induction period by considering theroughness effect. No negative value for Rf can be found. The highestamount of fouling is still calculated with the approaches by Burck

(1969) and Ceylan and Kelbaliyev (2003), again with an offset fork+ o30. More realistic results can be found by using the empiricalequation of Nunner (1956) and the model of Hughmark (1975),respectively. After an experimental runtime of approximately250 h fouling runs into asymptotic resistances, differing in theirabsolute value depending on the empirical approach. This results inthe calculation of different final deposit thicknesses, xf. The depositthickness can also be determined experimentally by volumetricmeasurements and may be compared to the calculated layerthickness according to each empirical approach. The constrictioneffects will be considered by extending the given approach in Eq.(16) to

Rf ðtÞ ¼1

Uf�

A

ðhi,0eNu,leNu,oÞAi�

xA

lAmþ

A

haAa

� �ð19Þ

The increase in Nusselt number eNu,o¼Nuo/Nu0 by accelerationeffects was determined from the correlation of Gnielinski (HEDH,1986).

Fig. 12 shows the relation of each calculated average thicknessconsidering the effects of roughness and constriction. All calculatedthicknesses are below the measured thickness. Taking into accountthe surface roughness of the fouling layer by using the equation ofNunner (1956), the estimated height of the deposit thicknessincreases by 65% and additionally 35% by considering the constric-tion effect. Using the empirical model of Hughmark (1975) thecalculated thickness is 144% higher. The highest thickness is

F. Albert et al. / Chemical Engineering Science 66 (2011) 499–509508

predicted by the models of Burck (1969) or Ceylan and Kelbaliyev(2003), which lies 16% below the measured thickness. Consideringthe unrealistic profile of Rf during the induction and roughnesscontrolled period the use of latter two approaches has to bescrutinized. Overall the asymptotic fouling resistance and thereforethe deposit thickness are underestimated when not accounting forthe roughness and constriction effects. The substitution of Nunners

and Hughmarks equations into the calculation of Rf seems to bemost appropriate for the given experiments in crystallizationfouling.

4. Conclusion

Fouling experiments in a double pipe heat exchanger withelectro-polished stainless steel tubes (SS 304EP) as well as withcommon drawn stainless steel tubes (SS 304) were conductedunder constant process conditions. Crystallization fouling of anaqueous CaSO4 solution was followed by three differentapproaches: fluid dynamics based on pressure drop measurements,heat transfer performance, as well as optical inspection via anendoscope. Crystal formation and fouling built-up on the heattransfer surface give rise to two effects: an increased surfaceroughness followed by an additional constriction of the flow crosssection as fouling progresses. These affect fluid dynamic as well asthermal performance of the heat exchanger. In the early phase offouling constriction effects may be neglected and the increase insurface roughness can be detected from pressure drop measure-ments. Four different literature models are applied to deduceintegral surface roughness from the pressure drop increase.Accounting for heat transfer enhancement through roughnesseliminates negative fouling resistances in the roughnesscontrolled phase.

In the subsequent crystal growth period the roughness of thefouling layer is considered constant. Therefore, any additionalpressure drop increase is attributed to constriction effects. Theincrease in heat transfer due to fluid acceleration to some degreecompensates for the heat transfer reduction due to fouling. Whenproperly accounting for this effect the corrected fouling resistancesare transferred to an equivalent area-averaged deposit layerthickness. The latter correlates very well with the experimentaldetermination of deposit thickness from volume filling. Apparentnegative fouling resistances are eliminated completely after con-sideration of roughness and constriction effects.

For further investigations of the influence of roughness effectsduring the initial stage of crystallization fouling, the present heatexchanger is modified to allow local temperature measurements.With this, the temperature gradient along the tube and localsupersaturation of the salt solution as well as local depositthicknesses can be calculated to obtain a differential view of thefouling process. This work is in progress. Elaboration of the detailedfouling topography by means of X-ray tomography measurementswill help to calculate local pressure losses.

Nomenclature

A area, pdL (m2)C constant (dimensionless)cP heat capacity (J kg�1 K�1)d diameter (m)h heat transfer coefficient (W m�2 K�1)k thermal conductivity (W m�1 K�1)k+ dimensionless roughness, ksdl

�1 (dimensionless)ks sand grain roughness (m)L representative length (m)

Nu Nusselt number, hdhk�1 (dimensionless)Dp pressure drop (Pa)Pr Prandtl number, ZcPk�1

_Q heat flux (W)r radius (m)Rf fouling resistance (m2 K W�1)Rfn asymptotic fouling resistance (m2 K W�1)

Re Reynolds number, wdhn�1 (dimensionless)St Stanton number, Nu Re�1 Pr�1 (dimensionless)T temperature (K)DT temperature difference (K)U overall heat transfer coefficient (W m�2 K�1)V volume (m3)w velocity (m s�1)x deposit thickness (m)

Greek letters

e effectiveness (dimensionless)F porosity, VH(VH+VS)�1 (dimensionless)c heat transfer efficiency (dimensionless)Z dynamic viscosity (Pa s)l friction factor (dimensionless)n kinematic viscosity (m2 s�1)r density (kg m�3)

Subscripts

b bulk phasec cooling sideC conef fouled surfaceh heating sideH hollowi innerm mean temperatureo outerS solidW wall0 smooth/clean surface

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