NUMERICAL INVESTIGATION OF SHORT ELLIPTICAL...

NUMERICAL INVESTIGATION OF SHORT ELLIPTICAL TWISTED TUBE FORREDUCED FOULING RATE IN STEAM CRACKING FURNACES.

*B. Indurain1,2, F. Beaubert¹, D. Uystepruyst¹, S. Lalot¹ and M. Couvrat²1 LAMIH UMR CNRS 8201, Polytechnic University Hauts-de-France, 59300, Valenciennes, France.

[email protected] (corresponding author)

2 Manoir Industries, 27108, Val de Reuil Cedex, Pitres, France

ABSTRACTIn the steam cracking industry of natural gas

or naphtha, fouling of tubular heat exchangers bycokes is one of the biggest issues regarding yieldsof valuable product and life span of the tubescomposing the furnace. Coke build up on the tubeswall and this growing carboneous layer has twomajor negative effects: 1) it increases pressure dropand 2) reduces heat transfer from the tube wall tothe processed fluid. Increasing wall shear stressyields higher friction forces at the wall of the tubewhich could reduce the coking rate. Previousstudies prove that minor change of tubescross section can both enhance wall shear stressand heat transfer by generating a swirling decayingflow. Using the open-source CFD softwareOpenFOAM, this study numerically investigateswall shear stress and pressure drop performances ofswirl decaying flow generated by differentelliptical cross-section twisted tube. One of theobjectives is to determine if minor modifications oftube geometry can generate swirling flow whichcould enhance wall shear stress at a reduce pressuredrop penalty. For a Reynolds number ranging from10, 000 to 100 ,000, it is shown that theinvestigated geometries could enhance heat transferby 90% at an increased pressure drop of 128%which yields a Performance Evaluation Criterion(PEC) of 1.44. The comparison between theperformances of the different geometries is carriedout using a newly defined PEC based on the bulktemperature, along with the usual PEC.

INTRODUCTIONSteam cracking of naphtha and ethane

produces about 85% of olefins made in the world,such as light olefins (ethylene, propylene, butene...)and aromatics [1]. The cracking reaction takesplace within the tubes of the steam crackingfurnaces at very high temperatures (above 1000 K)and produces the aforementioned products but alsocokes on the wall of the tubes [2, 3]. This growingcarboneous layer has several negative effects. First,coke build up decreases the cross-sectional area of

the gas flow resulting in higher pressure drop andloss of ethylene selectivity [4]. Secondly, the lowthermal conductivity of cokes weakens the heattransfer from the tube wall to the process gas.Consequently, the heat input is raised to counteractthe increased heat transfer resistance, leading tohigher tube metal temperature (TMT) and stillhigher coking rate. Eventually, either due to anexcessive pressure drop over the reactor or due tometallurgical constraints of the reactor tube alloy,production needs to be halted to decoke the reactor[5]. For obvious economics reasons coking ratemust be slowed down. To that end, metallurgydevelopments of tubes [6,7] or three-dimensionalreactor designs are used to enhance heat transfer,resulting in lower wall temperatures and/or higherwall shear stress and so to reduce coking rates asdeduced from the well known Ebert and Panchalmodel (see e.g. [8]). Designs can be divided intotwo classes based on the physical reason of heattransfer: increased internal surface area orenhanced mixing.

Van Goethem et al. [9] numerically studiedheat transfer and pressure drop of air flow inseveral heat transfer enhancers and among themthere were straight and helical internally finnedtube. For Reynolds numbers from 80,000 to350,000, they reported that these increased surfacetechnologies respectively enable an averageincrease in heat transfer of 51% and 66%compared to a straight tube yet at the expense of anaverage increased pressure drop of 67% and 92%.The better heat transfer performance of thehelically finned tube is linked to its ability togenerate a swirling flow and thus improving themixing of the gas which leads to a more effectiveand more homogeneous heating of the process gas.

Swirling flow increases mixing in the fluidcore section and results in increased shear stress atthe wall. The studies conducted byTorigoe et al. [10] and Györffy et al. [11] focusedon the heat transfer and pressure drop performancesof a single start internally ribbed tube calledMixing Element Radiant Tube (MERT) patented

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by Kubota in 1995 (seewww.kubotamaterials.com.products/mert.html fora brief description). They found with the latestversion of the MERT that the heat transfer isimproved by up to 40% while the pressure drop isincreased by up to 210%.

Although heat transfer is enhanced with theprevious technologies, this is at the cost of atremendous pressure drop increase. This drawbackis mainly due to the added material at the tubesurface. However, swirling flows could begenerated by other means, such as deforming thetube shape as with the Swirl Flow Tube (SFT)developed by Technip [12, 13]. Van Goethem et al.[9] have experimentally and numerically studiedthis design of tube. The increased mixing isobtained by changing the shape of the tube from astraight to a small amplitude helical tube. Theirresults showed that for Reynolds numbers rangingfrom 30,000 to 120,000, the SFT can achieve agood balance between enhanced heat transfer andimproved pressure drop with a 33% increase forboth. Those results prove that a mere modificationof the tube geometry could lead to a power efficientswirling flow.

Tubes with elliptical cross-sections have beenwidely studied and some of those researchesfocused on the heat transfer and pressure dropperformances of twisted elliptical tube.Tan et al. [14] conducted a parametric study of atwisted elliptical tube and they reported that thiskind of tube geometry offers an excellentPerformance Evaluation Criterion (PEC) as definedby Webb and Eckert [15] within the studiedReynolds number range with the highest PECreaching 1.725. It can also be concluded from theirstudy that the greater the aspect ratio of the ellipsethe higher the PEC and this is also true with thetwist pitch of the tube but up to given value. Thislatest result shows that continuous swirling flowcan become less efficient if it is maintained over atoo long distance. Thus, after reaching a fullydeveloped state, the swirling flow should decay andnot increase pressure drop further.

This paper presents some results of anumerical investigation on the heat transfer andpressure drop performance of a developing swirlingflow generated by a short length twisted tube withelliptical cross-section (SETET) and decayingdownstream of the SETET in a tube with a circularcross-section. Several configurations of the SETETare studied in order to find the configuration whichprovides the highest heat transfer enhancement atthe lowest pressure drop increase.

2. SHORT ELEMENT OF TWISTED ELLIPTICAL TUBE

The numeric test bench for the simulationsconsists of a tube composed of different elements.First of all, there is a twisted elliptical tube (TET)whose hydraulic diameter Dh is defined as:

Dh=4 AE

(1)

The twist operation of the elliptical cross-section consists in both a translation over adistance P and a 2π rotation along the tubesaxis. The length of the TET is LTET =20Dh andits inlet is considered as the origin of the axiscoordinate (z*=0). Upstream of the TET thereare two different elements, a transition tubeand a tube with a circular cross-section. Thelatter has the same hydraulic diameter of theTET and has a length Lup=40Dh. The purposeof this tube is to achieve a developed flowbefore entering the TET. The transition tube isused to have a smooth transition between thecircular and the elliptical cross-section tubesover a length Ltr=4Dh. Downstream of theTET, the same elements as upstream are usedbut the length of the tube with a circular cross-section is Ldown=32Dh so that the total length ofthe test bench is L=100Dh. LTET is only onefifth of L, that is why the TET is renamed hereas SETET. The computational domain can beseen on figure 1.

Fig. 1. Sketch of the numeric test bench withP=10Dh.

The geometric parameter of this study is thetwist pitch P and the aspect ratio of the ellipse c. Asit can be seen in table 1 the twist pitch P for agiven aspect ratio is tested.

Table 1. Tested geometric parameters with c the aspect ratio of the ellipse

Cases P (m) c

Case 1-1 20Dh 0.6

Case 1-2 10Dh 0.6

Case 1-3 5Dh 0.6

For every case five different Reynoldsnumbers (Re) are tested, they range from 10,000 to100,000 and Re is defined as:

Re=ρU b Dh

μ(2)



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3. SET UP OF THE NUMERICAL SIMULATIONS

The simulations are performed using the opensource CFD software OpenFOAM. OpenFOAM isan open source object oriented numericalsimulation toolkit developed in C++ and releasedunder GPL license by theOpenFOAM®Foundation [16]. As no experimentaldata are yet available with the investigated tubeconfiguration, a part of the numerical studyconducted by Tang et al. [17] on the heat transferand pressure drop performance of the flow in atwisted tube with elliptical cross-section wasreproduced in this study.

3.1 Test case of Tang et al. [17]The parameters of the elliptical cross-section

are the ellipse major and minor axis which arerespectively a=0.024 m and b=0.015 m. Thenumerical test bench, as shown on figure 2, iscomposed by a TET and two straight tubes with anelliptical cross-section upstream and downstreamof the TET. The hydraulic diameter of the TET isgiven by Tang et al. to be Dh=0.02 m, and the twistpitch is P=10Dh. Ultimately, the length of the TETis L=4P.

Fig. 2. Numeric test bench used by Tang et al. [17]

3.2. Boundary conditions and numerical schemes

The flow is considered steady, incompressible,turbulent with heat transfer and the flowing fluid iswater. Considering the boundary conditions, aconstant bulk velocity Ub based on the desiredReynolds number is imposed at the inlet along witha constant temperature T0=300 K. A constant walltemperature Tw=350 K is imposed, and a no-slipcondition is applied for the velocities. At the outlet,a constant pressure is imposed while null fluxes forthe velocity and the temperature are set.

The different components of the governingequations (continuity, momentum and energy) arediscretized using a second order bounded linearUPWIND scheme. The pressure-velocity linkedequation are solved using the SIMPLE algorithm.A k-ω SST turbulence model with a Low-Reapproach is used to reproduce the numerical workof Tang et al. [17]. At the inlet, the value of theturbulent kinetic energy k is set with the turbulentintensity and the specific dissipation rate ω isdetermined with the calculated value of k and theturbulent mixing length of the case. Thecorresponding formulas along with the governingequations can be found in Robertson et al. [18]. At

the outlet, a null flux boundary condition isimposed for both turbulent quantities and fixedvalues are imposed at the wall.

3.3. Validation of the numerical procedureTo quantify the pressure drop Δp along the

TET, the friction factor coefficient f is used and isdefined as:

f =2Δp Dh

ρU b2 L

(3)

The heat transfer along the TET is quantifiedusing the Nusselt number (Nu) defined as:

N u=h Dh

λ(4)

Heat transfer is calculated using a thermalenergy balance between the inlet and outlet of theTET and the Nusselt number can be rewritten as:

N u=m cp( T o−T i)

π λ LT L M T D

(5)

where:

T L M T D=T o−T i

ln (T w−T o

T w−T i)

(6)

The results of the comparison between thesimulations of the present study and theexperimental data of Tang et al. [17] are shown intable 2. It can be observed that the maximumdifferences between the results of the simulationsand the results from Tang et al. for Nu and f arerespectively 6.3% and 5.2%. Those differences aresufficiently small to consider that the adoptednumerical procedure is suitable to correctly predictheat transfer and pressure drop of a swirling flowgenerated by a twisted tube with elliptical cross-section. Therefore, this numerical procedure isadopted to study the different geometricconfigurations of SETET presented in table 1.

Table 2. Comparison between the results from thesimulations of the present study and theexperimental data from Tang et al [17].

Re 20,000 18,000 16,000 14,000

fTang [17] 0.0282 0.0294 0.0305 0.0322

f 0.0268 0.0279 0.0298 0.0311

Rel. dev 5.0% 5.2% 2.2% 3.2%

NuTang [17] 102.2 93.7 85.9 77.4

Nu 95.7 90.8 83.0 78.3

Rel. dev 6.3% 3.1% 3.4% 1.1%

4. NUMERICAL SIMULATIONS OF THE SETET

The same numerical configuration as in thevalidation process of part 3 is kept here. However,



the working fluid is now air and thethermodynamic properties used are summed up intable 3. One assumption is that, within the givenrange of encountered temperatures, thethermodynamic properties are kept constant.

Table 3. Thermodynamic properties of air at T=300 K [19]

cp (J/kgK) 1006

λ (W/mK) 0.024

μ (Pa.s) 1.91e-5

ρ (kg/m³) 1.205

Although the numerical procedure has beenvalidated, a mesh independent test study with case1-1 is undertaken to ensure that the results of thesimulations are not mesh sensitive.

4.1. Mesh independence testThe meshing process is achieved by using

cfMesh, an open source meshing softwaredeveloped by Dr. Franjo Juretic [20]. Threedifferent cartesian unstructured meshes were testedwith a refined mesh close to the wall of the tubeconsisting in 11 additional mesh layers. The threemeshes from the finest to the coarsest are notedmesh 1, mesh 2 and mesh 3 and they respectivelyhave 10,890,272, 7,632,400 and 5,330,459 cells.Mesh 2 is obtained with the same meshingparameters used for the validation case.

The Grid Convergence Index (GCI) methoddeveloped by Roache [21] is adopted here toconduct the mesh independence test. It is ageneralization of the Richardson extrapolation andit provides a uniform measure of convergence forgrid refinement studies. The GCI value representsthe resolution level and how much the solutionapproaches the asymptotic value and is defined as:

GC I i=1.25ei+1−ei

ei (rα−1 )

(7)

where the grid refinement ratio r in this study isr=1.43 and α is computed as follows [21]:

α=

ln (e1−e2

e2−e3)

ln(r)

(8)

For the sake of clarity, the GCI method is notdescribed here but can be found in [21,22]. Bothglobal and local quantities are investigated with theGCI method. The global quantities are the frictionfactor f and the Nusselt number Nu. The localquantities are averaged values in a plane located inz*=34 and they are the skin friction coefficient Cf

and the bulk temperature Tb respectively definedas:

C f =2τw

ρ U b2

(9)

and

T b=1

U b A∫AT uz d A (10)

The results of the grid refinement study aresummarized in table 4 and it can be noticed that theGCI between mesh 1 and 2 is lower than the GCIbetween mesh 2 and 3 except for the Nusseltnumber but the GCI is still low. Therefore, theresults of the simulations are less prone to changebetween mesh 1 and mesh 2. Furthermore, it iscomputationally less expensive to run simulationswith mesh 2, thus this latest mesh was chosen toperform all the other simulations for the parametricstudy.

Table 4. Order of accuracy and Grid Convergence Index (GCI) for several flow quantities and for the three meshes.

α GCI2

(%)GCI1

(%)

f 7.5 3.1 0.21

Nu 2.4 0.28 1.1

Cf 2.95 1.44 0.5

Tb 2.6 0.35 0.14

5. RESULTS AND DISCUSSION

5.1. Flow fieldFor the three cases, the swirling flow is

generated in the same way. As the flow progressesthrough the SETET it acquires a tangential velocitycomponent due to the geometry curvature.However, the lower the twist pitch of the SETETthe greater the curvature and therefore the higherthe intensity of the swirling flow as it can be seenon figure 3. In a cross-section of the SETETlocated at z*=10, which corresponds to half thelength of the twisted tube, the maximumdimensionless azimuthal velocity Uθ

* has beencalculated for case 1-1, 1-2 and 1-3 and isrespectively of 0.10, 0.28 and 0.53. As the twistpitch decreases, the maximum dimensionlesstangential velocity increases significantly whichleads to a greater mixing of the fluid, a longer flowpath and an improved heat exchange between theswirling flow and the wall of the tube. In thosesame cross-sections, the mean deviation angle ofthe flow calculated between the tube axial directionand the flow velocity vector for the three cases isrespectively of 9.2°, 16.9° and 24.5°. Again, thelower the twist pitch, the higher the mean deviationangle. This means that the wall of the twisted tubecould deflect more efficiently the axial flowyielding to an intense swirling motion.



Fig. 3. Swirling flow in the different SETET. Case1-1 (top), case 1-2 (middle) and case 1-3 (bottom)are all at Re=100,000.

In order to quantify the intensity of theswirling flow, a specific quantity is usually adoptedand defined by Kitoh [23] as the swirl number S:

S=∫0

R

r2uθ uz d r

R∫0

R

ru z2 d r

(11)

The evolution of S from z*=0 to z*=51 andfor the three different cases at the highest Reynoldsnumber is shown on figure 4, where the verticalbars delimitate the different phase of the swirlingflow as discussed in the following. It must benoticed that there are three major phases: 1) fromz*=0 to z*=20, the generation and development ofthe swirling flow, 2) at z*=20 the transitionbetween the SETET and the exit tube with circularcross-section where there is a huge drop of theswirl number and 3) from z*=24 to z*=51, thedecay of the swirling flow. In phase 1, between allof the three cases, there are large difference ofswirl numbers and the slopes are also greatlydifferent from one another. The sharpest slope isachieved with case 1-3 meaning that the swirlingflow is rapidly developing inside this SETET. Forevery case, there is a dramatic drop of the swirlnumber at z*=20, caused by the end of the curvedgeometry and the rather sharp transition between anelliptical and a circular cross-section. Moreover,the higher the swirl number, the larger the drop ofS.

Besides, it could also be observed thatwhatever length the SETET of case 1-1 might be, itwill never generate a swirling flow whose S is as

high as the intensity of the SETET of case 1-2 after10Dh or of case 1-3 after 5Dh. In addition, if onlyone twist pitch of every SETET is considered, itmust also be noticed that the shorter the length ofP, the greater the value of S.

Fig. 4. Evolution of the swirl number along theTET and downstream for the cases 1-1, 1-2 and 1-3at Re=100,000.

Ultimately, because of the logarithmic scale, itis easily observable that all of the three swirlingflows have the same decay in phase 3. Thecalculation of the slope or decay rate of case 1-1 to1-3 gives respectively a decay rate of 0.04, 0.041and 0.042. This specific behavior of the swirlingflows is shown on figure 5, where the graph hasbeen built as follows. The evolution of S from case1-3 is used and the last value of S at z*=51 isstored. Then, the closest value of S from case 1-2to the latest stored S is found and added to thegraph along with the subsequent values of S fromcase 1-2 and the latest value is stored. Then thisoperation is done once more between case 1-1 and1-2.

Fig. 5. Reconstruction of the Swirl number fromthe three cases at Re=100,000.

Although the pitch of the SETET has atremendous influence on the development of theswirling flow, it has very little regarding its decay.Figure 5 also illustrates that with case 1-3, theswirling flow could last over almost almost 70Dh

after the SETET.

5.2. Pressure DropThe swirling flow generated by the three

SETET are greatly different as previously seen onfigure 3 and 4. Hence it is important to study theevolution of the friction factor with the Reynoldsnumber, depending on the SETET. Figure 6features the friction factor ratio between the



SETET (f) and a straight tube (fp) where fp iscalculated with the correlation from Pethukov:

f p=(0.79 ln (Re)−1.64 )−2 (11)

while f is computed by using Eq. (3) between z*=0and z*=51.

Fig. 6. Evolution of f/fp with Re for cases 1-1 to1-3.

The transition between the elliptical cross-section and the circular cross-section might cause alarge pressure drop due to a sudden change of theflow topology as depicted with the sharp variationof the swirl number in phase 2 on figure 4. Pressureloss of case 1-2 are higher than case 1-1 but are inthe same range especially compared to case 1-3where the pressure drop are tremendously higher.

5.3. Heat TransferThe amount of heat exchanged between the

fluid and the wall depends also greatly on theswirling flow. The calculation of the bulktemperature Tb with Eq. (8) and its evolution fromz*=0 to z*=51 for every cases, as seen on figure 7,gives information on how effective the swirlingflow is to transport the heat from the wall to thebulk flow.

Fig. 7. Evolution of Tb along the TET anddownstream for cases 1-1 to 1-3 and for the straighttube at Re=100,000.

The swirling flow generated by the SETET ofcase 1-3 is more effective at increasing the bulktemperature than the two other SETET. Althoughthis increase is not really high, it means that theswirling flow enables a more effective heat transferbetween the wall of the tube and the flow. As aconsequence, for a given heat flux at the wall of thetube, the increased heat transfer will have two

major effects in steam cracking furnaces. First ofall, it will result in a diminution of the walltemperature and according to the coking model ofPlehiers [24] yield a lower coking rate. Secondly,because of the imparted swirling motion, it willlead to a more uniform radial temperaturedistribution which in turn decreases secondaryreactions which also participate to the cokeformation [25, 26]. Furthermore, more heat istransported by the rotating fluid as shown onfigure 8 which displays the ratio between the globalheat transfer obtained with an enhanced geometry(Nu) and the heat transfer obtained in a straighttube (Nup) where Nup is calculated with thecorrelation of Gneilinsky:

Nup=

f p

8(Re−1000) Pr

1+12.7 (f p

8)

0.5

Pr 0.6666−1

(12)

where Pr is the Prandtl number and is defined as:

Pr=μC p

λ(13)

The Nusselt number is calculated from Eq. (5)and the heat balance is done between z*=0 andz*=51.

Fig. 8. Evolution of Nu/Nup with Re for cases 1-1to 1-3.

It can be observed that both cases 1-1 and 1-2provide approximately the same heat transferenhancement and are both below the heat transferenhancement of case 1-3. All the SETET areefficient at enhancing heat transfer and theimprovement grows with the Reynolds number,except for case 1-1 at Re=100,000 where there is asudden drop of Nu/Nup. The improved heat transferand the relatively low pressure drop increase fromthe twisted tube is of particular interest for thesteam cracking industry because again it leads to alower TMT and provided that the coke depositionoccurs at the wall where the temperatures are thehighest to a lower coking rate [13, 26, 27].Similarly, considering the Ebert and Panchalmodel, the enhanced heat transfer of the SETETleads to a diminution of the deposition term byincreasing the heat transfer coefficient in thethermal boundary layer and by reducing the wall



temperature thus leading to a diminution of thefouling rate [8].

Even though every investigated SETETgenerate a swirling flow which increases pressuredrop, it also enhances significantly the heattransferred between the wall and the flowing fluid.To quantify the energetic efficiency of the SETET,the Performance Evaluation Criterion (PEC),proposed by Webb et al. [15] is used here and isdefined as:

PEC=Nu / Nup

3√f / f p

(14)

The evolution of the PEC for the differentcases is shown on figure 9.

Fig. 9. Evolution of PEC with Re for cases 1-1 to1-3.

Although the SETET of case 1-3 providesbetter heat transfer performance at the cost of ahigher pressure drop than the two other SETET, itcan be observed that all the studied geometrieshave approximately the same PEC with a slightlyhigher values for the SETET with the greatest twistpitch. Considering that the SETET of case 1-3generates the most intense swirling flow whichincreases both the wall shear stress and the heattransfer at the same PEC as the two other SETET,it is concluded that this SETET is the mostinteresting studied configuration.

6. THE BULK TEMPERATURE RELATED PEC

In the steam cracking industry, thetemperature of the processed gas is a primeparameter to achieve a better selectivity in highlyvaluable products (ethylene, propylene…). Thehigher the bulk temperature, the better theselectivity and also the lower the radial temperaturegradient and the lower the coking rate [25]

It was seen in section 5.3, on figure 7 thatevery configuration of SETET generates a swirlingflow which yields higher Tb along z* than in aturbulent flow in a straight tube. Thus, the requiredlength of tube in cases 1-1 to 1-3 to reach the samebulk temperature as the one at the end of a straighttube, here at z*=51, is shorter. This length isdenoted as Leq and new calculations of the frictionfactor and the Nusselt number with respectively

Eqs. (3) and (4) between z*=0 and z*=Leq areperformed to determine the PEC associated withthis reduction of tube material to achieve the sameTb as in a straight tube. This new number is denotedPECb.

The values of Leq for every cases is shown ontable 5 and from this table it is clear that theSETET from case 1-3 achieve the same Tb as in astraight tube within a dramatically shorter distance.Thus the total length of the tube with the SETET ofcase 1-3 could be reduced to a maximum of nearly65% at Re=80,000 and to a minimum of 17% atRe=100,000. It is also surprising to observe such anincrease of Leq between these two Reynoldsnumbers from case 1-3. It must also be noticed thatthe two other SETET are quite inefficient atreducing the length of tube required to obtain thesame Tb as in a straight tube.

Table 5. Leq obtained with cases 1-1 to 1-3 at every Reynolds number.

Re 105 8.10⁴ 5.10⁴ 3.10⁴ 1.10⁴

Case1-1 Leq

47.5Dh 48Dh 48Dh 48Dh 34.5Dh

Case1-2 Leq

46.5Dh 47Dh 47Dh 46Dh 35Dh

Case1-3 Leq

42.5Dh 18Dh 19Dh 20.5Dh 29.5Dh

The evolution of the PECb for the different cases is shown on figure 10.

Fig. 10. Evolution of PECb with Re for cases 1-1 to1-3.

From the latest figure it can be observed thatthe PECb of case 1-2 is below 1 for Re=10,000 andfor case 1-3 is below 1 for the two lowest Reynoldsnumbers, meaning that this solution causes morepressure drop than heat transfer enhancement.However, at higher Reynolds number the PECb

becomes higher than 1 and thus the generatedswirling flows are energetically efficient.

CONCLUSIONThis work presents a numerical study of

different geometry of short length twisted ellipticaltube (SETET) used to induced a swirling flow,followed by a transition tube and a tube with acircular cross-section. Three configurations ofSETET, whose length remain the same, are studied



and the tested parameter is the twist pitch P of theSETET. The Reynolds number range from 10,000to 100,000 and from the results of the study thefollowing conclusions can be drawn:

• With this kind of configuration theswirling flow could be decomposed intothree phases: a developing, transitioningand decaying.

• The SETET with the shortest twist pitchfeatures the highest swirl number S andthe best heat transfer enhancement at agiven Re but also the highest pressureloss.

• The better heat transfer that leads to ahigher bulk temperature is expected toyield a lower coking rate according to thecoking model of Plehiers [24].

• The PEC of the three cases are in the samerange and are above 1.

According to this last result, it can beconcluded that minor modification of tubegeometry or shape could generate a swirling flowwhich enhances heat transfer at a relative lowpressure drop penalty and which might also reducesignificantly the coking rate.

It was also shown in the last section of thisstudy that the swirling flow generated by theSETET with the lowest twist pitch can achieve thesame bulk temperature reached at the end of astraight tube within a shorter distance. Therefore,tube manufacturers could save money by using thisconfiguration of SETET and by shortening theirtubes. Furthermore, more heat is transferred withthe generated swirling flow, meaning that thetemperature at the wall is lower and therefore thatthe coking rate could be reduced thus extending runlengths and have less frequent shutting down fordecoking operations

Nevertheless, the large drop of swirl intensityin phase 2 is detrimental for the swirling flow andfuture work aims at creating another transitionwhich could reduce this swirl intensity gap.Furthermore, to reduce the pressure drop anotherparametric study with the aspect ratio c is expectedto be undertaken with the most interestingconfiguration of SETET investigated namely thecase 1-3.

ACKNOWLEDGMENTThe authors are extremely grateful for the

financial support provided by Manoir Industrieswithin the scope of the CIFRE convention2017/1437.

NOMENCLATUREA area of tube cross-section, m2

a major axis of the ellipse, mb minor axis of the ellipse, mCf skin friction coefficient, dimensionless

c aspect ratio of the ellipse, (b/a),dimensionless

cp specific heat capacity, J/kgKDh hydraulic diameter, mE circumference of tube cross-section, me quantity to evaluate for the GCIf friction factor coefficient, dimensionlessh heat transfer coefficient, W/m2Kk turbulent kinetic energy, J/kgL total length of the tested tube, m

mass flow rate, kg/sNu Nusselt number, dimensionlessP twist pitch, mPr Prandtl number, dimensionlessRe Reynolds number, dimensionlessR hydraulic radius, mr refinement ratio, dimensionlessS Swirl number, dimensionlessT temperature, KTMT tube metal temperatureU fluid velocity, m/sUθ

* dimensionless tangential velocity, (Uθ/Ub)z* dimensionless axial position (z/Dh)

α order of accuracy for the GCI,dimensionless

Δp pressure drop, Paλ thermal conductivity, W/mKμ dynamic viscosity, Pa.sρ fluid density, kg/m3

ω specific dissipation rate, 1/sτw wall shear stress, Pa

Subscripts0 inlet valueb bulkdown downstream tubeeq equivalentLMTD Logarithmic Mean Temperature

Differencei inlet of SETETo outlet of SETETp straight tubeTET twisted elliptical tubetr transition tubeup upstream tubew wallz axial component

θ tangential component

Superscripts¯ area averaged quantity

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