Energy efficiency in process industry – High-efficiency vortex (HEV) multifunctional heat exchanger

Energy ef fi ciency in process industry e High-ef fi ciency vortex (HEV) multifunctional heat exchanger

Akram Ghanem

, Charbel Habchi

, Thierry Lemenand

, Dominique Della Valle

, Hassan Peerhossaini

aThermofluids, Complex Flows and Energy Research Group, Laboratoire de Thermocinétique de Nantes, CNRS UMR 6607, Nantes University, 44306 Nantes, France

bEnergy and Thermo-Fluids Group ETF, School of Engineering, Lebanese International University LIU, PO Box 146404, Mazraa, Beirut, Lebanon

cONIRISeNantes, rue de la Géraudière, 44322 Nantes, France

dUniv Paris Diderot, Sorbonne Paris Cité, Institut des Energies de Demain (IED), Paris, France

a r t i c l e i n f o

Article history:

Received 21 May 2012 Accepted 25 September 2012 Available online 18 October 2012

Keywords:

Multifunctional heat exchanger Process intensification Heat transfer enhancement Streamwise vorticity Turbulence Vortex generator

a b s t r a c t

In the process industry, vortex generators are being increasingly incorporated in modern multifunctional heat exchangers/reactors to enhance heat and mass transfer and thus increase energy efficiency.

Longitudinal and transverse pressure-driven vortices and shear-instability-driven flow structures generated byflow separation behind the vortex generators play a crucial role in convective transport phenomena. The purpose of this work is to demonstrate experimentally the effects of hydrodynamics on the transfer processes accompanying suchflows. The high-efficiency vortex (HEV) is an innovative static mixer and a low energy consumption heat exchanger designed to exploit these types of vortices. Heat transfer results obtained in turbulent flow with embedded vorticity in this multifunctional heat exchanger are compared with numerical results in the literature. Both numerical and experimental results confirm the high energy efficiency of the HEV static mixerflow.

Ó2012 Elsevier Ltd. All rights reserved.

1. Introduction

Convective transport phenomena are strongly enhanced by transverse and longitudinal vortices because such vortices increase velocityfluctuations andflow momentum redistribution, leading to better heat and mass transfer and turbulent mixing with no external mechanical forces needed [1,2]. Transverse vortices are two-dimensionalflows with axes perpendicular to the mainflow direction, while longitudinal vortices have axes parallel to this direction, thus implying three-dimensional vortexflow. It has been shown that longitudinal vortices are more effective in improving heat transfer because they combine the main mechanisms of heat transfer intensification: development of three-dimensional turbu- lent layers, reduction of the laminar sublayer thickness near the wall and swirl movement of the streamwise vortex that enhances convective transfer[3,4]. Different types of vortices can be gener- ated either byflow separation behind vortex generators or turbu- lence promoters (such as the transient structures produced by

KelvineHelmholtz instabilities and the counter- or co-rotating vortices caused by pressure gradients upstream and downstream offlow perturbators)[1,2,4,5], or by the surface curvature where the centrifugal force produces longitudinal vortices (Dean and Görtler instabilities) [6e12], or by laminar or turbulent jets (annular vortices)[13,14].

Several types of vortex generators are used to generate longi- tudinal vorticity and complexflow structures, topologically similar to those encountered in the near-wall region of turbulent boundary layers[4,15]. These artificially generated structures can be used to intensify convective heat and mass transfer in open or internal flows such as those in multifunctional heat exchangers/reactors (MHE/R). MHE/R are increasingly used in industry because they can efficiently accomplish several unit operations such as mixing, heat and mass transfer, phase dispersion and chemical reactions, with low power consumption, better compactness, lower equipment costs and higher productivity than stirred vessels. Their use as static mixers in continuous processes is an interesting alternative to conventional agitation since comparable and sometimes better results can be achieved at lower cost. Motionless mixers typically have low energy consumptions and reduced maintenance requirements because they have no moving parts. They can provide homogenization of feed streams with minimum residence time.

Good mixing is achieved at lower shear rates than stirred vessels,

*Corresponding author. Thermofluids, Complex Flows and Energy Research Group, Laboratoire de Thermocinétique de Nantes, CNRS UMR 6607, Nantes University, 44306 Nantes, France. Tel.:þ33 6 07 53 31 61.

E-mail address:hassan.peerhossaini@univ-paris-diderot.fr(H. Peerhossaini).

Contents lists available atSciVerse ScienceDirect

Renewable Energy

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0960-1481/$esee front matterÓ2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.renene.2012.09.024

2.1. Vortex system

Vortex generators can be easily incorporated into compact channels or plain pipes to improve the convective transfer between the high- and low momentumfluids[26e30]. In addition to the vortices generated by vortex generators, shear layers are formed on the front and rear edges of the generator[31], creating an energy transport that enhances heat transfer locally and globally. High- velocityfluctuations caused by these shear layers, which can be characterized by the turbulent kinetic energy, may become unstable and lead to a self-sustained oscillatoryflow.

Trapezoidal vortex generators are of interest because they can provide coherent structures, similar to those found in natural turbulent boundary layers, with low power consumption compared to triangular and rectangular geometries[15e18]. When these tabs are set at a tilt angle relative to the tube wall, a pressure difference is generated between the area of high-momentum upstream (main flow) and that of low momentum downstream from the tab (wake zone) due to the velocity gradient, which in turn triggers a swirling motion in the form of longitudinal counter-rotating vortex pairs (CVP) shown inFig. 1. As generally observed, a counter-rotating vortex pair is generated at each side of the tab. A common radial flow in the tab center-plane is induced, transporting low- momentum fluid from the near-wall region toward the high- momentumfluid at the mixer centerline. This mechanism greatly enhances radial transfer. Whilefluid passes through the tab wake zone, it is stretched and folded over due to the swirling motion induced by the CVP. In addition, due to the KelvineHelmholtz instability, the shear layer generated at the edges of the vortex generator becomes unstable further downstream and gives rise to periodic “hairpin vortices” that propagate on the vortex pair [32,33], as shown inFig. 1.

On both sides of the tab symmetry plane, secondary counter- rotating vortices are also observed (Fig. 2b). These vortices result from the interaction of the high-radial velocityflow induced by the principal CVP with the relatively stagnantfluid between the wall and the CVP. The intersecting flow structures create an isolated zone and a hyperbolic point is thus generated at the splitting point of these four vortices. The secondary CVP is convected downstream with the main CVP until theflow encounters the next tab array, where the same process repeats.

2.3. Turbulent kinetic energy

The turbulent kinetic energy production and its dissipation rate are two important indicators of the intensity of transport phenomena responsible for mass and heat transfer enhancement [34].Fig. 3shows numerical simulations based on the investigation of the turbulent kinetic energy dissipation rate,ε(Habchiet al.[35]) and LIF visualizations (Mokraniet al.[36]) of the CVP and hairpin- like structures developed slightly downstream from thefirst tab array. The swirling motion of the CVP is clearly observed: it entrains radial mass transfer between the near-wall low velocityflow and the high-momentum flow in the mixer centerline. The common upflow induced by CVP ejects the near-wallfluid and forms the head of the hairpin-like structures, which interact further with CVP to intensify mixing. At the splitting point, the common upflow velocity induced by the CVP divides into two opposite tangential velocities in theflow cross section. It is clearly seen that the head of the hairpin vortices corresponds to positions of higher turbulence- energy dissipation that are located at the height of the tab.

Numerous studies [5,37,38] have shown that while flowing downstream from the tabs, CVP are transformed into hairpin-like structures that become the main contributors to the turbulent mixing process.

Fig. 4links the turbulent kinetic energy (TKE) distribution in the tube cross section 9 mm downstream from the tip of the fourth tab to the temperature contours. The numerical study was carried out by Mohand Kaciet al.[2]assuming a constant wall temperature of 360 K and an inlet temperature of 298 K. Theflow in the near-wall region is described by a“two-layer model”in which the Naviere Stokes equations are solved in the viscous sublayer. The limit of the viscous boundary layer is determined by the value of the wall Reynolds number:

Re_w ¼

r

m

wherer^{is the}fluid density,yis the distance from the wall,kis the turbulent kinetic energy, and m ^{is the} fluid viscosity. When Re_w<200, only the transport of the turbulence kinetic energy is computed, and the turbulent dissipation rate is related to the turbulence kinetic energy by the empirical formula:

Fig. 1.Flow structure produced downstream from a trapezoidal vortex generator[2].

ε ¼ k³²

l_ε (2)

where l_ε ¼ yc_l

1e^RewAε

(3)

withA_εandc_lconstants.

The highest TKE values occur in the shear layer shed from the tab tip edge. High-velocityfluctuations are created in this region due to the velocity gradient between the coreflow above the shear layer and the wake region beneath. It has been demonstrated in both experimental PIV[38]and DNS studies[5]that, due to Kelvine Helmholtz instability, this shear layer becomes more unstable and generates periodic hairpin-like structures convected downstream with the main CVP. It has also been shown[5,38]that the hairpin vortex heads coincide with the higher TKE values; this fact can be clearly seen inFig. 4a, where the higher TKE values form an arc

shape at the tip of the vortex generator, confirming that the TKE is carried by the heads of these unsteady transverse vortices.Fig. 4b shows the temperature contours in a tube cross section at 9 mm downstream from the fourth tab array.

The pair of counter-rotating vortices spirals theflow around its axis and redistributes the heat in the tube cross section. The commonflow in the tab symmetry plane transfers heat from the near-wall hot region to the cold zone at the tube centerline, thus further enhancing the radial heat transfer.

As for the effect of the tabs on the spatial evolution of the local fluid temperature, two longitudinal temperature profiles are pre- sented inFig. 5, one at a radial distance equal to the tab’s edge (r/R¼0.61, whereris the radial distance andRis the tube diam- eter), the other on the tube axis (r/R¼0). At the centerline, the overall temperature grows but without reaching the wall temper- ature. For the first three rows, the temperature on the heat exchanger axis does not vary because the arrival of hot particles in the core is delayed by the radial convection time. Beyond the third

Fig. 3.Interaction of hairpin-like structures with counter-rotating vortex pair, at a cross section 3 mm downstream fromfirst array: (a) Numerical results by Habchiet al.[35], Re¼15000, and (b) LIF visualizations by Mokraniet al.[36],Re¼1000.

Fig. 2.Streamwise velocity distribution (a) and velocity vectors (b) in the tube cross section at 9 mm downstream from the fourth tab’s tip (Re¼15000) (Mohand Kaciet al.[2]).

tab, however, the temperature starts a steady increase. On the other hand, in the shear region (r/R¼0.61) the temperature varies in a periodic way (a signature of the streamwise vortices[39]). The highest temperature is reached at the top of the tabs, since the tabs are in fact an extension of the tube wall and inject by thefin effect supplementary heat into theflow.

Designed to exploit the above vortex system, the HEV static mixer has shown high mass and heat transfer efficiency in turbu- lent mixing with low energy consumption compared to other multifunctional heat exchangers/reactors [40]. The results of numerical studies carried out on the HEV static mixer geometry to characterize theflow structure and its effects on heat and mass transfer show the great influence of vorticity on convective transfer in this type offlow: 500% improvement over turbulentflow in straight tubes[2]. To the best of our knowledge, however, there is no experimental data in the open literature to validate the numerical results.

The following sections present an experimental study based on heat transfer measurements to examine and quantify the improvement in turbulentflow with aligned vorticity generators compared to turbulent plain pipeflow. We also discuss the effects offlow structure on the thermal behavior of this heat exchanger.

3. Experimental apparatus and procedures 3.1. Flow loop and test section

Experiments are carried out in an openflow loop consisting of a reservoir from which the workingfluid (water) is circulated by a variable-speed gear pump. The reservoir temperature is main- tained constant by a thermostat so as to ensure constant initial conditions regardless of possible changes in the ambient temper- ature. The volume flow rate is measured by three parallelflow- meters with an accuracy of 2% over the measured range. Upstream of the flowmeters, a high-resolution ball valve is used further to adjust theflow rate after setting the required pump speed to cover the Reynolds numbers, which ranged between 2000 and 15,000 corresponding toflow rates between 130 L/h and 960 L/h. Before entering the test section, the fluid passes through a 2-m-long straight tube whose length is 100 times its inner diameter, suffi- cient to ensure a fully developed velocity profile at the inlet of the test section and thus eliminate entrance effects. The circuit is equipped with a safety valve and a pulsation damper to limit any eventual pressure fluctuations produced by the pump and to ensure continuity and stability offlow in the test section.

The test section shown in Fig. 6 is composed of a straight stainless steel tube in the walls of which six arrays of aligned trapezoidal vortex generators are inserted. Each array is constituted of four tabs inclined at 30 relative to the tube wall in theflow direction. The tube is 145 mm long, 22.7 mm in diameter and has wall thickness 1.15 mm. The distance between two successive tab rows is 22 mm.

At the test section inlet, the working fluid (water) properties taken at 25C are as shown inTable 1. Theflow Reynolds numberRe is defined by:

Re ¼ UmD

n

where U_m is the mean axial velocity, D is the heat exchanger diameter, and n^{is the} fluid kinematic viscosity. At each section, thermophysical properties of water are determined at the local fluid bulk temperatureTm.

3.2. Wall heating and temperature measurement

The experimental rig is shown inFig. 7. The HEV heat exchanger is housed inside a stainless steel heating cylinder of 55 mm inner Fig. 4.(a) Turbulent kinetic energy and (b) temperature distribution in tube cross section at 9 mm downstream from fourth tab’s tip[2].

Fig. 5.Axial profiles of mean temperature (Mohand Kaciet al.[2]:Twall¼360 K, Tinlet¼293 K,Re¼15000). Vertical lines show locations of mixing tabs.

diameter. The 10 mm annular gap between the heat exchanger and the heating cylinder is filled with heat-conducting grease with a thermal conductivitylof 0.7 W/mK. The outer cylinder is heated by the Joule effect by a continuous heating wire wound around it, as shown inFig. 7. This indirect heating technique is used to provide a uniform wall heatflux to the heat exchanger. The two ends of the heating wire are connected to a transformer; the electrical output needed to generate a 200 Watt uniform heatflux in the wire is controlled by adjusting the voltage (50 V) and the current (4 A) with a precision of 1%. The constant heatflux provided on the HEV outer wall is calculated from the temperature gradient across the annular gap. For this purpose temperature is measured at 15 different longitudinal positions by series of two sets of type-K thermocouple beads with an accuracy of0.5C, one set welded on the HEV heat exchanger outer wall and the other on the inner wall of the heating tube; thus there is a total of 30 thermocouples, each pair of which serves as a steady local heatfluxmeter. For heat flux measurements based on temperature gradients, the wall thermal resistance is neglected. Calibrated temperature sensors are used to measure the inlet and outlet water temperatures. The whole test section is insulated with a polystyrene boxfitted with a sensitive heatfluxmeter to measure convective losses.

In the experiments, the heatflux at the test wall is set by the transformer and the system is then allowed to reach thermal steady state for each value of flow Reynolds number. Inlet, outlet and longitudinal temperatures are measured continuouslyviaan‘Agi- lent’ data acquisition chain and numerically handled using

‘BenchLink Data Logger’software. The Fanning friction factorfis calculated in terms of pressure drop D^P as measured by two differential manometers covering all head losses with a precision depending on the measured value and varying between 0.1 and 0.25%. Pressure drop measurements are carried out under isothermal conditions.

Experimental uncertainties are evaluated for the derived quantities using the relative errors of measurement of their elementary terms as given by Eq.(5):

D

z Xⁿ

i¼1

vz

vx_i

D

wherezis the derived quantity depending onnvariables,x1,.,xn, whileD^zandD^xrepresent the absolute error in the calculation ofz and the measurement ofxrespectively.

We carried out repeatability and partial reproducibility tests on the experimental results. Experiments were repeatedly run by the same operator, with the same apparatus, and under the same conditions. Due to the test section complexity, it was not possible to carry out a complete reproducibility test in a completely different environment with different equipment. However, multiple measurements, under the same hydrodynamic and thermal conditions, were carried out by different operators using different measurement apparatus and longer time intervals in between.

Standard deviations of the corresponding measurements were calculated to ensure that they are commensurate and abide by research standards.

4. Results and discussion

In this section, experimental results are reported for different Reynolds numbers in terms of local convective heat transfer coef- ficient, friction factor and thermal performance in the HEV heat exchanger. The results are compared with those in the literature for the plain turbulent pipeflow and various types of heat exchangers.

4.1. Local convective heat transfer coefficient

Heat transfer enhancement in the HEV heat exchanger is the result of several concomitant mechanisms. The shear layer detached from the vortex generator is the site of high production of turbulent kinetic energy whose value increases in the longitudinal direction up to the fourth tab array[2,41]. Before the breakdown into turbulence, the KelvineHelmholtz instability in this layer generates hairpin vortices that produce a more uniform tempera- ture distribution in theflow cross section that intensifies the heat transfer. As the temperature of the vortex generator is very close to the heat exchanger wall temperature, it acts also as a thermalfin and thus injects additional heat into the mainflow. The tempera- ture evolution is related to the development of the thermal boundary layer, which in turn is controlled by the tab succession:

each tab row disrupts the wall boundary layer; the boundary layer is then regenerated on the heat exchanger’s wall before being disrupted again by the tab row next downstream. This successive disruption of the wall boundary layer contributes to temperature homogeneity, despite the presence of hot spots behind the tabs, due toflow recirculation. The heating tube inner wall temperature Teand the HEV wall temperatureTware measured at the different Fig. 6.HEV static mixer geometry: (a) tab dimensions and (b) global perspective view.

Table 1

Physical properties of workingfluid at the test section inlet.

Water r Cp n l Pr

kg m³ J kg¹K¹ m²s¹ Wm¹K¹ e

998 4186 10⁶ 0.60 6.96

longitudinal positions and are used to calculate the local heatflux densities4by:

4

l

eðTeT_wÞ (6)

whereeis the grease layer thickness. Experiments are run with constant wall heatflux. The heat flux is then averaged over 15 incremental segments making up the total heat exchanger wall.

From knowledge of the inlet fluid temperature to the heat exchanger, the averagefluid temperatures at the inlet and outlet of each segment are computed using a simple energy balance between the heat transferred through the wall surface and that transferred to the workingfluid calculated for a givenflow rate, specific heatCpand temperature gradient. The mean wall and bulk temperatures in each segment,TwandTmrespectively, are used to determineh,the local convective heat transfer coefficients:

h ¼

4

ðTwTmÞ (7)

The local Nusselt numbers,Nuare then calculated, taking into consideration the slight evolution of thefluid thermal conductivity kwith temperature:

Nu¼ hD

k

The spatial evolution of the local Nusselt number is plotted in Fig. 8for different Reynolds numbers.

The local heatflux densities are scattered around a mean value with a 5% maximum deviation. The uncertainties in the experi- mental data are determined and the maximum value associated with the local Nusselt numbers is estimated at 3.6%.

The increase in convective heat transfer along the tube is explained by the development of theflow. This process is strongly accelerated over that in the plain straight duct, by the destruction of the boundary layer at each tab array. It should be noted that the internal convective heat transfer does not reach a saturation plateau, meaning that the thermal boundary layers are not fully developed inside the tube length; this information should be useful in heat exchanger design. The vortically active central zone and theflow interruption by the protruding tabs in the near-wall region hinder the downstream thickening of the thermal

boundary layer, and the result isflatter temperature profiles and a more uniform heat distribution throughout the tube cross section.

This phenomenon ultimately results in higher convective transfer coefficients.

The pair of longitudinal vortices generates longitudinal vorticity and redistributes heat in the tube cross section. The secondaryflow in the symmetry plane of the tab transfers heat from the hot wall towards the cold region in the coreflow, increasing the radial heat transfer. Each row of vortex generators regenerates these vortices and breaks up the thermal boundary layer, thus enhancing heat transport phenomena. The increase in Reynolds number accentu- ates turbulent heat transfer and results in higher Nusselt numbers.

The spatial evolution can be assessed through the relative inlet- outlet increase in Nusselt number: in this study, the increase averages 9.6% for the Reynolds numbers run.

4.2. Global analysis and thermal performance

The thermal performance of a heat exchanger can be charac- terized by the global convective heat transfer coefficienthgor the Fig. 7.Test section and thermocouple positions.

Fig. 8.Local Nusselt number for different Reynolds numbers.

global Nusselt number Nug calculated using the longitudinally averaged heatflux density4gover the heat exchanger lengthL, the global average wall temperatureTwg, and the global averagefluid temperatureTmg. Experimental valueshgandNugas a function of Reynolds number are shown inTable 2.

Fig. 9presents the variation of global Nusselt number versus Reynolds number with error margin 3.6%. These results confirm the power law trend of the Nusselt number for heat exchangers;

however, the exponent seems rather low compared to those in the literature.

Gnielinski[42]provides a correlation for Nusselt numberNu₀in a straight plain pipe turbulentflow for Prandtl numbersPrranging from 0.5 to 200 and Reynolds numbers from 2300 to 510⁶:

Nu₀ ¼ ðf₀=8ÞðRe1000ÞPr 1þ12:7ðf0=8Þ¹⁼²

Pr²⁼³1 (9)

wheref0is the friction factor in a smooth-pipe turbulentflow given by:

f₀ ¼ 0:079Re¹⁴ (10)

The Gnielinski equation is in good agreement with experimental data obtained in a plain tube.

Fig. 9shows that the HEV global experimental Nusselt number, for a range of Reynolds numbers between 2000 and 15,000, varies from 45 to 115. The Nusselt number is generally expressed through a power law of Reynolds and Prandtl numbers:

Nu ¼ ARe^mPrⁿ (11)

whereA,mandnare constants to be determined in each geometry.

Correlations in the literature [43] show that the constant n is usually around 0.4 for turbulent flows. Then a plot of Nug/Pr^0.4 versusRegives the following correlation:

Nug ¼ 0:616Re^0:46Pr^0:4 (12)

Correlation (12) describes the global thermal behavior of the HEVflow over the range of Reynolds numbers studied and can be used as a design rule in new HEV heat exchanger applications.

When comparing Nu_g with Nu₀, current results confirm the numerical simulations of Mohand Kaci et al. [2] that predict a 500% increase in average convective heat transfer in the HEV flow for a matching range of Reynolds numbers. To characterize this relative enhancement, we define the rate of relative heat transfer intensification c ^(Eq. (13)) that reflects the increase in Nusselt number in the HEV heat exchanger compared to a turbu- lent tubeflow:

c

Nu₀ (13)

Fig. 10represents the relative intensification factorc^{with a 5%}

error margin and suggests that the vortical enhancement of heat transfer by HEV geometry increases the Nusselt number by between 800% and 200% over that in a turbulent tube flow for Reynolds numbers ranging between 2000 and 15,000, respectively.

The HEV produces considerable enhancement for the low Reynolds number zone with a relative enhancement that decreases for

higher Reynolds numbers. This decrease occurs because turbulent structures automatically start to appear in the plain tube that intensify convective transfer processes and reduce the sharp difference in Nusselt numbers in laminar regimes compared to the HEVflow.

4.3. Friction factor and energy efficiency

The Fanning friction factorfis related to pressure lossesD^Pby the Darcy-Weisbach equation (Eq.(14)). Over the length of the test section, the maximum pressure drop of 850 Pa was attained in the highest-Reynolds number run (Re¼15,000). Based on isothermal differential pressure measurements between the entrance and exit from the HEV heat exchanger, the friction factor is calculated and plotted against the Reynolds number:

f ¼

D

4 L

D

r

! (14)

Fig. 11compares the ratio of the HEVflow friction factor to that in a turbulent tubeflowf₀. Not surprisingly, the presence of the tab rows generates additional losses by friction due to a greater blockage andflow interruption and thus increased inertial forces in the boundary layer. The HEV friction factors, over the studied range

Table 2

Experimental values ofhgandNug.

Re 2160 4530 6390 8670 10,460 12,860 14,920

hg[Wm²K¹] 1192 1781 2076 2300 2549 2682 3023

Nug 45 67 79 87 96 101 114

Fig. 9.Global Nusselt numberNugas a function of Reynolds number.

0 2000 4000 6000 8000 10000 12000 14000 16000 0

100 200 300 400 500 600 700 800 900

Index χ (%)

Reynolds number, Re

Fig. 10.Convective heat transfer intensification index of CVP vs. flow Reynolds number.

of Reynolds number, are 15e19 times greater than those in a turbulent tubeflow. Between these two extrema, the variation of the friction factor ratio can be expressed by the power law

f

f₀ ¼ 11Re^0:054 (15)

The uncertainty in the friction factor calculations varies between 0.1 and 0.25% depending on the measured values of head losses. These values prove the HEV to be among the most efficient heat exchangers/mixers as shown inFig. 12, adapted from Thakur et al.[43]. Only the plain tubeflow and the helical tube exhibit smaller friction factors. However, the heat transfer in these geom- etries remains modest. The gain in heat transfer in other heat exchangers is accompanied by elevated pumping costs, with fric- tion factors reaching up to ten times those in the HEVflow, as for example in the Sulzer SMX[44]. The intermittent and relatively slight protuberance of the trapezoidal tabs into the core flow compared to the voluminous inserts in the Kenics, V-nozzle and Sulzer geometries allows freefluid passage in most of the cross section and is reflected in the moderate friction factors.

Another criterion for judging the energy efficiency of a heat exchanger is the Colburn factorj, given by:

j¼ Nu

Re Pr¹³ (16)

The Colburn factor quantifies the ratio of the thermal power transferred to the mechanical power consumed. For a givenfluid

and a specific range of Reynolds number, a higher Colburn factor indicates a higher efficiency of heat transfer. The comparison in Fig. 13of the Colburn factor for the HEV heat exchanger and other geometries shows the ability of the HEV flow to enhance heat transfer with moderate energy consumption. The HEV heat exchanger exhibits a Colburn factor around 0.01[2], representing a 500% improvement over the turbulent plain tubeflow (whose Colburn factor is around 0.002) for the same operating conditions.

The high friction factors of the Sulzer SMX are reflected in a low Colburn factor. The weak convective heat transfer in straight and helically coiled plain pipes shows relatively low Colburn factors even though energy costs are lower. The Helical Kenics, with its complex fabrication and maintenance processes, is the only geometry with energy efficiency higher than that of the HEV multifunctional heat exchanger.

5. Conclusions

An experimental thermal study is carried out to investigate heat transfer enhancement in HEV: a tubefitted with trapezoidal tabs acting as vortex generators and turbulence promoters. In the HEV multifunctional heat exchanger studied here, made up of six aligned arrays of four tabs each, a complex vortex system enhances radial heat and mass transfer. Local Nusselt numbers, calculated using temperature and heatflux values in the different sections, increase in the longitudinal direction and with Reynolds number.

A global analysis of the results based on the available literature describing the predictedflow structure is presented. The values of Nusselt number and friction factor in the tube equipped with vorticity generators are higher than those in a plain tube. The protuberance of the solid tabs in the flow produces additional losses compared to a plain tube, but simultaneously contributes to heat transfer by thefin effect and also by extra mixing of cold and hotfluid particles. The overall losses are moderate compared to those in similar devices. A classification of different heat exchangers based on the Colburn factor, which relates heat transfer intensification to power consumption, reveals the high-efficiency of the HEV compared to other geometries.

The experimental study validates the numerical results on the same geometry[2,41]and confirms the capacity of the HEV heat exchanger to improve convective heat transfer while keeping pressure losses relatively low.

In the HEV multifunctional heat exchanger/reactor, streamwise vorticity can be generated by a wide range of tab geometries in several configurations or even combinations of different vortex generators[45]. The alternated geometry, a variant of the current Reynolds number, Re

Fig. 11.Friction factor ratio of HEV as a function of Reynolds number.

Fig. 12.Friction factors of different heat exchangers (adapted from Thakur et al.[43]).

Fig. 13.Colburn factor for commercial heat exchangers (Mohand Kaci etal.[2]).

test section in which each row of trapezoidal tabs is rotated by 45 with respect to its predecessor, will be tested in future work. Recent numerical results[35]show the potential of such modified geom- etries in intensifying mass and heat transfer, but experimental validation is still needed.

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