Vortically enhanced heat transfer and mixing: state-of-the-art and recent results

Proceedings of the ASME 2012 Summer Heat Transfer Conference HT2012 July 8-12, 2012, Puerto Rico, USA

HT2012-58045

VORTICALLY ENHANCED HEAT TRANSFER AND MIXING: STATE OF THE ART AND RECENT RESULTS

ABSTRACT

Longitudinal and transverse pressure-driven vortices induced by shear instabilities behind vortex generators play a crucial role in convective transport phenomena. The proven influence of these turbulence promoters on heat and mass transfer enhancement has led to their incorporation in modern multifunctional heat exchangers/reactors. The purpose of this work is to demonstrate experimentally the effects of hydrodynamics on the transfer processes accompanying such flows. The high-efficiency vortex (HEV) is an innovative static mixer and a low-energy-consumption heat exchanger designed to exploit these types of vortices. Results obtained in turbulent flow with embedded vorticity in an HEV static mixer are compared with numerical results in the literature.

Both numerical and experimental results confirm the high energy efficiency of the HEV static mixer flow.

KEYWORDS

Heat transfer enhancement - Process intensification - Multifunctional heat exchangers - Vortex generator - Turbulence - Embedded streamwise vorticity

INTRODUCTION

The effects of transverse and longitudinal vortices on heat and mass transfer and on the mixing process have been widely studied due to their ability to increase velocity fluctuations and flow momentum redistribution, leading to better convective transfer and turbulent mixing without the need of external mechanical forces [1,2]. Transverse vortices are two- dimensional flows with axes perpendicular to the main flow direction, while longitudinal vortices have axes parallel to this

direction, thus implying three-dimensional vortex flow. 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 turbulent layers, reduction of the laminar sublayer thickness near the wall and swirl movement of the streamwise vortex that enhances convective transfer [3].

Different types of vortices can be generated either by flow separation behind vortex generators or turbulence promoters (such as the transient structures produced by Kelvin-Helmholtz instabilities and the counter- or co-rotating vortices caused by pressure gradients upstream and downstream of flow perturbators) [1-4], or by the surface curvature where the centrifugal force produces longitudinal vortices (Dean and Görtler instabilities) [5-6], or by laminar or turbulent jets (annular vortices) [7-8].

Several types of vortex generators are used to generate longitudinal vorticity and complex flow structures topologically similar to those encountered in the near-wall region of turbulent boundary layers [3,9]. These artificially generated structures can be used to intensify the convective heat and mass transfer in open flows or in internal flows such as those in multifunctional heat exchangers/reactors (MHE/R). MHE/Rs are widely 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 and higher productivity than stirred vessels [3–10]. Process intensification is a rapidly growing field aiming to develop new high- performance super-compact MHE/Rs. However, better performance is accompanied by an increase in pressure drop.

Akram Ghanem

Laboratoire de Thermocinétique, LTN Nantes, France

Thierry Lemenand

Laboratoire de Thermocinétique, LTN Nantes, France

Dominique Della Valle ONIRIS

Nantes, France

Charbel Habchi Lebanese International

University, LIU Beirut, Lebanon

Hassan Peerhossaini Laboratoire de Thermocinétique, LTN

Nantes, France

. This paper is organized as follows: the flow structure is first discussed. The experimental setup and the measurement techniques are then introduced. The results and discussion are presented afterwards, and finally some conclusions are drawn.

FLOW STRUCTURE AND TRANSPORT PHENOMENA Vortex System

In multifunctional heat exchangers-reactors, vortex generators can be easily incorporated into compact channels or plain pipes to improve the convective transfer between the high- and low-momentum fluid [11-12]. In addition to the vortices generated by vortex generators, shear layers are formed on the front and rear edges of the generator, creating an energy transport that enhances heat transfer locally and globally. High- velocity fluctuations caused by these shear layers, which can be characterized by the turbulent kinetic energy, result in flow

fluctuations and can form a self-sustained oscillatory flow when they become unstable. This is the case of the trapezoidal vortex generator, of interest due to its ability to enhance turbulent mixing, mass transfer and phase dispersion and to its generation of coherent structures similar to those found in natural turbulent boundary layers, with low power consumption compared to triangular and rectangular geometries [9]. 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 in Fig.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-momentum fluid at the mixer centerline. This mechanism greatly enhances radial transfer. While fluid passes through the tab wake zone, it is Nomenclature

D heat exchanger diameter (m) L heat exchanger length (m) f friction factor

j Colburn factor

h heat-transfer coefficient (Wm^-2K^-1) Nu Nusselt number

Pr Prandtl number Re Reynolds number T temperature (K) C_p specific heat (J kg^-1K^-1) U_m mean axial velocity (m/s) e grease layer thickness (m) k turbulent kinetic energy (m²s^-2)

Greek symbols



kinematic viscosity (m²s^-1)

 thermal conductivity of water (Wm^-1K^-1) λ thermal conductivity of grease (Wm^-1K^-1)

 fluid density (kg m^-3) φ heat flux density (Wm^-2)



turbulent energy dissipation rate (m²s^-3) Subscripts

w HEV wall m tube section mean e heating tube inner wall

b bulk

FIG. 1. FLOW STRUCTURE PRODUCED DOWNSTREAM FROM A TRAPEZOIDAL VORTEX GENERATOR

stretched and folded over due to the swirling motion induced by the CVP. This mechanism also occurs over the tabs further downstream.

In addition, due to the Kelvin-Helmholtz 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 [13], as shown in Fig. 1.

Mean Flow

Figure 2a, illustrating the mean streamwise velocity distribution, shows that the axial velocity above the tab is greater than that in the wake region; the low-pressure region thus created above the tab initiates a swirling motion that produces two large symmetric counter-rotating vortices. This large motion entrains fluid particle transfer between the low- momentum region in the tab wake and the high-momentum fluid in the core region, thus enhancing convective transfer downstream of the vortex generators. This counter-rotating vortex pair (CVP) is convected downstream with the main flow until it encounters the downstream tab where new CVPs are generated.

Secondary counter-rotating vortices are also observed on both sides of the tab symmetry plane, as shown in Fig. 2b.

These vortices are caused by the interaction of the high-radial- velocity flow induced by the principal CVP with the stagnant fluid between the wall and the CVP. 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 the flow encounters the next tab array.

Turbulent Kinetic Energy

Turbulent kinetic energy production and its dissipation rate are important indicators of the intensity of transport phenomena

responsible for mass and heat transfer enhancement. Figure 3 shows numerical simulations based on the investigation of the turbulent kinetic energy dissipation rate,



(Mohand Kaci et al. [2]) and LIF visualizations (Mokrani et al. [14]) of the CVP and hairpin-like structures developed slightly downstream from the first tab array. The swirling motion of the CVP is clearly observed: it entrains radial mass transfer between the near-wall low-velocity flow and the high-momentum flow in the mixer centerline. The common upflow induced by CVP ejects the near-wall fluid 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 the flow 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 [4-15] have shown that while flowing downstream from the tabs, CVPs are transformed into hairpin-like structures that become the main contributors to the turbulent mixing process.

Figure 4 links the turbulent kinetic energy (TKE) distribution in the tube cross-section at 9 mm downstream from the tip of the fourth tab to the temperature contours. The numerical study was carried out by Mohand Kaci et al. [2] assuming a constant wall temperature of 360 K and an inlet temperature of 298 K.

The flow in the near-wall region is described by the “two-layer model”, where the Navier–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:

w

Re



y k





⁽¹⁾

When Re_w < 200, only the transport of the turbulence kinetic energy is computed, and the turbulent dissipation rate is related

FIG. 2. STREAMWISE VELOCITY DISTRIBUTION (A) AND VELOCITY VECTORS (B) IN THE TUBE CROSS SECTION AT 9 MM DOWNSTREAM FROM THE FOURTH TABS’ TIP (Re = 15,000)

(MOHAND KACI ET AL. [2])

to the turbulence kinetic energy by the empirical formula:

32

k l

_

 

⁽²⁾

where

(1

Re^{w A}

)

l

_

 yc

l

 e

^{ } (3)

with

A

_ ^and

c

_l constants.

The maximum TKE values occur in the shear layer shed from the tab tip edge. In fact, high-velocity fluctuations are created in this region due to the velocity gradient between the core flow above the shear layer and the wake region beneath. It

has been demonstrated in both experimental PIV [17] and DNS studies [4] that, owing to Kelvin–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 [4,17] that the hairpin vortex heads coincide with the higher TKE values; this fact can be clearly seen in Fig. 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. Figure 4b represents the temperature contours in a tube-cross section at 9 mm downstream from the fourth tab array.

The pair of counter-rotating vortices spirals the flow around its axis and redistributes the heat in the tube cross-section. The common flow in the tab symmetry plane transfers heat from the FIG. 3. INTERACTION OF HAIRPIN-LIKE STRUCTURES WITH COUNTER-ROTATING VORTEX PAIR,

AT A CROSS SECTION 3 MM DOWNSTREAM FROM FIRST ARRAY: (A) NUMERICAL RESULTS BY HABCHI ET AL. [16], Re = 15,000, AND (B) LIF VISUALIZATIONS BY MOKRANI ET AL. [14], Re = 1000

FIG. 4. (A) TURBULENCE KINETIC ENERGY AND (B) TEMPERATURE DISTRIBUTION IN TUBE CROSS SECTION AT 9 MM DOWNSTREAM FROM FOURTH TAB TIP

(MOHAND KACI ET AL. [2]: TWALL= 360 K, TINLET= 298 K, Re = 15,000)

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 presented in Fig. 5, one at a radial distance equal to the tabs‟ edge (r/R = 0.61), the other on the tube axis (r/R = 0). At the centerline, the overall temperature grows but without reaching the wall temperature. 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 tab, however, the temperature starts a steady increase. On the other hand, in the shear region (r/R = 0.61) the temperature varies in a periodic way, a signature of the effect of the streamwise vortices. The highest temperature is reached at the top of the tabs, since the tabs are in fact an extension of the tube wall.

The HEV static mixer is an efficient heat exchanger designed to exploit the above vortex system and has shown high mass and heat transfer efficiency in turbulent mixing with low energy consumption compared to other multifunctional heat exchangers-reactors [18]. The results of numerical studies carried out on the HEV static mixer geometry to characterize the flow structure and its effects on heat and mass transfer show the great influence of vorticity on convective transfer in this type of flow: 500% improvement over turbulent flow in straight tubes [2].

In this paper we present an experimental study based on heat transfer measurements to examine and quantify the improvement of turbulent flow with aligned vorticity generators compared to turbulent straight pipe flow, and analyze the

effects of flow structure on the thermal behavior of this heat exchanger.

EXPERIMENTAL SETUP AND METHODS Hydraulic Loop and Test Section

Experiments are carried out in an open flow loop consisting of a reservoir from which the working fluid (water) is circulated by a variable-speed gear pump. The reservoir temperature is maintained constant by a thermostat so as to ensure constant initial conditions regardless of possible changes in the ambient temperature. The volume flow rate is measured by three parallel flowmeters with an accuracy of 2% over the measured range. Upstream of the flowmeters, a high-resolution ball valve is used further to adjust the flow rate after setting the required pump speed to cover the Reynolds numbers, which ranged between 2000 and 15000 corresponding to flow rates between 130 L/h and 960 L/h. Before entering the test section, the fluid passes through a 2-meter-long straight tube whose length is 100 times its inner diameter, 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 of flow in the test section.

The HEV 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 the flow 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 25°C are recapitulated as shown in Table 1

The flow Reynolds number is defined by:

U Dm

Re^  (4)

All thermophysical properties of water are determined at the fluid bulk temperature (T_b).

TABLE 1

PHYSICAL PROPERTIES OF WORKING FLUID

Water

 ^Cp   ^Pr

kg m^-3 J kg^-1K^-1 m² s^-1 Wm^-1K^-1 -

998 4186 10^-6 0.60 6.96

FIG. 5. AXIAL PROFILE OF MEAN TEMPERATURE ON THE HEAT EXCHANGER CENTERLINE (r/R = 0) AND ON AN AXIAL

LINE AT r/R = 0.61 (MOHAND KACI ET AL. [2]: TWALL = 360 K, TINLET = 293 K, Re = 15,000) (VERTICAL DASH-DOTTED LINES

SHOW LOCATIONS OF MIXING TABS)

Wall Heating and Temperature Measurement

The experimental rig is shown in Fig. 7. The HEV heat exchanger is housed inside a stainless steel heating cylinder of 55 mm inner diameter. The 10 mm annular gap between the heat exchanger and the heating cylinder is filled with heat- conducting grease of 0.7 W/mK thermal conductivity. The outer cylinder is heated by the Joule effect by a continuous heating wire wound around it, as shown in Fig. 7. This indirect heating technique is used to provide a uniform wall heat flux to the HEV heat exchanger. The two ends of the heating wire are connected to a transformer; the electrical output needed to generate uniform heat flux in the wire (200 W) is controlled by adjusting the voltage (50 V) and the current (4 A). The constant heat flux 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 sets of type-K thermocouple beads, one set welded on the HEV heat exchanger outer wall and the other on the inner wall of the heating tube; thus there are a total of 30 thermocouples, each pair of which serves as a steady local heat fluxmeter.

Calibrated temperature sensors are used to measure the inlet and outlet water temperatures. The whole test section is insulated with a polystyrene box fitted with a sensitive heat fluxmeter to measure convective losses.

In the experiments, water is pumped to the HEV test section. The heat flux 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 continuously via an

„Agilent‟ data acquisition chain and numerically handled using

„BenchLink Data Logger‟ software. The friction factor is calculated in terms of pressure drop as measured by two high- precision differential manometers (Digitron 2001P7 and Baratron 220DD) covering all head losses. Pressure drop measurements are carried out under isothermal conditions, i.e.

without heating the tube.

RESULTS AND DISCUSSION

In this section, the local convective heat transfer coefficient, friction factor and thermal performance in the HEV heat exchanger are reported for different Reynolds numbers. The results are compared with those in the literature for turbulent tube flow and other heat exchangers.

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 tabs array [2,19].

Before the breakdown into turbulence, the Kelvin-Helmholtz instability in this layer generates hairpin vortices that produce a more uniform temperature distribution in the flow 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 thermal fin and thus injects additional heat into the main flow. The temperature evolution is related to the development of the thermal boundary layer, which is in turn controlled by the tab succession: each tab row disrupts the wall boundary layer; the boundary layer is then regenerated on the heat exchanger wall before being disrupted again by the tab row next downstream. This successive disruption of the wall boundary layer contributes to heat- transfer enhancement. However, a disadvantage of the HEV heat exchanger is the hot spots generated behind the tabs due to flow recirculation.

The temperatures T_e and T_w measured at the different longitudinal positions are used to calculate the local heat flux densities using Eq. (5).

(T_e T_w) e

  (5)

a b

FIG. 6. HEV STATIC MIXER GEOMETRY (A) TAB DIMENSIONS AND (B) GLOBAL 3D VIEW

0,000 0,021 0,042 0,063 0,084 0,105 0,126 0,147 20

30 40 50 60 70 80 90 100 110 120 130 140 150

Re=14920 Re=12860 Re=10460 Re=8670 Re=6390 Re=4530 Re=2160

Local Nusselt number, Nu

Longitudinal position, z (m)

FIG. 8. LOCAL NUSSELT NUMBER FOR DIFFERENT

……….REYNOLDS NUMBERS Experiments are run at a constant wall heat flux condition;

however, the calculated local heat flux densities are scattered around a mean value with 5% maximum deviation. The longitudinally averaged flux density is then used as the heat source over 15 incremental longitudinal segments making up the total heat exchanger wall. From knowledge of the inlet fluid temperature to the heat exchanger, the average fluid temperatures at the entry and exit of each segment are consecutively calculated using a simple energy balance between the heat transferred through the incremental wall surfaces and that transferred to the working fluid. Then these (inlet and exit) temperatures are used to calculate a mean temperature in each segment, T_m. The local convective heat transfer coefficients, h are calculated using temperatures T_w and T_m:

( _{w m})

h T T

 

 (6)

The local Nusselt numbers are then calculated using Eq. (7), taking into consideration the slight evolution in the fluid thermal conductivity



with increased temperature:

Nu hD

  (7)

Fig. 8 shows the longitudinal evolution of the local Nusselt number calculated for different Reynolds numbers. The experimental data uncertainties are determined and the maximum uncertainty associated with the Nusselt number is estimated at 3.6%. The longitudinal increase of the Nusselt number is related to the increase in heat transfer coefficient, h, produced by the flow hydrodynamics. Each row of trapezoidal tabs regenerates the vortex pairs continuously, sustaining the radial transport phenomena that carry hot fluid from the wall region to the core flow homogenizing the cross-sectional

temperature and increasing the heat exchange between hot and cold fluid zones.

The convective heat transfer is also promoted by the increase in the Reynolds number. The turbulent structures thus created in the flow replace the parallel laminar streamlines, enhance fluid mixing and intensify the effect of the embedded vortical structures to produce higher Nusselt numbers.

The pair of longitudinal vortices generates longitudinal vorticity and redistributes heat in the tube cross section. The secondary flow in the symmetry plane of the tab transfers heat from near the hot wall towards the cold region in the core flow, increasing the radial heat transfer. These results confirm the numerical results of Habchi et al. [15] for the same flow and heat transfer conditions.

FIG. 7. TEST SECTION AND THERMOCOUPLE POSITIONS

TABLE 2

EXPERIMENTAL VALUES OF hGLOBAL AND NuGLOBAL

Re 2160 4530 6390 8670 10460 12860 14920

h_global [Wm^-2K^-1] 1192 1781 2076 2300 2549 2682 3023

Nu_g 45 67 79 87 96 101 114

Global Analysis and Thermal Performance

The thermal performance of a heat exchanger can be defined by the global convective heat transfer coefficient, hglobal or the global Nusselt number, which represents the ratio of convective to conductive heat transfer. The global Nusselt numbers are calculated using the longitudinally averaged heat flux density over the heat exchanger length



, the heat exchanger average wall temperature T_w , and the average fluid temperature T_m . Measured values of the global convective heat transfer coefficient hglobal and the global Nusselt number Nug are shown as a function of Reynolds number in Table II.

Fig. 9 shows the variation of global Nusselt number with Reynolds number. These results confirm those of previous numerical studies [2,19] which showed a great increase of the Nusselt number with Reynolds number: for all experiments in the current study, Nusselt number increases with Reynolds number. This increase is attributed, among other parameters, particularly to the enhancement of turbulence intensity. The growth of Nusselt number in the longitudinal direction reflects also the renewal of the thermal boundary layer after each row of vortex generators.

The Gnielinski equation [5] (Eq. (8)) gives a correlation for Nusselt number in turbulent tube flow Nu₀ for Prandtl numbers ranging from 0.5 to 200 and Reynolds numbers from 2300 to 5×10⁶:

0

0 1/ 2 2 / 3

( / 8)( 1000) 1 12.7( / 8) ( 1)

f Re Pr

Nu f Pr

 

  (8)

where f₀ is the friction factor in a smooth-pipe turbulent flow given by:

0.25 0 0.079

f  Re^ ₍₉₎

The Nusselt number is usually expressed as a function of Reynolds and Prandtl numbers through:

m n

NuARe Pr

(10) where A, m and n are constants to be determined in each geometry. Correlations in the literature [20] show that the constant n is usually around to 0.4 for turbulent flows. Then a plot of Nu/Pr^0.4 versus Re allows determination of constants A and m:

0.462 0.4

0.616

Nu Re Pr (11)

The correlation (11) cannot however, be generalized to flow regimes and flow conditions other than HEV. Nevertheless, it describes the thermal behavior of the HEV flow over the range of Reynolds numbers studied and can be used as a design rule in new HEV heat exchangers applications. The numerical study of Mohand Kaci et al. [2] predicts a 500% increase in average convective heat transfer in the HEV flow over a turbulent tube flow for a matching range of Reynolds numbers. Fig. 9 compares the global experimental Nusselt number Nu_g with those calculated using the Gnielinski correlation, Nu₀. The results confirm the numerical predictions of [2]: for the range of Reynolds numbers between 2000 and 15000, the average value of Nu_g in HEV is 85. In the low-Reynolds-number zone, where the flow is transitional in the plain tube and heat transfer is weak, the HEV heat exchanger shows relatively high Nusselt numbers.

We define the rate of relative heat transfer intensification  (Eq. 12) thatreflects the increase in Nusselt number in the HEV heat exchanger compared to a turbulent tube flow: When a fully turbulent regime is attained, the relative increase is less important, as shown in Fig. 10.

0 0

Nug Nu

 Nu

 (12)

2000 4000 6000 8000 10000 12000 14000 16000 0

20 40 60 80 100 120 140

Nu=0.616Re^0.462Pr^0.4

HEV - Experimental

Plain tube - Gnielinski correlation

Global Nusselt number, Nug

Reynolds number, Re

FIG. 9. GLOBAL NUSSELT NUMBER, Nug

7500 10000 12500 15000 0,0

0,2 0,4 0,6 0,8 1,0 1,2 1,4

Reynolds number, Re

Friction factor,f

Sulzer SMX V-Nozzle turbulators Sulzer SMV Helical Kenics

HEV-Present work HEV-Numerical (Mohand Kaci et al. [2]) Helical coiled tube Empty pipe

FIG. 12. EVOLUTION OF FRICTION FACTORS OF DIFFERENT EXCHANGERS (THAKUR ET AL. [20])

2000 4000 6000 8000 10000 12000 14000 16000 0

2 4 6 8 10 12 14 16 18 20 22

f / f0

Reynolds number, Re f / f

0 = 11 Re^0.054

FIG. 11. VARIATION OF FRICTION FACTOR RATIO, HEV/PLAIN TUBE

From this figure, it can be concluded that the vortical enhancement of heat transfer by HEV geometry increases the Nusselt number between 800% to 200% over that of a turbulent tube flow for the Reynolds numbers ranging between 2000 and 15000, respectively.

Friction Factor and Energy Efficiency

The Fanning friction factor f is related to pressure losses by the Darcy-Weisbach equation (Eq. 13). Over the length of the test section, the maximum pressure drop 850 Pa was attained in the highest-Reynolds-number run (Re=15000). 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:

2

4 2

m

f P

U L D 

 

 

  

   

(13)

Fig. 11 compares the ratio of the HEV flow friction factor to

that in a turbulent tube flow (denoted f₀). Not surprisingly, the presence of the tab rows generates additional losses by friction due to a greater blockage and flow interruption and thus increased inertial forces in the boundary layer. The HEV friction factors, over the studied range of Reynolds number, are 15 to 19 times greater than those in a turbulent tube flow.

In order to compare the HEV to other innovative heat exchangers/mixers producing similar heat-transfer enhancement with similar diameters, we present in Fig. 12 the friction factors of different geometries. The plot proves the HEV flow to be among the most efficient exchangers: only the empty-pipe flow and the helical tube exhibit inferior friction factors. However, the heat transfer in the geometries mentioned remains modest compared to the HEV flow. As for the other exchangers, the gain in heat transfer is accompanied with elevated pumping costs, with friction factors reaching up to ten times those of the HEV flow, as for example in the case of the Sulzer SMX.

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

13

j Nu RePr

 ₍₁₄₎

The Colburn factor quantifies the ratio of the thermal power transferred to the mechanical power consumed. For a given fluid and a specific range of Reynolds number, a higher Colburn factor indicates a higher quality of heat transfer.

Numerical studies by Mohand Kaci et al. [2] show a Colburn factor of 0.01 for HEV flow, representing an improvement of 500% over the turbulent plain-tube flow (j = 0.002). Again, the comparison in Fig. 13 of the Colburn factor for HEV flow with that for other geometries shows the HEV‟s capacity to enhance heat transfer with moderate energy consumption. The high

2000 4000 6000 8000 10000 12000 14000 16000 0

100 200 300 400 500 600 700 800 900

(Nug / Nu0) %

Reynolds number, Re 0 0

(%) Nu^g Nu

  Nu^

FIG. 10. INDEX OF RELATIVE INTENSIFICATION OF CONVECTIVE TRANSFER, 

7500 10000 12500 15000 0,000

0,002 0,004 0,006 0,008 0,010 0,012 0,014 0,016 0,018

Colburn factor,j

Reynolds number, Re Sulzer SMX

V-Nozzle turbulators Sulzer SMV Helical Kenics

HEV - Numerical results [2]

Helical coiled tube

Empty pipe

FIG. 13. COLBURN FACTOR FOR COMMON COMMERCIAL HEAT

EXCHANGERS (MOHAND KACI ET AL. [2])

friction factors of the Sulzer SMX mentioned above are reflected in a low Colburn factor. The weak convective transfer in empty pipes, whether straight or helical, keep the values of their Colburn factors relatively low even if their energy costs are less. For the range studied, the Helical Kenics with its complex fabrication and maintenance processes is the only geometry with a efficiency superior to the HEV‟s.

CONCLUSIONS AND PERSPECTIVES

An experimental apparatus is constructed to study the heat- transfer enhancement in a tube fitted with trapezoidal tabs acting as vortex generators and turbulators. A thorough thermal study is carried out over the different flow regimes in which the evolution of the local and global Nusselt numbers is monitored.

A global analysis of the results based on the available literature describing the predicted flow structure is presented and the energetic costs of the process intensification are assessed. The values of Nusselt number and friction factor in the tube equipped with vorticity generators are higher than those in a plain tube. The vorticity produced in the turbulent flow in the HEV multifunctional heat exchanger-reactor is the main factor in the enhanced transfer. The protuberance of the solid tabs in the flow produces additional losses over a plain tube, but simultaneously contributes to heat transfer by the fin effect and also by extra mixing of cold and hot fluid particles. Therefore, the overall effect of losses remains moderate and tolerable compared to those produced in similar devices. The experimental study validates the numerical results of [2,19] and confirms the capacity of the HEV heat exchanger to improve convective heat transfer while producing moderate pressure losses.

A variant of the current test section is under construction in which the tab arrays are no longer aligned but instead are alternated so that each row of trapezoidal tabs is rotated by 45º with respect to its predecessor. Recent numerical results [16]

have shown the interest of such modified geometry in terms of mass and heat transfer, but still need experimental validation.

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