International Conference on Renewable Energy: Generation and Applications, ICRE-2012 UAE University, Al Ain, UAE 4-7 March, 2012
Energy Efficiency in Process Industry – High- Efficiency Vortex (HEV) Multifunctional Heat
Exchanger
Akram Ghanem
1 Thermofluids, Complex Flows and Energy Research Group, Laboratoire de Thermocinétique, CNRS UMR 6607, Nantes University, rue Christian Pauc, 44306 Nantes, France
1, Charbel Habchi2, Thierry Lemenand1, Dominique Della Valle1,3, Hassan Peerhossaini1
2 Fluid Mechanics, Heat and Thermodynamics Group, School of Engineering, Lebanese International University LIU, Beirut, Lebanon
3 ONIRIS – Nantes, rue de la Géraudière - 44322 Nantes, France
Abstract - 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 by flow 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 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 HEV are compared with numerical results in the literature. Both numerical and experimental results confirm the high efficiency of the HEV static mixer flow.
Keywords
Multifunctional heat exchangers - Process intensification - Heat transfer enhancement - Streamwise vorticity - Turbulence - Vortex generator.
I. INTRODUCTION
Convective transport phenomena are strongly enhanced by transverse and longitudinal vortices [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 a 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) [5-8], or by laminar or turbulent jets
(annular vortices) [9-10].
This paper is organized as follows: the flow structure is discussed in section 2; section 3 describes description the experimental setup and the measurement techniques. The results and discussion are presented in section 4 and section 5 draws some conclusions.
II. VORTEX GENERATION AND FLOW STRUCTURE 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 trapezoidal vortex generator, which has been widely studied due to its ability to enhance turbulent mixing and mass transfer with low power consumption compared to triangular and rectangular geometries [13]. 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). 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 [6], as shown in Fig. 1(b). The HEV static mixer is an efficient heat exchanger designed to exploit the above vortices and has shown high mass and heat transfer efficiency in turbulent mixing with low energy consumption
compared to other multifunctional heat exchangers-reactors [12].
Numerical studies have been carried out on the HEV static mixer geometry to characterize the flow structure and its effects on heat and mass transfer [2]. The results show the great influence of vorticity on convective transfer in this type of flow: 500% improvement over turbulent flow in straight tubes.
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.
III. EXPERIMENTAL APPARATUS AND PROCEDURES A. Flow 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, sufficient 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. 1(a) 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 as shown in Table 1.
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) Cp specific heat (J kg-1K-1) Um mean axial velocity (m/s) e grease layer thickness (m)
Greek symbols
ν
kinematic viscosity (m2s-1)κ thermal conductivity of water (Wm-1K-1) λ thermal conductivity of grease (Wm-1K-1) ρ fluid density (kg m-3)
φ heat flux density (Wm-2) Subscripts
w HEV wall m tube section mean e heating tube inner wall
b bulk
Fig. 1. (a) HEV geometry and (b) flow structure produced behind a trapezoidal vortex generator
TABLE I
PHYSICAL PROPERTIESOF WORKING FLUID
Water
ρ Cp ν κ Pr
kg m-3 J kg-1K-1 m2 s-1 Wm-1K-1 -
998 4186 10-6 0.60 6.96
The flow Reynolds number is defined by:
Re U Dm
= ν (1)
All thermophysical properties of water are determined at the fluid bulk temperature (Tb).
B. Wall Heating and Temperature Measurement
The experimental rig is shown in Fig. 2. 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 Figure 2. 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 a 200 watt uniform heat flux in the wire is controlled by adjusting the voltage (50 V) and the current (4 A) with a precision of 1%. 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 two sets of type-K thermocouple beads with an accuracy of ± 1.5°C, 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 differential manometers (Digitron 2001P7 and Baratron 220DD) 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, i.e. without heating the tube.
Experimental uncertainties are evaluated for the derived quantities using the relative errors of measurement of their elementary terms as given by Eq. (2):
1
1 n
i i i
z z x
z z = x
∆ = ∂ ∆
∑
∂ (2)where z is the derived quantity depending on n variables, x1...xn, while ∆z and ∆x represent the absolute error in the calculation of z and the measurement of x respectively.
IV. 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.
A. 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 and 15]. 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 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 heat-transfer enhancement.
Fig. 2. Test section and thermocouple positions
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. 3. Local Nusselt number for different Reynolds numbers
2000 4000 6000 8000 10000 12000 14000 16000
0 20 40 60 80 100 120 140
Nu=0.616Re0.462Pr0.4
HEV - Experimental
Plain tube - Gnielinski correlation
Global Nusselt number, N
u g
Reynolds number, Re Fig. 4. Global Nusselt number, Nug
However, a disadvantage of the HEV heat exchanger is the hot spots generated behind the tabs due to flow recirculation. The temperatures Te and Tw measured at the different longitudinal positions are used to calculate the local heat flux densities using Eq. (3):
(T Te w) e
ϕ =λ − (3)
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, Tm. The local convective heat transfer coefficients, h are calculated using temperatures Tw and Tm:
( w m)
h T T
= ϕ
− (4)
The local Nusselt numbers are then calculated using Eq.
(5), taking into consideration the slight evolution in the fluid thermal conductivity
κ
with increased temperature:Nu hD
= κ (5)
Fig. 3 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 local and global Nusselt numbers 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.
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. [1] for the same flow and heat transfer conditions.
B. 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
ϕ
, the heat exchanger average wall temperature Tw , and the average fluid temperature Tm . 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. 4 shows the variation of global Nussselt number with Reynolds number. These results confirm those of our previous numerical studies [2 and 15] which showed an important 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. (6)) 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 ( / 8)(0 1/ 21000)2/3
1 12.7( / 8) ( 1)
f Re Pr
Nu f Pr
= −
+ − (6)
2000 4000 6000 8000 10000 12000 14000 16000 0
100 200 300 400 500 600 700 800 900
χ = (∆ Nug / Nu0) %
Reynolds number, Re
0 0
(%) Nug Nu *100 χ = Nu−
Fig. 5. Index of relative intensification of convective transfer, χ
2000 4000 6000 8000 10000 12000 14000 16000 0
2 4 6 8 10 12 14 16 18 20 22 24
f / f0
Reynolds number, Re f / f0 = 11 Re0.054
Fig. 6. Variation of friction factor ratio, HEV/plain tube TABLE II
EXPERIMENTAL VALUES OF hglobalAND Nuglobal
where f0 is the friction factor in a smooth-pipe turbulent flow given by:
0.25 0 0.079
f = Re− (7)
The numerical studies of Mohand Kaci et al. [2] predict a 500% increase in average convective heat transfer in the HEV flow over a turbulent tube flow for a matching range of Reynolds numbers. Figure 4 compares the global experimental Nusselt number Nug with those calculated using the Gnielinski correlation in a turbulent tube flow, Nu0. The results confirm the numerical predictions of [2]:
for a range of Reynolds numbers between 2000 and 15000, the average value of Nug 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. When a fully turbulent regime is attained, the relative increase is less important, as shown in Fig. 5 with a 5% error margin.
From this figure, it can be concluded that the vortical enhancement of heat transfer by HEV geometry increases the Nusselt number by between 800% to 200% over that of a turbulent tube flow for the Reynolds numbers ranging between 2000 and 15000, respectively.
We define the rate of relative heat transfer intensification χ (Eq. 8) thatreflects the increase in Nusselt number in the HEV heat exchanger compared to a turbulent tube flow (see Fig. 5):
0 0
Nug Nu χ Nu−
= (8)
The Nusselt number is generally a function of Reynolds and Prandtl numbers through:
Re Prm n
Nu A= (9)
where A, m and n are constants to be determined in each geometry. Correlations in the literature [16] show that the constant n is usually around to 0.4 for turbulent flows. Then a plot of Nu/Pr0.4 versus Re gives the following correlation:
0.462 0.4
0.616Re Pr
Nu= (10)
The above correlation 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.
C. Friction Factor and Energy Efficiency
The Fanning friction factor f is related to pressure losses by the Darcy-Weisbach equation (Eq. 11). 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:
4 2
2m f P
U L
D ρ
= ∆
(11)
Fig. 6 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. The uncertainty of the friction factor calculations varies between 0.1 and 0.25%
depending on the measured values of head losses.
Re 2160 4530 6390 8670 10460 12860 14920
hglobal [Wm-2K-1] 1192 1781 2076 2300 2549 2682 3023
Nug 45 67 79 87 96 101 114
7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 -0,2
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. 7. Evolution of friction factors of different exchangers (adapted from Thakur et al. [14])
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 reults [2]
Helical coiled tube Empty pipe
Fig. 8. Colburn factor for common commercial heat exchangers (Mohand Kaci et al. [2])
Compared to other innovative heat exchangers/mixers producing similar heat-transfer enhancement with similar diameters, these values prove the HEV flow to be among the most efficient exchangers, as shown in Fig. 7.
Another criterion for judging the energy efficiency of a heat exchanger is the Colburn factor j, given by
13
Re Pr
j= Nu (12)
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 of the Colburn factor for HEV flow with that for other geometries plotted in Fig. 8
.
shows the HEV’s capacity to enhance heat transfer while producing moderate energy consumption.
V. CONCLUSIONS AND PERSPECTIVES
Heat-transfer enhancement in a tube fitted with trapezoidal tabs acting as vortex generators and turbulators is investigated experimentally. 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 of enhanced transfer. The protuberance of the solid tabs in the flow produces additional losses compared to a plain tube, but simultaneously contributes to heat transfer by the fin effect and also 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 [2,15] and confirms the capacity of the HEV heat exchanger to improve convective heat transfer while keeping pressure losses moderately low.
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