ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2015, Vol. 56, No. 4, pp. 569–579. c Pleiades Publishing, Ltd., 2015.
Original Russian Textc C. Habchi, T. Lemenand, D. Della Valle, A. Al Shaer, H. Peerhossaini.
EXPERIMENTAL STUDY OF THE TURBULENT FIELD BEHIND A PERFORATED VORTEX GENERATOR
UDC 532.517:629.7 C. Habchia, T. Lemenandb, D. Della Vallec, d,
A. Al Shaere, and H. Peerhossainif
Abstract: The influence of the wake vortex arising behind a perforated tab on the mixing process in heat exchangers and chemical reactors is analyzed. The preliminary step of this study, i.e., investigation of the turbulent field generated by a single perforated tab, is presented here. For this aim, laser Doppler velocimetry measurements are conducted downstream from a perforated trapezoidal vortex generator placed in a wind tunnel. It is shown that two shear layers are generated by the tab. The first shear layer is located at the upper edge of the tab, and the other is ejected from the perforation edges. These shear layers are characterized by high turbulent kinetic energy levels, which are profitable for meso-mixing enhancement. Finally, a spectral study shows that the turbulent macro-scale is nearly the same for typical locations in the shear layers shed from the tab and perforation edges.
Keywords: vorticity, turbulent kinetic energy, turbulence power spectra, laser Doppler velocimetry.
DOI:10.1134/S0021894415040045
INTRODUCTION
The production of vorticity in industrial flows is an important issue for many engineering applications, such as mass and heat transfer intensification [1–6], as well as boundary layer separation control in aeronautics and automotive aerodynamics [7–11]. Vorticity can be generated by using either spatial or temporal perturbations, or a combination of both. An example of temporal perturbations is a pulsatile mean flow, which causes velocity gradients within the bulk flow, and, thus, transverse vortices may be produced [12]. Spatial perturbations can be encountered with the development of instabilities due to centrifugal forces, for example, the Dean roll cells in curved channels [13, 14] or the G¨ortler vortices in the case of concave surfaces [15]. The use of turbulence promoters also appears to be very efficient to generate a complex set of coherent structures, which may combine transverse and longitudinal vortices [7].
Generally, two types of vortices are created downstream from the vortex generator, due to pressure gradients between the wake region behind the vortex generator and the bulk region in the free stream [16]. The first type consists in longitudinal vortices, which appear usually as pairs of counter-rotating vortices in the flow cross section.
aNotre Dame University, Louaize, Lebanon; charbel.habchi@hotmail.fr. bLUNAM University, IMIS IS- TIA, Angers, France; Thierry.LEMENAND@univ-angers.fr. cLUNAM University, LTN CNRS UMR 6607, Nantes, France. dONIRIS, Food Processing Dept., GEPEA, Nantes, France; dominique.dellavalle@oniris-nantes.fr.
eLebanese International University LIU, Mechanical Engineering Dept., Beirut, Lebanon; ali.alshaer@liu.edu.lb;
fUniversite Paris Diderot, Paris, France; hassan.peerhossaini@univ-paris-diderot.fr. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 4, pp. 36–47, July–August, 2015. Original article submitted October 10, 2013.
569
4 5
6 7
x z y
1
2
3
Fig. 1. Basic flow structures generated by a trapezoidal vortex generator: (1) necklace vortex (ωx,0,0);
(2) hairpin vortices (ωx,±ωy,±ωz); (3) primary CVP (0,0,±ωz); (4) secondary CVP (0,0,±ωz); (5) re- verse vortices (−ωx,0,0); (6) transverse vortices (recirculation flow) (0,±ωy,0); (7) tab.
These counter-rotating vortex pairs (CVPs) that form on the trailing edges are very efficient for heat and mass transfer [17, 18]. The second type of vortices is caused by deformation and breakdown of the boundary layer ejected from the top edge of the vortex generator. Due to the orientation of the vortices, they entrap the fluid and favour the formation of a dead zone. Both types of vortices may themselves break up in hairpin transient vortices due to the Kelvin–Helmholtz instability, as in the case of trapezoidal tabs [4, 19–21].
These main flow structures downstream from a trapezoidal vortex generator are represented in Fig. 1 [19].
A recirculation region is observed directly behind the tab. This recirculation region has a negative effect on the residence time distribution (RTD) and, as a consequence, on macro-mixing. Therefore, the perforation in the tab is used to generate a high-momentum flow to break the recirculation region.
Many types of vortex generators can be found in the open literature, which differ mainly by their shape [7, 11, 17]. While most of the studies are aimed to analyze the flow structure and its effect on mass and heat transfer by using experimental techniques or numerical computations, the study of the turbulence statistics and its properties is less developed for vortex generators [22]. In fact, this issue is fundamental for understanding the effect of vortex generators on the evolution of the turbulent kinetic energy and its dissipation rate. Actually, these two properties can be adopted for local quantification of the mixing process in the turbulent regime. Mixing in the turbulent regime is a multi-scale process that can be defined merely by three parallel steps, the largest scales
“feeding” the smaller ones [23].
1. The first mechanism is the macro-mixing process related to the mean velocity distribution leading to the homogeneity at the mixer scale. The related mechanism is advection by the mean flow, generally characterized by the P´eclet number.
2. The second mechanism, the meso-mixing process, corresponds to disintegration of large vortices in the inertial range of the turbulence spectrum and can be characterized by the turbulent kinetic energy.
3. Finally, the third mechanism, the micro-mixing process, is the reduction of the local gradients due to the effect of the engulfment and deformation at the Kolmogorov scale and laminar stirring till the molecular diffusion scales.
In this scheme, the role of the vortex generators is to favor macro-mixing by means of convective radial transfer due to the formation of trailing vortices similar to that on plane wing edges. Associated mechanisms increase the production of turbulence in the shear layer resulting from flow acceleration on the tab top and secondary
1
80mm 2
70mm
60mm
40mm
20mm
Fig. 2.Dimensions of the trapezoidal perforated vortex generator: (1) air flow; (2) wind tunnel base.
instabilities (hairpins) around the trailing vortices. This leads to enhancement of meso- and micro-mixing in the vicinity of the tab.
Nevertheless, the hydrodynamic obstruction due to the tab leads to the formation of a wake that tends to entrap a small fluid volume near the wall that exchanges poorly with the environment, with unfavorable consequences on the residence time distribution [4]. To thwart this negative effect, the idea is to break the wake vortex with a circular perforation in the center of the tab, which induces a fluid jet in the orifice, intended to introduce the high-velocity fluid into the wake region of the low-velocity fluid.
Nuntadusit et al. [24] carried out heat transfer measurements and numerical simulations on a surface equipped with perforated ribs and showed that heat transfer improvement and recirculation region size reduction can be observed due to the jet-like flow.
To evaluate the efficiency of this geometric modification on the global flow and its influence on the mixing mechanisms, it is necessary to understand the hydrodynamics induced by this new geometry.
The present paper describes an experimental study with the use of laser Doppler velocimetry (LDV) to analyze the velocity distribution and turbulence statistics downstream from a perforated trapezoidal tab in a wind tunnel.
1. EXPERIMENTAL SETUP
The experimental setup and measurement technique are described in this section.
1.1. Wind Tunnel and Vortex Generator Dimensions
The perforated trapezoidal vortex generator represented in Fig. 2 consists on an aluminum tab 0.5 mm thick and 70 mm high. Its largest base 80 mm wide is attached to the wind tunnel base with an angle of 90◦, while its tip is 60 mm wide. The perforation is a circle with a radius of 10 mm, and its center is located at its plane of symmetry and at 40 mm from the wind tunnel base. The trapezoidal tab is painted in black to avoid reflection of the laser beam.
The LDV measurements are performed in a 5-m wind tunnel with a square section with a side of 300 mm.
As shown in Fig. 3, a centrifugal fan is used to drive the air flow into the test section. The centrifugal fan is driven by an electric motor whose maximum power is 5 kW supplied by a 220-V AC current. The rotational speed of the motor can be regulated by a frequency controller to deliver air velocity ranging from 5 to 12 m/s. This velocity is measured by a Pitot static tube connected to a digital converter to regulate the air flow rate. In the present study, two velocities are investigated, 1 and 6 m/s, corresponding to the Reynolds numbers of 7000 and 42 000, respectively. A honeycomb followed by a convergent segment is located downstream from the fan to stabilize the air flow before its entering the test section. Therefore, the turbulence intensity at the test section entrance does not exceed 5%. A paraffin–oil generator is placed upstream of the test section to produce smoke as a tracer for LDV measurements. The sides of the test section are glass panels with optical quality.
4 5 6
7 8
9
1 2
3
Fig. 3. Schematic view of the wind tunnel and experimental benchmark: (1) centrifugal fan;
(2) diffuser; (3) honeycomb; (4) preconditioner; (5) Pitot static tube; (6) test section; (7) smoke generator; (8) laser source; (9) LDV system.
1.2. LDV Measurements and Data Acquisition
The measurements are performed by a Dantec LDV system equipped with a 10-W argon-ion laser source and two signal-processing units (57N20 BSA and 57N35 BSA enhanced models). The measurement head is equipped with a 160-mm focal lens.
It is shown that a validated sampling particle number of 35 000 is needed to obtain the statistical convergence for velocity fluctuations and mean velocity. The data-acquisition rate is ranging between 1 and 2 kHz.
The LDV system calibration is performed with accuracy of 2.5%. Moreover, to ensure the reproducibility of LDV measurements, the experiments are iterated four times for profiles at different locations in the symmetry plane of the test section for the highest flow velocity. The relative standard deviation for the mean and root-mean-square (RMS) velocities depends on the location in the measurement volume. It reaches 8% in the near-wall region because of the low velocity and remains at about 4% in the bulk region. The global standard deviation corresponding to the maximum uncertainty is evaluated as √
2.52+ 82 = 8.4%. By using the sampling rate uncertainty method of Benedict and Gould [25], the confidence level is determined to be 95%; in addition, 25% of the data present an error smaller than 1%, and the remaining 75% have an error smaller than 10%. The measurements must be performed at sufficiently short time intervals to detect high-frequency fluctuations. Laser Doppler velocimetry allows such fast measurements by optimizing seeding and optical adjustments. As LDV measurements are not performed at constant time intervals, the data are resampled according to the method suggested by Host-Madsen and Caspersen [26]. The measurements are taken in the central plane of the vortex generator, at locations shown in Fig. 4.
2. RESULTS AND DISCUSSIONS
The results obtained from the LDV measurements are discussed in this section.
2.1. Average Velocity Field
The mean axial velocity profiles in the symmetry plane are shown in Fig. 5 forz/h= 0.71 and Re = 7000 and 42 000.
The Reynolds number in the present study is defined as Re =U∞h/ν,
whereU∞is the mean flow velocity,h= 70 mm is the vortex generator height, andν is the kinematic viscosity.
As observed in Fig. 5, the velocity profiles are qualitatively similar for both Reynolds numbers, with a trans- verse development of four regions that can be distinguished by the changes in the curvature of the velocity profiles.
Region I (0 < y/h < 0.43) under the orifice is dominated by low negative velocities and small gradients revealing the presence of a recirculation vortex near the wind channel base.
z/h y/h
0.14
0 0.29 0.43 0.71 1.00 2.00
0 0.43 0.57 0.71 1.00 2.00
Fig. 4.Locations of the measurement profiles downstream from the vortex generator.
1.0
I II III IV
1.5 0.5
0 0
0.8 0.6 0.4 0.2 1.0 1.8 1.6 1.4 1.2 2.0
_0.5 y/h
U/U1 1
2
Fig. 5. Velocity profiles for z/h= 0.71: regions with different curvatures of the velocity profiles are denoted by I–IV; Re = 7000 (1) and 42 000 (2).
Region II (0.43< y/h <0.71), which is the orifice region, presents a local maximum for the velocity nearly equal to the bulk velocity in the channel, showing the efficient jet effect due to the orifice. The velocity profile in this region has a parabolic shape.
Region III (0.71< y/h <1.40) coincides with the shear layer ejected from the upper edge of the tab with a low absolute velocity behind the solid part of the obstacle.
Region IV (y/h >1.40) is the free stream above the tab, whereU/U∞ = 1.0 and the perturbation due to the obstacle vanishes.
Figure 6 shows the dimensionless mean axial velocity distributions at six locations (see Fig. 4) downstream from the vortex generator for Re = 42 000. The inflection points and the maxima are highlighted to show the statistical path of the jet-like flow and of the shear layers.
0.8
0.6 1.0
0.4
0.2 1.2 1.4 1.6 1.8 2.0
0 0.5 1.0 1.5 2.0 y/h
z/h 1
2 3 4
2.2
Fig. 6.Dimensionless mean axial velocity distributions in six locations represented in Fig. 4: points1–3are inflection points, i.e., shear layer shed from the upper edge of the tab (1) and shear layer caused by the accelerating flow that exits from the perforation (2, 3); the maximum velocities are denoted by points4.
z/h y/h
U/U1
0.5 1.0 1.5 2.0
1.1 0.9 0.7 0.5 0.3 0.1 _0.1 _0.3
0 0.5 1.0 1.5 2.0
Fig. 7.Contours of the velocity field for Re = 42 000.
The shear layer shed from the upper edge of the tab is characterized by the maximum velocity gradients and, thus, can be defined by the inflection points (∂2U/∂y2 = 0) marked as points 1 in Fig. 6. Normally, under certain conditions, this shear layer deforms and then detaches due to the Kelvin–Helmholtz instability and gives rise to a periodic sequence of horseshoe vortices [21].
The other inflection points2and 3correspond to the shear layer caused by the accelerating flow that exits from the perforation. Under certain conditions, this shear layer can be destabilized and detaches to form a sequence of ring-shaped vortices that take the form of the perforation.
Moreover, it is observed that the jet thickness increases downstream from the tab, while the fluid flow velocity decreases. A similar behavior is typical for free jets. Finally, the maximum velocities (points4) are obtained at the perforation center and tend to decrease in the downstream direction due to viscous effects (see Fig. 6).
This is confirmed by Fig. 7, which shows the velocity contours obtained by triangulation smoothing of discrete points of LDV measurements. The effect of the jet induced by the perforation is clearly visible downstream from the vortex generator as it generates a high-momentum fluid flow whose velocity is almost equal to that of the free stream at a distance z/h ≈ 1. The effect of the perforation vanishes after a distance z/h ≈ 2 due to
Mean flow velocityU, fluctuating velocityu, and turbulent kinetic energyk at five different locations downstream from the vortex generator
z/h y/h U, m/s u·103, m/s k·105, m2/s2
Free stream 6.00 5.05 3.83
0.14 0.50 1.98 20.64 63.87
1.14 0.93 12.24 22.47
0.71 0.50 1.65 15.77 37.31
1.14 0.78 5.22 4.09
viscous effects. The shear layer (points 1 in Fig. 6) is clearly observed in Fig. 7. It separates the free stream with a high velocity from the flow in the wake behind the vortex generator whose velocity is twice smaller than the free-stream velocityU∞. In the wake region, it is observed in Fig. 7 that the flow structure is modified due to the presence of the perforation. In the upper half (0.5< y/h <1.0), the mean flow velocity increases, and the jet brakes the recirculation region, which was formed due to the presence of the trapezoidal vortex generator [19].
Meanwhile, in the lower half (y/h <0.5), the jet has no significant influence on the hydrodynamic structure, and negative velocities are observed due to the recirculation region, which persists for a distance z/h ≈2. However, this recirculation region is less important than that for a completely trapezoidal vortex generator [19].
2.2. Turbulent Kinetic Energy
Figure 8 presents the profiles of the turbulent kinetic energy (TKE) normalized byU∞2 and the profiles of the mean axial velocity normalized byU∞ for different locations downstream from the vortex generator. It can be observed that the TKE maxima coincide with the inflection points in the velocity profiles, which correspond to the maximum gradients of velocity and, hence, to the maximum turbulence production rates. The high TKE value in the primary maximum is due to the fact that the shear layer ejected from the perforation is highly unstable and generates energetic coherent structures. The secondary maximum on the TKE profile corresponding toz/h= 0.14 (see Fig. 8a) coincides with the upper inflection point where the shear layer is ejected from the upper edge of the vortex generator. This means that the instability of this shear layer occurs far away from the vortex generator, while the shear layer ejected from the orifice is highly unstable near the vortex generator.
Figure 9 shows the TKE distributions downstream from the vortex generator. This figure shows that the inflection points coincide with the maximum values of the turbulent kinetic energy, especially at the lower edge of the perforation. It can be observed that there is no significant effect of the vortex generator on the TKE profile at z/h >1. To maintain high TKE levels, hence, a successive row of vortex generators must be added at this distance from each other to provide good meso-mixing.
The table represents the measured values of the mean flow velocity, fluctuating velocity, and turbulent kinetic energy at five different locations. The first one is in the free-stream flow with a high mean velocity and a low turbulent field. In the other positions, which are the primary and secondary maxima in the shear layers, the velocity is almost one third of the free-stream velocity or even smaller. The turbulent kinetic energy reaches about 16 times that in the free-stream region due to higher fluctuating velocities in the shear layers, especially near the vortex generator. The highest values ofkare observed in the shear layer shed from the perforation, which are three to nine times greater than that in the shear layer shed from the upper edge of the vortex generator.
2.3. Spectral Study
The energy spectra multiplied by the frequencyf, namely, the pre-multiplied spectra f E are presented in Fig. 10 at the inflection points obtained previously for z/h= 0.43. The values of lnf are shown on the abscissa axis. The TKE is proportional to the area between each curve and the abscissa axis:
k= 2π Uconv
∞ 0
E(f)df= 2π Uconv
∞ 0
f E(f)dln (f) (Uconv is the convective velocity).
16
12 20 24
8 4 0
_8 _4
0.8
0.6 1.0 1.2
0.4 0.2 0
0 0.5 1.0 1.5 2.0
_0.4 _0.2
I II
I y/h
(b) (a)
U/U1 (k/U12).103
(k/U12).103 16
12 20 24
8 4 0
_8 _4
0.8
0.6 1.0 1.2
0.4 0.2 0 0
0.5 1.0 1.5 2.0
_0.4 _0.2 y/h
U/U1 1
2
Fig. 8. Mean axial velocity U/U∞ and turbulent kinetic energyk/U∞2 for z/h= 0.14 (a) and 0.71 (b) for Re = 42 000: the primary and secondary maxima are denoted by I and II, respectively;
points1and2show the mean axial velocity and turbulent kinetic energy, respectively.
The−2/3 power in the pre-multiplied spectraf E(f) corresponds to the inertial subrange, which is charac- terized by a−5/3 power when plotting the energy spectrumE(f) directly versus the frequency.
In Fig. 10, the valuesy/h= 0.50, 0.71, and 1.26 correspond, respectively, to the inflection points (see Fig. 6), andy/h= 0.61 corresponds to the maximum velocity at the center of the perforation.
The inflection points corresponding to the orifice-induced shear layer (y= 0.50 and 0.71) are characterized by a high TKE value, which are almost two-fold that at the jet center and in the shear layers. Both spectra are much more energetic than the others: they are higher approximately by two orders of magnitude.
Moreover, it can be observed that the maximum of the pre-multiplied spectraf E(f) almost coincides with the turbulent macro-scale, which is the limit of the convective inertial range. In fact, the smaller the macro-scale, the more efficient the micro-mixing process, which is characterized by the turbulent energy dissipation rate ε, as given by Batchelor’s model [27] based on the dimensional analysis:
ε=Au3/Λ;
0.8
0.6 1.0
0.4
0.2 1.2 1.4 1.6 1.8 2.0
0 0.5 1.0 1.5 2.0 y/h
z/h 1
2 3 4
2.2
Fig. 9. Dimensionless turbulent kinetic energy distributions downstream from the vortex generator at six locations (see Fig. 4) for Re = 42 000: points 1–3are the maxima; points4show the inflection points.
10 0 fE
1
2 3
5
4
102 103 104 f,Hz
1.8.10-4
6.0 .10-5 1.2.10-4 1.2.10-2 1.0 .10-2 8.0 .10-3 6.0 .10-3 4.0 .10-3 2.0 .10-3
Fig. 10. Pre-multiplied turbulent spectrafE(f) versus the frequency f for z/h= 0.43, Re = 42 000, andy/h= 0.50 (1), 0.61 (2), 0.71 (3), and 1.26 (4); curve5is the power-law function with the power index of−2/3.
therefore, we have
ε≈u3.
Here A is a constant depending on the flow configuration, Λ is the integral length, and uis the RMS deviation of the fluctuating velocity at the turbulent macro-scale. Hence, as Λ is more or less constant in the present study (determined by the geometry), we haveε≈u3; therefore, the maximum values ofεcoincide with those for the TKE.
This leads us to conclude that micro-mixing is the most efficient in the shear layers, similar to the meso-mixing process.
CONCLUSIONS
Vorticity generation is a fundamental issue for different engineering applications in order to intensify heat and mass transfer, and many methods can be used for this purpose. The present study deals with a perforated trapezoidal vortex generator, which can combine turbulent promoters and free jet mechanisms. Laser Doppler velocimetry is used to determine the velocity distributions downstream from the vortex generator and to study the turbulence statistics.
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