- Email: [email protected]
On the dependence of an empty flanged diffuser performance on flange height: Numerical simulations and PIV visualizations
Renewable Energy 56 (2013) 123e128
Contents lists available at SciVerse ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
On the dependence of an empty flanged diffuser performance on flange height: Numerical simulations and PIV visualizations M. Kardous a, *, R. Chaker a,1, F. Aloui a,1, S. Ben Nasrallah b, 2 a b
Research and Technology Center of Energy (CRTEn), Borj Cedria Technopark, BP. 95, Hammam-Lif 2050, Tunisia National Engineering School of Monastir, Avenue Ibn El Jazzar, 5019 Monastir, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 May 2012 Accepted 30 September 2012 Available online 20 November 2012
Flanged diffuser shrouding small wind turbine, is among the most tested devices for increasing wind energy. The height of the flange is between the geometric futures of the diffuser that contributes efficiently in improving diffuser performances. Results obtained from numerical simulations and PIV visualizations show that when a flange is mounted at the outlet area of the diffuser, two contra-rotating vortices were created at this location. These two vortices move away from each other in the flow direction as the flange height increases and they seem to lengthen in the streamwise direction and to extend in the two directions when the flange height becomes taller. A critical ratio (Flange height/Inlet section diffuser diameter ¼ 0.1) has been found. Beyond this value, due to the remoteness of vortices from the flange, the flange height seems to be without significant effect on increasing wind velocity. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Flanged diffuser Wind energy Flange height Simulations PIV measurements
1. Introduction It’s well known that rising fossil fuel consumption is strongly associated to the increasing greenhouse gas emissions, which contributes widely to the global warming and consequently to climatic changes. Hence, over the last decades, many countries have invested in developing renewable energy technologies such as wind energy systems which have taken on an exceptional evolution with an annual growth rate reaching about 30%. Wind energy increases as the cubic of the wind speed, consequently any increment in wind velocity approaching wind turbine leads to a large increase in wind energy output. Several research teams have strived to set up new technologies that accelerate wind at the rotor disk. This approach, could present new opportunities to extract energy even for small wind velocities which is not the case with conventional wind turbines. Diffuser shrouding wind turbine is among the most tested devices for accelerating wind. It consists of a funnel-shape structure which shrouds conventional wind turbine to enhance its efficiency (Figs. 1 and 2). Researches carried out between the 1950s and 1990s, had mainly concerned diffusers with large open angle and had focused on controlling boundary layers by various flow
* Corresponding author. Tel.: þ216 24 66 9085; fax: þ216 79 325 825. E-mail address: [email protected] (M. Kardous). 1 Tel.: þ216 24 66 9085; fax: þ216 79 325 825. 2 Tel.: þ216 98 262 931; fax: þ216 73 50 05 14. 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.09.061
slots to increase the mass flow inside the diffuser [1e8]. Unfortunately, the high cost of the energy produced by the proposed diffusers doesn’t let them reach the commercialization stage. It should be noted that the general economic context where these researches had been performed did not promote developing renewable energy. However, due to the increase of oil prices in the early 1990s, diffuser for increasing wind energy has become an attractive research topic. Hence, various types and shapes of diffusers have been studied [9e14]. Most of these relevant research activities have led to very promising results. In particular, the flanged diffuser with smoothly curved inlet section suggested more recently by [12,14], is one of the very interesting wind-acceleration systems. By using the one dimension momentum theory it’s easy to demonstrate that, for an empty diffuser without flange, the wind velocity (u) and pressure (p) at the inlet inside the diffuser can be described by the following equations:
u ¼ wd $uN
(1)
1 p ¼ pN þ 1 w2d r$u2N 2
(2)
where uN and pN refer respectively to the velocity and pressure located far in front of the diffuser. wd is a dimensionless coefficient larger than 1. It obviously means that the velocity u at the narrow section inside the diffuser is greater than uN and pressure p is smaller than atmospheric pressure pN. Coefficient wd depends on
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M. Kardous et al. / Renewable Energy 56 (2013) 123e128
Fig. 2. Geometric characteristics of the tested diffuser.
Fig. 1. Design of the tested diffuser.
diffuser geometric characteristics and it describes the twofold effect of the continuity and the magnitude of the adverse pressure located behind the diffuser. When a flange is mounted at the exit area of the diffuser, an additional adverse pressure is created behind this location inducing an additional acceleration (wFlange $uN) at the inlet section. In this case, expressions of u and p become as follows:
u ¼ wd $uN þ wFlange $uN ¼
wd þ wFlange $uN
2 i 1 h r$u2N p ¼ pN þ 1 wd þ wFlange 2
(3)
(4)
In equations (3) and (4), coefficient wFlange represents the changes of velocity and pressure induced by the flange effect. Even if the flanged diffuser increases efficiently wind speed, the physical process remains unclear and a lack of information regarding which could be the optimal flange height is recorded. The aim of this paper is to try to improve the understanding of this process which also could find value in other applications. 2. Procedures 2.1. Numerical simulations and wind tunnel experiments In order to investigate the effect of flange height on the wind acceleration in the inlet section of the diffuser, we adopt an approach based on numerical simulations and wind tunnel experiments performed in the wind tunnel of the Energy Research and Technologies Center e Tunisia. Particle-Image-Velocimetry (PIV) technique is also used to get a better understanding of the flow field structure downstream as well as upstream of the diffuser. The studied flanged diffuser has a curved inlet section. Its length (L), the diameter of its narrow section (Da) and its open angle (q) are respectively 342 mm, 194 mm and 12 . The ratio (L/Da ¼ 1.76) is of the same order of those used in previous simulations and experimental works [11,15e17]. Ten flange heights (H) were tested. The ratio H/Da is ranged from 0 (no flange) to 60%. This range of values is of the same order of magnitude that used by in other works [16]. Numerical simulations have been carried out by using FLUENT 6.3 which is a useful computer program for modeling fluid flow in complex geometry. Since the flanged diffuser is axisymetric two-
dimensional simulations (2D) were performed on only the half of the diffuser. The physics of air flow around and within the diffuser is governed by the incompressible NaviereStokes equations. These equations could be solved using a volume-finite method and a first order discretization scheme [18]. All simulations were done for a steady-state flow with a 106 convergence criterion. Under those conditions, six RANS (Reynolds Averaged NaviereStokes) turbulence models available in Fluent were used. Among them, the standard keu turbulence model, has led to results in good agreement with experimental and numerical data of Abe et al. [11], and also agree with our experimental data as showed below in this paper. The computational domain was constructed using GAMBIT. It was taken rectangular with 15 Da long and 10 Da height. The diffuser was set at 5 Da from the entrance area of the domain. It was meshed into about 10,500 quadrilateral cells gradually condensed toward the diffuser using the structured mesh (Fig. 3). 140 cells were in streamwise direction and 75 cells in the traverse direction. At the entrance of the domain (inflow boundary), free stream was initialized with a mean velocity of 5 m s1. The other boundaries conditions of the computational domain were chosen as follows: “Atmospheric pressure” at the exit section (outflow boundary), a “symmetry line” for the bottom and top section and “wall” for the external faces of the diffuser. To insure that computational conditions do not significantly affect the simulations results, four Reynolds number values and three grid systems had been tested. No significant differences between the obtained maximum velocities were detected. Coefficient wd and the sum wd þ wFlange can be determined by dividing the wind velocity (u) at any point inside the diffuser by the upstream wind velocity (vN) respectively for the diffuser without flange and the flanged one. Only values obtained at several points along the diffusers centerline are discussed for describing the effect of the diffuser height on the airflow. However for evaluating the diffuser accelerating wind flow, all analyses will be based on calculating wd and wFlange for the maximum recorded velocity. Results of simulations had been compared to our experimental data and to other results available in the literature. 2.2. PIV tests PIV tests were performed at ReD ¼ 66,438, in closed loop wind tunnel. The dimensions of the test section were 800 mm (width) 1000 mm (depth) 4000 mm (length). The free stream
M. Kardous et al. / Renewable Energy 56 (2013) 123e128
125
Fig. 3. Computational domain and mesh.
velocity was monitored via a Pitot tube positioned 10 Da upstream from the diffuser, and it was proved to be constant during the test within a 1% uncertainty. The air temperature variations were considered negligible for the current tests. The PIV system was a commercial 2D PIV system from Dantec dynamics. A double pulsed Nd-YAG laser had been used. This delivers energy of 2 65 mJ that illuminate the smoke used as flow seeding with a 1 mm thick sheet. The flow is seeded with micrometer-sized droplets generated by a smog generator. The size of the particles is about 1 mm. The wind tunnel was equipped with two optical accesses for the camera and the laser. A flow Sens camera had been used with a resolution of 1600 1200 pixels, recording double fullframe particle images. The camera is equipped with a 60 mm objective lens at a diaphragm aperture of 2.8. The system: camera and laser, had operated at frequency of 10 Hz. The size of the measurement area had been 168 mm 160 mm. Studio DynamicsÒ software, from Dantec Dynamics was used to compute the instantaneous velocity field. The 1600 1200 pixels images were processed using adaptive correlation. The interrogation window is fixed to 32 32 pixels, providing a spatial resolution of approximately 3.3 3.3 mm2. The overlap ratio between adjacent interrogation windows is 50%, providing instantaneous velocity fields with 99 74 vectors. Subsequently, mean velocity fields were calculated as the average of 500 instantaneous velocity fields. 3. Results and discussions As expected, the most important events in terms of air dynamics had occurred at both ends of the flanged diffuser. All the simulated and experimented diffusers had generated low-pressure region behind the diffuser outlet section, allowing air flow to accelerate inside the narrow inlet section where the maximum of wind velocity was recorded. The same result was found from analysis of PIV measurements (Fig. 4). Upstream, streamlines converge as approaching the
diffuser inlet section, while downstream, due to the flange located at the exit area; two vortices are generated producing an additional adverse pressure. A quantitative analysis of these structures is presented at the end of this part (page 5). A similar result was also obtained by Toshimitsu et al. [19]. Comparison between experimental and simulated set of data for the same diffuser characteristics shows a satisfactory agreement since the difference between the two methods gives an error less than 12% with a correlation coefficient R2 ¼ 0.93 (Fig. 5). This is reassuring about the consistency of the results obtained by both methods. For the diffuser without flange (H ¼ 0), the wind velocity ratio wd was found equal to 1.58, This means that the diffuser without flange is responsible of a wind velocity increase rate of about 58%. For the flanged diffuser, the sum wd þ wFlange was found between 1.64 and 1.81. The contribution of the flange only (wFlange) in increasing wind velocity is calculated to be between 13% and 23%. Fig. 6, illustrates the variation of the ratio u/uN versus a dimensionless length H/Da. It clearly shows two distinct linear zones (two slopes) for two ranges of the ratio H/Da. The first linear zone (zone 1) corresponds to the range of ratios H/Da between 0 and 0.1, and the second one (zone 2) to those bigger than 0.1. The flange height for which H/Da ¼ 0.1 is considered as a critical height (HC) it corresponds to a maximum recorded wind velocity (uC). For the first zone of the curve, wind velocity increases significantly and linearly with the flange height. The slope is equal to 1.245 and the wind velocity ratio passes from 1.58 (no flange) to 1.71 for HC. The ratio u/uN versus H/Da can be described by the following suggested expression:
u=uN ¼ 1:245$H=Da þ 1:577
for H=Da ¼ 0:1
(5)
Values of u/uN deduced from simulations are very well reproduced by equation (5) with a correlation R2 ¼ 0.98.
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M. Kardous et al. / Renewable Energy 56 (2013) 123e128
Fig. 4. Streamlines of wind flow upstream the diffuser (left) and downstream the diffuser (right) ((a) and (b) simulations; (c) and (d) PIV results).
When the ratio H/Da exceeds the critical value of 0.1 (the second linear zone), the slope becomes too small. It passes from 1.245 to 0.206, then the flange height seems to have no more significant effect on increasing wind velocity. This confirms result obtained by Abe et al. [11]. Indeed, HC needs to be six times bigger to increase the ratio uC/uN only about 5%, at the same time, the effort exerted by the wind on the diffuser could be 2.36 times greater. This will compromise the mechanical stability of the diffuser induced by the interaction Fluid-Structure. This effect is more visible when we refer to uC and HC by plotting u/uC vs. ratio H/HC (Fig. 7).
Otherwise, due to the differences between wind velocities located on the periphery of the outlet section of the diffuser, an internal shear layer is created (Fig. 8). This layer, which is closely related to the intensity of the axial wind velocities, is responsible for the formation of vortices generated by the KelvineHelmholtz instability. Only one vortex is created when the ratio H/Da is less than the critical value Hc/Da and two contra-rotating vortices beyond it. These ones can be completely characterized by their sizes and by the coordinate of their centers.
Fig. 5. u/uN vs. x/D simulations and experimental results.
Fig. 6. Variation of the ratio u/uN versus a dimensionless length H/Da.
M. Kardous et al. / Renewable Energy 56 (2013) 123e128
Fig. 7. Ratio u/uc vs. ratio H/Hc (simulations).
In our case, three lengths D1, D2 and D3 had been chosen to describe the dynamic of the two vortices (Fig. 9). D1 and D2 represent the horizontal distances between the flange and the centers of the two vortices and D3 represents the distance between the two centers. For simulations, the position of the center of a vortex is the point where the wind velocity reaches a zero value. These lengths were deduced graphically in both cases (simulations and experiments). Fig. 10, gives a comparison between simulations and experimental values of D1, D2 and D3; a 22.5% overestimation of simulations lengths values, is observed. Analysis of obtained data shows that the three distances (D1, D2 and D3) increase linearly with the height of the flange. This means that vortices move in the flow direction as the flange height increases. When we had plotted these distances against the flange height (H), we found that the data points were very well aligned along a straight line (Fig. 11). The slope values indicate that the vortex 2 moves slightly faster than the vortex 1 and the two vortices move away from each other more slowly. This finding is also highlighted by Fig. 12 which displays, for each flange height, zero isovelocity contour that passes by the centers C1 and C2 of the two swirls and delimits the swirling zone located downstream. As flange height increases, swirls seem to
Fig. 9. Distances characterizing vortices located downstream the flange.
Fig. 10. D1, D2 and D3 value’s obtained by both methods.
Fig. 8. Shear layer located at the periphery of the diffuser outlet section.
Fig. 11. Distances (D1, D2 and D3) of vertices as a function of flange height.
127
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M. Kardous et al. / Renewable Energy 56 (2013) 123e128
contra-rotating vortices were created at this location. The effect of these vortices was assessed on the base of the position of their centers. Analysis of data shows that vortices move in the flow direction as the flange height increases. 5- The no significant effect of flange height observed from HC can be explained by the remoteness of vortices from the flange.
References
Fig. 12. Expansion of vortices generated by the KelvineHelmholtz instability located downstream the diffuser with the increase of the flange height (Full and empty markers represent respectively the centers C1 and C2).
lengthen in the streamwise direction and to extend in the two directions when the flange height becomes taller. At the same time flange height becomes without significant effect to increase wind velocity. This clearly suggests that beyond a certain flange height (HC) and therefore from certain position of the vortices, the value of the depression located directly downstream of the diffuser undergoes trivial changes which are inadequate to increase the wind velocity at the inlet section of the diffuser. 4. Conclusion Numerical simulations, Particle-Image-Velocimetry visualizations and wind tunnel experiments had been carried out to get a better understanding of the effect of the flange height on wind velocity increase at the inlet section of an empty flanged diffuser. Ten flange heights (H) with a ratio (H/Da) ranged from 0 (no flange) to 60%, were tested. Results show that: 1- When a flange is mounted at the diffuser exit area, an additional acceleration of the wind occurs at its inlet section. 2- The diffuser without flange is responsible of a wind velocity increase rate of about 58% while for the flanged one, this rate ranged from 64 to 81%. The contribution of the flange only is calculated to be between 13 and 23%. 3- A critical ratio HC/Da ¼ 0.1 has been found. Beyond this value, the flange height seems to be without significant effect to increase wind velocity. 4- Due to the differences between wind velocities located on the periphery of the outlet section of the diffuser, two
[1] Lilley GM, Rainbird WJ. A preliminary report on the design and performance of ducted windmills. Cranfield, UK: College of Aeronautics; 1956. CoA Rep. 102. [2] Oman RA, Foreman KM. Advantages of the diffuser-augmented wind turbine. In: Wind Energy Conversion Systems Workshop Proceeding Washington DC June 1113 1973. [3] Gilbert BL, Oman RA, Foreman KM. Fluid dynamics of diffuser-augmented wind turbines. J Energy Nov. 1978;2(6):368e74. [4] Kogan A, Seginer A. Shrouded aerogenerator design study II, axisymmetrical shroud performance. In: Proc. 5th Annu. Conf. on Aviation and Astronotic. Israel: Tel-Aviv; 1963. [5] Igra O. Compact shrouds for wind turbines. Energy Conversion 1977;16:149e 57. [6] Igra O. Research and development for shrouded wind turbines. Energ Conversion and Management 1981;21:13e48. [7] Dick E. Power limits for wind energy concentrator systems. Wind Engineering 1986;10(2):98e115. [8] Flay RG, Phillips DG, Richards PJ. Development of diffuser augmented wind turbine designs in New Zealand. In: Proc. EWEC 1999 Conference, 1e5 March, Nice, France; 1999. p. 349e52. [9] Van Bussel GJW. The science of making more torque from wind: diffuser experiments and theory revisited. Journal of Physics: Conference Series 2007; 75:1e11. IOP Publishing Ltd. [10] Hansen MOL, Sorensen NN, Flay RGJ. Effect of placing a diffuser around a wind turbine. Wind Energy 2000;3(4):207e13. [11] Abe K, Ohya Y. An investigation of flow fields around flanged diffusers using CFD. Journal of Wind Engineering and Industrial Aerodynamics 2004; 92:315e30. [12] Abe K, Nishida M, Sakurai A, Ohya Y, Kihara H, Wada E, Sato K. Experimental and numerical investigations of flow fields behind a small wind turbine with a flanged diffuser. Journal of Wind Engineering and Industrial Aerodynamics 2005;93:951e70. [13] Ohya Y, Karasudani T, Sakurai A. Development of high-performance wind turbine with a brimmed diffuser. Journal of the Japan Society Aeronautical Space Sciences 2002;50:477e82 (in Japanese). [14] Ohya Y, Karasudani T, Sakurai A. Development of high-performance wind turbine with a brimmed diffuser: part II. Journal of the Japan Society Aeronautical Space Sciences 2004;52(604):210e3 (in Japanese). [15] Watson SJ, Infield DG, Barton JP, Wylie SJ. Modelling of the performance of a building-mounted ducted wind turbine. Journal of Physics: Conference Series 2007;75:7. [16] Matsushima T, Takagi S, Muroyama S. Characteristics of a highly efficient propeller type small wind turbine with a diffuser. Renewable Energy 2006;31: 1343e54. [17] Ohya Y, Karasudani T, Sakurai A, Abe KI, Inoue M. Development of a shrouded wind turbine with a flanged diffuser. Journal of Wind Engineering and Industrial Aerodynamics 2008;96:524e39. [18] ANSYS: FLUENT user guide documentation: chapter 25 using the solver, section 8.1. First-order accuracy vs. second-order accuracy. [19] Toshimitsu K, Kikugawa H, Sato K, Hosoi T. Experimental and numerical investigation of performances and flow fields of the wind turbine with the flanged-diffuser for sinusoidally oscillating wind velocity. In: Proc. 3rd Asian Joint Workshop on Thermophysics and Fluid Science, Matsue, Japan; Sept 2010. p. 10e3.
Contents lists available at SciVerse ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
On the dependence of an empty flanged diffuser performance on flange height: Numerical simulations and PIV visualizations M. Kardous a, *, R. Chaker a,1, F. Aloui a,1, S. Ben Nasrallah b, 2 a b
Research and Technology Center of Energy (CRTEn), Borj Cedria Technopark, BP. 95, Hammam-Lif 2050, Tunisia National Engineering School of Monastir, Avenue Ibn El Jazzar, 5019 Monastir, Tunisia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 5 May 2012 Accepted 30 September 2012 Available online 20 November 2012
Flanged diffuser shrouding small wind turbine, is among the most tested devices for increasing wind energy. The height of the flange is between the geometric futures of the diffuser that contributes efficiently in improving diffuser performances. Results obtained from numerical simulations and PIV visualizations show that when a flange is mounted at the outlet area of the diffuser, two contra-rotating vortices were created at this location. These two vortices move away from each other in the flow direction as the flange height increases and they seem to lengthen in the streamwise direction and to extend in the two directions when the flange height becomes taller. A critical ratio (Flange height/Inlet section diffuser diameter ¼ 0.1) has been found. Beyond this value, due to the remoteness of vortices from the flange, the flange height seems to be without significant effect on increasing wind velocity. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Flanged diffuser Wind energy Flange height Simulations PIV measurements
1. Introduction It’s well known that rising fossil fuel consumption is strongly associated to the increasing greenhouse gas emissions, which contributes widely to the global warming and consequently to climatic changes. Hence, over the last decades, many countries have invested in developing renewable energy technologies such as wind energy systems which have taken on an exceptional evolution with an annual growth rate reaching about 30%. Wind energy increases as the cubic of the wind speed, consequently any increment in wind velocity approaching wind turbine leads to a large increase in wind energy output. Several research teams have strived to set up new technologies that accelerate wind at the rotor disk. This approach, could present new opportunities to extract energy even for small wind velocities which is not the case with conventional wind turbines. Diffuser shrouding wind turbine is among the most tested devices for accelerating wind. It consists of a funnel-shape structure which shrouds conventional wind turbine to enhance its efficiency (Figs. 1 and 2). Researches carried out between the 1950s and 1990s, had mainly concerned diffusers with large open angle and had focused on controlling boundary layers by various flow
* Corresponding author. Tel.: þ216 24 66 9085; fax: þ216 79 325 825. E-mail address: [email protected] (M. Kardous). 1 Tel.: þ216 24 66 9085; fax: þ216 79 325 825. 2 Tel.: þ216 98 262 931; fax: þ216 73 50 05 14. 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.09.061
slots to increase the mass flow inside the diffuser [1e8]. Unfortunately, the high cost of the energy produced by the proposed diffusers doesn’t let them reach the commercialization stage. It should be noted that the general economic context where these researches had been performed did not promote developing renewable energy. However, due to the increase of oil prices in the early 1990s, diffuser for increasing wind energy has become an attractive research topic. Hence, various types and shapes of diffusers have been studied [9e14]. Most of these relevant research activities have led to very promising results. In particular, the flanged diffuser with smoothly curved inlet section suggested more recently by [12,14], is one of the very interesting wind-acceleration systems. By using the one dimension momentum theory it’s easy to demonstrate that, for an empty diffuser without flange, the wind velocity (u) and pressure (p) at the inlet inside the diffuser can be described by the following equations:
u ¼ wd $uN
(1)
1 p ¼ pN þ 1 w2d r$u2N 2
(2)
where uN and pN refer respectively to the velocity and pressure located far in front of the diffuser. wd is a dimensionless coefficient larger than 1. It obviously means that the velocity u at the narrow section inside the diffuser is greater than uN and pressure p is smaller than atmospheric pressure pN. Coefficient wd depends on
124
M. Kardous et al. / Renewable Energy 56 (2013) 123e128
Fig. 2. Geometric characteristics of the tested diffuser.
Fig. 1. Design of the tested diffuser.
diffuser geometric characteristics and it describes the twofold effect of the continuity and the magnitude of the adverse pressure located behind the diffuser. When a flange is mounted at the exit area of the diffuser, an additional adverse pressure is created behind this location inducing an additional acceleration (wFlange $uN) at the inlet section. In this case, expressions of u and p become as follows:
u ¼ wd $uN þ wFlange $uN ¼
wd þ wFlange $uN
2 i 1 h r$u2N p ¼ pN þ 1 wd þ wFlange 2
(3)
(4)
In equations (3) and (4), coefficient wFlange represents the changes of velocity and pressure induced by the flange effect. Even if the flanged diffuser increases efficiently wind speed, the physical process remains unclear and a lack of information regarding which could be the optimal flange height is recorded. The aim of this paper is to try to improve the understanding of this process which also could find value in other applications. 2. Procedures 2.1. Numerical simulations and wind tunnel experiments In order to investigate the effect of flange height on the wind acceleration in the inlet section of the diffuser, we adopt an approach based on numerical simulations and wind tunnel experiments performed in the wind tunnel of the Energy Research and Technologies Center e Tunisia. Particle-Image-Velocimetry (PIV) technique is also used to get a better understanding of the flow field structure downstream as well as upstream of the diffuser. The studied flanged diffuser has a curved inlet section. Its length (L), the diameter of its narrow section (Da) and its open angle (q) are respectively 342 mm, 194 mm and 12 . The ratio (L/Da ¼ 1.76) is of the same order of those used in previous simulations and experimental works [11,15e17]. Ten flange heights (H) were tested. The ratio H/Da is ranged from 0 (no flange) to 60%. This range of values is of the same order of magnitude that used by in other works [16]. Numerical simulations have been carried out by using FLUENT 6.3 which is a useful computer program for modeling fluid flow in complex geometry. Since the flanged diffuser is axisymetric two-
dimensional simulations (2D) were performed on only the half of the diffuser. The physics of air flow around and within the diffuser is governed by the incompressible NaviereStokes equations. These equations could be solved using a volume-finite method and a first order discretization scheme [18]. All simulations were done for a steady-state flow with a 106 convergence criterion. Under those conditions, six RANS (Reynolds Averaged NaviereStokes) turbulence models available in Fluent were used. Among them, the standard keu turbulence model, has led to results in good agreement with experimental and numerical data of Abe et al. [11], and also agree with our experimental data as showed below in this paper. The computational domain was constructed using GAMBIT. It was taken rectangular with 15 Da long and 10 Da height. The diffuser was set at 5 Da from the entrance area of the domain. It was meshed into about 10,500 quadrilateral cells gradually condensed toward the diffuser using the structured mesh (Fig. 3). 140 cells were in streamwise direction and 75 cells in the traverse direction. At the entrance of the domain (inflow boundary), free stream was initialized with a mean velocity of 5 m s1. The other boundaries conditions of the computational domain were chosen as follows: “Atmospheric pressure” at the exit section (outflow boundary), a “symmetry line” for the bottom and top section and “wall” for the external faces of the diffuser. To insure that computational conditions do not significantly affect the simulations results, four Reynolds number values and three grid systems had been tested. No significant differences between the obtained maximum velocities were detected. Coefficient wd and the sum wd þ wFlange can be determined by dividing the wind velocity (u) at any point inside the diffuser by the upstream wind velocity (vN) respectively for the diffuser without flange and the flanged one. Only values obtained at several points along the diffusers centerline are discussed for describing the effect of the diffuser height on the airflow. However for evaluating the diffuser accelerating wind flow, all analyses will be based on calculating wd and wFlange for the maximum recorded velocity. Results of simulations had been compared to our experimental data and to other results available in the literature. 2.2. PIV tests PIV tests were performed at ReD ¼ 66,438, in closed loop wind tunnel. The dimensions of the test section were 800 mm (width) 1000 mm (depth) 4000 mm (length). The free stream
M. Kardous et al. / Renewable Energy 56 (2013) 123e128
125
Fig. 3. Computational domain and mesh.
velocity was monitored via a Pitot tube positioned 10 Da upstream from the diffuser, and it was proved to be constant during the test within a 1% uncertainty. The air temperature variations were considered negligible for the current tests. The PIV system was a commercial 2D PIV system from Dantec dynamics. A double pulsed Nd-YAG laser had been used. This delivers energy of 2 65 mJ that illuminate the smoke used as flow seeding with a 1 mm thick sheet. The flow is seeded with micrometer-sized droplets generated by a smog generator. The size of the particles is about 1 mm. The wind tunnel was equipped with two optical accesses for the camera and the laser. A flow Sens camera had been used with a resolution of 1600 1200 pixels, recording double fullframe particle images. The camera is equipped with a 60 mm objective lens at a diaphragm aperture of 2.8. The system: camera and laser, had operated at frequency of 10 Hz. The size of the measurement area had been 168 mm 160 mm. Studio DynamicsÒ software, from Dantec Dynamics was used to compute the instantaneous velocity field. The 1600 1200 pixels images were processed using adaptive correlation. The interrogation window is fixed to 32 32 pixels, providing a spatial resolution of approximately 3.3 3.3 mm2. The overlap ratio between adjacent interrogation windows is 50%, providing instantaneous velocity fields with 99 74 vectors. Subsequently, mean velocity fields were calculated as the average of 500 instantaneous velocity fields. 3. Results and discussions As expected, the most important events in terms of air dynamics had occurred at both ends of the flanged diffuser. All the simulated and experimented diffusers had generated low-pressure region behind the diffuser outlet section, allowing air flow to accelerate inside the narrow inlet section where the maximum of wind velocity was recorded. The same result was found from analysis of PIV measurements (Fig. 4). Upstream, streamlines converge as approaching the
diffuser inlet section, while downstream, due to the flange located at the exit area; two vortices are generated producing an additional adverse pressure. A quantitative analysis of these structures is presented at the end of this part (page 5). A similar result was also obtained by Toshimitsu et al. [19]. Comparison between experimental and simulated set of data for the same diffuser characteristics shows a satisfactory agreement since the difference between the two methods gives an error less than 12% with a correlation coefficient R2 ¼ 0.93 (Fig. 5). This is reassuring about the consistency of the results obtained by both methods. For the diffuser without flange (H ¼ 0), the wind velocity ratio wd was found equal to 1.58, This means that the diffuser without flange is responsible of a wind velocity increase rate of about 58%. For the flanged diffuser, the sum wd þ wFlange was found between 1.64 and 1.81. The contribution of the flange only (wFlange) in increasing wind velocity is calculated to be between 13% and 23%. Fig. 6, illustrates the variation of the ratio u/uN versus a dimensionless length H/Da. It clearly shows two distinct linear zones (two slopes) for two ranges of the ratio H/Da. The first linear zone (zone 1) corresponds to the range of ratios H/Da between 0 and 0.1, and the second one (zone 2) to those bigger than 0.1. The flange height for which H/Da ¼ 0.1 is considered as a critical height (HC) it corresponds to a maximum recorded wind velocity (uC). For the first zone of the curve, wind velocity increases significantly and linearly with the flange height. The slope is equal to 1.245 and the wind velocity ratio passes from 1.58 (no flange) to 1.71 for HC. The ratio u/uN versus H/Da can be described by the following suggested expression:
u=uN ¼ 1:245$H=Da þ 1:577
for H=Da ¼ 0:1
(5)
Values of u/uN deduced from simulations are very well reproduced by equation (5) with a correlation R2 ¼ 0.98.
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Fig. 4. Streamlines of wind flow upstream the diffuser (left) and downstream the diffuser (right) ((a) and (b) simulations; (c) and (d) PIV results).
When the ratio H/Da exceeds the critical value of 0.1 (the second linear zone), the slope becomes too small. It passes from 1.245 to 0.206, then the flange height seems to have no more significant effect on increasing wind velocity. This confirms result obtained by Abe et al. [11]. Indeed, HC needs to be six times bigger to increase the ratio uC/uN only about 5%, at the same time, the effort exerted by the wind on the diffuser could be 2.36 times greater. This will compromise the mechanical stability of the diffuser induced by the interaction Fluid-Structure. This effect is more visible when we refer to uC and HC by plotting u/uC vs. ratio H/HC (Fig. 7).
Otherwise, due to the differences between wind velocities located on the periphery of the outlet section of the diffuser, an internal shear layer is created (Fig. 8). This layer, which is closely related to the intensity of the axial wind velocities, is responsible for the formation of vortices generated by the KelvineHelmholtz instability. Only one vortex is created when the ratio H/Da is less than the critical value Hc/Da and two contra-rotating vortices beyond it. These ones can be completely characterized by their sizes and by the coordinate of their centers.
Fig. 5. u/uN vs. x/D simulations and experimental results.
Fig. 6. Variation of the ratio u/uN versus a dimensionless length H/Da.
M. Kardous et al. / Renewable Energy 56 (2013) 123e128
Fig. 7. Ratio u/uc vs. ratio H/Hc (simulations).
In our case, three lengths D1, D2 and D3 had been chosen to describe the dynamic of the two vortices (Fig. 9). D1 and D2 represent the horizontal distances between the flange and the centers of the two vortices and D3 represents the distance between the two centers. For simulations, the position of the center of a vortex is the point where the wind velocity reaches a zero value. These lengths were deduced graphically in both cases (simulations and experiments). Fig. 10, gives a comparison between simulations and experimental values of D1, D2 and D3; a 22.5% overestimation of simulations lengths values, is observed. Analysis of obtained data shows that the three distances (D1, D2 and D3) increase linearly with the height of the flange. This means that vortices move in the flow direction as the flange height increases. When we had plotted these distances against the flange height (H), we found that the data points were very well aligned along a straight line (Fig. 11). The slope values indicate that the vortex 2 moves slightly faster than the vortex 1 and the two vortices move away from each other more slowly. This finding is also highlighted by Fig. 12 which displays, for each flange height, zero isovelocity contour that passes by the centers C1 and C2 of the two swirls and delimits the swirling zone located downstream. As flange height increases, swirls seem to
Fig. 9. Distances characterizing vortices located downstream the flange.
Fig. 10. D1, D2 and D3 value’s obtained by both methods.
Fig. 8. Shear layer located at the periphery of the diffuser outlet section.
Fig. 11. Distances (D1, D2 and D3) of vertices as a function of flange height.
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contra-rotating vortices were created at this location. The effect of these vortices was assessed on the base of the position of their centers. Analysis of data shows that vortices move in the flow direction as the flange height increases. 5- The no significant effect of flange height observed from HC can be explained by the remoteness of vortices from the flange.
References
Fig. 12. Expansion of vortices generated by the KelvineHelmholtz instability located downstream the diffuser with the increase of the flange height (Full and empty markers represent respectively the centers C1 and C2).
lengthen in the streamwise direction and to extend in the two directions when the flange height becomes taller. At the same time flange height becomes without significant effect to increase wind velocity. This clearly suggests that beyond a certain flange height (HC) and therefore from certain position of the vortices, the value of the depression located directly downstream of the diffuser undergoes trivial changes which are inadequate to increase the wind velocity at the inlet section of the diffuser. 4. Conclusion Numerical simulations, Particle-Image-Velocimetry visualizations and wind tunnel experiments had been carried out to get a better understanding of the effect of the flange height on wind velocity increase at the inlet section of an empty flanged diffuser. Ten flange heights (H) with a ratio (H/Da) ranged from 0 (no flange) to 60%, were tested. Results show that: 1- When a flange is mounted at the diffuser exit area, an additional acceleration of the wind occurs at its inlet section. 2- The diffuser without flange is responsible of a wind velocity increase rate of about 58% while for the flanged one, this rate ranged from 64 to 81%. The contribution of the flange only is calculated to be between 13 and 23%. 3- A critical ratio HC/Da ¼ 0.1 has been found. Beyond this value, the flange height seems to be without significant effect to increase wind velocity. 4- Due to the differences between wind velocities located on the periphery of the outlet section of the diffuser, two
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