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Computational analysis of a solar energy induced vortex generator
Applied Thermal Engineering 98 (2016) 1036–1043
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Computational analysis of a solar energy induced vortex generator Abdullah Mohiuddin a, Eray Uzgoren b,* a b
Sustainable Environment and Energy Systems, Middle East Technical University, Northern Cyprus Campus, Mersin 10, Turkey Mechanical Engineering Program, Middle East Technical University, Northern Cyprus Campus, Mersin 10, Turkey
H I G H L I G H T S
• • • •
A novel device mimicking dust devils is proposed for solar energy applications. CFD model is devised to analyze influence of geometric parameters on the swirl. Parametric study on device geometry reveals optimal vane height and width. Vortex stability and torque strength increase at vane angles greater than 30°.
A R T I C L E
I N F O
Article history: Received 20 October 2015 Accepted 1 January 2016 Available online 12 January 2016 Keywords: Solar updraft tower Free convection OpenFOAM Buoyancy induced vortex
G R A P H I C A L
A B S T R A C T
Hot rising air acquires swirl due to vane angle for better power production opportunities Turbine
Air
A B S T R A C T
This study presents a computational analysis of a device that mimics dust devils in a controlled environment in order to explore its capacity as an energy conversion apparatus in solar energy applications. Concept is built upon the buoyancy effect over a heated plate surrounded by stationary vertical thin plates (vanes), which cause swirl in the raising air. The novelty of the paper is that it is the first parametric study that investigates effects of vane width, vane height, number of vanes, and vane angle on the vertical flow rate of the proposed device. It is found that (i) the optimal vane width is 1.4R, (ii) reduction in spacing between the vanes improves vertical flow strength, (iii) minimum vane height is 1.4R, and (iv) high vane angles increase swirl and hence vortex stability to yield better torque production opportunities with the high air speeds away from the vertical centerline. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The idea of harvesting energy through rising air has been explored in various renewable energy applications. One promising example is the solar updraft towers, which generate mechanical energy in terms of turbine shaft work from rising hot air that is heated by solar energy [1,2]. According to a recent review by Zhou and Xu on solar updraft towers [3], one of the fundamental challenges is related to the low energy conversion efficiency owing to
* Corresponding author. Tel.: +903926612925; fax: +903926612999. E-mail address: [email protected] (E. Uzgoren). http://dx.doi.org/10.1016/j.applthermaleng.2016.01.005 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
limitations related to tower’s height. Reasonable energy conversion efficiencies are only possible for towers with heights ranging from 100 m and 1000 m but construction of such towers bring additional challenges related to construction materials’ availability, investment cost, and environmental concerns. Zhang et al. [4] recently proposed a device to replace the tower by a vertical columnar vortex. Such a vortex can be formed with the help of vertical planes (vanes) beneath the solar panels, guiding warm air tangentially toward the center of the collectors at a certain angle so that the rising air acquires tangential and radial velocity. This idea was previously used by Fitzjarrald [5] in 1973 in an experimental setup with 20 vanes to study naturally occurring dustdevils, which are small-sized vertical columnar vortices with high
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
Cyclic
III, VI
Heated plate
Computational domain
Wall
Vanes
1037
θ
II, V
h I,IV Φ Cyclic
Vanes R
c
Surrounding floor Surrounding floor
Fig. 1. Flow geometry, computational domain and boundary conditions.
concentrations of kinetic energy. Simpson et al. [6] used a similar setup to explore its power generation capabilities through a turbine placed at the top of the vanes. They used a heated square plate surrounded by 12 planar aluminum vanes, each of which was 35 cm in width and 60 cm in height. They were able to demonstrate the formation of a meter scale vortex of 4 m high and a core diameter of 5–25 cm, which was able to spin a rotor at 15–25 rpm at a plate temperature 22 °C higher than the ambient temperature. While they investigated power production opportunities at various temperature differences, they did not focus on scaling of geometrical parameters. Zhang et al. [4] investigated geometrical scaling of a similar device with 8 curved vanes through experiments on a prototype with 2 m radius and numerical analyses for 20 and 200 m radii. They observed that the maximum speed scales with Froude number and identified that the tangential velocity increased the most when the vane angle was changed from 30° to 60°. Michaud and Monrad [7,8] demonstrated the energy conversion potential based on a thermodynamic model as part of commercialization opportunities within cooling towers of already existing power plants. Natarajan [9] used CFD simulations to explore the flow induced by such a device. Device proposed by Refs. 4–9 relies on the swirl of the uprising air owing to vanes, which direct air to flow tangentially to the convective plume. These studies have mostly reported vortex formation at meter scale and it is still not clear whether similar flow conditions for vortex growth are attainable at larger scales for costeffective commercial applications [7]. Furthermore, such large scale applications would also require certain measures to be taken for flow control to relieve safety and environmental concerns [8]. Thus, a better understanding of flow’s characteristics is needed. The present study investigates the influence of geometrical and physical parameters of such a device on the flow field using numerical analysis tools. Specifically, vertical flow features are examined through simulations of various vane widths, various vane spacing, various vane heights, and vane angles to understand their role so that better designs can be developed for power production purposes. 2. Methodology Numerical simulations are carried out using OpenFOAM, opensource finite volume based computational fluid dynamics software [10]. Basic flow geometry is shown in Fig. 1, which consists of a circular heated plate at an elevated temperature surrounded by an unheated floor. Both circular heated plate and floor are open to the
atmosphere. The heated plate is surrounded by a number of vertical thin flat plates, referred to vanes throughout the paper. Vertical vanes are considered as the core focus of this paper, as they guide the entrained flow off the center to form a vortex. Numerical experiments are carried out to investigate the influence of vane width, vane height, vane angle and heated plate’s radius. Vane angle is the angle between the vane and an imaginary radial line stretched from the center of heated surface, vane width is the horizontal vane length, and vane height is the distance from the floor to the top of the vane as shown in Fig. 1.
2.1. Numerical method The governing equations for incompressible fluid flow including the Boussinesq approximation are given as follows:
∇u = 0
(1)
∂u ⎞ ρo ⎛⎜ + (u ⋅∇ ) u⎟ = −∇p + μ∇ 2u + ρo (1 − βΔT ) g ⎝ ∂t ⎠
(2)
The scalar transport-diffusion equation for the temperature is given as follows:
∂T + (u ⋅∇ ) T = α∇ 2T + ϕ ∂t
(3)
Equations (1)–(3) are solved using OpenFOAM’s buoyantBoussineqPimpleFoam, which is a precompiled solver using a pressure-based method for incompressible transient flows with Boussinesq approximation for the buoyant forces. Standard k–ε twoequation turbulence model is used in simulations. Specifics of simulation setup are summarized in Table 1, while readers can refer to Ref. 11 for additional details. Flow domain is defined by a truncated circular plate in shape of a piece of pie (sector) with a span characterized by the span angle as shown in Fig. 1. All vertical sides of the sector except vanes are modeled using cyclic boundary condition for all transport variables. Vertical vanes, heated plate and surrounding wall are considered as isothermal walls. Outer circumferential vertical surface switches between constant pressure/temperature for inflow and zero pressure/temperature gradient for outflow conditions. Simulations are initialized with zero velocity field and ambient temperature and carried out until reasonable steady state conditions are satisfied,
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A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
Table 1 Details of simulation setup. OpenFOAM v2.3.1 Hexahedral structured Finite volume buoyantBoussinesqPimpleFoam PISO Scheme Interpolation Implicit Euler Gauss Linear Gauss Linear/Upwind Gauss Gauss linear uncorrected
Radial Outflow
Vane
Software/Tool Mesh Method Solver Pressure–velocity coupling Discretization Time Gradient Divergence Laplacian Turbulence Model Two-equation model Boundary conditions Outer vertical surface Top surface Isothermal walls Span’s lateral vertical surface
Radial Inflow
RAS k–ε ( C μ = 0.09 , C1 = 1.44 , C 2 = 1.92 , σ ε = 1.3 ) Velocity Temperature pressureInletOutlet inletOutlet inletOutlet inletOutlet fixedValue fixedValue cyclic cyclic Fig. 2. Velocity field and vertical flow rate within the vane region.
such that the variation of two independent points in time becomes negligible. 2.2. Computational grid and verification Structured grid, based on mostly hexahedra cells with wedges at the sector’s center, is generated for each case represented by a different set of geometrical parameters. Each grid consists of six blocks as marked with I–VI in Fig. 1. Blocks I–III for the vane region while blocks IV–VI are placed on the top of lower blocks I–III. This setting makes it possible to use different spacing in different blocks. The proposed cyclic model is verified using sector spans of φ = 18°, 30°, 42°, 60° against a complete circular plate excluding vertical vanes. All domains are meshed with the same uniform cell spacing, i.e. 1.2° in angular direction, 0.032 m in axial direction and 0.04 m in radial direction. The heated plate is imposed at a constant surface temperature at 314 K, while both the surrounding floor and ambient air are at 307 K. It is found that root mean square error (RMSE) based on the velocity field for different angular widths with respect to the full circular mesh remained in the order of 10−6 and hence validates the use of cyclic conditions independent of the sector span. Grid convergence is also studied with the same conditions at a sector span of 30° by changing the grid spacing in all directions. Root mean square error for the velocity field is computed for each simulation with respect to the grid with 86,000 cells. Overall order of accuracy of the numerical scheme is found to be approximately 1.50 throughout simulations using three additional mesh spacing. Columnar vortex’s tangential velocity variation at z/h = 0.5 is compared against the theoretical vortex models such as Rankine vortex model, Burgers vortex model, and empirical model of Vatistas et al. [12], which have been used by several authors to represent dust devils [13–17]. Tangential velocity field obtained by our model agrees very well with the empirical vortex model for concentrated vortices as proposed by Vatistas et al. [12]. 3. Results and discussion 3.1. General description of the flow field Vertical flow is considered to characterize the convective vortex, as the flow primarily happens as a result of the buoyancy force. Radial inflow and any subsequent swirling motion are considered to be secondary mechanisms of columnar vortex formation. Fig. 2 presents qualitative description of the flow field with respect to the variation of the vertical flowrate. Vertical flow rate provides
information about the radial inflow through the vanes, which can help distinguish regions of radial inflow, growth and decay of the column in the vertical direction. This is as a result of continuity, which suggests that the flow rate in the vertical direction increases as a result of entrained air from the surroundings in the radial direction. Increase in average vertical velocity signifies radial inflow, which is at maximum near the bottom, where the temperature gradient is large. Increase in vertical flow continues but at a decreasing rate and reaches a maximum around mid-height of the vane. It continues to decay with elevation, but at a slower rate than the bottom half. The slope becomes weaker when the flow has tangential velocity component. Significant amount of radial inflow happens near the bottom, which triggers tangential velocity component owing to the vane angle. Vane angles greater than 0° helps the formation of a vortex and delays radial outflow. Investigations are based on a normalized flow rate, calculated at over a fixed area above the heated plate as follows: 2Π
R
Vz ∫0 ∫0 uz rdθ dr = Vzc uzc (π R 2 )
(4)
When the numerator of Eq. (4) is represented by the mean axial velocity, normalized flow rate also represents a ratio of average vertical speed to a characteristic vertical speed. Characteristic vertical speed, uzc , can be obtained by matching Reynolds number to squareroot of Grashof number as follows:
uzc = g βΔTR
(5)
Furthermore, Eq. (4) can be viewed as the Froude number, the ratio of inertia to the buoyant forces.
Fr =
Vz = Vzc
uz ,m g βΔTR
(6)
A similar form of Froude number was also used by Zhang et al. [4] with a slight difference as they defined Froude number as the ratio of maximum speed to the characteristic speed as given in Eq. (5). 3.2. Parametric study A columnar vortex with high and concentrated kinetic energy relies on the strength and growth of the vertical flow, caused by accumulating higher magnitudes of radial inflow and tangential velocity component preventing radial outflow. Geometrical
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
Vane width 0.4R
Vane width R
Vane width 1.4R 0.25
0.05
)1⁄2
0.20
0.04
Δ
0.15
0.03
⁄(
Vz / Vzc
0.06
0.02
1039
Vane width 1.6R
0.10 0.05
0.01
0.00
0 0
0.2
0.4
0.6
0.8
0
1
0.2
0.4
z/h
0.6
0.8
1
r/R
Fig. 3. Vertical flow rate along the vane height and vertical velocity profile at the vane’s mid-height, z = 0.5 h.
angle of 0°. It is found that increasing the vane height continuously causes an increase in the magnitude of the vertical flow rate, suggesting that the height also has an important role in terms of flow similarity. For vane heights less than 1.2R of the plate, flow behaves different than those with heights above 1.4R. The location of the peak vertical flow rate, as marked with filled markers, is about 0.4R for a vane width of R, while peak’s elevation is pushed in the upward direction for both taller and shorter vanes. In addition, the increase in vertical velocity magnitude from a vane height of 1.2R to 1.4R is much larger than the increase from 1.4R to 1.6R. Curvefit on the peak Froude number reveals its relation to the vane height as follows:
parameters are investigated for their influence on the flow field. These parameters are, namely, vane width, the vane height, the spacing between vanes and the vane angle. Following Ref. 6, flow conditions for the base case are as follows: R = 0.5 m, h = 1.2R , c = 0.8R , θ = 30° and N = 12 ; To = 306 K and Tp = 328 K . Effects of vane width, vane height, and spacing between vanes are considered first at a vane angle of 0°, at which no or negligible tangential velocity is anticipated. The temperature difference is 22 °C. The interplay between the radial inflow, which is directed exactly to the center, but guided through the vanes, is observed to characterize the influence of the vanes. Fig. 3 shows the influence of vane width from 0.4R to 1.6R on the vertical flow rate and the corresponding vertical velocity profile in radial direction at an elevation of 0.5h. It is observed that nondimensional vertical velocity improves when vane width is increased up to 1.4R. Increasing the vane width greater than 1.4R does not cause any significant change in the non-dimensional vertical velocity profile. Peaks of vertical velocity happen around an elevation of 0.5h for all vane widths. The maximum velocity occurs at r = 0.4R when vane width is 0.4R and it gets closer to the center as the width increases. The velocity profile remains the same for widths 1.4R and 1.6R, indicating viscous effects related to vane’s boundary layer do not influence the upward flow significantly. This suggests that the width of the vanes should at least be 1.4R to have larger flow rates. Fig. 4 shows the variation of vertical flow rate when the vane height is varied from 0.6R to 1.6R for a vane width of 1.4R and a vane
(7)
Fig. 5 shows the influence of the spacing between the vanes through simulations of 6, 12 and 18 vanes. Large spacing between the vanes shows a reduced vertical flow rate, and increase in the number of vanes causes the flow rate continue to increase and shifts the location of peak flow rate upward, yielding better stability. The vertical velocity variation in radial direction in Fig. 5 shows that the peak vertical velocity is higher near the centerline for 6 vanes (60° spacing) while it decays quicker away from the radius than those with more vanes. Increasing number of vanes from 6 to 12 causes the peak shift away from the center of the plate. Even though the peak is located at a different radial location for each case, the average
Vane height 0.6R
Vane height 0.8R
Vane height R
Vane height 1.2R
Vane height 1.4R
Vane height 1.6R
0.08
0.50
0.07
0.45
)1⁄2
0.35
Δ
0.40
0.06
0.30
0.05 0.04
0.25
⁄(
Vz / Vzc
⎧h1.5 h ≤ 1.2R ⎩ h h ≥ 1.4R
(Vz Vzc )peak ∼ ⎨
0.03
0.20 0.15
0.02
0.10
0.01
0.05 0.00
0 0
0.2
0.4
0.6
z/h
0.8
1
0
0.2
0.4
0.6
0.8
1
r/R
Fig. 4. Vertical flow rate for various vane heights and corresponding peak vertical velocity profiles at locations shown by filled markers.
1040
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
0.06
0.40
6 vanes 12 vanes 18 vanes
0.20 0.15
0.03
18 vanes
0.25
Δ
0.04
12 vanes
0.30
⁄(
Vz / Vzc
)1⁄2
0.05
6 vanes
0.35
0.10 0.05
0.02
0.00 0
0.2
0.4
z/h
0.6
0.8
1
0
0.2
0.4
r/R
0.6
0.8
1
Fig. 5. Vertical flow rate for different numbers of vanes and velocity profiles at locations shown by filled markers.
and tangential velocities are largest there. The peak of the tangential velocity is higher for vane angles greater than 25°, which illustrates vortex strengthening and improved kinetic energy when the vanes have an angle of 25° or more. Fig. 7 shows peak vertical velocity variation for various vane angles. The peak of vertical flow rate increases when the vane angle is higher than 30° (tanθ = 0.57), while it gets saturated for vane angles of 45° and 50°. For smaller vane angles, i.e. 15° and 25°, the vertical velocity profile is similar to the one presented at height of 0.2 R in Fig. 6. For higher angles, vertical velocity profiles at peaks are also similar to those with smaller angles but with higher magnitude especially away from the radius. The major difference between high and small vane angles is that high vane angle cases have a significantly larger tangential velocity profile, i.e. four times more in magnitude than that of 15° vane angle. The peak of the tangential
vertical flow is shown to increase with number of vanes due to the improved flow for r/R > 0.3. Lastly, vertical flow rate and corresponding radial velocity profiles are examined for vane angles between 15° and 50°. Fig. 6 shows the non-dimensional vertical velocity for a radius of R = 0.5 m, a vane width of 1.4R, and a vane height of R at 22 °C temperature difference. The peak increases with the vane angle, showing that induced tangential velocity continues to bring additional radial inflow. At lower elevations, i.e. z smaller than 0.2h, the vertical flow rate for all angles are the same despite the differences in vertical and tangential velocity profiles at 0.2R. At lower vane angles, the velocity profile is similar as the formation of a central plume, i.e. vertical velocity is maximum at the centerline and decreases continuously with r. For vane angles greater than 25°, maximum speed happens around r = 0.2R, as both vertical
15º
25º
35º
45º
0.20
0.20
0.04
0.16
0.16
0.035
0.12
Δ
0.12
Δ 0.08
0.08
q
⁄(
0.03
⁄(
Vz / Vzc
)1⁄2
)1⁄2
0.045
0.04
0.025
0.04
0.00
0.02
0
0.2
0.4
0.6
0.8
0.00
0
1
z/h
0.2
0.4
0.6
0.8
1
0
r/R
0.5
1
r/R
0.5
1
tan( )
1.5
0.01 0.00
0.00
0
0.02
)1⁄ 2 Δ q
⁄(
0.05
⁄(
Δ
0.10
)1⁄2
0.042 0.04
15º 25º 35º 45º 50º
0.038 0.036
Peak of Vz / Vzc
0.044
Fig. 6. Vertical flow rate and velocity profiles at variation z = 0.2 R for various vane angles.
0
0.2
0.4 0.6 r/R
0.8
1
0
0.2
0.4 0.6 r/R
Fig. 7. Peak vertical flow rate and corresponding velocity profiles at various vane angles.
0.8
1
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
Fig. 8 shows that Swirl number is high at lower elevations for each vane angle, and it follows a similar pattern of decay in the upward direction.
1.2
Swirl No
1
15º
25º
30º
40º
45º
50º
35º
0.8
3.3. Flow-similarity estimation
0.6
In order flow to reach speeds suitable for wind turbines, i.e. greater than 3 m/s, it is necessary to consider flow similarity when temperature difference or size changes. Both together represent the amount of energy input to the system. For this purpose, the similarity of the flow is studied when the system is exposed to different temperature differences and various sizes of the same flow geometry. The base case is modified for vane height and vane width as follows: h = 1.4 R , and c = 1.4 R . Fig. 9 shows the non-dimensional average vertical velocity with height at temperature differences ranging from 12 °C to 20 °C. Features of the flow field agree well for all temperatures considered, and the vertical velocity scales with the square root of temperature difference between the heated plate and the ambient. Geometric scaling is investigated on the same geometry by changing the radius, the vane width and the vane height using the same scaling factor, S, ranging from 0.6 to 1.4. As the device is to be used with air, the thermo-physical properties are kept the same for all cases. Fig. 10 shows that the non-dimensional average vertical velocity continuously decreases when the device is enlarged. This indicates that using Froude number alone does not yield dynamically similar flows as the flow field features become different with geometric scaling. In fact, the peak of the normalized velocity is found to decay with S−2 as shown in Fig. 10. The differences in the flow features are illustrated through the streamline plots presented in Fig. 11. For the case with S = 0.6, circulation zone at the edge of the vane region influences the radial
0.4 0.2 0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
h/H Fig. 8. Swirl number variation for various vane angles. Dash lines represent fitted power curves.
velocity happens about 0.6R, which would yield better torque extraction opportunities. Swirl number (Sw) provides a comparison between the tangential and axial components of velocities at a particular elevation. This information is useful in determining the angle of attack of the turbine blade, which can be used to utilize tangential velocity more at high Swirl numbers. Swirl number is computed and plotted against scaled elevation levels for different vane angles in Fig. 8 using the following equation:
uz uθ r 2dr
(8)
R
R∫ uz 2rdr 0
0.5
0.07 0.06
)1⁄2
0.4
0.05
0.04
Δ
Vz / Vzc
ΔT 12°C ΔT 14°C ΔT 16°C ΔT 18°C ΔT 20°C
0.45 0.35 0.3 ΔT 12°C ΔT 14°C ΔT 16°C ΔT 18°C ΔT 20°C
0.03 0.02 0.01
⁄(
R
0
0.25 0.2 0.15
0.1 0.05
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
z/h
0.6
0.8
1
r/R
Fig. 9. Vertical flow rate and velocity profile for various temperature differences.
0.25
0.06
1,4 S 1,2 S 1S 0,8 S 0,6 S
0.15
0.05
Peak of Vf / Vfc
0.2
Vz / Vzc
Sw
∫ =
1041
0.1 0.05
0.04 0.03 Vf /Vfc = 0.02S -2.10
0.02 0.01
0 0
0.2
0.4
0.6
z/h
0.8
1
0 0.6
0.8
1
1.2
Scaling factor S
Fig. 10. Vertical flow rate characterized by the scaling factor.
1.4
z
Vane
1.4R
Vane
1.96R
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
0.84R
1042
z r
0.6R
0.6(R+c)
Vane
z r
R
R+c
r
1.4R
1.4(R+c)
Fig. 11. Streamlines obtained for the scaled geometry using S = 0.6, S = 1.0, and S = 1.4. Colors represent the vertical velocity magnitude, red for maximum and blue for minimum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
inflow characteristic near the heated plate. This causes higher average flow over the heated plate. On the other hand, when the scaling parameter, S, increases, circulation gets weaker causing a decay in the magnitude of radial inflow and hence the vertical flow over the heated plate. The weakening of the circulation zone is related to the enlarged spacing between the vanes and how it compares to the viscous effects. Fixing the spacing between the vanes around the heated plate instead of the angle can be considered for higher radial inflow and allow the possibility of realistic power applications through an enlarged space. 4. Conclusion A numerical model is developed using OpenFOAM to investigate flow characteristics of a device that mimics dust-devils in a controlled environment. A cyclic grid is utilized to reduce the computational time, memory space and post processing time and following results are found:
• • • • • •
Vane width should at least be 1.4R to obtain maximum vertical speed. Beyond 1.4R, it is found that there is no improvement. Increasing the vane height improves radial inflow. Vane spacing should be decreased for larger flowrates. Increasing vane angle improves the magnitude of tangential velocities, which cause improved vortex stability and delay for radial outflow. Swirl number is higher at higher vane angles and lower heights, and decreases with height obeying power law. Froude number alone is not sufficient to describe the flow similarity due to the interplay between the vane spacing and the viscous effects.
It is concluded that columnar vortex flows can be obtained through changing the vane width, height, spacing and angle to redistribute the concentration of energy from the center to the distances away from center for higher yield of energy.
Nomenclature
c Fr g h N p R r S Sw t T u V z
Vane width [m] Froude number ≡ ratio of flow inertial force to gravitational force [dimensionless] Gravitational acceleration [m s−2] Vane height [m] Number of vanes Pressure [Pa] Radius of the heated plate [m] Position in radial direction [m] Scaling factor ≡ ratio of plate radius to the reference plate radius [dimensionless] Swirl number ≡ ratio of axial flux of the tangential momentum to axial flux of axial momentum [dimensionless] Time [s] Temperature [K] Velocity vector [m s−1] Vertical volumetric flow rate [m3 s−1] Position in axial direction [m]
Greek symbols α Thermal diffusivity [m2 s−1] Coefficient of thermal expansion [K−1] β μ Dynamic viscosity [Pa s] ν Kinematic viscosity [m2 s−1] φ Span angle [degrees] ρ Density [kg m−3] θ Vane angle [degrees] ϕ Source term in energy equation [K/s] Subscripts c Characteristic m Mean/average o Reference p Plate r Radial component z Axial component
Acknowledgement References This research was supported by a Marie Curie International Reintegration Grant within the 7th European Community Framework Programme (Project 268426).
[1] Z. Zou, S. He, Modeling and characteristics analysis of hybrid cooling-towersolar-chimney system, Energy Convers. Manage. 95 (2015) 59–68.
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[2] K. Chen, J. Wang, Y. Dai, Y. Liu, Thermodynamic analysis of a low-temperature waste heat recovery system based on the concept of solar chimney, Energy Convers. Manage. 80 (2014) 78–86. [3] X. Zhou, Y. Xu, Solar updraft tower power generation, Sol. Energy (2014). In press. [4] M. Zhang, X. Luo, T. Li, L. Zhang, X. Meng, K. Kase, et al., From dust devil to sustainable swirling wind energy, Sci. Rep. 5 (2015) 8322. [5] D.E. Fitzjarrald, A laboratory simulation of convective vortices, J. Atmos. Sci. 30 (5) (1973) 894–902. [6] M.W. Simpson, A.J. Pearlstein, A. Glezer Power generation from concentrated solar-heated air using buoyancy-induced vortices. International Conference on Renewable Energies and Power Quality (ICREPQ’13), Bilbao (Spain), March 20-22, 2013. [7] L. Michaud, B. Monrad, Energy from convective vortices, Appl. Mech. Mater. 283 (2013) 73–86. [8] Atmospheric vortex engine. (accessed 12.04.15).
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[9] D. Natarajan Numerical simulation of tornado-like vortices (Ph.D. thesis), The University of Western Ontario, 2011. [10] OpenFOAM® Documentation.
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Applied Thermal Engineering j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / a p t h e r m e n g
Research Paper
Computational analysis of a solar energy induced vortex generator Abdullah Mohiuddin a, Eray Uzgoren b,* a b
Sustainable Environment and Energy Systems, Middle East Technical University, Northern Cyprus Campus, Mersin 10, Turkey Mechanical Engineering Program, Middle East Technical University, Northern Cyprus Campus, Mersin 10, Turkey
H I G H L I G H T S
• • • •
A novel device mimicking dust devils is proposed for solar energy applications. CFD model is devised to analyze influence of geometric parameters on the swirl. Parametric study on device geometry reveals optimal vane height and width. Vortex stability and torque strength increase at vane angles greater than 30°.
A R T I C L E
I N F O
Article history: Received 20 October 2015 Accepted 1 January 2016 Available online 12 January 2016 Keywords: Solar updraft tower Free convection OpenFOAM Buoyancy induced vortex
G R A P H I C A L
A B S T R A C T
Hot rising air acquires swirl due to vane angle for better power production opportunities Turbine
Air
A B S T R A C T
This study presents a computational analysis of a device that mimics dust devils in a controlled environment in order to explore its capacity as an energy conversion apparatus in solar energy applications. Concept is built upon the buoyancy effect over a heated plate surrounded by stationary vertical thin plates (vanes), which cause swirl in the raising air. The novelty of the paper is that it is the first parametric study that investigates effects of vane width, vane height, number of vanes, and vane angle on the vertical flow rate of the proposed device. It is found that (i) the optimal vane width is 1.4R, (ii) reduction in spacing between the vanes improves vertical flow strength, (iii) minimum vane height is 1.4R, and (iv) high vane angles increase swirl and hence vortex stability to yield better torque production opportunities with the high air speeds away from the vertical centerline. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The idea of harvesting energy through rising air has been explored in various renewable energy applications. One promising example is the solar updraft towers, which generate mechanical energy in terms of turbine shaft work from rising hot air that is heated by solar energy [1,2]. According to a recent review by Zhou and Xu on solar updraft towers [3], one of the fundamental challenges is related to the low energy conversion efficiency owing to
* Corresponding author. Tel.: +903926612925; fax: +903926612999. E-mail address: [email protected] (E. Uzgoren). http://dx.doi.org/10.1016/j.applthermaleng.2016.01.005 1359-4311/© 2016 Elsevier Ltd. All rights reserved.
limitations related to tower’s height. Reasonable energy conversion efficiencies are only possible for towers with heights ranging from 100 m and 1000 m but construction of such towers bring additional challenges related to construction materials’ availability, investment cost, and environmental concerns. Zhang et al. [4] recently proposed a device to replace the tower by a vertical columnar vortex. Such a vortex can be formed with the help of vertical planes (vanes) beneath the solar panels, guiding warm air tangentially toward the center of the collectors at a certain angle so that the rising air acquires tangential and radial velocity. This idea was previously used by Fitzjarrald [5] in 1973 in an experimental setup with 20 vanes to study naturally occurring dustdevils, which are small-sized vertical columnar vortices with high
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
Cyclic
III, VI
Heated plate
Computational domain
Wall
Vanes
1037
θ
II, V
h I,IV Φ Cyclic
Vanes R
c
Surrounding floor Surrounding floor
Fig. 1. Flow geometry, computational domain and boundary conditions.
concentrations of kinetic energy. Simpson et al. [6] used a similar setup to explore its power generation capabilities through a turbine placed at the top of the vanes. They used a heated square plate surrounded by 12 planar aluminum vanes, each of which was 35 cm in width and 60 cm in height. They were able to demonstrate the formation of a meter scale vortex of 4 m high and a core diameter of 5–25 cm, which was able to spin a rotor at 15–25 rpm at a plate temperature 22 °C higher than the ambient temperature. While they investigated power production opportunities at various temperature differences, they did not focus on scaling of geometrical parameters. Zhang et al. [4] investigated geometrical scaling of a similar device with 8 curved vanes through experiments on a prototype with 2 m radius and numerical analyses for 20 and 200 m radii. They observed that the maximum speed scales with Froude number and identified that the tangential velocity increased the most when the vane angle was changed from 30° to 60°. Michaud and Monrad [7,8] demonstrated the energy conversion potential based on a thermodynamic model as part of commercialization opportunities within cooling towers of already existing power plants. Natarajan [9] used CFD simulations to explore the flow induced by such a device. Device proposed by Refs. 4–9 relies on the swirl of the uprising air owing to vanes, which direct air to flow tangentially to the convective plume. These studies have mostly reported vortex formation at meter scale and it is still not clear whether similar flow conditions for vortex growth are attainable at larger scales for costeffective commercial applications [7]. Furthermore, such large scale applications would also require certain measures to be taken for flow control to relieve safety and environmental concerns [8]. Thus, a better understanding of flow’s characteristics is needed. The present study investigates the influence of geometrical and physical parameters of such a device on the flow field using numerical analysis tools. Specifically, vertical flow features are examined through simulations of various vane widths, various vane spacing, various vane heights, and vane angles to understand their role so that better designs can be developed for power production purposes. 2. Methodology Numerical simulations are carried out using OpenFOAM, opensource finite volume based computational fluid dynamics software [10]. Basic flow geometry is shown in Fig. 1, which consists of a circular heated plate at an elevated temperature surrounded by an unheated floor. Both circular heated plate and floor are open to the
atmosphere. The heated plate is surrounded by a number of vertical thin flat plates, referred to vanes throughout the paper. Vertical vanes are considered as the core focus of this paper, as they guide the entrained flow off the center to form a vortex. Numerical experiments are carried out to investigate the influence of vane width, vane height, vane angle and heated plate’s radius. Vane angle is the angle between the vane and an imaginary radial line stretched from the center of heated surface, vane width is the horizontal vane length, and vane height is the distance from the floor to the top of the vane as shown in Fig. 1.
2.1. Numerical method The governing equations for incompressible fluid flow including the Boussinesq approximation are given as follows:
∇u = 0
(1)
∂u ⎞ ρo ⎛⎜ + (u ⋅∇ ) u⎟ = −∇p + μ∇ 2u + ρo (1 − βΔT ) g ⎝ ∂t ⎠
(2)
The scalar transport-diffusion equation for the temperature is given as follows:
∂T + (u ⋅∇ ) T = α∇ 2T + ϕ ∂t
(3)
Equations (1)–(3) are solved using OpenFOAM’s buoyantBoussineqPimpleFoam, which is a precompiled solver using a pressure-based method for incompressible transient flows with Boussinesq approximation for the buoyant forces. Standard k–ε twoequation turbulence model is used in simulations. Specifics of simulation setup are summarized in Table 1, while readers can refer to Ref. 11 for additional details. Flow domain is defined by a truncated circular plate in shape of a piece of pie (sector) with a span characterized by the span angle as shown in Fig. 1. All vertical sides of the sector except vanes are modeled using cyclic boundary condition for all transport variables. Vertical vanes, heated plate and surrounding wall are considered as isothermal walls. Outer circumferential vertical surface switches between constant pressure/temperature for inflow and zero pressure/temperature gradient for outflow conditions. Simulations are initialized with zero velocity field and ambient temperature and carried out until reasonable steady state conditions are satisfied,
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Table 1 Details of simulation setup. OpenFOAM v2.3.1 Hexahedral structured Finite volume buoyantBoussinesqPimpleFoam PISO Scheme Interpolation Implicit Euler Gauss Linear Gauss Linear/Upwind Gauss Gauss linear uncorrected
Radial Outflow
Vane
Software/Tool Mesh Method Solver Pressure–velocity coupling Discretization Time Gradient Divergence Laplacian Turbulence Model Two-equation model Boundary conditions Outer vertical surface Top surface Isothermal walls Span’s lateral vertical surface
Radial Inflow
RAS k–ε ( C μ = 0.09 , C1 = 1.44 , C 2 = 1.92 , σ ε = 1.3 ) Velocity Temperature pressureInletOutlet inletOutlet inletOutlet inletOutlet fixedValue fixedValue cyclic cyclic Fig. 2. Velocity field and vertical flow rate within the vane region.
such that the variation of two independent points in time becomes negligible. 2.2. Computational grid and verification Structured grid, based on mostly hexahedra cells with wedges at the sector’s center, is generated for each case represented by a different set of geometrical parameters. Each grid consists of six blocks as marked with I–VI in Fig. 1. Blocks I–III for the vane region while blocks IV–VI are placed on the top of lower blocks I–III. This setting makes it possible to use different spacing in different blocks. The proposed cyclic model is verified using sector spans of φ = 18°, 30°, 42°, 60° against a complete circular plate excluding vertical vanes. All domains are meshed with the same uniform cell spacing, i.e. 1.2° in angular direction, 0.032 m in axial direction and 0.04 m in radial direction. The heated plate is imposed at a constant surface temperature at 314 K, while both the surrounding floor and ambient air are at 307 K. It is found that root mean square error (RMSE) based on the velocity field for different angular widths with respect to the full circular mesh remained in the order of 10−6 and hence validates the use of cyclic conditions independent of the sector span. Grid convergence is also studied with the same conditions at a sector span of 30° by changing the grid spacing in all directions. Root mean square error for the velocity field is computed for each simulation with respect to the grid with 86,000 cells. Overall order of accuracy of the numerical scheme is found to be approximately 1.50 throughout simulations using three additional mesh spacing. Columnar vortex’s tangential velocity variation at z/h = 0.5 is compared against the theoretical vortex models such as Rankine vortex model, Burgers vortex model, and empirical model of Vatistas et al. [12], which have been used by several authors to represent dust devils [13–17]. Tangential velocity field obtained by our model agrees very well with the empirical vortex model for concentrated vortices as proposed by Vatistas et al. [12]. 3. Results and discussion 3.1. General description of the flow field Vertical flow is considered to characterize the convective vortex, as the flow primarily happens as a result of the buoyancy force. Radial inflow and any subsequent swirling motion are considered to be secondary mechanisms of columnar vortex formation. Fig. 2 presents qualitative description of the flow field with respect to the variation of the vertical flowrate. Vertical flow rate provides
information about the radial inflow through the vanes, which can help distinguish regions of radial inflow, growth and decay of the column in the vertical direction. This is as a result of continuity, which suggests that the flow rate in the vertical direction increases as a result of entrained air from the surroundings in the radial direction. Increase in average vertical velocity signifies radial inflow, which is at maximum near the bottom, where the temperature gradient is large. Increase in vertical flow continues but at a decreasing rate and reaches a maximum around mid-height of the vane. It continues to decay with elevation, but at a slower rate than the bottom half. The slope becomes weaker when the flow has tangential velocity component. Significant amount of radial inflow happens near the bottom, which triggers tangential velocity component owing to the vane angle. Vane angles greater than 0° helps the formation of a vortex and delays radial outflow. Investigations are based on a normalized flow rate, calculated at over a fixed area above the heated plate as follows: 2Π
R
Vz ∫0 ∫0 uz rdθ dr = Vzc uzc (π R 2 )
(4)
When the numerator of Eq. (4) is represented by the mean axial velocity, normalized flow rate also represents a ratio of average vertical speed to a characteristic vertical speed. Characteristic vertical speed, uzc , can be obtained by matching Reynolds number to squareroot of Grashof number as follows:
uzc = g βΔTR
(5)
Furthermore, Eq. (4) can be viewed as the Froude number, the ratio of inertia to the buoyant forces.
Fr =
Vz = Vzc
uz ,m g βΔTR
(6)
A similar form of Froude number was also used by Zhang et al. [4] with a slight difference as they defined Froude number as the ratio of maximum speed to the characteristic speed as given in Eq. (5). 3.2. Parametric study A columnar vortex with high and concentrated kinetic energy relies on the strength and growth of the vertical flow, caused by accumulating higher magnitudes of radial inflow and tangential velocity component preventing radial outflow. Geometrical
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Vane width 0.4R
Vane width R
Vane width 1.4R 0.25
0.05
)1⁄2
0.20
0.04
Δ
0.15
0.03
⁄(
Vz / Vzc
0.06
0.02
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Vane width 1.6R
0.10 0.05
0.01
0.00
0 0
0.2
0.4
0.6
0.8
0
1
0.2
0.4
z/h
0.6
0.8
1
r/R
Fig. 3. Vertical flow rate along the vane height and vertical velocity profile at the vane’s mid-height, z = 0.5 h.
angle of 0°. It is found that increasing the vane height continuously causes an increase in the magnitude of the vertical flow rate, suggesting that the height also has an important role in terms of flow similarity. For vane heights less than 1.2R of the plate, flow behaves different than those with heights above 1.4R. The location of the peak vertical flow rate, as marked with filled markers, is about 0.4R for a vane width of R, while peak’s elevation is pushed in the upward direction for both taller and shorter vanes. In addition, the increase in vertical velocity magnitude from a vane height of 1.2R to 1.4R is much larger than the increase from 1.4R to 1.6R. Curvefit on the peak Froude number reveals its relation to the vane height as follows:
parameters are investigated for their influence on the flow field. These parameters are, namely, vane width, the vane height, the spacing between vanes and the vane angle. Following Ref. 6, flow conditions for the base case are as follows: R = 0.5 m, h = 1.2R , c = 0.8R , θ = 30° and N = 12 ; To = 306 K and Tp = 328 K . Effects of vane width, vane height, and spacing between vanes are considered first at a vane angle of 0°, at which no or negligible tangential velocity is anticipated. The temperature difference is 22 °C. The interplay between the radial inflow, which is directed exactly to the center, but guided through the vanes, is observed to characterize the influence of the vanes. Fig. 3 shows the influence of vane width from 0.4R to 1.6R on the vertical flow rate and the corresponding vertical velocity profile in radial direction at an elevation of 0.5h. It is observed that nondimensional vertical velocity improves when vane width is increased up to 1.4R. Increasing the vane width greater than 1.4R does not cause any significant change in the non-dimensional vertical velocity profile. Peaks of vertical velocity happen around an elevation of 0.5h for all vane widths. The maximum velocity occurs at r = 0.4R when vane width is 0.4R and it gets closer to the center as the width increases. The velocity profile remains the same for widths 1.4R and 1.6R, indicating viscous effects related to vane’s boundary layer do not influence the upward flow significantly. This suggests that the width of the vanes should at least be 1.4R to have larger flow rates. Fig. 4 shows the variation of vertical flow rate when the vane height is varied from 0.6R to 1.6R for a vane width of 1.4R and a vane
(7)
Fig. 5 shows the influence of the spacing between the vanes through simulations of 6, 12 and 18 vanes. Large spacing between the vanes shows a reduced vertical flow rate, and increase in the number of vanes causes the flow rate continue to increase and shifts the location of peak flow rate upward, yielding better stability. The vertical velocity variation in radial direction in Fig. 5 shows that the peak vertical velocity is higher near the centerline for 6 vanes (60° spacing) while it decays quicker away from the radius than those with more vanes. Increasing number of vanes from 6 to 12 causes the peak shift away from the center of the plate. Even though the peak is located at a different radial location for each case, the average
Vane height 0.6R
Vane height 0.8R
Vane height R
Vane height 1.2R
Vane height 1.4R
Vane height 1.6R
0.08
0.50
0.07
0.45
)1⁄2
0.35
Δ
0.40
0.06
0.30
0.05 0.04
0.25
⁄(
Vz / Vzc
⎧h1.5 h ≤ 1.2R ⎩ h h ≥ 1.4R
(Vz Vzc )peak ∼ ⎨
0.03
0.20 0.15
0.02
0.10
0.01
0.05 0.00
0 0
0.2
0.4
0.6
z/h
0.8
1
0
0.2
0.4
0.6
0.8
1
r/R
Fig. 4. Vertical flow rate for various vane heights and corresponding peak vertical velocity profiles at locations shown by filled markers.
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0.06
0.40
6 vanes 12 vanes 18 vanes
0.20 0.15
0.03
18 vanes
0.25
Δ
0.04
12 vanes
0.30
⁄(
Vz / Vzc
)1⁄2
0.05
6 vanes
0.35
0.10 0.05
0.02
0.00 0
0.2
0.4
z/h
0.6
0.8
1
0
0.2
0.4
r/R
0.6
0.8
1
Fig. 5. Vertical flow rate for different numbers of vanes and velocity profiles at locations shown by filled markers.
and tangential velocities are largest there. The peak of the tangential velocity is higher for vane angles greater than 25°, which illustrates vortex strengthening and improved kinetic energy when the vanes have an angle of 25° or more. Fig. 7 shows peak vertical velocity variation for various vane angles. The peak of vertical flow rate increases when the vane angle is higher than 30° (tanθ = 0.57), while it gets saturated for vane angles of 45° and 50°. For smaller vane angles, i.e. 15° and 25°, the vertical velocity profile is similar to the one presented at height of 0.2 R in Fig. 6. For higher angles, vertical velocity profiles at peaks are also similar to those with smaller angles but with higher magnitude especially away from the radius. The major difference between high and small vane angles is that high vane angle cases have a significantly larger tangential velocity profile, i.e. four times more in magnitude than that of 15° vane angle. The peak of the tangential
vertical flow is shown to increase with number of vanes due to the improved flow for r/R > 0.3. Lastly, vertical flow rate and corresponding radial velocity profiles are examined for vane angles between 15° and 50°. Fig. 6 shows the non-dimensional vertical velocity for a radius of R = 0.5 m, a vane width of 1.4R, and a vane height of R at 22 °C temperature difference. The peak increases with the vane angle, showing that induced tangential velocity continues to bring additional radial inflow. At lower elevations, i.e. z smaller than 0.2h, the vertical flow rate for all angles are the same despite the differences in vertical and tangential velocity profiles at 0.2R. At lower vane angles, the velocity profile is similar as the formation of a central plume, i.e. vertical velocity is maximum at the centerline and decreases continuously with r. For vane angles greater than 25°, maximum speed happens around r = 0.2R, as both vertical
15º
25º
35º
45º
0.20
0.20
0.04
0.16
0.16
0.035
0.12
Δ
0.12
Δ 0.08
0.08
q
⁄(
0.03
⁄(
Vz / Vzc
)1⁄2
)1⁄2
0.045
0.04
0.025
0.04
0.00
0.02
0
0.2
0.4
0.6
0.8
0.00
0
1
z/h
0.2
0.4
0.6
0.8
1
0
r/R
0.5
1
r/R
0.5
1
tan( )
1.5
0.01 0.00
0.00
0
0.02
)1⁄ 2 Δ q
⁄(
0.05
⁄(
Δ
0.10
)1⁄2
0.042 0.04
15º 25º 35º 45º 50º
0.038 0.036
Peak of Vz / Vzc
0.044
Fig. 6. Vertical flow rate and velocity profiles at variation z = 0.2 R for various vane angles.
0
0.2
0.4 0.6 r/R
0.8
1
0
0.2
0.4 0.6 r/R
Fig. 7. Peak vertical flow rate and corresponding velocity profiles at various vane angles.
0.8
1
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
Fig. 8 shows that Swirl number is high at lower elevations for each vane angle, and it follows a similar pattern of decay in the upward direction.
1.2
Swirl No
1
15º
25º
30º
40º
45º
50º
35º
0.8
3.3. Flow-similarity estimation
0.6
In order flow to reach speeds suitable for wind turbines, i.e. greater than 3 m/s, it is necessary to consider flow similarity when temperature difference or size changes. Both together represent the amount of energy input to the system. For this purpose, the similarity of the flow is studied when the system is exposed to different temperature differences and various sizes of the same flow geometry. The base case is modified for vane height and vane width as follows: h = 1.4 R , and c = 1.4 R . Fig. 9 shows the non-dimensional average vertical velocity with height at temperature differences ranging from 12 °C to 20 °C. Features of the flow field agree well for all temperatures considered, and the vertical velocity scales with the square root of temperature difference between the heated plate and the ambient. Geometric scaling is investigated on the same geometry by changing the radius, the vane width and the vane height using the same scaling factor, S, ranging from 0.6 to 1.4. As the device is to be used with air, the thermo-physical properties are kept the same for all cases. Fig. 10 shows that the non-dimensional average vertical velocity continuously decreases when the device is enlarged. This indicates that using Froude number alone does not yield dynamically similar flows as the flow field features become different with geometric scaling. In fact, the peak of the normalized velocity is found to decay with S−2 as shown in Fig. 10. The differences in the flow features are illustrated through the streamline plots presented in Fig. 11. For the case with S = 0.6, circulation zone at the edge of the vane region influences the radial
0.4 0.2 0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
h/H Fig. 8. Swirl number variation for various vane angles. Dash lines represent fitted power curves.
velocity happens about 0.6R, which would yield better torque extraction opportunities. Swirl number (Sw) provides a comparison between the tangential and axial components of velocities at a particular elevation. This information is useful in determining the angle of attack of the turbine blade, which can be used to utilize tangential velocity more at high Swirl numbers. Swirl number is computed and plotted against scaled elevation levels for different vane angles in Fig. 8 using the following equation:
uz uθ r 2dr
(8)
R
R∫ uz 2rdr 0
0.5
0.07 0.06
)1⁄2
0.4
0.05
0.04
Δ
Vz / Vzc
ΔT 12°C ΔT 14°C ΔT 16°C ΔT 18°C ΔT 20°C
0.45 0.35 0.3 ΔT 12°C ΔT 14°C ΔT 16°C ΔT 18°C ΔT 20°C
0.03 0.02 0.01
⁄(
R
0
0.25 0.2 0.15
0.1 0.05
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
z/h
0.6
0.8
1
r/R
Fig. 9. Vertical flow rate and velocity profile for various temperature differences.
0.25
0.06
1,4 S 1,2 S 1S 0,8 S 0,6 S
0.15
0.05
Peak of Vf / Vfc
0.2
Vz / Vzc
Sw
∫ =
1041
0.1 0.05
0.04 0.03 Vf /Vfc = 0.02S -2.10
0.02 0.01
0 0
0.2
0.4
0.6
z/h
0.8
1
0 0.6
0.8
1
1.2
Scaling factor S
Fig. 10. Vertical flow rate characterized by the scaling factor.
1.4
z
Vane
1.4R
Vane
1.96R
A. Mohiuddin, E. Uzgoren/Applied Thermal Engineering 98 (2016) 1036–1043
0.84R
1042
z r
0.6R
0.6(R+c)
Vane
z r
R
R+c
r
1.4R
1.4(R+c)
Fig. 11. Streamlines obtained for the scaled geometry using S = 0.6, S = 1.0, and S = 1.4. Colors represent the vertical velocity magnitude, red for maximum and blue for minimum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
inflow characteristic near the heated plate. This causes higher average flow over the heated plate. On the other hand, when the scaling parameter, S, increases, circulation gets weaker causing a decay in the magnitude of radial inflow and hence the vertical flow over the heated plate. The weakening of the circulation zone is related to the enlarged spacing between the vanes and how it compares to the viscous effects. Fixing the spacing between the vanes around the heated plate instead of the angle can be considered for higher radial inflow and allow the possibility of realistic power applications through an enlarged space. 4. Conclusion A numerical model is developed using OpenFOAM to investigate flow characteristics of a device that mimics dust-devils in a controlled environment. A cyclic grid is utilized to reduce the computational time, memory space and post processing time and following results are found:
• • • • • •
Vane width should at least be 1.4R to obtain maximum vertical speed. Beyond 1.4R, it is found that there is no improvement. Increasing the vane height improves radial inflow. Vane spacing should be decreased for larger flowrates. Increasing vane angle improves the magnitude of tangential velocities, which cause improved vortex stability and delay for radial outflow. Swirl number is higher at higher vane angles and lower heights, and decreases with height obeying power law. Froude number alone is not sufficient to describe the flow similarity due to the interplay between the vane spacing and the viscous effects.
It is concluded that columnar vortex flows can be obtained through changing the vane width, height, spacing and angle to redistribute the concentration of energy from the center to the distances away from center for higher yield of energy.
Nomenclature
c Fr g h N p R r S Sw t T u V z
Vane width [m] Froude number ≡ ratio of flow inertial force to gravitational force [dimensionless] Gravitational acceleration [m s−2] Vane height [m] Number of vanes Pressure [Pa] Radius of the heated plate [m] Position in radial direction [m] Scaling factor ≡ ratio of plate radius to the reference plate radius [dimensionless] Swirl number ≡ ratio of axial flux of the tangential momentum to axial flux of axial momentum [dimensionless] Time [s] Temperature [K] Velocity vector [m s−1] Vertical volumetric flow rate [m3 s−1] Position in axial direction [m]
Greek symbols α Thermal diffusivity [m2 s−1] Coefficient of thermal expansion [K−1] β μ Dynamic viscosity [Pa s] ν Kinematic viscosity [m2 s−1] φ Span angle [degrees] ρ Density [kg m−3] θ Vane angle [degrees] ϕ Source term in energy equation [K/s] Subscripts c Characteristic m Mean/average o Reference p Plate r Radial component z Axial component
Acknowledgement References This research was supported by a Marie Curie International Reintegration Grant within the 7th European Community Framework Programme (Project 268426).
[1] Z. Zou, S. He, Modeling and characteristics analysis of hybrid cooling-towersolar-chimney system, Energy Convers. Manage. 95 (2015) 59–68.
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[2] K. Chen, J. Wang, Y. Dai, Y. Liu, Thermodynamic analysis of a low-temperature waste heat recovery system based on the concept of solar chimney, Energy Convers. Manage. 80 (2014) 78–86. [3] X. Zhou, Y. Xu, Solar updraft tower power generation, Sol. Energy (2014). In press. [4] M. Zhang, X. Luo, T. Li, L. Zhang, X. Meng, K. Kase, et al., From dust devil to sustainable swirling wind energy, Sci. Rep. 5 (2015) 8322. [5] D.E. Fitzjarrald, A laboratory simulation of convective vortices, J. Atmos. Sci. 30 (5) (1973) 894–902. [6] M.W. Simpson, A.J. Pearlstein, A. Glezer Power generation from concentrated solar-heated air using buoyancy-induced vortices. International Conference on Renewable Energies and Power Quality (ICREPQ’13), Bilbao (Spain), March 20-22, 2013. [7] L. Michaud, B. Monrad, Energy from convective vortices, Appl. Mech. Mater. 283 (2013) 73–86. [8] Atmospheric vortex engine.
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[9] D. Natarajan Numerical simulation of tornado-like vortices (Ph.D. thesis), The University of Western Ontario, 2011. [10] OpenFOAM® Documentation.