Numerical analysis on overall performance of Savonius turbines adjacent to a natural draft cooling tower

Energy Conversion and Management 99 (2015) 41–49

Contents lists available at ScienceDirect

Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Numerical analysis on overall performance of Savonius turbines adjacent to a natural draft cooling tower M. Goodarzi ⇑, R. Keimanesh Bu_Ali Sina University, Hamedan, Iran

a r t i c l e

i n f o

Article history: Received 21 September 2014 Accepted 9 April 2015 Available online 22 April 2015 Keywords: Savonius turbine Cooling tower Wind Power generation

a b s t r a c t Two large Savonius turbine have been proposed to use near the radiators of a natural draft dry cooling tower instead of previously proposed solid windbreakers. A numerical procedure has been used to predict the flow field unsteadily, and calculate the cooling improvement and power generation in turbines. Numerical results showed that rotating turbines could improve cooling capacity as the same order of solid windbreakers. It was surprisingly concluded that presence of cooling tower near Savonius turbine increased its power generation. Ultimately, it was concluded that overall improvement of the proposed arrangement was considerable from thermal and clean energy production viewpoints. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Steam power plants are frequently used to generate the electrical energy. Cooling tower is usually used to reject the heat from the steam turbine’s condenser. Two different types of cooling towers, i.e., wet cooling tower and dry cooling tower, are designed for this purpose. Today, dry cooling towers are more preferable than the wet cooling towers, because the water resources are decreasing all around the world. Natural draft dry cooling tower (NDDCT) is able to reject a large amount of heat to the atmosphere without applying mechanical draft facilities. This characteristic makes NDDCT more favorable for high capacity power plants. Unfortunately, NDDCT’s performance significantly decreases under crosswind condition [1]. Many researchers numerically studied the thermal and hydraulic performances of NDDCTs among them Du Preez and Kroger [2], We et al. [3], Su et al. [4], and Al-Waked and Behnia [5] can be addressed. They concluded that accelerated flow near the sideward radiators reduced the local outdoor pressure of the airflow and decreased the airflow crossing the radiator. Besides, the deflected plume throttled the passage of the warmed air flow exiting the tower stack, and consequently, increased the indoor pressure. These unfavorable effects decrease the cooling performance of the NDDCT under crosswind condition. It is worth to mention that the former effect decreases cooling performance more than the later one. Several proposals have been proposed for decreasing the unfavorable wind effects. Many researchers proposed windbreaker ⇑ Corresponding author. Tel.: +98 8138292625; fax: +98 8138292631. E-mail address: [email protected] (M. Goodarzi). http://dx.doi.org/10.1016/j.enconman.2015.04.027 0196-8904/Ó 2015 Elsevier Ltd. All rights reserved.

walls for decelerating airflow near the sideward radiators [6–8]. Recently, Goodarzi and Kiemanesh [9] proposed the radiator-type wind breakers with greater improvement compared to the solid windbreakers. There are a few proposals for decreasing throttling effect among them the oblique exit plane proposed by Goodarzi [10] can be addressed. Wind breakers are also used inside the cooling towers and considerably affect its thermal performance [11]. From momentum viewpoint, windbreakers decrease the momentum of the airflow near the sideward radiators to increase the local outdoor pressure. But, from energy viewpoint, windbreakers decrease the kinetic energy of the airflow at this location. Windbreakers change this energy to friction work and dissipate it to the ambient. Wind turbines are used to produce power from wind kinetic energy. They are generally divided into two classes: turbines with horizontal axis and turbines with vertical axis. The operation of a turbine with horizontal axis depends on wind direction. These types of wind turbines are used at regions with high wind-velocity. They produce power at high rotation velocity and low axial torque. But, the operation of a turbine with vertical axis is independent of the wind direction. These types of wind turbines operate at low rotation velocity and large axial torque. Savonius turbine is a wind turbine with vertical axis. It was created for the first time by the Finnish engineer Sigurd Savonius [12]. A simple type of this turbine consists of two blades each one is a half part of a cylinder. Fig. 1 schematically shows a two blades Savonius turbine. As Fig. 1 shows, this turbine has a simple structure with large surface against the airflow. Its simplicity in fabrication and operation has encouraged the researchers to study this turbine with more details. It was experimentally studied to find its

42

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

Nomenclature a A Cm C1e, C2e, d D gi G h H I k kv M p P Pr Prt Q Qh ~ r Ri Sij T ui U

distance ratio area torque coefficient Cl standard coefficients for k–e turbulent model distance between cooling tower and turbine centers diameter gravitational acceleration component generation term in turbulent model convective heat transfer coefficient turbine blade height percent of improvement turbulent kinetics energy pressure loss coefficient torque pressure production term in turbulent model, power Prandtle number turbulent Prandtle number heat transfer rate source term in energy equation distance vector between blade element and rotor center source term in momentum equation tensor of deformation rate temperature velocity component wind velocity

characteristic performance [13], or to find its optimum configurations and performance [14,15]. Fujisawa et al. [16–22] studied Savonius turbine from several viewpoints. They experimentally visualized flow field in the blades of turbine by measuring velocity, pressure, and aerodynamics characteristics. Altan and Atilgan [23] improved performance of the turbine by performing an experimental setup and numerical simulation for their modified geometries. D’Alessandro et al. [24] developed a new computational approach for simulating unsteady performance of Savonius turbine. They showed that fluctuations of aerodynamics characteristics made from variable rotation speed were negligible so that rotation speed could be assumed invariable during numerical simulation. Today, engineers focus on renewable energy. Therefore, wind turbine takes more attention so that experimental and numerical studies are going to increase in the research centers. Among the recent studies on Savonius turbine, experimental and/or numerical studied of Mohamed et al. [25], Roy and Saha [26], Zhou and Rempfer [27], Shaheen et al. [28], Kacprzak et al. [29], Nasef et al. [30], and Sarma et al. [31] show the importance of the subject. It should be concluded from previous paragraphs that wind is useful from power generation viewpoint, while it is unfavorable from NDDCT operation viewpoint. It seems that installing two large Savonius turbines instead of windbreakers near the sideward radiators may increase the NDDCT cooling efficiency, while wind turbines can generate considerable electrical power at the same time. A simplified numerical modeling is used in this article to investigate the flow field, rate of power generation by wind turbines, and cooling improvement of the cooling tower under crosswind condition. 2. Numerical modeling 2.1. Governing equations Air density variation in the cooling tower is so small that the flow can be assumed incompressible. Therefore, Boussinesq

Vn xi Z

normal velocity i-th coordinate direction vertical direction

Symbols

a

angle of rotation compressibility coefficient turbulent energy dissipation C, Ct molecular and turbulent thermal diffusion coefficients c cooling efficiency k tip-speed ratio l, lt molecular and turbulent viscosities m, mt molecular and turbulent dynamic viscosities q density rk, rt, re standard coefficients for k–e turbulent model sij stress tensor x angular velocity b e

Subscript 0 ar D n r t tur

absence of turbine/cooling tower condition for reference temperature design value normal direction radiator cooling tower turbine

approximation [32] predicts the resulted buoyancy force, which should be included in the vertical momentum equation. Since Grashof number is greater than the critical value [32], flow regime is inherently turbulent. Governing equations for unsteady, buoyant, and turbulent flow including heat transfer are continuity, momentum, and energy equations associated with a suitable turbulence model [32]. The well-known standard k–e model [33] has been used to model the turbulent flow as a simple model, because the main aim of the present study is to analyze the overall performance of a cooling tower using Savonius turbines as windbreakers. Conservative forms of the governing equations in an inertial reference frame are presented by the following equations

@ðquj Þ ¼ 0:0 @xj

ð1Þ

@ðqui Þ @ðquj ui Þ @p @ sij þ ¼ þ  qbðT  T ar Þg i þ Ri @t @xj @xi @xi

ð2Þ

  @ðqTÞ @ðquj TÞ @ @ þ ¼ ð C þ Ct Þ T þ Qh @t @xj @xj @xj

ð3Þ

@ðqkÞ @ðquj kÞ @ þ ¼ @t @xj @xj @ðqeÞ @ðquj eÞ @ þ ¼ @t @xj @xj







mþ

mt @ k þPþGe rk @xj

mþ

mt @ e e2 e þ C 1e ðP þ GÞ  C 2e re @xj k k







They are associated with the following relations

sij ¼ ðl þ lt ÞSij ; P ¼ mt Sij Sij ; G ¼ gb ¼

  1 @ui @uj þ 2 @xj @xi

ð4Þ

mt @T ; Sij rt @z

ð5Þ

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

mt ¼

43

2 lt k l l ¼ C l ; C ¼ ; Ct ¼ t q e Pr Prt

and the following standard constants

C l ¼ 0:09;

C 1e ¼ 1:44;

C 2e ¼ 1:92;

rk ¼ 1:0; re ¼ 1:3; rt

¼ 1:0 In the above equations, ui, p, q, l, and lt denote velocity components in inertial reference frame, static pressure, air density, molecular viscosity, and turbulent viscosity, respectively. In addition, T and Tar are local and reference temperatures of the airflow, respectively. b denotes the air compressibility coefficient, gi refers to each component of gravitational acceleration vector along each coordinate direction, and Sij is the tensor of deformation rate. Bottom radiators of the cooling tower are modeled as smooth and permeable surfaces. Ri provides the airflow pressure drop across the radiators in the momentum equation. Pressure drop across the radiator is usually computed based on the pressure drop coefficient, kv, and normal velocity component, Vn

1 Dp ¼ kv qV 2n 2

ð6Þ

The pressure drop coefficient depends on the normal velocity component [34,35]

kv ¼ 13:03V 0:24 þ 0:436 n

ð7Þ

Meanwhile, the source term, Qh, provides the rate of heat transferring to the airflow across the radiators in the energy equation. The rate of heat transfer across the radiators is computed from the following equation

Q r ¼ Ar hðT r  TÞ

ð8Þ

where Ar denotes the radiator surface, h is convective heat transfer coefficient, and Tr refers to radiator temperature. An experimental correlation [34,35] relates the convectional heat transfer coefficient to the normal velocity component

h ¼ 2035:2V 0:515 n

ð9Þ

2.2. Sliding mesh The basic idea of the present study is to apply two Savonius turbines instead of two solid windbreakers in order to improve cooling efficiency of the cooling tower during wind condition and generate power from wind kinetic energy. Fig. 2 schematically shows the proposed layout. This figure shows that two Savonius turbines are installed near the bottom radiators normal to wind direction as conventional solid windbreakers are done. There is a symmetry plane along the wind direction, so that one-half of the physical domain can be considered for numerical simulation. Fig. 3 shows the physical domain which was modeled for numerical simulation in the present study. Since turbine blades rotate during time intervals, physical domain is decomposed to two separated regions; a cylindrical rotating region around the Savonius turbine, and a fixed region containing cooling tower. Fig. 4 shows a top view of the physical domain. Two separated regions have a common interface boundary. Two grid systems should be used for these regions in the manner that they have consistence face cells on the common interface. Meanwhile, a suitable time interval should be used to interpolate all variables between two regions across the coincided interface. All computational cells within the rotational region have the same rotation speed of the turbine blades. Rigid body rotation of the cells within the rotational region induces Coriolis acceleration, which must be included in the transport equations. A Sliding Mesh

Fig. 1. Schematic sketch of a Savonius turbine.

Method (SMM) [36] was used in the present numerical approach to consider the rotational fluxes and corresponding virtual acceleration in an inertial frame [37]. Details of this approach and how to apply it in a numerical computation based on the inertial frame are extensively presented in [36,37].

2.3. Boundary and initial conditions Fig. 2 schematically shows the boundary conditions used in the numerical computation. All gradients of the dependent variables are set to zero normal to the symmetry plane. Ground and solid walls of the cooling tower and turbine blades are insulated surfaces at which the no-slip condition associated with the wall function

Fig. 2. Schematic view of turbines and cooling tower.

44

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

Fig. 3. Simulated physical domain including prescribed boundary conditions.

Fig. 4. Top-view of simulated physical domain including rotational region.

approach [33] are used. The far field boundary is located as far as possible from the cooling tower at where all dependent variables are merely invariant. All dependent variables are linearly extrapolated from the inner cells at the outflow boundary. An experimental fully developed velocity profile corresponding to the velocity of 10 m/s at the middle height of the radiators is used as the inlet velocity profile [10]

UðzÞ ¼ 5:265z0:2548

ð10Þ

where z denotes the vertical distance from the ground level in meter. Many researchers frequently used this velocity profile for comparing their results with other references. As was presented in the previous section, a special procedure including interpolation across the common interface between the rotational and fixed regions must be used [36]. Initial condition for unsteady computation was performed by a steady simulation of the flow field over the cooling tower and turbine when fixing the turbine at starting position.

2.4. Other numerical details A commercial finite volume CFD code (FLUENT) was used. A second order upwind scheme was used to compute fluxes on cell faces, while a central scheme was used to discrete diffusive terms. Final discrete algebraic systems of equations were implicitly solved with SIMPLE algorithm [38] to couple the velocity and pressure fields. Numerical computation continued until all dependent variables reached to the invariant values within each time step. Time step was selected so that both convergence criteria and coincidence of corresponding cell faces over the interface between rotational and fixed regions are met during all intervals. Grid points were appropriately concentrated toward the solid walls and all surfaces near which there might be large gradients of dependent variables. Several grid systems have been examined for each geometrical case study at steady condition to find the optimal grid system. Different distributed parameters such as pressure coefficient at the symmetry line on the exit plane of the tower stack have been drawn for several grid systems. The optimal grid systems were

45

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

3.1. Model validation In order to validate the results of the present numerical method, total heat transfer rate of the cooling tower in the absence of turbines was computed under normal condition. Numerical model predicted the total heat transfer rate as 273 MW compared to the practical reported design value of 277 MW. It shows 1% difference between the predicted and reported values. Cooling efficiency of the cooling tower is defined by the following equation

c¼

Q  100 QD

ð11Þ

where Q denotes the rate of heat rejection at windy condition, while QD is the corresponding design value at normal condition. Present computed cooling efficiency is compared with reported values in Table 1 at the prescribed wind velocity. Comparison shows good agreement among the present and referenced results. An unsteady simulation was performed to compute the torque coefficient of the Savonius turbine in the absence of cooling tower under the wind condition. Wind condition was defined by the wind velocity profile described in Eq. (10). Tip-speed ratio is defined as

k¼

Fig. 5. Cooling tower dimensions.

selected when the graphs of two successive fine grid systems acceptably coincided on each other.

3. Results and discussions Fig. 5 shows geometrical dimensions of the cylindrical cooling tower. Total height of the tower is 120 m, base and exit diameters of the tower are 100, and 60 m, respectively, and radiator height is 17 m. Turbine height is equal to radiator height, and total diameter of the turbine blades, Dtur, is 20 m. Fig. 6 shows geometrical parameters used in the present study. This figure defines angle of rotation for Savonius turbine with respect to transverse direction as the reference direction. Referring to Fig. 6, distance ratio is defined as a = 2d/Dt.

xDtur

ð12Þ

2U

where x and U are turbine angular velocity and averaged wind velocity, respectively. Tip speed ratio was set to 1.0 in the present study. Torque coefficient should be computed at steady periodic operation of turbine. Steady periodic operation begins after the startup process. Fig. 7 shows the variation of cooling efficiency of the cooling tower during startup process following by steady periodic operation. Torque coefficient is defined as the following relation

Cm ¼

4M

qADtur U 2

;

A ¼ HDtur

ð13Þ

where M is total torque exerted on the turbine axis, A is projected area of the turbine blades, and H denotes the height of turbine blade. Total torque is computed from integrating differential torque exerted on differential surface of turbine blades over the front and back areas of blades. Differential torque consists of differential torques exerted by pressure and shear stress forces on blade elements,

Mz ¼

Z A

r  pd~ ð~ AÞz þ

Z A

r  ss d~ ð~ AÞz

ð14Þ

where ~ r denotes the distance vector between blade element and rotor center. The obtained result was compared with that was reported by D’Alessandro et al. [24] in Fig. 8. This figure shows the variation of torque coefficient when turbine turns in the range 0–180° at steady periodic operation. Two set of results quantitatively vary in this turning range, but there is quantitatively difference between the curves. There are several reasons for this quantitatively difference. The most important one is that D’Alessandro et al. [24] used 2D numerical model for simulating the flow field, while 3D numerical model was used in the present study. In fact, there are two frictionless endplates in 2D numerical model, whereas they do not present in 3D model. Additionally, there are a few geometrical differences between the two types of modeled turbines. Fig. 9 shows top views of the two types of Table 1 Cooling efficiency at crosswind condition (U = 10 m/s).

Fig. 6. Geometrical parameters description.

c (%)

Al-Waked and Behnia [5]

Zhai and Fu [7]

Present

74

75

74.5

46

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

Fig. 11 shows percent of cooling improvement for three distance ratios. It is obviously similar to Fig. 10. Again, this figure shows that when turbines are installed far from cooling tower, percent of cooling improvement decreases. Distance ratio of 1.3 is corresponding to the case in which tip of turbine blades become tangential to the radiators of the cooling tower. Therefore, Fig. 11 declares that maximum improvement that can be enhanced by turbine installation could be 25%, which is surprisingly greater than that has been reported for solid wall windbreakers with same dimensions [7], i.e. 16%. 3.3. Power generation In addition to improvement in cooling capacity of the cooling tower operation, turbines generate some power that could be used to electricity production. Fig. 12 shows torque variation during the one-half of complete turbine rotation. It shows that exerted torque on the advancing blade substantially increases when turbine is

Fig. 7. Cooling efficiency variation during startup and steady periodic intervals.

Fig. 9. Cross sections of the present turbine and turbine that was modeled by D’Alessandro et al. Fig. 8. Torque coefficient variation in one-half period of turbine rotation.

turbines. As this figure shows, blade connections to the axis are different. Besides, wind velocity is uniform in 2D model, while Eq. (10) is used for wind velocity profile with ground boundary condition at z = 0 for 3D modeling. Meanwhile, tip-speed ratio was 0.735 in 2D model, while it is 1.0 in the present 3D modeling. 3.2. Cooling improvement Wind turbine partially blocks the accelerated flow near the sideward radiators. Therefore, it seems that turbine can decelerate the airflow at this region in the manner that cooling efficiency of the cooling tower increases. Fig. 10 shows cooling efficiency of the cooling tower during one-half period of turbine turning for three distance ratios. It shows that cooling efficiency decreases when turbines are installed far from cooling tower. The percent of cooling improvement in the presence of turbines can be calculated by the following equation

Ist ¼

Q  Q0  100 Q0

ð15Þ

where Q0 denotes the rate of heat rejection in the absence of turbines at wind condition.

Fig. 10. Cooling efficiency variation in one-half period of turbine rotation for three distance ratios.

47

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

3.4. Flow field analysis Fig. 13 shows flow field near the sideward radiators at the height 10 m above the ground level. Note that in the absence of turbine velocity vectors are tangential to the sideward radiators with greater magnitude compared to those presented at the frontal and rearward regions. Therefore, the intake airflow at sideward radiators is less than two other mentioned regions. In the presence of turbine, especially at the angular position denoted by a = 90°, velocity vectors are directed to the sideward radiators in the manner that intake airflow is increased over this portion of radiators. Of course, at the angular position denoted by a = 0°, turbine presence could not increase the intake airflow over the sideward radiators, because of less obstruction against the accelerated tangential flow. Considering velocity magnitudes around the concave and convex surfaces of the advancing and returning blades shows that there are regions with high and low velocities over these blades, which demonstrate low and high pressure regions, respectively. Greater velocity and pressure differences between these region lead to Fig. 11. Cooling improvement variation in one-half period of turbine rotation for three distance ratios.

installed closer to the cooling tower, while it negligibly decreases on the returning blade. Therefore, it seems that closer turbine installation to the cooling tower increases the turbine power generation. How does affect the presence of cooling tower on turbine performance? A dimensionless parameter is introduced in the present study to find the answer for this question. It is the percent of improvement in turbine power generation and is defined as follows

Ip ¼

P  P0  100 P0

Table 2 Percents of power generation and overall improvements for three distance ratios. Distance ratio a

Power generation improvement Ip (%)

Overall improvement Itt (%)

1.3 1.4 1.5

25 22.6 19.9

18.7 17 15

ð16Þ

where P and P0 are averaged turbine power generations in the presence and absence of cooling tower, respectively. It computed for three distance ratios and is tabulated in Table 2. Tabulated results shows that percent of improvement in turbine power generation increases as turbine is installed closer to the cooling tower. It may be ultimately increased up to 25%. Therefore, Savonius turbine has better performance near cooling tower at wind condition.

Fig. 12. Torque exerted on turbine axis during one-half rotation for three distance ratios.

Fig. 13. Vector plots near sideward radiators in the absence and presence of turbine.

48

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49

Fig. 14. Vector plots around the turbine for different distance ratios.

greater torque exerted on turbine axis. Fig. 13 illustrates that these differences are higher at angular position denoted by a = 90°. Fig. 14 shows velocity vectors around the turbine at the same height of Fig. 13. Vector plots are presented for different distance ratios. All vector plots are presented at the angular position denoted by a = 90°. This figure shows that the presence of the cooling tower changes the pattern of the separation flow behind the turbine. Cooling tower accelerates the tangential flow over the frontal face of the returning blade, which decreases the pressure over it. At the same time, cooling tower makes the rear separating flow to be formed closer to the returning blade. Additionally, cooling tower makes a contraction passage between the sideward radiators and advancing blade of turbine. Generated vena-contract flow passage at this region accelerates the airflow compared to the situation in which cooling tower is not present. Therefore, both frontal high-pressure region and rear separating flow over the advancing blade are amplified. These effects on the advancing and returning blades of the turbine lead to greater torque or power generation on turbine axis. As Fig. 14 shows, these favorite effects decrease with increasing in distance ratio. 3.5. Overall improvement Another dimensionless parameter is needed to declare the overall improvement in system performance. It can be define by the sum of averaged improvement in cooling capacity of the cooling tower and power generation of the Savonius turbines. Therefore, the following equation is introduced in the present study

Itt ¼

ðQ  Q 0 Þ þ P  100 QD

ð17Þ

Overall improvement in percent are calculated for three distance ratios at the prescribed wind condition, i.e. Eq. (1). They are tabulated in Table 2. Tabulated result shows that overall improvement may be ultimately up to 18.7% of the design cooling capacity of the cooling tower.

4. Conclusion Wind turbines are used to produce clean energy from kinetics energy stored in the wind. Despite the favorite potential of the wind energy from energy production viewpoint, wind unfavorably decreases cooling efficiency of a natural draft cooling tower from thermal viewpoint. Present numerical study was conducted to investigate the simultaneous applications of cooling tower and a particular type of wind turbines, both qualitatively and quantitatively. Numerical results show that, Savonius wind turbines can be used as windbreakers to improve cooling efficiency of the cooling tower and generate power from a renewable energy source simultaneously. Although large Savonius turbine may be impractical, a farm of distributed small Savonius turbines around a large cooling tower seems to be practical. Meanwhile, two medium Savonius turbine near a small cooling tower is practical from operational viewpoint.

References [1] Kapas N. Behavior of natural draught cooling towers in wind. CMFF 30, Budapest, Hungary; 2003. [2] Du Preez AF, Kroger DG. Effect of wind performance on a pry pooling power. J Heat Recov Syst CHP 1993;13:139–46. [3] We QD, Zhang BY, Liu KQ, Meng XZ. A study of the unfavorable effects of wind on the cooling efficiency of dry cooling towers. J Wind Eng Ind Aerodynam 1995;54:633–43. [4] Su MD, Tang GF, Fu TS. Numerical simulations of fluid and thermal performance of a dry cooling tower under cross wind condition. J. Wind Eng Ind Aerodynam 1999;79:289–306. [5] Al-Waked R, Behnia M. The performance of natural draft dry cooling towers under crosswind: CFD study. Int J Energy Res 2004;28:147–61. [6] Du Preez AF, Kroger DG. The effect of the heat exchanger arrangement and windbreaker walls on the performance of natural draft dry cooling towers subjected to crosswinds. J Wind Eng Ind Aerodynam 1995;58:293–303. [7] Zhai Z, Fu S. Improving cooling efficiency of dry-cooling towers under crosswind conditions by using wind-breaker methods. Appl Therm Eng 2006;26:1008–17. [8] Al-Waked R, Behnia M. Enhancing performance of wet cooling tower. Energy Convers Manage 2007;48:2638–48.

M. Goodarzi, R. Keimanesh / Energy Conversion and Management 99 (2015) 41–49 [9] Goodarzi M, Keimanesh R. Heat rejection enhancement in natural draft cooling tower using radiator-type windbreakers. Energy Convers Manage 2013;71:120–5. [10] Goodarzi M. A proposed stack configuration for dry cooling tower to improve cooling efficiency under crosswind. J Wind Eng Ind Aerodynam 2010;98:858–63. [11] Lu Y, Guan Z, Gurgenci H, Hooman K, He S, Bharathan D. Experimental study of crosswind effects on the performance of small cylindrical natural draft dry cooling towers. Energy Convers Manage 2015;91:238–48. [12] Savonius SJ. The S-rotor and its application. Mech Eng 1931;53:333–8. [13] Khan MH. Model prototype performance characteristics of Savonius rotor windmill. Wind Energy 1978;2(2):75–85. [14] Ushiyama I, Nagai H. Optimum design configurations and performance of Savonius rotors. Wind Eng 1988;12(1):59–75. [15] Saha UK, Rajkumar MJ. On the performance analysis of Savonius rotor with twisted blades. Renew Energy 2006;31:1776–88. [16] Fujisawa N. Velocity measurements and numerical calculations of flow fields in and around Savonius rotors. J Wind Eng Ind Aerodynam 1996;59: 39–50. [17] Fujisawa N. On the torque mechanism of Savonius rotors. J Wind Eng Ind Aerodynam 1992;40:277–92. [18] Fujisawa N, Gotoh F. Experimental study on the aerodynamic performance of a Savonius rotor. J Solar Energy Eng, Trans ASME 1994;116:148–52. [19] Fujisawa N, Gotoh F. Pressure measurements and flow visualization study of a Savonius rotor. J Wind Eng Ind Aerodynam 1992;39:51–60. [20] Fujisawa N, Taguchi Y. Visualization and image processing of the flow in and around a Savonius rotor. J Flow Visual Image Proc 1993;1:337–46. [21] Fujisawa N, Shirai H. Experimental investigation on the unsteady flow field around a Savonius rotor at the maximum power performance. Wind Eng 1987;11(4):195–206. [22] Fujisawa N, Gotoh F. Visualization study of the flow in and around a Savonius rotor. Exp Fluids 1992;12:407–12. [23] Altan BD, Atilgan M. An experimental and numerical study on the improvement of the performance of Savonius wind rotor. Energy Convers Manage 2008;49:3425–32.

49

[24] D’Alessandro V, Montelpare S, Ricci R, Secchiaroli A. Unsteady Aerodynamics of a Savonius wind rotor: a new computational approach for the simulation of energy performance. Energy 2010;35:3349–63. [25] Mohamed MH, Janiga G, Pap E, Thévenin D. Optimal blade shape of a modified Savonius turbine using an obstacle shielding the returning blade. Energy Convers Manage 2011;52:236–42. [26] Roy S, Saha UK. An adapted blockage factor correlation approach in wind tunnel experiments of a Savonius-style wind turbine. Energy Convers Manage 2014;86:418–27. [27] Zhou T, Rempfer D. Numerical study of detailed flow field and performance of Savonius wind turbines. Renew Energy 2013;51:373–81. [28] Shaheen M, El-Sayed M, Abdallah S. Numerical study of two-bucket Savonius wind turbine cluster. J Wind Eng Ind Aerodynam 2015;137:78–89. [29] Kacprzak K, Liskiewicz G, Sobczak K. Numerical investigation of conventional and modified Savonius wind Turbines. Renew Energy 2013;60:578–85. [30] Nasef MH, El-Askary WA, Abdel-hamid AA, Gad HE. Evaluation of Savonius rotor performance. Static and dynamic studies. J Wind Eng Ind Aerodynam 2013;123:1–11. [31] Sarma NK, Biswas A, Misra RD. Experimental and computational evaluation of Savonius hydrokinetic turbine for low velocity condition with comparison to Savonius wind turbine at the same input power. Energy Convers Manage 2014;83:88–98. [32] Gebhart B. Buoyancy-induced flows and transport. Textbook ed. Hemisphere Publishing Corporation; 1988. [33] Launder BE, Spalding DB. The numerical computation of turbulent flow. Comput Meth Appl Mech Eng 1974;3:269–89. [34] EGI, The Heller System, Budapest; 1984. [35] EGI. Thermo technical and aerodynamic design/calculation/characteristics of the dry cooling plant system heater, vol. A. Budapest Institute of Engineering; 1985. [36] FLUENT users’ guide release 6.3.26. USA: ANSYS Inc; 2006. [37] Hirsch C. Numerical computation of internal and external flows. 2nd ed. Elsevier; 2007. [38] Patankar S. Numerical heat transfer and fluid flow. New York: Hemisphere Publishing Corporation, McGraw Hill Book Co.; 1980.