Effects of flow area changes on the potential of solar chimney power plants

Energy 51 (2013) 400e406

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Effects of flow area changes on the potential of solar chimney power plants Atit Koonsrisuk *, Tawit Chitsomboon * School of Mechanical Engineering, Institute of Engineering, Suranaree University of Technology, Muang District, Nakhon Ratchasima 30000, Thailand

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 September 2012 Received in revised form 25 November 2012 Accepted 30 December 2012 Available online 29 January 2013

The solar chimney power plant is a solar power plant for electricity generation by means of air flow induced through a tall chimney. Guided by a theoretical model, this paper uses CFD technology to investigate the changes in flow properties caused by the variations of flow area. It is found that the sloping collector roof affects the plant performance. The divergent-top chimney leads to augmentations in kinetic energy at the chimney base significantly. The proper combination between the sloping collector roof and the divergent-top chimney can produce the power as much as hundreds times that of the conventional solar chimney power plant. Ó 2013 Elsevier Ltd. All rights reserved.

Keywords: Solar chimney power plant Solar energy Divergent top solar chimney Convergent top solar chimney Performance enhancement

1. Introduction The solar chimney power plant is a power plant proposed to generate electricity in large scale by transforming solar energy into mechanical energy. The schematic of a typical solar chimney power plant is sketched in Fig. 1. It consists of a transparent circular roof or solar collector with a chimney at its center and a turbine, which is generally installed at the chimney’s base. Solar radiation penetrates the roof and heats the air underneath as a result of the greenhouse effect. Due to buoyancy effect, the heated air flows up the chimney and induces a continuous flow from the roof perimeter towards the chimney. Mechanical energy can be extracted from the energy of the flowing air to turn an electrical generator. Research works on solar chimney power plants started around 1970s, after the construction of a 50 kW prototype in Manzanares, Spain. This pilot plant operated from the year 1982e1989 and was connected to the local electric network between 1986 and 1989 [1,2]. Tests conducted have shown that the prototype plant operated reliably and the concept is technically viable. Since then several studies on solar chimney power plants have been carried out. One common finding in the literature is that the plant efficiency is very low, and that it increases with the plant size. As a result, only * Corresponding authors. Tel.: þ66 44 224515; fax: þ66 44 224613. E-mail addresses: [email protected], [email protected] (A. Koonsrisuk), tabon@ sut.ac.th (T. Chitsomboon). 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.12.051

large-scale plants, in which the chimney heights are 1000 m or more, were proposed in the literature, e.g. [3e5]. The effects of various geometrical parameters on the plant performance were examined by several researchers. Padki and Sherif [6] reported that the power and efficiency could be increased by tapering the top end of the chimney. In contrast, Chitsomboon [7] developed a mathematical model and it showed that, as the chimney top is made convergent, the power and efficiency does not increase but stays relatively constant. Von Backström and Gannon [8] employed a one-dimensional compressible flow model for the calculation of the thermodynamic variables as functions of several parameters, including the chimney area change. The study showed that, for a given chimney height, an increase in area ratio leads to augmentations in static pressure in the chimney. Based on a mathematical model, Schlaich [3] reported that optimal dimensions for a solar chimney do not exist. However, if construction costs are taken into account, thermoeconomically optimal plant configurations may be established for individual sites. It was shown in [9] that the characteristics of a system with a sloped collector roof are a weak function of the ratio of the collector inlet flow area and collector exit flow area. Koonsrisuk and Chitsomboon [10] investigated the predictions of 5 mathematical models proposed in the literature with the numerical results of ANSYS-CFX and revealed that the roof diameter and chimney height are the most important geometric dimensions for solar chimney design. Zhou et al. [11] reported the maximum chimney height in order to avoid

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Collector. The one-dimensional steady compressible flow in a variable-area passage is considered here. It is assumed that the solar heat gain is totally absorbed by the air under the roof. In the absence of friction and heat loss, the conservation equations in differential form are as follows

dr

dV dA þ ¼ 0 V A

(2)

¼ VdV

(3)

Energy : cp dT þ VdV ¼ dq

(4)

Continuity :

r

þ

dp

Momentum :

r

dp dr dT   ¼ 0: r p T

State equation :

(5)

_ and the height of the roof is given by hr ¼ a$r Let dq ¼ q00 dAr =m where a is the constant and r is the roof radius. Combining all equations, we have

dp ¼


 _ 2 dA m q00 dr :  _ p Tr 3 a2 r A3 2pmc

(6)

Next we assume that q00 , cp, r and T are approximately constant. Integrate from the entrance to the outlet of the collector, Eq. (6) becomes,

_2 m p2 ¼ p1  2r1

Fig. 1. Schematic layout of solar chimney power plant.

negative buoyancy, and the optimal chimney height for maximum power output. They found that the maximum height and the optimal height increase with collector radius. Ming et al. [12] did the steady axisymmetric numerical simulations on the solar chimney and reported that the optimum height-to-diameter ratio (hc/dc) of a chimney ranges from 6 to 8. While Kashiwa et al. [13] found that if hc/dc is not large enough, then the outside wind at the chimney top level can have a strong influence on the air updraft inside the chimney. In [13], a value of hc/dc ¼ 12 is considered sufficient to generate and maintain the updraft. The objective of the presented study is to quest for a better design of the solar chimney power plant and to focus on increasing the plant performance by controlling the flow area of the system. It is guided by the theoretical investigation along with the CFD-based design analysis. Based on the results of the computational simulation, the influence of the flow area parameters of the solar chimney on the behavior of the air flow is assessed. The area parameters analyzed are the areas at the collector entrance and chimney exit, while the areas at the collector exit and the chimney entrance were kept constant. 2. Derivation of theoretical model

1 1  2 2 A2 A1

_ q00 m þ 4pa2 r1 cp T1

! 1 1 :  r22 r12

(7)

Chimney. The air movement inside a chimney is assumed a frictionless adiabatic process. The system of equations for a onedimensional steady compressible flow in a variable-area chimney is as follows

Continuity :

Momentum :

dr

r

dV dA þ ¼ 0 V A

(8)

þ gdz ¼ VdV

(9)

þ

dp

r

Energy : cp dT þ VdV þ gdz ¼ 0 State equation :

dp dr dT   ¼ 0: r p T

(10)

(11)

Combining Eqs. (8)e(11) gives

_2 dp ¼ rgdz þ m

dA

rA3

:

(12)

Integrating between chimney’s inlet and outlet yields

p3 ¼ p4 þ r3 ghc þ

In this simple analysis the power generated by a solar chimney power plant as shown in Fig. 1 can be expressed as [14]

!

_2 m 2r3

! 1 1 :  A24 A23

(13)

For a variable area collector and chimney, let assume that

(1)

A1 ¼

pffiffiffiffiffi nr A2

(14)

_ becomes larger when p3 is amplified and p2 Eq. (1) shows that W is attenuated. To determine the geometry layout that can fulfill this, the governing equations for the movement of air within the collector and chimney are considered separately.

A4 ¼

pffiffiffiffiffi nc A3 :

(15)

_ m

_ m _ ¼ Dp z  ðp  p2 Þ: W rturb turb ðr2 þ r3 Þ=2 3

where nr and nc are the constants and their values depend on the roof slope and chimney shape. For example, nr¼(r1/r2)2 for

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a constant-height collector, nc ¼ 1for a constant-area chimney, nc < 1for a convergent-top chimney, and nc > 1for a divergent-top chimney. Substituting Eqs. (7) and (13)e(15) into Eq. (1), we get an approximation of Eq. (1) as follows:

_ ¼  W

" _ _2 m m ðr2 þ r3 Þ=2 2r3

_ q00 m  4pa2 r1 cp T1

! 1  nc nr  1 þ nc A23 nr A22 !# 1 1  r22 r12

(16)

It should be noted that when the heat loss and friction are not included in the analysis, the power is not a function of the shape of collector or chimney. An order of magnitude analysis reveals that, on the right-hand side of Eq. (16), the first term is much greater than the second term. Thus Eq. (16) becomes 3

_ m _ Wz  2

r2

! 1  nc n r  1 þ nc A23 nr A22

(17)

_ and r2 will be changed correWhen nr and nc are changed, m _ may be increased spondingly. However, Eq. (17) suggests that W when nc > 1 and nr < 1. In other words,

A1 < A2

(18)

and

A3 < A4 :

(19)

This finding makes recommendations regarding the arrangement of plant’s area ratio. To evaluate it, the numerical simulations of several solar chimneys with different collector and chimney’s shapes were carried out to investigate the varying behavior of the plant performances.

3. Computational work The plant layouts studied in this work are schematically depicted in Fig. 2aef. They are: (a) a constant-height collector with a constant-area chimney (see Fig. 2a), (b) a sloping collector with a constant-area chimney (see Fig. 2b), (c) a constant-height collector with a convergent-top chimney (see Fig. 2c), (d) a constant-height collector with a divergent-top chimney (see Fig. 2d), (e) a sloping collector with a convergent-top chimney (see Fig. 2e), and (f) a sloping collector with a divergent-top chimney (see Fig. 2f). Their details are listed in Table 1. To investigate the effects of flow area variation, we define the dimensionless measures

AR12 ¼ A1 =A2

(20)

and

AR43 ¼ A4 =A3 :

(21)

Generally, the solar chimneys that have been investigated in the literature have the same layout as configuration (a). The collector is customarily of a circular shape, while its height is relatively constant with some inclination angle, and the chimney is modeled as a constant-diameter tube. As a result, configuration (a) is chosen to be the reference plant in this study. Its collector has a diameter of 200 m and a height of 2 m, and it has a 100 m high chimney with a diameter of 8 m [15]. So AR12a ¼ 25 and AR43a ¼ 1. The commercial CFD code “ANSYS-CFX” has been proven to be a reliable tool to simulate the flow in solar chimney [16]. Consequently, the numerical model had been built using ANSYS-CFX in this work. In ANSYS-CFX, compressible equations for the conservation of mass, momentum and energy equations are solved for the whole plant using a control volume technique. The steady transport equations can be written in general form as follows:

  V$ ruf  Gf Vf ¼ Sf

(22)

Fig. 2. Schematic layout of (a) reference plant; (b) a sloping collector with a constant-area chimney; (c) a constant-height collector with a convergent-top chimney; (d) a constantheight collector with a divergent-top chimney; (e) a sloping collector with a convergent-top chimney; (f) a sloping collector with a divergent-top chimney.

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Table 1 List of models illustrated in Fig. 2. Configuration

Objective

Remark

(a) A constant-height collector with a constant-area chimney

Reference plant.

(b) A sloping collector with a constant-area chimney (c) A constant-height collector with a convergent-top chimney (d) A constant-height collector with a divergent-top chimney (e) A sloping collector with a convergent-top chimney (f) A sloping collector with a divergent-top chimney

Investigate the system when A1 < A2 and A4 ¼ A3. Investigate the effect of A3>A4 on the system with a constant-height collector.

A simple geometry version of the conventional solar chimney power plant cf. Eq. (18)

Adopt the idea from [6]

Investigate the effect of A3
cf. Eq. (19)

Investigate the combined effect ofA1A4.

e

Investigate the combined effect of A1
e

The buoyancy term in the momentum equation and the solar heat gain in the energy equation are given as

SM



 ¼ r  rref g

SE ¼ q00 =hr :

Fig. 3. Computational domain: (a) 5 axis-symmetric section; (b) Side view of the domain.

(23) (24)

where rref is the reference operating density specified at the inlet fluid condition of 308 K and 1 atm absolute pressure. The equations were discretized by a non-staggered grid scheme. A high resolution upwind differencing scheme was applied for the convective terms of equations. The convergence criterion was that the normalized residuals for mass, momentum and energy equations were required to be below than 107. A solar chimney is a cylindrical structure, so an axis-symmetric representation is assumed. As a result, a 5-degree pie shape of the plant was simulated as shown in Fig. 3a. An unstructured, nonuniform mesh was constructed. In order to ensure the accuracy of the numerical results, a grid dependence study was realized. Furthermore, the adaptive grid refinement algorithm locally refined the mesh only where needed based on regionally velocity variation. It should be mentioned that the numerical procedure used in this study had already been carefully calibrated and validated in [16] to achieve a satisfactory level of confidence. In addition, it should be noted that the turbine was not included in the simulation. The boundary conditions used are shown in Fig. 3b. At the center of the plant, axis-symmetric conditions were utilized. At the walls, free-slip and adiabatic boundary conditions were used. These conditions were applied at the roof, transition section, chimney wall and ground surface. The total pressure and temperature are prescribed at the roof inlet (reference pressure ¼ 101,325 Pa, total pressure ¼ 0 Pa (gauge), static temperature ¼ 308 K) and the flow direction was set as normal to the roof perimeter. At the chimney top, the ‘outlet’ boundary condition with zero static gauge-pressure is imposed.

configuration (b) increases a little when compare with configuration (a). One can notice that (p1p2)b < (p1p2)a while (p3p4)b z (p3p4)a. For configuration (c), p3,c > p3,a and p2,c > p2,a in such a way that (p2p3)c z (p2p3)a. On the other hand, p3,d < p3,a and p2,d < p2,a and we found that (p2p3)d > (p2p3)a. It was found that the simulation of configuration (e) had convergence difficulties. To mitigate the problem, instead of testing the case of A1 < A2 together with A3 > A4, we traded off configuration (e) to the case of A1 ¼ A2 together with A3 > A4. In that case we found that p3,e > p3,a and p2,e > p2,a in the manner that (p2p3)e z (p2p3)a. For configuration (f) it appears that (p2p3)f > (p2p3)a. It is important to notice that the pressure change inside the system does not show a strong sensitivity to the change of AR12 (configuration (b)), as it does to the change of AR43 (configuration (d)).

4. Results and discussion Fig. 4 shows the gauge pressure distributions inside the plants. It should be noted that the gauge pressures were scaled so that they are equal zero at the chimney top. It can be observed that (p2p3) of

Fig. 4. Effect of area variation on the pressure profiles.

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Fig. 7. Effect of AR12on the flow power (scaled by the flow power of prototype at position 3). Fig. 5. Effect of area variation on the mass flow rate (scaled by the mass flow rate of the reference case).

When we combine the effect of changing AR12 and AR43 together (configuration (f)), however, the reduction of AR12 can yield a vacuum pressure inside the system as shown in Fig. 4. The favorable flow behavior when A1 < A2 can be explained in the following way. In accord with the principle of conversation of mass, the acceleration required for the flow to move from the collector inlet to the collector outlet for a system with A1 < A2 is significantly less than that required by the flow in a conventional system (configuration (a)). Refer to Eq. (3), the smaller acceleration required leads to the larger (p1p2). Also, the favorable flow behavior when A3 < A4 can be explained in the following way. The flow area is increasing along the divergent-top chimney for a system with A3 < A4, this affects the flow velocity and can reduce the flow acceleration, resulting in the decrease of the pressure gradient across the chimney. Order of magnitude analysis reveals that the pressure drop due to the flow acceleration along the

chimney is significantly large compared with other pressure drops. Therefore using the appropriate AR43 can increase (p2p3) significantly. The effect of the flow area variation on the mass flow rate is presented in Fig. 5. The mass flow ratio depicted in Fig. 5 is defined as the mass flow rate of the test cases divided by the mass flow rate of the reference case, in which AR12 ¼ 25 and AR43 ¼ 1. The results show that varying AR12 does not affect the mass flow rate for the system with a constant-area chimney. On the other hand, an increase in AR43 produces an increase in the mass flow rate. The augmentation of mass flow rate is observed in cases of varying AR43 andAR12 > 0.75, except the case of AR12 ¼ 0.25 and AR43 ¼ 8 in which the flow recirculation occurred around the chimney exit. Fig. 6 shows the temperature rise across the roof. It is presented in dimensionless form and defined as the ratio of the temperature rise of the test cases to the temperature rise of the reference case. The values of temperature rise are consistent with the differences in mass flow rates presented in Fig. 5, since, in accordance with the conservation of energy principle, a higher mass flow rate should give a lower temperature rise for an equal amount of energy input.

Fig. 6. Effect of area variation on the collector temperature rise (scaled by the temperature rise of the reference case).

Fig. 8. Effect of AR43 on the flow power (scaled by the flow power of prototype at position 3).

A. Koonsrisuk, T. Chitsomboon / Energy 51 (2013) 400e406 Table 2 Power at the chimney base scaled by the power of the reference case, the square of _ 32 =q00 Ar . AR43 and the efficiency at chimney entrance, h ¼ 100  0:5mV AR43

(AR43)2

Power

h (%)

Note

1 0.25 0.5 0.75 2 4 8 16

1 0.06 0.25 0.56 4 16 64 256

1 0.06 0.25 0.54 4.27 18.49 69.07 179.16

0.36 0.02 0.09 0.19 1.54 6.66 24.89 64.55

Reference case e e e e e e e

Note: all test cases use the constant-diameter chimney.

_ 2 =2) Figs. 7 and 8 present the sensitivity of the flow power (¼mV with respect to the changes of AR12 and AR43, respectively. The ordinates of the figures are the normalized power, which is the power of the test cases scaled by the power at position 3 of the reference case, while the abscissas are the positions depicted in Fig. 1. The chimney diameter of the test cases in Fig. 7 is constant. It is obvious that the power at position 1 is a function of AR12 and a sloping roof leads to the power reduction inside the chimney. Although decreasing AR12 can increase the power at position 1 notably (leads to the option to install the turbine at position 1), but this power rise is still lower than the power inside the chimney. Further inspection reveals that the collector efficiency _ p DT=q00 Ar ) of the system with a sloping collector and a con(¼mc stant-area chimney is a weak function of AR12, and its overall ef_ 32 =q00 Ar ) is relatively constant. ficiency (¼0:5mV It is apparent in Fig. 8, in which the roof height is constant, that the power at position 3 is a strong function of AR43. It should be noted that the case of AR43 ¼ 16offers higher power than that of AR43 ¼ 32 due to the flow recirculation occurring near the chimney exit when AR43 ¼ 32. Table 2 presents the normalized power at the chimney base (position 3); the square of AR43 of each case is also shown. It is observed that the power increases in proportion to (AR43)2 when AR ranges between 0.25 and 8 and at a lower rate thereafter. This quadratic trend is suggested by Eq. (17). It would seem that there is an upper bound on AR43 that can boost up the power. Too high AR43 would eventually lead to boundary layer separation. Friction that comes with high velocity would also reduce the benefit. Further inspection of Table 2 shows that the efficiency also increases as AR43 increases. Efficiency in this case is defined as power at

Fig. 9. Combined effect of AR12 and AR43 on the flow power (scaled by the flow power of prototype at position 3).

405

chimney base divided by the total solar heat gain. This definition is unfair to the convergent-top case because its potential is at the top, not at the base. However, numerical results reveal that the power at the top of the convergent chimney remains the same as the constant area case. So, its potential remains unchanged in relation to the constant area case. The combined effect of AR12 and AR43 was shown in Fig. 9. Because the flow velocity of the cases of AR12 ¼ 0.25 is very high, so the flow recirculation is presented when AR43 > 1. This is the reason that the power of the cases of AR12 ¼ 0.25 is less than those of AR12 ¼ 0.5. As observed in the plots of pressure and mass flow rate that the ‘proper’ combination between AR12 and AR43 offers the largest power. It was found that the ‘proper’ combination depends on the whole size of the plant. In any case, it is evident that high AR43 leads to augmentation in power at the chimney base. This suggests the potential of harnessing more turbine power from the high AR43 system. 5. Conclusion A solar chimney system with varying flow area was studied and its performance was evaluated. Theoretical analysis suggests that the solar chimney with sloping collector and divergent-top chimney would perform better than that of a conventional system. CFD calculations show that a divergent chimney helps increase the static pressure, mass flow rate and power over that of the constant area chimney. For the convergent chimney, the power remains the same as the constant area case. The sloping collector helps increase the static pressure across the roof and the power at the roof entrance. The system with the sloping collector and divergent-top chimney of chimney area ratio of 16 can produce power as much as 400 times that of the reference case. Acknowledgments This research was sponsored by the SUT Research and Development fund of Suranaree University of Technology (SUT), Thailand. References [1] Haaf W, Friedrich K, Mayr G, Schlaich J. Solar chimneys: part I: principle and construction of the pilot plant in Manzanares. Int J Sol Energy 1983;2: 3e20. [2] Haaf W. Solar chimneys: part II: preliminary test results from the Manzanares plant. Int J Sol Energy 1984;2:141e61. [3] Schlaich J. The solar chimney. Stuttgart, Germany: Edition Axel Menges; 1995. [4] Nizetic S, Ninic N, Klarin B. Analysis and feasibility of implementing solar chimney power plants in the Mediterranean region. Energy 2008;33(11): 1680e90. [5] Zhou XP, Bernardes MA, dos S, Ochieng RM. Influence of atmospheric cross flow on solar updraft tower inflow. Energy 2012;42(1):393e400. [6] Padki MM, Sherif SA. On a simple analytical model for solar chimneys. Int J Energ Res 1999;23:289e94. [7] Chitsomboon T. The effect of chimney-top convergence on efficiency of a solar chimney. In: Proceeding of the 13th national mechanical engineering conference, Thailand; 1999. [8] Von Backström TW, Gannon AJ. Compressible flow through solar power plant chimneys. J Sol Energ-T ASME 2000;122(3):138e45. [9] Koonsrisuk A. Mathematical modeling of sloped solar chimney power plants. Energy 2012;47(1):582e9. [10] Koonsrisuk A, Chitsomboon T. Accuracy of theoretical models in the prediction of solar chimney performance. Solar Energy 2009;83(10):1764e71. [11] Zhou XP, Yang JK, Xiao B, Hou G, Xing F. Analysis of chimney height for solar chimney power plant. Appl Therm Eng 2009;29:178e85. [12] Ming T, deRichter RK, Meng F, Pan Y, Liu W. Chimney shape numerical study for solar chimney power generating systems. Int J Energ Res 2011. http:// dx.doi.org/10.1002/er.1910. [13] Kashiwa BA, Kashiwa CB. The solar cyclone: a solar chimney for harvesting atmospheric water. Energy 2008;33(2):331e9. [14] Koonsrisuk A, Chitsomboon T. Mathematical modeling of solar chimney power plants. Energy, http://dx.doi.org/10.1016/j.energy.2012.10.038; 2012.

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[15] Koonsrisuk A, Chitsomboon T. A single dimensionless variable for solar tower plant modeling. Sol Energy 2009;83(12):2136e43. [16] Koonsrisuk A, Chitsomboon T. Dynamic similarity in solar chimney modeling. Sol Energy 2007;81(12):1439e46.

Nomenclature a: constant A: flow area, m2 Ar: roof area, m2 AR12: ratio of the collector inlet area to the collector outlet area AR43: ratio of the chimney outlet area to the chimney inlet area cp: specific heat capacity at constant pressure, J/(kg K) g: gravitational acceleration, m/s2 hc: chimney height, m hr: roof height above the ground, m _ mass flow rate, kg/s m: nc,nr: constants p: pressure, Pa q: heat transfer rate per unit mass, W/kg q00 : insolation, W/m2

r: roof radius SE: source term in the energy equation, W/m3 SM: source term in the momentum equations, N/m3 Sf: source term T: absolute temperature, K u: velocity vector V: flow velocity, m/s _ flow power, W W: z: Cartesian coordinate in vertical direction z: approximately equal Greek symbols

Dp: pressure drop, Pa f: flow variable Gf: diffusion coefficient, Ns/m2 r: density, kg/m3 Subscripts 1,2,3,4: positions as depicted in Fig. 1 a,b,c,d,e,f: plant configurations as shown in Table 1 ref: reference state turb: turbine