Effect of chimney shadow on the performance of wind supercharged solar chimney power plants: A numerical case study for the Spanish prototype

0 Introduction

Energy is of paramount importance to developing countries, such as China and India.However, due to environmental issues, including pollution and the greenhouse effect related to the use of fossil fuels,supplying energy becomes increasingly difficult.The largescale development of renewable and clean energy power generation is the best possible solution to reduce carbon emissions [1].One of the most promising sources of clean energy is solar energy, which has the advantages of low cost and no harmful emissions [2].A solar chimney power plant(SCPP) is a simple and clean option for the large-scale use of solar energy.In 1903, Cabanyes proposed the concept of the SCPP and stated that a typical SCPP is mainly composed of three parts: a solar collector, chimney, and turbine [3].The first SCPP was built in Manzanares, Spain in 1982 and operated automatically for approximately 7 years, which demonstrated the feasible operation of the SCPP.The preliminary test results and energy balance, design criteria,and costs of the Spanish prototype SCPP were reported in reference [4-5].In 2002, Zhou et al [6] built China’s first experimental SCPP setup in Wuhan to investigate the temperature distribution in the SCPP.The Jinshawan solar chimney power plant, built in Wuhai, China, was connected to the grid for power generation in October 2010.Compared with the Spanish prototype SCPP, the power generation efficiency of this power station is very low because the total height of the chimney is 53.0 m.Nonetheless, this power station can generate electricity through a mix of solar and wind energy by setting ventilation doors to increase the power output [7-8].

The traditional SCPP has the advantages of a simple structure, easy design, convenient materials, and low maintenance costs [9].The SCPP does not require fossil fuels for operation.Consequently, this power plant does not cause any greenhouse gas emissions, being a completely eco-friendly renewable energy application.Compared with the parabolic trough solar thermal power generation, dish solar thermal power generation, and tower solar thermal power generation [10-12], the energy conversion efficiency of the SCPP, which is considered only for power generation,is lower.There are two main methods to address the limitations of current SCPPs.One is to optimize the internal structure and dimension parameters of the SCPP [13-16].The other is to combine other appropriate technologies to form a multi-technology coupled comprehensive system.For example, the SCPP can be combined with photovoltaic power generation [17], building ventilation [18],external heat sources [19], and wind power [20].A wind supercharged SCPP combined with seawater desalination(WSSCPPCSD) and wind supercharged SCPP (WSSCPP),in which the wind pressure ventilator is placed at the exit of the chimney, were proposed in references [21-22].This system can greatly improve the system performance,offering a promising option for the commercialization of SCPPs.

In reference[23], Mullett found that the height of the chimney had a direct effect on the overall efficiency of the SCPP, which was approximately 1% when the chimney height was 1,000 m.Li et al [24] proposed a non-steadystate simplified model of the SCPP and a power quality factor to evaluate the power generation efficiency and stability of the system.They found that the power quality factor was positively correlated with the chimney height and negatively correlated with the radius of the solar collector.In reference [25], based on the Spanish prototype,the maximum chimney height necessary to avoid negative buoyancy and the optimal chimney height corresponding to the maximum power output were presented and verified.Therefore, it can be concluded that the height of the chimney has an important influence on the performance of the SCPP.

Many studies on numerical methods adopting computational fluid dynamics (CFD) have been conducted to predict the performance of the SCPP.In reference [26],numerical simulations of the Spanish prototype SCPP were performed and the effect of the turbine rotational speed was analyzed.Gholamalizadeh et al.reference [27-28]performed a 3-D simulation using the two-band radiation model to study the influence of the greenhouse effect.In reference [29-30], the authors developed a small-scale SCPP and conducted numerical simulations to analyze the effect of the divergence angle of the chimney, ambient temperature, solar flux, and turbine efficiency on the air flow and performance parameters of the SCPP.

Radiation heat transfer is a non-negligible factor in the greenhouse effect and must be studied in numerical simulations of the SCPP.In reference [31], Guo et al.conducted a numerical simulation incorporating the discrete ordinate (DO)radiation model and found that the radiation heat transfer in the collector could not be ignored, otherwise the heat loss could be underestimated.A 2-D mathematical model based on the radiation heat transfer in the collector was proposed, and the radiation model was implemented in ANSYS Fluent as a userdefined function (UDF) [32].A numerical simulation of the solar-enhanced natural draft dry cooling tower showed that the heat transfer process could be predicted more accurately using the above radiation model [33].

In addition, due to the effect of the solar elevation angle,the chimney forms a shadow area in the solar collector.The power output of the SCPP may be overestimated if the influence of the chimney shadow is neglected [34].In the case of the WSSCPPs, the chimney height is 209.6 m when the height of the wind supercharging ventilator is 15 m.This indicates that the chimney shadow area of a WSSCPP is larger than that of a SCPP for the same incident angle.For a wind supercharged system, it is critical to study the influence of the chimney shadow to accurately predict the performance of the system.Therefore, in this study, the chimney shadow effect and radiation heat transfer are considered to calculate the system performance more accurately, which is important for the design and construction of SCPP systems.

In this study, 3-D numerical simulations of a SCPP and WSSCPP at a solar ray incident angle of 0 to 30° were performed using the ANSYS Fluent software.The DO radiation model and coordinates of the solar ray vectors were incorporated to improve the accuracy of predicting the actual performance of the SCPP systems.In addition,a parametric study was performed by varying the solar incident angle from 0° to 30° to explore the chimney shadow effect.

1 Methodology

1.1 Physical model

The basic model of a WSSCPP is shown in Fig.1; it mainly consists of four parts: a solar collector, vertical chimney, turbine, and wind pressure ventilator.The main dimensions of the physical model are derived from the Spanish prototype, as presented in Table 1.The transition section, which connects the collector and chimney, is designed as a bell-shaped transition to reduce the flow loss.

Fig.1 Schematic diagram of the WSSCPP

Table 1 Main parameters of the Spanish prototype

Parameter Value/m Chimney height 194.6 Chimney radius 5.08 Collector radius 122 Average height of the collector roof 1.85 Thermal energy storage layer thickness 5.0 Solar radiation intensity 850 W/m2 Actual power output 37.0 kW Turbine speed in the grid connection mode 100 rpm

1.2 Mathematical model

In this simulation, the airflow in the SCPP is considered to be a steady-state, incompressible flow.The flow in the SCPP is a type of buoyancy-driven flow and its strength is usually measured by the Rayleigh number.The Rayleigh number in the Spanish prototype is higher than 1010, which indicates that the flow is turbulent.The Boussinesq model is adopted in the simulation.

where ρ is the air density and ρ0 is the density of ambient air; T is the air temperature and T0 is the ambient temperature; β is the thermal expansion coefficient, which is equal to 1/T0.

The generalized equation governing the entire system can be expressed as:

where φ is the generalized dependent variable, which can represent 1, v, T, k, and ε of the continuity equation, N-S equation, and energy equation; Γφ is the universal diffusivity and Sφ is the universal source term.

The blocking effect of the collector roof on the ground long-wave radiation is the key aspect governing the heating function of a SCPP.As the discrete ordinate (DO) radiation model can be used to model semi-transparent and opaque walls, this model is adopted to solve the radiative transfer equation.The radiative heat transfer equation is given by:

whereis the position vector, is the direction vector, is the scattering direction vector, α is the spectral absorption coefficient, n is the refractive index, σs is the scattering coefficient, σ is the Stefan - Boltzmann constant, I is the spectral intensity, φ is the phase function, and Ω′ is the solid angle.

The entries in the table represent the X coordinates, where

Y=0 and Z=1.

The incident angle of the solar rays directly determines the area of the shadow region.In this study, the effect of the chimney shadow was investigated by setting the direction of the incident solar rays, and the solar ray-tracing algorithm was employed.The sun rays are assumed to be beams of parallel light and the incident angle (θ) is the angle between the incident solar ray and Z-axis, as shown in Fig.2.Table 2 lists the coordinates of the solar ray vectors at different incident angles.

Table 2 Coordinates of the ray vectors at different incident angles

θ (°) SCPP WSSCPP 0 0 0 5-0.087489 -0.094232 10 -0.176327 -0.189918 15 -0.267949 -0.288603 20 -0.36397 -0.392025 25 -0.466308 -0.502251 30 -0.57735 -0.621853

Fig.2 Incidence of solar rays

The related performance parameters are calculated as:

Turbine shaft power Ptur:

where nt is the turbine rotational speed and M is the torque.

Turbine efficiency ηtur:

where m˙ is the mass flow rate and Δp is the turbine pressure difference.

Collector efficiency ηcol:

where cp is the specific heat capacity, ΔT is the collector temperature rise, rcol is the radius of the collector, and S is the solar radiation intensity absorbed by the collector.

1.3 Mesh generation

The ANSYS ICEM 16.0 software was used for meshing.The unstructured grid method is adopted in the turbine region while the other parts are structured grids.The grids of each domain are connected by a sliding mesh interface.The fluid domain, solid domain, and fluid-solid interface are created in the process of collector region meshing.Locally thickened meshes are employed in the transition section.Fig.3 shows the mesh of the computational domain.The number of mesh elements is optimized with respect to the variation in the mass flow rate and collector temperature rise.In the simulation, the number of grid elements is approximately 5,466,000.

Fig.3 Mesh distribution in the domain

1.4 Boundary conditions and solution method

The simulation was performed using the ANSYS Fluent 16.0 software, and the boundary conditions are presented in Table 3.The standard k-ε turbulence model coupled with the enhanced wall function was employed.The DO radiation model and solar ray tracing were selected to model the solar irradiation and sun direction vector.The temperatures at the bottom and sides of the heat storage layer are set to 298.15 K.The interface between the heat storage layer and airflow domain is set as a “coupled” boundary.The collector roof is set as a semi-transparent material with a thickness of 5 mm and as a “mixed” boundary.The multiple reference frame(MRF) model is used for the turbine region, and the other walls are adiabatic boundaries.The SIMPLEC algorithm is used for the pressure-velocity coupling scheme.

Table 3 Boundary conditions

Place Type Value Collector inlet Pressure inlet Ta=298.15 K Chimney outlet Pressure outlet pgage= 0 Pa for the SCPP pgage= -64.5 Pa for the WSSCPP Collector roof Wall Mixed: h =10 W/(m2·K)Ground surface Wall Coupled Heat storage Wall T= 298.15 K Chimney Wall Adiabatic

2 Results and discussion

2.1 Validation

The validation of the numerical simulation is presented in Table 4.The turbine pressure drop is 89.2 Pa, and the turbine shaft power is 39.03 kW when the turbine rotational speed is 100 rpm.As shown in Table 4, the errors between the present simulation and the Spanish experimental data for the temperature rise, outlet velocity, and power are 1.14%, 7.95%, and 5.48%, respectively.The power output and outlet velocity in our simulation are slightly higher than the experimental power generation.This can be attributed to the bell-shaped transition section, which may reduce the flow loss.Hence, it can be concluded that the simulation performed in this study can predict the operational parameters of a SCPP accurately.

Table 4 Validation of the numerical method

Parameters Temperature rise/K Outlet velocity/(m/s) Power /kW Spanish prototype [2] 17.5 8.8 37.0 Gholamalizadeh [12] 17.2 9.0 36.1 Present simulation 17.3 9.5 39.03

2.2 Flow field analysis

Fig.4 shows the temperature distributions of the collector roof, heat storage layer surface, and Z=1 plane of the SCPP when the incident angle is 25°.The shadow directly results in a sudden temperature drop of the shadow area.It can be observed that the temperature of the shadow area is lower than that of the adjacent area.This difference is more obvious on the surface of the heat storage layer.The maximum and minimum temperatures of the heat storage layer surface are 344.4 K and 292.89 K, respectively.There are still some unshaded areas in the +X direction when the incident angle is 25°.Therefore, the distributions of the solar radiation and temperature in the entrance area of the collector are axisymmetric.

Fig.4 Temperature distributions in the SCPP when the incident angle is 25°

Fig.5 shows the temperature distributions of the axial plane in the SCPP at incident angles of 0° and 25° and the WSSCPP at 25°.From Fig.5, it can be seen that the temperature distribution is symmetrical when the incident angle is 0°.Compared to the distributions of SCPP-0° and SCPP-25°, the temperatures of the collector roof, heat storage layer, and airflow exhibit a small difference, which becomes more significant in the shadow area.Due to the chimney shadow, a low-temperature area is generated on the surface of the heat storage layer in the shadow area.In the low-temperature area, the airflow tends to heat the collector roof and heat storage layer by convection heat transfer,which can result in heat loss of the airflow.Consequently,the airflow temperature in the +X direction of the shadow area is lower than that in the -X direction of the unshaded region.The shadow area of the WSSCPP is larger owing to the wind pressure ventilator.Under the suction force of the negative pressure generated by the wind pressure ventilator,the air mass flow rate increases, the air velocity increases,and the air heating time reduces.Thus, the collector temperature rise of the WSSCPP is smaller than that of the SCPP.

Fig.5 Temperature distributions of the axial plane in the SCPP and WSSCPP

The airflow is heated by the collector roof and heat storage layer surface as it enters the collector.The temperature of air increases while its density decreases.Concurrently, the air flows toward the center of the collector because of the pumping effect of the chimney.However, the temperature of the airflow in the shadow area is higher than that of the collector roof and heat storage layer surface.The two parts will be heated by the airflow.This is the reason for the temperature of the air in the shadow area being lower than that in the adjacent area.As the temperature of the airflow in the unshaded area increases, the temperature difference between the shaded and unshaded areas at the collector center increases.

Fig.6 shows the air velocity and streamline distributions of the SCPP and WSSCPP collectors when the incident angle is 25°.As shown in Fig.6, the air is heated and converges at the center of the collector in the radial direction.Once the airflow enters the shaded area, it flows downward along with simultaneous backflow.The temperature of the airflow in the shadow area decreases,increasing the air density.The airflow then flows downward.On the other hand, the air still keeps flowing to the center of the collector because of the chimney.There is a backflow and an air stagnant zone in the collector.In addition, heat exchange occurs via air mixing between the air in the shaded and non-shaded areas, resulting in a loss of momentum.As a result, mixed, cluttered streamlines are formed near the shadow area.For the WSSCPP, the negative pressure at the chimney outlet results in a higher airflow velocity, which restrains the backflow.

Fig.6 Velocity and streamline distributions in the SCPP and WSSCPP collectors when the incident angle is 25°

2.3 Influence of the incident angle on the SCPP and WSSCPP performance

The shadow area of the chimney is directly determined by the height of the chimney and incident angle.The effects of the incident angle on the SCPP and WSSCPP performance cannot be ignored.The incident angles were set to 0°, 5°, 10°, 15°, 20°, 25°, and 30° to investigate the effects of the chimney shade on the system performance.

Fig.7 and Fig.8 show the variations in the chimney outlet velocity, collector temperature rise, collector efficiency, and turbine efficiency versus the incident angle.The chimney outlet velocity, collector temperature rise, and collector efficiency increase with an increase in the incident angle.The variation in the turbine efficiency is relatively small.

Fig.7 Chimney outlet velocity and collector temperature rise versus the incident angle

Fig.8 Collector efficiency and turbine efficiency versus the incident angle

The solar radiation absorbed by the collector decreases due to the chimney shadow.In contrast, the lowtemperature area on the heat storage layer surface becomes larger, resulting in more heat loss.This will aggravate the imbalance of the temperature distribution in the collector and lead to a decrease in the collector efficiency.As a result, the temperature and density differences between the air inside and outside the system decrease.This results in a reduction in the total pressure drop and air velocity at the chimney outlet.

By comparing the curves of the WSSCPP and SCPP, it can be seen that the chimney outlet velocity of the WSSCPP is higher than that of the SCPP but that the collector temperature rise and collector efficiency are both less than those of the SCPP.The shadow area of the WSSCPP is larger due to the wind pressure ventilator.Because of the negative pressure at the chimney outlet, the average velocity of the WSSCPP is higher, resulting in a shorter air heating time.This can also enhance the convective heat transfer between the airflow and surface of the heat storage layer in the shadow area, leading to more heat loss.Therefore,compared with the SCPP, the collector efficiency and collector temperature rise of the WSSCPP are lower.

Fig.9 shows the variations in the turbine shaft powers of the SCPP and WSSCPP versus the incident angle.It can be seen that the turbine shaft powers of the SCPP and WSSCPP decrease with an increase in the incident angle.When the incident angle increases from 0° to 30°, a 22.4% decrease in the turbine shaft power of the SCPP and a 13.7% decrease in the turbine shaft power of the WSSCPP are observed.This indicates that the chimney shadow greatly reduces the power outputs of the SCPP and WSSCPP, which is detrimental to the operation of the system.The temperature rise and turbine pressure drop decrease as the incident angle increases.Thus, the turbine pressure difference and power output decrease.In addition, in the WSSCPP, the negative pressure at the chimney outlet results in a faster airflow,which weakens the effect of airflow sinking and backflow.Consequently, the decrease in the turbine shaft power is relatively small compared with the SCPP.

Fig.9 Turbine shaft power versus the incident angle

2.4 Influence of the chimney shadow

To study the effects of chimney shadows more comprehensively, we investigated the shadow effects in the SCPP, WSSCPP, and WSSCPPCSD.In reference [22], the authors combined desalination with the WSSCPP and used MATLAB to simulate the desalination process.However,the temperature distribution calculated with MATLAB did not reflect the influence of the chimney shadow.In reference[34], the effect of the incident angle was categorized into two parts: the ratio of the shadow area to the total collector area and the incident angle.In this study, the collector area loss caused by the chimney shadow is expressed in terms of the decrease in the collector radius.Therefore, the shadow effect of the chimney can be calculated quantitatively.Then,the performance parameters of the SCPP, SCPPCSD, and WSSCPPCSD with the equivalent radius were calculated.The loss coefficient is defined as the product of the ratio of the effective area and the cosine of the incident angle to describe the effect of the chimney shadow.

Fig.10 shows a comparison between the results of this study and those reported by reference[34].It can be observed that the results of the estimation methods are consistent.The main reason for the difference in the simulations is the different settings of the average height of the collector roof and the transition section.Guo et al.set the collector as a parallel plate with a height of 1.85 m[34].In our simulations, the slope of the collector roof was considered, and the transition section was optimized.

Fig.10 Comparison between the estimation and simulation models

Fig.11 shows the variation of the turbine shaft power and freshwater yield of the SCPP, WSSCPP, and WSSCPPCSD.The variation trend of the turbine shaft power with the incident angle is consistent with the numerical simulations.Compared with the turbine shaft power, the freshwater yield of the WSSCPPCSD significantly decreases.The freshwater yield of the WSSCPPCSD reduces by 15.93% when the incident angle changes from 0° to 30°.This finding indicates that neglecting the chimney shadow can lead to an overestimation of the WSSCPPCSD performance.

Fig.11 Variation of the turbine shaft power and freshwater yield

3 Conclusion

In this study, numerical simulations using the DO radiation model and ray-tracing algorithm were conducted to investigate the shadow effect of a wind supercharging chimney.The accuracy of predicting the actual SCPP performance is improved when the effects of the solar altitude angle are considered, which provides a reference for the commercialization of the SCPP and WSSCPPCSD.The study was performed based on the specifications and geometry of a Spanish power plant.A parametric study was performed by varying the incident angle from 0° to 30° to study the chimney effect using the ANSYS Fluent software.The main conclusions of this study are as follows:

(1) A shadow area is created on the collector area due to the shadow effect of the chimney.As a result, the temperatures of the collector roof and heat storage layer surface in the shadow area decrease suddenly.The airflow flows downward once it enters the shadow area, along with simultaneous backflow.For the WSSCPP, the concurrent backflow in the shadow area is weakened because of the negative pressure produced by the wind pressure ventilator.

(2) The turbine shaft powers of the SCPP and WSSCPP decline by 22.4% and 13.7%, respectively, when the incident angle increases from 0° to 30°.Ignoring the chimney shadow can lead to an overestimation of the power outputs of the SCPP and WSSCPP.

(3) The results of the estimation methods presented in this study are similar to those reported in reference [34].The freshwater yield of the WSSCPPCSD reduces by 15.93% when the incident angle changes from 0° to 30°.It is important to consider the chimney shadow effect when estimating the performance in the design and cost analysis of WSSCPPCSD systems.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No.51976053) and College Students Innovation and Entrepreneurship Training Program (No.202010294024).

Declaration of Competing Interests

The authors have no conflicts of interest to declare.