Scaled Designs of Solar Chimneys for Different Locations

Abstract

A global motivation to reduce reliance on fossil fuels and transition to cleaner, renewable energy sources propels studies of innovative technologies to harness solar energy. This paper investigates the viability of a promising renewable energy technology, solar chimney power plants (SCPPs), in a domestic context. Using a scalable mathematical model, including thermodynamic processes within the collector, chimney, and turbine generator, the power output of SCPPs is assessed across five global locations with varying annual energy requirements: Aswan, Egypt, Cornwall, UK, Melbourne, Australia, Quito Ecuador, São Paulo Brazil. This research predicts a plant’s performance under differing plant geometries and meteorological inputs such as ambient temperature and solar irradiance, revealing that Aswan, Quito, and São Paulo can reliably produce year-round power, while Cornwall and Melbourne may need a supplementary energy supply in the winter months. The model establishes a linear relationship between collector radius and chimney height for each region to minimize geometry whilst fulfilling annual energy requirements, demonstrating that reducing one component size increases the other to maintain the required output. These geometries inform discussions of technology implementation, including the integration of an air-source heat pump (ASHP) to enhance performance, though it was found that the SCPP may not meet the power demand of the ASHP in Melbourne winter. Some lifecycle factors of the Melbourne and Quito plants are considered to assess the environmental viability of the technology.

1. Introduction

The ‘dangerous climate change guardrail’ of 1.5 °C global temperature rise represents a pivotal threshold, beyond which the world may reach a point of no return in the face of global warming [1]. The United Nations Paris Agreement aims to mitigate this risk by targeting a 45% reduction in emissions by 2030, with the ultimate goal of achieving net zero emissions by 2050 [2]. However, with fossil fuels currently supplying around 80% of the world’s energy [3] and current projections indicating a 9% increase in emissions by 2030 compared to 2010 [4], achieving the Paris Agreement targets requires a radical shift in energy production away from fossil fuels and towards clean, renewable sources.

A solar chimney power plant (SCPP), shown in Figure 1, is a promising renewable energy technology that utilizes well-known principles and relatively inexpensive materials for construction to create electricity from solar radiation with low carbon emissions. These principles are the greenhouse effect, the buoyancy effect, and the conversion of kinetic energy into electrical energy via a turbine generator.

Figure 1a displays the three main components of a SCPP. The collector is constructed from a transparent material, such as glass, PVC, or plastic film, which is elevated above the ground and open around the perimeter. The collector uses the greenhouse effect to heat the ground below using both direct and diffuse solar radiation, which, combined with the buoyancy effect and an open perimeter, creates a solar-induced convective airflow that is driven towards the center of the collector. Here, a turbine captures the kinetic energy before the air rises up from the chimney and returns to the atmosphere, as shown in Figure 1b. The air continuously moves through the system, driven by the pressure difference between the air outside and inside the SCPP. The numbered locations in Figure 1b is referenced throughout this report as subscripts following the corresponding parameters.

Although large-scale SCPPs have been widely studied, research on small-scale SCPPs and their domestic application remains limited. The motivation behind this research is to investigate the technical, practical, and environmental viability of the domestic application of a SCPP in various locations around the globe, with the aim to forecast system performance, considering dimensional and meteorological parameters.

The main objectives of this paper are as follows:

• Devise a mathematical model to predict the performance of solar chimney systems in different locations with varying dimensions;
• Compare and analyze the results of the systems in different locations and for different energy requirements;
• Discuss the feasibility and practical implementation of their domestic application in different locations.

A Python-based mathematical model was developed to simulate the thermodynamic processes validated using experimental data. Hourly meteorological data spanning a year for five distinct global locations were used to compute the hourly power output over the course of that year. Varying the system dimensions was used to understand the impact on the power output through modeling. This allowed for an examination of the relationship between required energy generation and minimum system size, considering location-specific meteorological parameters. The results obtained informed a discussion on the feasibility, practicality, and environmental impact of implementing SCPP technology in diverse geographical locations, providing insights for further discussions on its application.

2. A Review of the Solar Chimney Power Plant (SCPP)

The concept of using rising hot air in a chimney to propel a turbine was first presented as a ‘smoke jack’ by Leonardo da Vinci around 1480 [5]. In 1903, Isidoro Cabanyes introduced an early form of a SCPP, outlining a ‘projecto de motor solar’ or ‘solar engine project’ that featured a collector that heats air, connected to a building with a chimney. In this setup, the heated air flows through the chimney and rotates a fan, thereby generating electricity [6]. The first SCPP prototype was constructed in Manzanares, Spain, by the engineering firm Schlaich & Partners in 1982 [7], as seen in Figure 2.

The Manzanares prototype was constructed with a thick collector cover made from various plastic films and glass, a reinforced concrete chimney, a blackened bitumen collector floor, and a vertical axis turbine with four blades, designed for a peak power output of 50 kW [9]. Some key dimensional parameters are listed in

Table 1. Manzanares SCPP key parameters from Refs. [7,9].

Dimensional Parameters		Operating Parameters
Collector Radius, rcoll [m]	122	Ambient Temperature, T1 [°C]	23.4
Collector Height, Hcoll [m]	1.85	Solar Irradiance, I [W/m2]	850
Chimney Radius, rch [m]	5.08	Ambient Pressure, p1 [Pa]	92,930
Chimney Height, Hch [m]	194.6

alongside operating parameters from 2 September 1982 at midday.

The Manzanares pilot plant was commissioned in 1982 and was in operation for 15,000 h between 1986 and 1989, running for an average of 8.9 h a day with 95% reliability. The prototype was constructed with the purpose of performing tests and experiments in order to design larger plants with the potential of producing 200 MW of power [8]. Although the Spanish prototype produced a large dataset, it is still one of the only large-scale plants that has ever been constructed, resulting in a scarcity of validation points for subsequent studies.

There were plans for the construction of a large SCPP in Mildura, Australia, capable of generating 200 MW. With a chimney constructed from cement and steel at a height of 1 km and a collector diameter of 10 km, this plant came with an expected cost of AU$1.67 billion [10], making it difficult to secure funding and resulting in the eventual rejection of the plans [11].

Ghalamchi et al. [12] conducted a study to obtain experimental results on varying geometric dimensions on a pilot SCPP with a collector diameter and chimney height of 3 m. They concluded that reducing the collector inlet height had a positive impact on the performance of the chimney. Lal et al. [13] built a small SCPP in Kota, India, with a collector diameter of 12 m and a chimney height of 8 m, producing around 5 W of electrical power at an irradiance of 820 W/m². These results informed the development of a computational model to estimate the optimum location for the turbine at a height of 0.25–1 m inside the chimney tower. A small SCPP was constructed in Aswan, Egypt, by Mekhail et al. [14], measuring 6 m in both collector diameter and chimney height with a recorded maximum power of 0.85 W for an irradiance of 1000 W/m². This study aimed to expand on the mathematical model reported by Koonsrisuk et al. [15] in order to predict the performance of a larger plant. In Texas, a SCPP was constructed with a variable chimney height from 0.203 to 7.52 m by Raney et al. [16] to investigate the necessary size for a 35 W output. They concluded from their study that this would require a chimney height of 15 m and a collector radius of 60 m, stating that the characteristic equations of the flow still apply to small scale SCPPs.

Haaf et al. [9] first developed an analytical model to predict the performance of the Manzanares plant. They reported that if the collector radius is increased, output is also increased; however, this resulted in reduced efficiency. Also, increasing the chimney height increases the efficiency of the SCPP. They also reported that the momentary efficiency should not be a design requirement, and the most important design factor should account for the average power output over long periods of time. Zhou et al. [17] used a theoretical model to study the effect of chimney height and concluded that the optimum chimney height for the Manzanares plant is 615 m for a peak power output of 102.2 kW. Cuce et al. [18] developed a computational fluid dynamics model to investigate the effect of altering geometry on a variety of parameters. They found that mass flow rate is a key parameter of system performance and is equal to 1122.1 kg/s for the Manzanares plant with an irradiance of 1000 W/m².

A mathematical model was used by Koonsrisuk et al. [15,19] to investigate the power production of a SCPP based on the geometry. They reported that the power generated per unit of land area is proportional to the length scale of the power plant, although this cannot increase indefinitely as other losses are introduced as the system increases in size, altering the simple model. Setareh [20] developed a comprehensive mathematical model, similar to the one used in this paper. They proposed that the collector heat loss coefficient is not a fixed value but instead is calculated from a variety of dimensional, environmental, and material parameters. They included the effect of ambient wind in the model and stated that increasing wind velocity has a “remarkable positive effect” on the performance of the plant.

Haaf et al. [9] reported on the effect of environmental factors such as the local climate, where a lower ambient temperature leads to increased efficiency of the system. Also, the collector characteristics, such as floor solar absorption and cover transmissivity, determine how much of the solar radiation is converted to thermal energy. Haaf et al. [7] found that dust deposits on the collector cover influenced the transmissivity, but for smooth materials such as polyester, the dust adhesion was extremely low and, after rain showers, only decreased the transmission value by up to two percent. Kreetz [21] proposed using black plastic pipes filled with water under the collector as a form of thermal storage, with his numerical model indicating that this would make 24 h power production possible. Das et al. [22] reported in depth on a variety of materials and their properties that can be used in the construction of the SCPP components as well as the corresponding effect on the performance of the plant.

There are several methods reported to calculate the power output of the SCPP system, as outlined in

Table 2. Reported methods for calculating power output.

Reference Source	Type of Study	Method	In This Paper?
Haaf et al. [9]/Raney et al. [16]	Numerical/Experimental	Electrical power production—accounts for chimney height and collector, turbine, and frictional efficiencies	No
Lal et al. [13]	Experimental and Numerical	Electrical power production—accounts for chimney height and collector and generator efficiencies	No
Zhou et al. [17]	Mathematical	Electrical power production—accounts for turbine generator efficiency, pressure difference over the turbine and collector area	No
Mekhail et al. [14]/Setareh [20]	Mathematical and Experimental/Mathematical	Available turbine power—accounts for the pressure potential and volume flow rate over the turbine	Yes
Koonsrisuk et al. [15]	Mathematical and Numerical	Available turbine power—accounts for the pressure potential in the collector and does not model the turbine	No

, resulting in some discrepancies between model results.

Haaf et al. [9] used this method to design the Manzanares pilot plant with a maximum power capacity of 50 kW. However, the actual maximum output of the plant was 36 kW [7], and this difference was attributed to losses over the turbine.

Aside from the pilot plant in Manzanares, all of the subsequent experimental studies have been limited to laboratory-sized plants, with [22] reporting that chimney height values are limited to 0.2–12 m. This gives a basic understanding of the real flow behavior to inform mathematical and numerical studies. On the other hand, the wide range of numerical and analytical studies all focus on large-scale commercial plant sizes, with [22] reporting that chimney height values studied are between 123 and 1500 m, and therefore, research into domestic SCPP’s is very limited. The main findings from all these studies indicate that an increase in the size of the system increases the power output.

For the purpose of this paper, the effect of ambient wind is neglected for modeling simplicity and mathematical tractability. The collector loss coefficient is also set at a fixed value, establishing uniformity throughout the models. This is a good assumption and justified later through a sensitivity study of the parameters contributing to power output. The power output chosen for use in this report is consistent with that of Mekhail et al. [14] and Setareh [20] due to the smaller number of input parameters, resulting in a simpler model and ensuring consistency for each location.

3. Methodology

3.1. Location

Initially, 10 to 15 locations were considered across all continents but were eventually reduced to 5 for the purpose of this paper. The locations shown in Figure 3 were selected to represent a variety of latitude, longitude, altitude, and terrain. Two locations are located each in the Northern and Southern Hemispheres, and one location is on the Equator.

Previous studies have investigated the potential for SCPPs in Aswan [14], Victoria, Australia [11], and Brazil [23], supporting the decision to report on these locations. No studies have been conducted on SCPPs in the UK, so the southwest region was selected due to having the highest global horizontal irradiance and being the most feasible across twenty locations in 2019 according to [24]. Quito was selected for its equatorial position as well as its high altitude. As altitude increases, the atmospheric pressure decreases, highlighting the effect of atmospheric pressure and air buoyancy on the output of the Quito plant.

Another selection criterion was the variation in average household energy use across the different locations, presenting an opportunity for conducting location-specific studies to determine the minimum dimensions necessary for each area.

Table 3. Average annual domestic electricity consumption.

Location	UK	Victoria, Australia	Egypt	Brazil	Ecuador
Power Consumption [kWh]	2700 [25]	4600 [26]	2600 [27]	1700 [28]	1600 [29]

outlines the average yearly domestic power consumption for each location.

3.2. Meteorological Data

An online database was used to obtain hourly data over the years 2007 and 2023 in a .csv format for the following parameters: air temperature, global horizontal irradiance, and surface pressure [30]. The 2023 data were averaged over 4-weekly intervals to produce the plots in Figure 4 and show a similar trend for average temperature and irradiance at each location. The seasonal variation for each location is observed, where the peaks for each location reflect the summer according to the hemisphere. The Quito plant shows a steady year-round irradiance and temperature due to its equatorial location.

3.3. Modeling

When devising the model, some assumptions were made in order to simplify the problem and ensure a consistent approach throughout. The following main assumptions are outlined below:

• Air acts as an ideal gas, allowing for the application of the ideal gas Llaw (IGL), i.e., low temperatures or high pressure conditions do not apply. Air has the properties listed in

  Table 4. Properties of air used in the analysis [19].

  Property [units]	R [J/kgK]	ν [m2/s]	cp [J/kgK]
  Value	287	1.6 × 10−5	1006

  ;
• One-dimensional, steady-state airflow in order to simplify the continuity, energy, and momentum equations;
• The absorptivity of the collector ground material is equal to 0.9 [7,18,20,31].
• The transmissivity of the collector roof material is equal to 0.85 [9,18,31].
• The collector heat loss coefficient is equal to 15 [8,19].
• The turbine efficiency has been investigated and reported over a wide range in Ref. [32]; however, for the purpose of this report, it is equal to 0.83 in accordance with the Manzanares pilot plant [9].
• Only GHI is considered in the model as it is the sum of the direct and diffuse irradiance received on a horizontal surface.

The following analysis closely follows the procedure set out in [14,15,19,20]. The pressure difference in the collector is calculated according to Equation (1), derived from the continuity, momentum, and energy equations for the flow in the collector assuming a low Mach flow [14,15,19,20].

$$p_2=p_1+\left({\displaystyle \frac{{\dot{m}}^2}{2{\rho }_1}}\right)·\left({\displaystyle \frac{1}{A_2^2}}-{\displaystyle \frac{1}{A_1^2}}\right)-\left({\displaystyle \frac{\dot{m}{q}^{″}}{2\pi H_{coll}^2{\rho }_1{c}_p{T}_1}}\right)·\mathit{log}{\displaystyle \frac{r_{ch}}{r_{coll}}}$$

(1)

In [20], the temperature change in the collector is also derived from the continuity, momentum, and energy equations with the assumption of a low Mach flow:

$$T_2=T_1+\left({\displaystyle \frac{q^{″}{A}_{coll}}{\dot{m}{c}_p}}\right)-\left({\displaystyle \frac{{\dot{m}}^2}{2{\rho }_1^2{c}_p}}\right)·\left({\displaystyle \frac{1}{A_2^2}}-{\displaystyle \frac{1}{A_1^2}}\right)$$

(2)

Equation (3) is used to calculate the air density at each chimney component:

$$\rho ={\displaystyle \frac{p}{RT}}$$

(3)

The mass flow rate is calculated using Equation (4) and is assumed to be constant throughout:

$$\dot{m}=\rho VA$$

(4)

The velocity of air at each point is calculated using Equation (5) [9,22]:

$$V=\sqrt{2g{H}_{ch}\left({\displaystyle \frac{∆T}{T_1}}\right)}$$

(5)

The solar heat flux absorbed by the collector floor can be calculated using Equation (6) [20]:

$$q^{″}=I·{\alpha }_g·{\tau }_c-U_L\left({\displaystyle \frac{1}{2}}\left(T_2-T_1\right)\right)$$

(6)

Equation (7) is the dry adiabatic lapse rate equation, which shows the temperature decrease with an increase in height, assuming the air is unsaturated [19]:

$$T=T_{\infty }{\displaystyle \frac{g}{c_p}}z$$

(7)

The pressure at the chimney exit is calculated using the hydrostatic equation and Equations (3) and (7) [19]:

$$p_4=p_1{\left(1-{\displaystyle \frac{g{H}_{ch}}{c_p{T}_1}}\right)}^{{\displaystyle \frac{c_p}{R}}}$$

(8)

Equation (7) can be applied to the temperature change in the chimney tower to calculate the temperature at the chimney exit in Equation (9) [19]:

$$T_4=T_3-{\displaystyle \frac{g}{c_p}}{H}_{ch}$$

(9)

The pressure at the chimney base is calculated by combining Equations (3) and (9) with the hydrostatic equation and then integrating the derived equation to obtain Equation (10) [20]:

$$p_3=p_4{\left(1-{\displaystyle \frac{g{H}_{ch}}{c_p{T}_3}}\right)}^{-{\displaystyle \frac{c_p}{R}}}$$

(10)

Draught equation is used to calculate the pressure difference across the turbine by calculating the other pressure losses in the system and subtracting them from the total pressure potential [20,33].

$$∆p_{turb}=∆p_{pot}-(∆p_{coll,i}+∆p_{turb,i}+∆p_{coll,f}+∆p_{ch,f}+∆p_{dyn})$$

(11)

The total pressure potential is regarded as the pressure difference between the column of cold air outside the chimney tower and the column of hot air inside, as calculated in Equation (12) [14,19,20].

$$∆p_{pot}={(p}_1-p_4)-\left(p_3-p_4\right)=p_1-p_3$$

(12)

The inlet pressure drops, and pressure drops due to kinematic energy loss of the outlet flow are computed using Equation (13) [20].

$$∆p=K{\displaystyle \frac{\rho V^2}{2}}$$

(13)

where K is the pressure loss coefficient and is equal to 1, 0.25, and 1 in Δp_coll,i, Δp_turb,i, and Δp_dyn, respectively [20]. The frictional pressure drop in the collector and chimney is estimated from the Darcy–Weisbach equation, as show in Equation (14) [20].

$$∆p={\displaystyle \frac{fL}{2D_h}}\rho V^2$$

(14)

Darcy’s friction factor is calculated as shown in Equation (15) [33,34].

$$f={\left[-1.8log\left(\left({\displaystyle \frac{6.9}{{Re}_{D_h}}}\right)+{\left({\displaystyle \frac{\raisebox{1ex}{$\epsilon $}\!\left/ \!\raisebox{-1ex}{$D_h$}\right.}{3.75}}\right)}^{1.11}\right)\right]}^{-2}$$

(15)

where the wall surface roughness of the glass collector and concrete chimney is considered to be equal to zero and 0.002 m, respectively [33]. The Reynold’s number is calculated using Equation (16).

$$Re={\displaystyle \frac{V{r}^2}{\nu }}$$

(16)

The temperature change across the turbine is calculated using Equation (17), following the first law of thermodynamics [20].

$$T_3=T_2-{\displaystyle \frac{P}{{\dot{m}c}_p}}$$

(17)

where the power output is a product of the turbine efficiency, volume flow rate, and pressure drop over the turbine, as shown in Equation (18) [14,18,19,20,33].

$$P={\eta }_T·{\displaystyle \frac{2\dot{m}}{{\rho }_2+{\rho }_3}}·∆p_{turb}$$

(18)

The model was computed using Python following the procedure developed in the flowchart shown in Figure 5. As mass flow rate is a key performance parameter [18], the model accounts for this by iterating for $\dot{m}$, a variation of the models proposed in previous studies. This model has the capacity to compute hourly data points over a year-long period, ensuring that the outcome data retains this level of granularity. This approach provides a more accurate representation of the output compared to relying on computed averages as input parameters.

Validation of the model was carried out using the dimensions and parameters of the Manzanares pilot plant, as listed in Table 1. These results were compared to the measured experimental outputs at the Manzanares plant on 2 September 1982 at midday, and the results are shown in

Table 5. Comparison of measured experimental outputs and calculated theoretical outputs.

Parameter	Measured Output	Model Output	Error [%]
Collector Temperature Difference, ΔT12 [°C]	17.5	18.4	5
Turbine Pressure Difference, ΔP13 [Pa]	−135	−125	7.7
Power Output, P [kW]	36	38.1	5.7

[7]. The theoretical estimates closely match the experimental observations, with errors consistently under 6% for the power output of the plant, validating the reliability of the model to provide consistent results at this level of model fidelity. It can be seen that the model slightly overestimates the power output, possibly as a result of the assumption made to use fixed loss coefficients and the exclusion of any electrical system inefficiencies.

In addition, a basic sensitivity study was performed using the data from Table 1 to determine the effect on the model output when varying the input parameters. The results can be seen in Figure 6. This study highlights a negative correlation between ambient temperature and the power output of the system, and conversely, the power output increases with increasing solar irradiance, consistent with other findings [8,9]. An important practical note on this relationship is that ambient temperature tends to increase alongside rising solar irradiance, as shown later in Figure 7b, using the Melbourne meteorological data from 29 December 2023. Therefore, ambient temperature and irradiance will have a lower limit on the performance of the plant, beyond which the air under the collector will not produce a convective air flow, and the plant will not operate.

4. Results Analysis

4.1. Power Output

Initially, the power outputs of each location were computed using the Manzanares plant dimensions in order to compare their performances. The highest output days in 2023 are shown in Figure 7a, alongside the irradiance and temperature plot for the highest output day in Melbourne in Figure 7b. It is evident from Figure 7 that the daily power production closely follows the irradiance level throughout the day.

The peak data for each location are listed in

Table 6. Peak power output data 2023.

Location	Date	T1 [°C]	I [W/m2]	p1 [Pa]	P [kW]
Melbourne	29/12/2023	18	1066	102,900	52.2
Aswan	01/05/2023	29	1077	100,980	49.1
Cornwall	15/05/2023	13	819	102,080	42.5
Quito	06/09/2023	19	1094	67,310	49.8
Sao Paulo	06/11/2023	22	1114	92,070	51.8

. For these dates, the ambient temperature and irradiance of Melbourne and Quito are very similar; however, the power output in Melbourne is higher than Quito. This difference is the result of the lower ambient pressure in Quito due to the higher altitude of the city, suggesting that the performance of a SCPP decreases as altitude increases.

Figure 7a illustrates that there is a small variation in the annual peak power output in every location; however, when considering the annual power output in Figure 8, there is a large variation by location. The plot in Figure 8b closely resembles the irradiance plot in Figure 4b, suggesting that the irradiance has a dominating effect on the output of the SCPP and that output is proportional to irradiance. Figure 8 indicates a decline in the average power output in the winter months in Melbourne and particularly Cornwall, where the output approaches zero at the beginning and end of the year, indicating that this technology may not provide year-round power in regions with low levels of irradiance.

The annual energy production by location is compared in

Table 7. Annual energy production in kWh in 2007 and 2023.

			Location
Year	Cornwall, UK	Melbourne, Australia	Aswan, Egypt	São Paulo, Brazil	Quito, Ecuador
2007	45,400	69,100	100,000	72,300	83,900
2023	46,600	64,400	104,800	80,300	92,800

for the years 2007 and 2023. It can be seen that energy production in four out of the five locations increases from 2007 to 2023; this is likely a result of fluctuating annual irradiance.

4.2. Dimensional Study

Using the Manzanares plant parameters in Table 1, the effect of varying the dimension of each individual component was investigated with the other geometries remaining fixed. The findings for 2023 Aswan meteorological data are displayed in Figure 9. Figure 9a indicates that there is a minimum collector radius and chimney height in order for the plant to operate; however, changing the collector height and chimney radius has little impact on the performance of the system after this point. Conversely, with an increase in collector radius and chimney height, the power output increases. Figure 9b suggests that on a small scale, the scale factor for each component is approximately equal when considering the Manzanares plant dimensions and the domestic energy demand.

The relationship between the ratios of chimney height and collector radius was considered for the Manzanares geometry by firstly keeping the collector radius constant and running the model with the chimney height as a varying ratio of the collector radius. Secondly, it was ran with a constant chimney height and the collector radius as a varying ratio of the chimney height. For the Manzanares plant, the ratio chimney height to collector radius is 1.595. The outcome is displayed in Figure 10, indicating that for both cases, the performance of the plant is proportional to an increase in this ratio. However, according to Figure 10b, enlarging the collector radius to exceed the chimney height increases the capacity of the plant significantly more than having the chimney height larger than the collector radius. When considering the applicability of this relationship to a domestic scenario, a reduction in the floor area occupied by the system may be preferred.

The Manzanares pilot plant’s dimensions were scaled down for each location to observe the effect on the annual energy production, as illustrated in Figure 11, demonstrating a clear relationship between increasing energy production with an increase in the scale factor of the plant. Figure 11b is used to initially estimate the minimum scale factor of the Manzanares plant dimensions for each location, and this value was iterated through the model to find the minimum scale factor for the annual energy requirement, as shown in

Table 8. Minimum scale factor of the Manzanares SCPP to achieve the average annual household energy consumption by location.

	Cornwall, UK	Quito, Ecuador	Aswan, Egypt	Melbourne, Australia	São Paulo, Brazil
Scale Factor	0.388	0.26	0.293	0.417	0.279
Chimney Height [m]	75.5	50.6	57	81.1	54.3
Collector Radius [m]	47.3	31.7	35.7	50.8	34

. While identifying this scale factor serves as a good initial step in determining the minimum geometries, it overlooks the optimization of design and geometries for maximizing the power output. Instead, it uses the same design and component ratios as the Manzanares pilot plant.

The scale factors from Table 8 were used to update and fix the chimney radius and collector height. The model was iterated around the chimney heights and collector radii to determine a linear relationship between the two parameters to fulfill the annual energy requirement. The results are displayed in Figure 12 alongside the least squares regression model for each location for 2007 and 2023. It is visible from the regression models that minimizing one major plant dimension will lead to an increase in another plant dimension, and therefore, there is not a single set of optimum geometries. Accordingly, the regression model for each location can be used in practice to determine the chimney height appropriate for a collector radius corresponding to the ground area that is available for construction.

The correlation coefficient for each regression line was calculated in

Table 9. Correlation coefficients for the linear relationship between chimney height and collector radius in 2007 and 2023.

	Cornwall, UK	Quito, Ecuador	Aswan, Egypt	Melbourne, Australia	São Paulo, Brazil
2007	−0.994	−0.982	−0.995	−0.985	−0.984
2003	−0.981	−0.978	−0.987	−0.996	−0.977

, indicating a strong negative correlation for each location and therefore imparting confidence in the regression fit.

The collector radius was calculated for a 70 m chimney height for each location using the 2023 regression models. A comparison of the SCPP sizes can be seen in Figure 13. The magnitude of the size of the plant reflects the scale of the annual energy requirement by location, suggesting that the most dominating factor of plant size is the energy requirement of the region in which it is located, rather than meteorological factors. The annual energy requirement of the Cornwall plant is only 100 kWh more than the Aswan plant; however, the radius of the Aswan plant is 60% of the Cornwall plant due to the higher irradiance levels in Aswan, proposing that irradiance is the second biggest factor attributed to plant dimensions.

Using these dimensions, the results in Figure 14 were produced to observe the plant performance in 2023 in terms of annual energy production. Evidently, the production in Aswan, São Paulo, and Quito is steady year-round due to the consistent irradiance levels throughout all of the seasons, indicating that the technology could produce a reliable energy supply throughout the year. In contrast, the plants in Melbourne and Cornwall have a much higher peak output during the summer months due to their size. During the winter months, the output drops significantly, evidencing the potential need for a supplementary energy supply or suitable energy storage to ensure the energy demand can be met during these periods. This is especially pertinent in Cornwall, where the power production falls to nearly zero from November to February.

Taking a chimney height of 70 m and using the regression models, the percentage change in the dimension of the radius between 2007 and 2023 is shown in

Table 10. Percentage change in the size of the collector radius from 2007 to 2023 for a 70 m chimney height.

	Cornwall, UK	Quito, Ecuador	Aswan, Egypt	Melbourne, Australia	São Paulo, Brazil
Change in collector radius [%]	0.6	−14	−5.1	4.4	−10.7
Change per year [%]	0.04	−0.87	−0.32	0.28	−0.67

. Assuming a steady change over the time period, the percentage change per year was calculated in order to forecast how the plant may perform in the future.

The results indicate that the performance of plants constructed in Quito, Aswan, and São Paulo will increase annually, whereas the performance of plants constructed in Cornwall and Melbourne would decrease annually, suggesting the need for constructing the plants with a larger collector radius to ensure viability in the future. However, as this change was only measured over two years, this would need to be tested over a continuous period to better determine the trend over time.

Although Figure 13 displays one combination of the minimum required dimensions, an observation regarding the practicality of installation and the maintenance of SCPPs shows that the roof height is too small for convenient access to the turbine. However, as illustrated in Figure 9, increasing the roof height does not change the annual energy production; hence for an applied system, the roof should be at least 1 m in height.

The slenderness ratio is the ratio of the length of the chimney to the radius. In [35], the authors report that chimneys with a slenderness ratio of up to 11.6 satisfy the permissible tensile stress for winds between 30 and 50 m/s, meaning that chimneys with a 70 m height require a radius of at least 6 m in order to comply with this ratio. Even for the largest plant in Melbourne, this would mean that the chimney radius would need to be more than doubled.

5. Hybridization and Lifecycle Analyses

5.1. Hybrid Options and Selection

There are many options for the extension of this SCPP model in order to make the system more effective, as reported in [36]. Five options were considered as follows:

• Photovoltaic (PV) panels: They are located under the collector cover. Crystalline silicon PV panels become 0.2–0.5% less efficient for each 1 °C rise in temperature. The convective air flow through the SCPP would maintain a lower surface temperature on the PV panels and therefore increase the efficiency. However, the heat absorbed by the PV panels would alter the collector properties and consequently reduce the power output of the SCPP [37];
• Air-source heat pump (ASHP): It is located between points three and four in the chimney tower (as shown in Figure 1b). ASHPs are used to provide a more sustainable option for heating buildings by absorbing heat from the outside air and transferring it to an indoor space;
• Electricity storage: As an SCPP does not constantly generate power, energy storage such as large batteries could be incorporated into the design to harness the available energy. This would introduce more inefficiencies in the system; however, it could help minimize the size of the plant to ensure the annual energy demand can be met;
• Thermal storage: As discussed in [21], this would include the use of a material to absorb some of the solar energy to be slowly released throughout the night or other periods where the plant would otherwise be inactive to allow for constant power generation. This would however decrease the peak power output as the convection-induced airflow during sunlight hours would be reduced.
• Turbine design: This has been studied in [32] and [15] to explore alternative options for increasing the performance of the SCPP, such as blade design, the number of blades, the position of the turbine, and the number of turbines.

A multi criteria decision analysis (MCDA) was conducted to determine which option to study in more detail, as shown in

Table 11. Multi criteria decision analysis for hybridization study of the SCPP system.

Criteria	Weight	PV Panels		ASHP		Electricity Storage		Thermal Storage		Turbine Design
	↓ ∑1 ↓	Rating (1–5)	Score	Rating (1–5)	Score	Rating (1–5)	Score	Rating (1–5)	Score	Rating (1–5)	Score
Cost	0.1	1	0.1	4	0.4	2	0.2	5	0.5	3	0.3
Maintenance	0.1	2	0.2	3	0.3	5	0.5	5	0.5	3	0.3
Modularity	0.125	4	0.5	4	0.5	1	0.1	2	0.3	2	0.3
Efficiency	0.25	1	0.3	5	1.3	4	1	3	0.8	2	0.5
Service Life	0.175	5	0.9	5	0.9	3	0.5	2	0.4	4	0.7
Embodied CO2	0.25	1	0.3	3	0.8	2	0.5	5	1.3	4	1
	FINAL SCORE	2.2		4.1		2.9		3.6		3.1

, using a range of criteria relevant to the literature review conducted earlier. The technology selected for further investigation was ASHP as it provided a higher score in this qualitative approach. To test the sensitivity of this decision outcome to the weightings used, the MCDA was performed with equal criteria weightings as well as those initially determined, and the outcome was unchanged.

5.2. Analysis of a SCPP/ASHP Hybrid Plant

ASHPs operate via a reversed Carnot cycle, where a refrigerant is passed through the following components:

• Compressor: isentropic compression requiring work input;
• Condenser: isobaric heat rejection to maintain domestic temperature;
• Expansion valve: throttling;
• Evaporator: isobaric heat absorption from hot chimney air.

An ASHP could be incorporated into the SCPP system with the evaporator located between points three and four in the chimney (see Figure 1b). In order to assess the benefit of this hybrid option, the work input to the compressor must be calculated, as shown in Equation (20). Taking two winter days in Melbourne as an example, this can be calculated using the parameters in

Table 12. Parameters from Melbourne for ASHP calculations.

Date	Time	I [W/m2]	P [kW]	T1 [°C]	T3 [°C]	$\dot{\mathit{m}}$ of Chimney Air [kg/s]
07/07/2023	02:00 p.m.	345	1	14	25.9	130
17/08/2023	01:00 p.m.	203	0.52	12	19.9	108.9

, some of which have been generated by the model.

First, the rate of heat transfer to the heated space (Q_H) can be calculated using Equation (19) by making the following assumptions:

• The desired room temperature is 20 °C, and it takes 30 min (1800 s) to reach this temperature from ambient when the heating is turned on;
• The average size of a one-story Melbourne house is 593 m³ [38];
• The density of air is 1.3 kg/m³, making the mass of the air inside the house equal to 770 kg [39].

$$Q=\dot{m}{c}_p∆T$$

(19)

The coefficient of performance (COP) is the ratio of the useful heat transfer to the work input and is used as a measure of efficiency of the heat pump. Currently, the best ASHPs on the market offer a maximum COP of around five [40]. Using this value and Equation (19), the required work input to the ASHP can be calculated from Equation (20).

Using Equations (20) and (21), the rate of heat transfer from the hot chimney air (Q_L) can also be calculated, and from Equation (19), the additional temperature change in the chimney air (ΔT₃₄) can be deduced.

$$W_{in}={\displaystyle \frac{Q_H}{COP}}$$

(20)

$$COP={\displaystyle \frac{Q_H}{Q_H-Q_L}}$$

(21)

The outcome of these calculations can be seen in

Table 13. Melbourne ASHP calculation results.

Date	QH [W]	Win [W]	QL [W]	ΔT34 [K]
07/07/2023	2582	516	3098	0.024
17/08/2023	3442	689	4130	0.038

. When comparing this with Table 12, it can be observed that the work input required for the compressor is greater than the power output on 17 August 2023. However, on 7 July 2023, as the solar irradiance and ambient temperature are greater, there is an increase in the power output of the SCPP and a decrease in Q_H, suggesting that there are minimum temperatures and irradiance levels for the viability of the technology.

This simple process could be included as a model extension to determine the periods of viability for this hybrid option at all locations. It would be integrated into the second iterative process in Figure 5, where Equation (9) would become

$$T_4=T_3-\left({\displaystyle \frac{g}{c_p}}{H}_{ch}+{∆T}_{34}\right)$$

(22)

Although this technology may be plausible, it would decrease the power available for alternative uses, so it may be necessary to increase the size of the SCPP to produce sufficient power for domestic use as well as the ASHP. Hybridizing the SCPP also introduces logistical complexities, such as the installation of an electrical system that is capable of powering the ASHP directly from the SCPP turbine generator.

5.3. Lifecycle Considerations

When considering the viability of a renewable energy system, both the direct and indirect environmental impact must be assessed to ensure a net positive impact. For the purpose of this study, the carbon footprint throughout the life cycle of the SCPP for only two locations were evaluated: Quito and Melbourne. They were selected to represent the extremes in the annual energy consumption and also to reflect the range of SCPP sizes, with Quito being the smallest and Melbourne being the largest. The availability of materials used in the construction of the largest components of the SCPP were considered, as outlined in

Table 14. Availability of materials in Quito and Melbourne.

Material	Quito	Melbourne
Glass	Limited availability—5 manufacturers nationwide, 1 manufacturer in Quito [41]	Readily available—Numerous manufacturers in Melbourne [41]
PVC	Readily available—Numerous manufacturers nationwide [42]	Readily available—Numerous manufacturers nationwide [43]
Soil	Readily available	Readily available
Bitumen	Limited availability—Import only [44]	Limited availability—2 manufacturers nationwide, 74km from Melbourne [45]
Copper	Readily available—Mined in Ecuador [46]	_
Graphite	_	Readily available—Mined on the East Coast of Australia [47]
Concrete	Limited availability—1 pre-cast concrete plant nationwide, 200km from Quito [48]	Readily available—Numerous pre-cast concrete plants in Melbourne [49]

, in order to reduce emissions associated with transportation. Copper and graphite were included as location-specific materials due to their local sourcing through the mining of the materials.

The properties of the collector materials are defined in

Table 15. Properties of collector materials.

Collector Cover			Collector Floor
Material	Transmissivity	CO2 footprint of primary production [kg/kg]	Material	Solar Absorptivity	CO2 footprint of primary production [kg/kg]
Glass	0.88 [22]	0.72 [50]	Soil	0.80 [51]	-
PVC	0.83 [22]	2.80 [50]	Bitumen	0.91 [7]	0.13 [50]
			Copper	0.64 [52]	3.90 [50]
			Graphite	0.84 [52]	16.1 [50]

. Increased transmissivity and absorptivity of the material will lead to a greater power output of the plant, as evidenced in Figure 6. Therefore, the material’s properties should be an important consideration to ensure a reduced size and increased power density, thereby reducing its environmental impact.

Based on the information in Table 14 and Table 15, a basic EcoAudit using the Ashby method was conducted on the following materials, using the dimensions displayed in Figure 13 [50]:

• Quito: PVC collector cover, soil collector floor, and concrete chimney;
• Melbourne: glass collector cover, bitumen collector floor, and concrete chimney.

These materials were selected for a combination of maximized thermo-physical properties alongside local availability and minimized CO₂ footprint. The results can be seen in Figure 15 for the two locations.

Based on a typical 50-year service life [53], the equivalent annual environmental burden from the construction and disposal of a SCPP in Quito is equal to 11,300 kg, and in Melbourne, it is equal to 52,100 kg. Although the footprint of Melbourne is comparatively much higher, the bitumen collector ground accounts for 21% of the footprint of the material, whereas the soil floor accounts for 0% of the Quito footprint. Moreover, the dimensions of the Melbourne plant are larger than those of the Quito plant and therefore so is the output, as shown in

Table 16. Annual energy output in 2023 with different materials.

	Quito, Ecuador	Melbourne, Australia
Chimney Height [m]	70	70
Collector Radius [m]	22.9	56.8
Energy Output [kWh]	1240	4800

[50]. The output values in Table 16 were the result of computing the model with the stated dimensions and the material properties listed in Table 15. When considering the effect of these properties, the wall roughness of each material remains unchanged in the model to enable a better comparison of each plant.

It can be seen that with the materials available locally to Quito, the plant dimensions would need to be increased in order to meet the average annual household energy demand, increasing the CO₂ footprint of the plant. On the other hand, with these materials, the output of the Melbourne plant exceeds the output required, indicating that there is scope to decrease the size of the plant and consequently decrease the CO₂ footprint. The use of soil as the collector floor in the Melbourne plant would help to mitigate some of the material footprint; however, this would necessitate a plant with larger dimensions and therefore increase the footprint elsewhere. From the data in Table 16, the annual CO₂ avoided through the use of a SCPP in Quito is 870 kg and 3350 kg in Melbourne [54], as shown in Figure 15 in the ‘use’ stage, meaning that the net annual CO₂ footprint is 10,430 kg for Quito and 48,750 kg for Melbourne.

6. Conclusions

The research reported in this paper utilized a validated mathematical model of a SCPP to determine the effect of varying dimensional and environmental parameters on the output of the plant. From this, a regression model for five different locations was developed to establish the minimum necessary geometries of the plants based on the regional energy requirement. The simple model used produces results closely mirroring experimental data; however, it fails to account for electrical system inefficiencies and loss coefficients that are influenced by geometric, environmental, and material parameters. The simplified modeling also did not take into account ambient wind conditions, even though their inclusion is reported as positively beneficial to SCPP peformance.

Some of the key findings from this research are as follows:

• The smallest collector radius of all the plants studied is in Quito and is approximately 25 m, corresponding to a chimney height of approximately 70 m. Decreasing the radius more than this would lead to an increase in chimney height because of the strong negative correlation between the two dimensions;
• Aswan, Quito, and São Paulo can reliably produce year-round power; however, Cornwall and Melbourne may need a supplementary energy supply in the winter months;
• Hybridizing the system with an ASHP could enhance the overall performance of the plant. However, there are days when the power generated by the plant is insufficient to power the ASHP compressor, suggesting that there are optimum environmental conditions for this technology;
• The material selection for the construction of the SCPP influences the plant performance and is the greatest contributor to the carbon footprint. The net annual CO₂ footprint is 10,430 kg for Quito and 48,750 kg for Melbourne, the smallest and largest plant, respectively.

From these findings, it can be concluded that the domestic application of a solar chimney power plant is not currently feasible without some form of hybridization technology to improve power output, power availability, and efficiency. This is because the required dimensions to fulfill the average annual household energy requirement for all locations are too large to be practically applicable to individual households. Furthermore, the direct and indirect CO₂ emissions involved in the construction of the SCPP far outweigh the environmental benefit for both plants studied with a 50-year service life.

There is scope to expand on this research and improve the model developed. Suggestions for further work include conducting experimental studies to establish a database of electrical system losses and loss coefficients for a variety of dimensions, as well as environmental factors. The inclusion of ambient wind in the model could produce a more accurate outcome, providing the true influence on the power output, which is reported as being positively beneficial to performance of the plant. Research could also be carried out on the effect of the mass flow rate, developing a method to calculate the mass flow rate rather than assuming it. Apart from the continuation of studies on dimensional changes and plant performance, researchers are also investigating features to improve power through inclined collectors [55] and divergent chimneys [56], and in time, these should be modeled and included when comparing design when validated at various scales. A complete LCA would obtain a more accurate representation of the environmental impact of the system at any scale and include locally sourced materials for construction. A scalable cost analysis method would be essential to assess the economic viability of the system in any setting and has also been proposed by [57]. Detailed quantitative studies of all hybrid options with SCPPs are required for a viability assessment in domestic locations. Finally, the optimization of SCPP design to determine the ideal dimensional and environmental parameters would aid in the identification of optimum climates and regions for viable construction.