Keywords

Solar chimney power plant; collector; energy storage layer; chimney

6.1 Introduction

The solar chimney power plant (SC) system was first proposed in the late 1970s by Professor J. Schlaich and tested with a prototype model in Manzanares, Spain in the early 1980s [1,2]. Compared with the traditional power generation systems, the system has the following advantages: easier to design, more convenient to draw materials, higher operational reliability, fewer running components, more convenient maintenance and overhaul, lower maintenance expense, no environmental contamination, continuous stable running, and longer operational lifespan. It has the potential to meet the power needs of developing countries and territories, especially in deserts where there is a shortage of electric power, with extensive application prospects.

As the SC systems could make significant contributions to the energy supplies of those countries where there is plenty of desert land, which is not being utilized, in recent years, many researchers have made research reports on this technology and have carried out tracking studies on SC systems. Pasumarthi and Sherif [3,4] developed a mathematical model to study the effects of various environment conditions and geometry on the flow and heat transfer characteristics and output power of the solar chimney, and they also developed three different models in Florida and reported the experimental data to assess the viability of the solar chimney concept. Lodhi [5] presented a comprehensive analysis of the chimney effect, power production, efficiency, and estimated the cost of the SC setup in developing nations. Bernardes et al. [6] presented a theoretical analysis of a solar chimney, operating on natural laminar convection under steady state. Gannon and Backström [7] presented an air standard cycle analysis of the SC for the calculation of limiting performance, efficiency, and relationship between the main variables including chimney friction, system, turbine, and exit kinetic energy losses. Gannon and Backström [8] presented an experimental investigation of the performance of a solar chimney turbine. The measured results showed that the solar chimney turbine presented has a total-to-total efficiency of 85–90% and total-to-static efficiency of 77–80% over the design range. Later, the same authors [9] presented analytical equations in terms of turbine flow and load coefficient and degree of reaction, to express the influence of each coefficient on turbine efficiency. Bernardes et al. [10] established a rounded mathematic model for an SC system on the basis of energy-balance principle. Pastohr et al. [11] carried out a two-dimensional steady-state numerical simulation study on the whole SC system which consists of the energy storage layer, the collector, the turbine, and the chimney, and obtained the distributions of velocity, pressure, and temperature inside the collector. Schlaich et al. [12] made an analysis on the operation principle of an SC system and predicted the commercial application prospects of large-scale SC systems. Ming et al. [13] developed a comprehensive model to evaluate the performance of an SC system, in which the effects of various parameters on the relative static pressure, driving force, power output, and efficiency have been further investigated. Pretorius and Kröger [14] evaluated the influence of a developed convective heat transfer equation, more accurate turbine inlet loss coefficient, quality of collector roof glass, and various types of soil on the performance of a large-scale SC system. Bilgen and Rheault [15] designed an SC system for power production at high latitudes and evaluated its performance. Koonsrisuk and Chitsomboon [16] proposed dimensionless variables to guide the experimental study of flow in a small-scale solar chimney and employed a computational fluid dynamics methodology to explore the results that were used to prove the similarity of the proposed dimensionless variables. Maia et al. [17–19] gave detailed theoretical evaluations of the influence of geometric parameters and materials on the behavior of the airflow in a solar chimney prototype and analyzed the airflow characteristics of the systems which can be used as a dryer for agriculture. Ming et al. [20] carried out numerical simulations on the SC systems coupled with a 3-blade turbine using the Spanish prototype as a practical example and presented design and simulation of a MW-graded SC system with a 5-blade turbine, the results of which show that the coupling of the turbine increases the maximum power output of the system and the turbine efficiency is also relatively rather high. Ming et al. [21] established different mathematical models for the collector, the chimney, and the energy storage layer and analyzed the effect of solar radiation on the heat storage characteristics of the energy storage layer. Zhou et al. [22,23] presented some experimental and numerical results of a pilot SC equipment. Ming et al. [24] presented a simple analysis on the thermal performance of solar chimney power generation systems.

The energy storage layer, without which the whole system could not operate continuously during the night, undoubtedly plays a significant role in the power output of a solar chimney system. Part of the solar radiation is absorbed by the energy storage layer during the daytime, and is released during the night or days with cloudy weather. Pastohr et al. [11] presented a numerical simulation result in which the energy storage layer was regarded as solid. The energy storage layer, however, can be treated as aporous medium as there is air flowing inside the solid matrix, especially when the solar chimney systems are built in Gobi or the desert land in the northwest of China with the energy storage layer made of gravel or sand. In this chapter, unsteady conjugate numerical simulations of the solar chimney system with the energy storage layer, the collector, and the chimney are carried out. However, it is not necessary to take the turbine into consideration for a 2-D axisymmetric flow, as the 2-D turbine can only describe the flow and heat transfer characteristics of the system with an ideal pressure drop at a certain place. In addition, the effects of the heat storage characteristics of the energy storage layer on the air flow and heat transfer characteristics of the system is also taken into consideration.

6.2 Numerical Models

6.2.1 System Description

The physical model of the Spanish solar chimney power generating system prototype shown in Fig. 6.1 [11] is selected as a physical model for the numerical simulation. The prototype has a chimney that is 200 m in height and 5 m in radius, and a collector that is 122 m in radius and 2 m in height. The solid matrix of the energy storage layer is soil or gravel with a large heat capacity.

However, the analysis described in this chapter is based on some simple assumptions shown as follows: (1) Axisymmetric flow of air in the collector is assumed, that is, nonuniform heating of the collector surface in terms of the sun’s altitude angle is neglected. (2) An average value for the optical properties is considered to estimate the radiation incident on the absorber surface. Therefore, the transmittance of beam radiation during early sunshine hours would be considerably lower than the average value of the transmittance. (3) The Boussinesq approximation is assumed to be valid. This approximation neglects all variations of properties except for density in the momentum equation. (4) The solar radiation is thought to be transient with time, but the ambient temperature and wind speed are assumed constant. This assumption is advanced only by considering that it is a little difficult to get a convergent simulation result if the ambient parameters were set to be transient with time.

6.2.2 Theoretical Modeling

The Continuity equation, Navier-Stokes equation, energy equation, and $\kappa -\epsilon$ equations can be used to describe the air flow and heat transfer in the collector and chimney shown as follows:

$\frac{\partial \rho }{\partial t}+\frac{\partial (\rho u)}{\partial x}+\frac{1}{r}\frac{\partial (\rho v)}{\partial r}=0$ (6.1)

(6.1)

$\frac{\partial (\rho u)}{\partial t}+\frac{\partial (\rho uu)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rvu)}{\partial r}=\rho g\beta (T-T_{\infty })+\frac{\partial }{\partial x}\left(\left(\mu +{\mu }_t\right)\frac{\partial u}{\partial x}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left((\mu +{\mu }_t)r\frac{\partial u}{\partial r}\right)$ (6.2)

(6.2)

$\frac{\partial (\rho v)}{\partial t}+\frac{\partial (\rho uv)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rvv)}{\partial r}=\frac{\partial }{\partial x}\left((\mu +{\mu }_t)\frac{\partial v}{\partial x}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left((\mu +{\mu }_t)r\frac{\partial v}{\partial r}\right)$ (6.3)

(6.3)

$\frac{\partial (\rho T)}{\partial t}+\frac{\partial (\rho uT)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rvT)}{\partial r}=\frac{\partial }{\partial x}\left(\left(\frac{\mu }{\mathit{Pr}}+\frac{{\mu }_t}{{\sigma }_T}\right)\frac{\partial T}{\partial x}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left(r\left(\frac{\mu }{\mathit{Pr}}+\frac{{\mu }_t}{{\sigma }_T}\right)\frac{\partial T}{\partial r}\right)$ (6.4)

(6.4)

$\frac{\partial (\rho \kappa )}{\partial t}+\frac{\partial (\rho \kappa u)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rv\kappa )}{\partial r}=\frac{\partial }{\partial x}\left(\left(\mu +\frac{{\mu }_t}{{\sigma }_{\kappa }}\right)\frac{\partial \kappa }{\partial x}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left(\left(\mu +\frac{{\mu }_t}{{\sigma }_{\kappa }}\right)r\frac{\partial \kappa }{\partial r}\right)+G_{\kappa }-\rho \epsilon$ (6.5)

(6.5)

$\frac{\partial (\rho \epsilon )}{\partial t}+\frac{\partial (\rho \epsilon u)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rv\epsilon )}{\partial r}=\frac{\partial }{\partial x}\left(\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial x}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left(\left(\mu +\frac{{\mu }_t}{{\sigma }_{\epsilon }}\right)r\frac{\partial \epsilon }{\partial r}\right)+\frac{\epsilon }{\kappa }(c_1{G}_{\kappa }-c_2\rho \epsilon )$ (6.6)

(6.6)

where, $G_{\kappa }$ represents the generation of turbulence kinetic energy due to the mean velocity gradients defined as: $G_{\kappa }=-{\mu }_t\left(2\left({\left(\frac{\partial u}{\partial x}\right)}^2+{\left(\frac{\partial v}{\partial r}\right)}^2+{\left(\frac{v}{r}\right)}^2\right)+{\left(\frac{\partial u}{\partial r}+\frac{\partial v}{\partial x}\right)}^2\right)$. ${\sigma }_T$, ${\sigma }_{\kappa }$, and ${\sigma }_{\epsilon }$ are the turbulent Prandtl numbers for T, $\kappa$, and $\epsilon$, respectively, and $c_1$ and $c_2$ are two constants for the turbulent model:$c_1=1.44$, $c_2=1.92$, ${\sigma }_T=0.9$, ${\sigma }_{\kappa }=1.0$, ${\sigma }_{\epsilon }=1.3$, ${\mu }_t=\frac{c_{\mu }\rho {\kappa }^2}{\epsilon }$, and $c_{\mu }=0.09$.

The heat transfer and flow in the energy storage layer may be very complicated, and it is necessary to consider the collector, the chimney, and the storage medium as a whole system. As the material used for energy storage can be regarded as a porous medium, the Brinkman–Forchheimer Extended Darcy model [25] is used to describe the flow in the convective porous-layer, which can be expressed as follows.

$\frac{\partial \rho }{\partial t}+\frac{\partial (\rho u)}{\partial x}+\frac{1}{r}\frac{\partial (\rho v)}{\partial r}=0$ (6.7)

(6.7)

$\begin{array}{l}\frac{1}{\phi }\frac{\partial (\rho u)}{\partial t}+\frac{1}{{\phi }^2}\left(\frac{\partial (\rho uu)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rvu)}{\partial r}\right)=\rho g\beta (T-T_e)+\frac{\partial }{\partial x}\left({\mu }_m\frac{\partial u}{\partial x}\right)\hfill \\ +\frac{1}{r}\frac{\partial }{\partial r}\left(r{\mu }_m\frac{\partial u}{\partial r}\right)-\frac{\mu u}{K}-\frac{\rho F}{\sqrt{K}}\sqrt{u^2+v^2}u\hfill \end{array}$ (6.8)

(6.8)

$\begin{array}{l}\frac{1}{\phi }\frac{\partial (\rho v)}{\partial t}+\frac{1}{{\phi }^2}\left(\frac{\partial (\rho uv)}{\partial x}+\frac{1}{r}\frac{\partial (\rho rvv)}{\partial r}\right)=\frac{\partial }{\partial x}\left({\mu }_m\frac{\partial v}{\partial x}\right)\hfill \\ +\frac{1}{r}\frac{\partial }{\partial r}\left(r{\mu }_m\frac{\partial v}{\partial r}\right)-{\mu }_m\frac{v}{r^2}-\frac{\mu u}{K}-\frac{\rho F}{\sqrt{K}}\sqrt{u^2+v^2}v\hfill \end{array}$ (6.9)

(6.9)

${\rho }_m{c}_{p,m}\left(\frac{\partial T}{\partial t}+\frac{\partial (uT)}{\partial x}+\frac{1}{r}\frac{\partial (rvT)}{\partial r}\right)=\frac{\partial }{\partial z}\left({\lambda }_m\frac{\partial T}{\partial x}\right)+\frac{1}{r}\frac{\partial }{\partial r}\left(r{\lambda }_m\frac{\partial T}{\partial r}\right)$ (6.10)

(6.10)

where, $\phi$, ${\rho }_m$, $c_{p,m}$, ${\mu }_m$, and ${\lambda }_m$ are the porosity, apparent density, specific capacity, dynamic viscosity, and apparent thermal conductivity of the porous medium, respectively: ${\rho }_m=(1-\phi ){\rho }_s+\phi {\rho }_a$,$c_{p,m}=(1-\phi )c_{p,s}+\phi c_{p,a}$,${\lambda }_m=(1-\phi ){\lambda }_s+\phi {\lambda }_a$,${\mu }_m=\mu /\phi$, the parameters with subscripts s and a denote the corresponding parameters of the solid and air in the energy storage layer, respectively. K, F, and $d_b$ are the permeability, the inertia coefficient, and the particle diameter of the energy storage layer, respectively.

$K={d_b}^2{\phi }^3/(175{(1-\phi )}^2)$ (6.11)

(6.11)

$F=1.75{\phi }^{-1.5}/\sqrt{175}$ (6.12)

(6.12)

6.2.3 Boundary Conditions and Initial Conditions

(1) Boundary conditions for the side-faces of the energy storage layer

${\frac{\partial T}{\partial r}|}_{r=R}=0,u=0,v=0$ (6.13)

(6.13)

There might be heat transfer phenomenon between the outside face of the energy storage layer and the material nearby. Therefore, a simplification of this boundary as shown in Eq. (6.13) may overestimate the local temperature profile of the energy storage layer near this location.

(2) Boundary conditions for the chimney wall

${\frac{\partial T}{\partial r}|}_w=0,u=0,v=00$ (6.14)

(6.14)

(3) Boundary conditions for the collector inlet and chimney outlet
According to the analysis by Pastohr et al. [11], the static pressure difference $\mathrm{\Delta }p$ between the collector inlet and the environment at the same height is 0 Pa, and temperature approximately equals the environment temperature. In addition, the boundary condition for the chimney outlet should be the pressure outlet, and the pressure at this location should also be equal to that of the environment at the same height:

$\mathrm{\Delta }{p}_{inlet}=0,T_{inlet}=T_e$ (6.15)

(6.15)

Similar to the method applied by Pastohr et al. [11], the absorption of the solar radiation is considered as a source term in the energy storage layer with a thickness of 0.1 mm. In addition, the boundary condition for the bottom of the energy storage layer could be selected as a constant temperature condition as the temperature distribution 5 m below the surface varies slightly. The boundary conditions for the solar chimney system are shown in Ref. [24].

(4) Initial conditions
It can be easily seen from the boundary conditions shown above that ${\varphi }_{solar}$ will change with time during a day. Therefore, the solar radiation, the air temperature in the environment, and the initial conditions of the system should be given as follows to analyze the unsteady heat transfer and flow characteristics of the solar chimney system:

$\begin{array}{cc}\begin{array}{cc}\begin{array}{cc}t=0,& T_e=const,\end{array}& u=0,\end{array}& v=0\end{array}$ (6.16)

(6.16)

${\varphi }_{solar}={\varphi }_{solar,\max }\sin \left(\frac{t-1440n}{720}\pi \right)0\le t-1440n<720n=0,1,\dots ,4$ (6.17)

(6.17)

${\varphi }_{solar}=0720\le t-1440n<1440n=0,1,\dots ,4$ (6.18)

(6.18)

where, n is the ordinal number of the sunny days which varies from 0 to 4, and ${\varphi }_{solar,\max }$ is the maximum value of the solar radiation including the beam radiation, diffuse sky radiation, and ground-reflected radiation.

6.3 Reliability of the Simulation Method

In order to confirm the reliability of the numerical simulation carried out in this paper, comparison between the experimental results of the SC prototype in Spain and the simulation results is necessary and carried out as follows. Some parameters of the SC prototype in Spain are set as follows: solar radiation, 1040 W/m²; absorptance of the ground, 0.56~0.67; permeability of the collector, 0.8; ambient temperature, 303K. When soil thickness is within 0~5 cm, the average thermal conductivity is about 0.7 W/m K; when soil thickness is within 5~10 cm, the average thermal conductivity is about 1.2 W/m K; when soil thickness is within 10~15 cm, the average thermal conductivity is about 1.5 W/m K.

The comparison between the measured and numerical simulation results is shown in Table 6.1. It can be easily seen that the numerical simulation results agree well with the measured results, which indicates that the simulation method applied in this paper is reliable. The cause for the errors listed in Table 6.1 is the uncertainty of specific parameters such as the density of gasoloid in the air, air humidity, optical parameters, and the property parameters.

6.4 Results and Discussion

One of the most attractive advantages of the solar chimney systems is the continuous electricity supply regardless of the weather conditions and day–night cycle, and the cardinal part of the system to realize this advantage is the energy storage layer. The thermal performance of the energy storage layer plays an important role in the power output of the solar chimney system with time. It is clear that the power output of the system is affected by the chimney inlet velocity which is nearly equal to the chimney outlet velocity, while the surface temperature of the energy storage layer has significant influence on the air velocity of the chimney inlet, and the average temperature of the whole energy storage layer also notably affects the power output of the system especially when there is no solar radiation at night or on cloudy days. Hence, we should give a detailed description of the temperature distribution of the system and the air velocity of the chimney outlet with the variation of solar radiation.

Fig. 6.2 gives a description of the velocity distributions of the solar chimney system with an energy storage layer made of soil. It can be seen from this figure that the velocity inside the collector and chimney is about several meters per second, whereas it is rather small inside the energy storage layer, and the air velocity of the whole system increases with the solar radiation, and the maximum velocity lies at the bottom of the tower. Simulation results indicate that the temperature inside the chimney is only 304K when the solar radiation is 200 W/m², and reaches 321K when the solar radiation is 800 W/m², which shows that solar radiation has a significant influence on the air temperature of the chimney. Further results of numerical simulation with a certain solar radiation and comparison of different models can be found in Ref. [21].

Fig. 6.3 shows the variations of bulk temperature of different energy storage layers with time, where 0 of the abscissa is 06:00 in the morning of the first day. From the figure, we can see that the bulk temperature of the gravel energy storage layer changes more notably than that of the soil energy storage layer during the five days. For a given day, the change scope of bulk temperature of the gravel system is about 1K, which is nearly 80% larger than that of the soil system. This is because the heat capacity of soil is much higher than that of gravel, and therefore the temperature of the gravel energy storage layer changes more notably than that of the soil energy storage layer. As time goes on, the maximum temperature of the soil energy storage layer gradually reaches that of the gravel energy storage layer, and the difference is very small on the fifth day. In contrast, the difference of the minimum temperature between the two types of energy storage layers becomes more and more notable. For the soil energy storage layer, the temperature difference between the day and night decreases gradually, this is because the energy storage increases, and the temperature of the energy storage layer will not decrease significantly even though large amounts of heat energy dissipates from the energy storage layer during the night. In addition, there is a lag effect on the solar radiation for the maximum and minimum temperature of different types of energy storage layer. For the first day, the maximum temperature of the energy storage layer occurs at about 16:00 and the minimum temperature occurs at about 04:00 the next day, but these values come comparatively later in the subsequent days. This phenomenon shows that the energy storage layer has thermal inertia characteristics and has a very notable effect on energy storage. In addition, the overall trend of the bulk temperature seems to increase continuously and show no sign of stabilizing; the reason is that for a 5 m energy storage layer, simulation with 5 days of energy storage is not enough, only when the energy released is equal to the energy storage will the numerical results stabilize.

The variations of the surface temperature of the energy storage layer with time are shown in Fig. 6.4. From this figure, we can see that there is a more notable variation of the surface temperature of the gravel energy storage layer than that of the soil energy storage layer. By comparison, the maximum temperature of the gravel energy storage layer is 15K higher than that of the soil energy storage layer, while the minimum temperature of the former is 2K lower than that of the latter.

The surface temperature of the energy storage layer has a very significant effect on the performance of the solar chimney system. Heat transfer is an irreversible process accompanied with exergy loss to some extent. The higher the surface temperature of the energy storage layer, the larger the temperature difference between the energy storage layer surface and the air inside the collector, and the larger the extent of irreversibility of the heat transfer process, which results in a larger entropy generation. According to the definition of exergy loss, which is the product of environment temperature and entropy generation, the exergy loss caused by the heat transfer process from the higher temperature of the surface of the energy storage layer to the air inside the collector is comparatively larger, and the collector efficiency therefore decreases. As a result, shown in Fig. 6.4, the extent of irreversibility caused by the heat transfer process by using the soil energy storage layer is less than that by using the gravel energy storage layer, with a comparatively lower exergy loss. This is very beneficial for the increase of the power output efficiency of the solar chimney system. In addition, the higher the surface temperature of the energy storage layer, if we look inside the temperature gradient of the energy storage layer with a constant temperature of the bottom of the energy storage layer, the larger the temperature difference between the surface and the bottom of the energy storage layer, the greater the temperature gradient inside, and the larger the energy loss from the bottom of the energy storage layer to the deeper soil which could never be used again by the solar chimney system. On the other hand, a comparatively larger temperature gradient inside the energy storage layer will also result in larger exergy loss from the system.

Hence, the effects of the surface temperature of the energy storage layer on the solar chimney systems could be described at least in two aspects: (1) The higher the surface temperature of the energy storage layer, the larger the energy loss from the bottom of the energy storage layer based on the first law of thermodynamics. (2) The higher the surface temperature of the energy storage layer, based on the second law of thermodynamics, the higher the extent of irreversibility during the heat transfer process both inside the energy storage layer and from the energy storage layer surface to the air inside the collector, and the larger the exergy loss during the energy transfer process. Therefore, in order to decrease the energy loss and exergy loss and also to increase the efficiency of the solar chimney system, it is a very effective approach to decrease the surface temperature of the energy storage layer.

There are several methods to decrease the surface temperature of the energy storage layer. In the first way, material with high heat capacity could be selected as the energy storage medium, which could decrease the surface temperature of the energy storage layer effectively. It is thus effective to pave water pipes on the ground inside the collector instead of other energy storage material, since there may be large amounts of energy stored in the water without large temperature differences for the solar chimney system. Secondly, applying material with a comparatively larger thermal conductivity as an energy storage medium can also decrease the surface temperature of the energy storage layer. With the same heat transfer rate, the temperature difference is smaller in the material whose thermal conductivity is higher, and it is therefore useful to adopt a composite energy storage layer with the upper using higher thermal conductivity material and the lower using comparatively lower thermal conductivity, as this kind of energy storage layer could decrease the surface temperature of the energy storage layer with a comparatively smaller amount of energy loss from the bottom to the deeper soil. In addition, different kinds of plants such as flowers and vegetables could be cultivated at different places inside the collector, which can improve the air quality and humidity and also decrease the surface temperature of the energy storage layer.

Figs. 6.5 and 6.6 show the variations of the chimney outlet parameters with time. Air flows inside the collector absorbing energy from the surface of the energy storage layer, and the amount of energy absorbed has an effect on the air temperature and velocity. The larger the amount of energy absorbed by the air, the higher the air temperature and velocity of the airflow of the chimney outlet, while the lower the amount of energy absorbed by the air, the lower the air temperature and velocity of the chimney outlet. When soil is selected as the energy storage medium, the daytime temperature and velocity of the airflow of the chimney outlet from 05:00 to 21:00 will be higher than that when gravel is selected. The temperature and velocity of the outlet at night from 21:00 to 05:00 will be lower for soil than for gravel. The reason is that the thermal conductivity of soil is lower than that of gravel, which results in a comparatively higher temperature difference between the energy storage layer surface and the air inside the collector under the same solar radiation, this creates a comparatively higher heat transfer rate between the energy storage layer surface and the air, where the heat transfer coefficient is corresponding to the air velocity which increases with the increase of the temperature difference between the energy storage layer surface and the air.

The energy storage layer, which can absorb and store solar energy during sunny days and release heat energy to the air inside the collector at nights or on rainy and cloudy days, plays an important role in the continuous fluid flow, heat transfer, and power output of the solar chimney system. Another aim of the energy storage layer is to decrease the system power output difference between the day and night by decreasing the variations of the chimney outlet parameters, especially air velocity. If the variations are too large, the variation of power output of the solar chimney with time will be very large. It can be seen from Figs. 6.5 and 6.6 that the variation scales of the chimney outlet parameters with time are very large. A possible method to decrease these differences is to replace soil and gravel with a kind of energy storage layer made of a new type of composite material whose thermal conductivity decreases as temperature increases, and another possible method is to use a kind of material whose thermal conductivity is higher than that of the gravel but lower than that of the soil. Therefore, heat conduction of the energy storage layer has a complicated effect on the power output characteristic of the solar chimney system. A comparatively higher heat conduction of the energy storage layer will decrease the surface temperature of the energy storage layer, which will result in the decreases of energy loss and exergy loss from the system. On the other hand, a higher heat conduction of the energy storage layer will decrease the heat transfer resistance between the surface of the energy storage layer and the air inside the collector. Hence, care must be taken with the thermal conductivity and heat capacity of the energy storage layer for the power output performance of the solar chimney systems.

Further study will consider the effects of the absorptivity and absorptance of the canopy, and the porosity of the energy storage layer on the performance of the solar chimney system. In addition, research on the performance of the solar chimney system by changing both the turbine pressure drop and the solar radiation will also be valuable.

6.5 Conclusions

Unsteady numerical simulations on the solar chimney system with an energy storage layer were carried out, and the energy storage layer was regarded as a porous medium. Numerical simulation results show that:

Nomenclature

A Collector area, m²

c Constant

c_p Specific heat, kJ/(kg·K)

$d_b$ Particle diameter of the porous layer, m

F Inertia coefficient of the porous layer

g Gravitational acceleration, m/s²

h Convection heat transfer coefficient, W/(m²·K)

K Permeability of the porous media

p Pressure, Pa

Pr Prandtl number

t Time, s

T Temperature, K

$u$ Velocity, m/s

$v$ Velocity, m/s

Greek symbols

$\alpha$ Thermal diffusivity; absorptance of the collector canopy to the solar radiation energy

$\beta$ Thermal expansion coefficient, 1/K

$\varphi$ Heat transfer rate, W

$\tau$ Transmissivity of the body

$\sigma$ Turbulent Prandtl numbers for T, $\kappa ,$ and $\epsilon$; Stefan-Boltzmann constant.

$\rho$ Density of the material, kg/m³

$\epsilon$ Emissivity of the body surface

$\phi$ Porosity

$\mu$ Dynamic viscosity, kg/(m·s)

$\lambda$ Thermal conductivity, W/m

$\mathrm{\Delta }$ Difference

Subscript

a Air inside the collector

c Canopy

chim Chimney

down Bottom of the energy storage layer

e Environment

m Apparent value of the energy storage layer

s Solid matrix of the energy storage layer; surface of the energy storage layer

w Wall of the chimney