Investigation of Solar Collector Design Parameters Effect onto Solar Stirling Engine Efficiency

The performance of a solar-powered heat engine, operating in a Stirling cycle is studied in this work. Also the influence of design parameters on both the optimum solar receiver temperature and overall efficiency is considered. The analysis has also clearly brought out the effect of solar collector design parameters such as concentration ratio, overall heat-loss coefficient, and heat engine parameter on the overall efficiency of solar Stirling power systems. Operation of a solar Stirling engine depends not only on the design parameters of the Stirling engine but also on the design parameters of the heat source, i.e. the solar collector. In the following, a thermodynamic analysis of a solar Stirling engine has been conducted to see the impact of solar collector design parameters on the operation of a solar Stirling engine. A theoretical approach to the determination of optimum working temperature has been described by Sootha et al. [14]. This subject has also been approached by other authors within a different scope and theoretical framework [15-24]. A study on the optimum operation of a solar converter in combination with a Stirling of Ericsson heat engine has also been conducted by Badescu [18,25]. Analysis Solar energy is incident on a solar collector which is coupled to a Stirling engine as the heat source. The incident energy on the collector includes the direct solar radiation incident on the collector as well as the radiation absorbed from the atmosphere. The collector loses some of its energy to the surroundings by convection and radiation. The rest of the thermal energy is delivered to the Stirling engine. Therefore, the energy balance on the collector is given by [25-28]. D O R C T Q Q Q Q Q + = + + (1) Where D Q and O Q are the energy fluxes absorbed from the sun (short wave) and from the atmosphere (long wave), respectively. Also, R Q is the flux or radiant energy emitted by the converter, C Q is the rate of thermal convective losses and T Q is the rate of thermal energy delivered to the Stirling engine. The energy flux absorbed from the sun is ( ) ( ) D d d b b Q I I C τα τα = + (2) ( )d τα and ( )b τα are the receiver effective absorptance-transmittance for diffuse and direct(beam) radiation, respectively, while C is Stirling engine Sun


Introduction
Thermodynamic cycles have been widely used in conversion of solar radiation energy into the electrical power. Use of solar collector systems in Stirling engine has been investigated in recent literatures [1][2][3][4][5]. Most applications of solar collector systems in Stirling engines are in space power and terrestrial power plant systems in which entirely directed at the electrical power generation. Less attention has been accomplished in small scale terrestrial applications such as in domestic application [6][7][8][9][10][11][12]. In recent studies [13,14] it has been identified that the Stirling engine has good potential for meeting continuous power requirements in the 5 to 20 kW range for electrical power generation and water pumping requirements in third world countries.
The dish-Stirling system, comprises of a parabolic dish collector (which is made up a dish concentrator and a thermal absorber) and a Stirling heat engine located at the focus of the dish, tracks the sun and focuses solar energy into a cavity absorber where solar energy is absorbed and transferred to the Stirling engine to heat its displacer hotend, thereby creating a solar powered Stirling heat engine, as shown in Figure 1.  Operation of a solar Stirling engine depends not only on the design parameters of the Stirling engine but also on the design parameters of the heat source, i.e. the solar collector. In the following, a thermodynamic analysis of a solar Stirling engine has been conducted to see the impact of solar collector design parameters on the operation of a solar Stirling engine. A theoretical approach to the determination of optimum working temperature has been described by Sootha et al. [14]. This subject has also been approached by other authors within a different scope and theoretical framework [15][16][17][18][19][20][21][22][23][24]. A study on the optimum operation of a solar converter in combination with a Stirling of Ericsson heat engine has also been conducted by Badescu [18,25].

Analysis
Solar energy is incident on a solar collector which is coupled to a Stirling engine as the heat source. The incident energy on the collector includes the direct solar radiation incident on the collector as well as the radiation absorbed from the atmosphere. The collector loses some of its energy to the surroundings by convection and radiation. The rest of the thermal energy is delivered to the Stirling engine. Therefore, the energy balance on the collector is given by [25][26][27][28].
Where D Q and O Q are the energy fluxes absorbed from the sun (short wave) and from the atmosphere (long wave), respectively. Also, R Q is the flux or radiant energy emitted by the converter, C Q is the rate of thermal convective losses and T Q is the rate of thermal energy delivered to the Stirling engine.
The energy flux absorbed from the sun is τα are the receiver effective absorptance-transmittance for diffuse and direct(beam) radiation, respectively, while C is Stirling engine Sun Concentrator the concentration ratio of the direct solar radiation; d I and b I are irradiances of the solar diffuse and direct(beam) radiation, respectively.
We assume that the energy flux absorbed from the atmosphere is τα is the effective receiver absorptance-transmittance product for atmospheric radiation; σ is the Stefan-Boltzmann constant and Sky T is the equivalent black-body temperature of the sky [16-18, 25, 26,29].
T is the ambient absolute temperature. The rate of radiative energy loss from the collector is given by Where ε and T are solar collector emissivity and temperature of the solar collector, respectively.
The rate of thermal convective losses is given by [16][17][18]25,27,28] ( ) Where U is the overall converter convective heat loss coefficient of the collector.
The thermodynamic efficiency of a Stirling cycle is given by [ in equation (1), we have the rate of the thermal energy delivered to the Stirling engine: We define the following non dimensional ratio If T Q is the rate of thermal energy delivered to the Stirling engine, then the power produced by the Stirling engine is For the maximum power production Substituting equation (8) into (7) and then applying equation (9), we have [25] ( ) ( )

Result and Discussion
A selectively coated collector system with typical values of emissivity ε = 0.1, overall heat loss coefficient (U = 4Wm -2 K -1 ), (ατ) b = 0.8, (ατ) d = 0.5, (ατ) O = 0.5 has been considered. Figure 2 shows the dependence of the overall efficiency of a solar Stirling system on the Stirling engine parameter and the concentration ratio of the collector system. It is evident from the figure 2 that the overall efficiency of the system is less dependent on increasing values of the engine parameter and increases with the increasing concentration ratio. Figure 3 shows the variation of the ratio of optimum operating temperature with concentration ratio for various values of engine parameters. By fixed concentration ratio and decreasing engine parameters, caused optimum operating temperature ratio increased. Also in fixed engine parameters by increasing concentration result, optimum temperature ratio increased. values in comparison to the system based on a concentrating collector of moderate concentration(C=200)( Figure 5). It is because radiative losses are of a predominant nature for concentrating collectors. Figure 4 and 5 shown that with increased overall heat loss coefficient in constant concentration ratio, overall efficiency of Stirling power system decreased which this reduction for flat plate solar collector is more rapidly than concentrating collector. The result shows that concentrating collector-based Stirling power systems are considerably more efficient in comparison to those based on flat plate collectors.

Conclusions
Overall efficiency of Stirling power system has strong dependence on the concentration ratio. As seen maximum system efficiency obtained on optimum operating temperature ratio which optimum operating temperature ratio dependence to concentration ratio and engine parameters. Therefore, performance of Stirling power system is very sensitive to changing in concentration ratio. As show in Figure  2 in the constant engine parameters by increasing concentration ratio, efficiency is increased. Also in constant concentration ratio by increasing overall heat loss coefficient slop of efficiency reduction of system is decreased by this reason we don't recommend using of flat plate solar collector.