OPEN ACCESS
This paper analyses the performances of a DishStirling concentrating solar system using a Stirling engine for the production of electrical and thermal energy. In particular, with focus on the receiver, its performance was evaluated considering two different plant solutions: “naked” receiver (without hot chamber) and receiver provided with hot chamber.
The DishStirling system under study includes a MICROGEN linear piston Stirling engine of 4 kW total rated power (3 kW thermal and 1 kW electric). The minimum engine starting temperature is 190 °C, while the maximum operating temperature is 565 °C. The analysis is developed through the setting up of a calculation model in MatLab, through which it is possible to predict the dynamic behaviour of the concentratorreceiverStirling engine system and quantify the energy productivity in various operating conditions. The simulations results show that the use of a hot chamber allows improvement of the system performance which, as regards the thermal power, is quantified in an increase of over 70%.
(Presented at the AIGE Conference 2015)
DishStirling, Hot chamber, Thermalelectric performance.
Electrical and thermal energy can be produced, for small users, by means of solar thermal technology at mediumhigh temperature (CSP technologies, Concentrating Solar Power) such as the “parabolic dish focus point” technology. Direct solar radiation is collected on a reflective surface formed by parabolic mirrors and focused on the focal point; the mirrors track the sun with a rotation movement about two orthogonal axes, in order to collect all the direct components of the radiation throughout the day; the heat at a high temperature is transferred to a fluid and used in a Stirling engine, placed in contact with the absorber, to produce electrical and thermal energy directly. The DishStirling system has already been produced and marketed in Italy [1].
In this work a mathematical model has been developed to simulate the absorber of the DishStirling system equipped with hot chamber, in order to analyse the system performance in relation to its electrical and thermal energy production. The hot chamber has the function of creating a sort of black cavity: the solar rays, impacting on the dish, are concentrated towards the entrance of the hot chamber hole in which, apart from small losses, they remain confined and absorbed after a series of reflections and absorptions. In this way, therefore, only a very small part of the concentrated energy is able to escape from the chamberabsorber system: this energy is that of the rays which, once reflected, again escape through the hole.
In this work in order to test the improvement in performances resulting from the use of the hot chamber, a
comparison between a system with absorber without hot chamber and a system with absorber provided with hot chamber was performed.
Figure 1 shows the layout of the DishStirling system analysed.
Figure 1. Layout of the DishStirling system
The concentrator of a CSP system is made from reflective materials able to direct most of the incident solar rays onto it with minimum optical losses. The reflective surface is generally made of aluminium or of silver deposited on glass or plastic plates.
The reflection ρ_{p} and convergence F coefficients of the parabola were assumed, respectively, at 0.89 and 0.98. The geometric form that ensures minimal optical losses for this type of application is the revolution paraboloid, which, in this case, has a collecting area of 10 m^{2}.
The receiver, the element of the concentration system that absorbs the solar rays and transfers the heat to the working fluid of the Stirling engine, has a trunkconical geometry as shown in Figure 2.
The head of the Stirling engine is housed in the cavity of the receiver. The heat transfer between the receiver and the head of the engine is by conduction, once the solar rays have been absorbed (Figure 3).
In this study, the engine used in the concentration system is a linear piston Stirling engine with a total rated output of 4 kW. Figure 4 shows the characteristic curves of the engine supplied by the manufacturer.
Figure 2. Representation of the receiver
Figure 3. Heat transfer receiverengine
Figure 4. Stirling Engine characteristic curves
From the same figure, it is also possible to deduce the range of temperature in which the engine operates: the minimum ignition temperature is 190 °C, and the maximum temperature, beyond which the engine may suffer irreversible deformations, is 565 °C.
From the experimental curves provided by the manufacturer, polynomial Eq.s were deduced according to the absorber temperature T_{ass}, to calculate the electrical power produced by the engine and the total thermal power absorbed:
$P_{\mathrm{el}}=2.865 \cdot \mathrm{T}_{\mathrm{ass}}532.5$ (1)
^{$\mathrm{Q}_{\mathrm{u}}=\mathrm{a} \cdot \mathrm{T}_{\mathrm{ass}}^{6}+\mathrm{b} \cdot \mathrm{T}_{\mathrm{ass}}^{5}+\mathrm{c} \cdot \mathrm{T}_{\mathrm{ass}}^{4}+\mathrm{d} \cdot \mathrm{T}_{\mathrm{ass}}^{3}+\mathrm{e} \cdot \mathrm{T}_{\mathrm{ass}}^{2}+\mathrm{f} \cdot \mathrm{T}_{\mathrm{ass}}+\mathrm{g}$} (2)
The coefficients of Eq.(2) are shown in Table 1.
Table 1. Coefficients of Eq.(2)
a 
4.10067788608900E12 
b 
1.08524735176741E08 
c 
1.18255068023595E05 
d 
6.79967723330480E03 
e 
2.19320377318078E+00 
f 
3.73113244062248E+02 
g 
2.80263239880726E+04 
Unlike the traditional DishStirling system, the system under study is characterized by an absorber enclosed in a hot chamber in order to achieve the characteristics of a black cavity and increase the performance of the entire plant (Figure 5).
Figure 5. Receiver provided with hot chamber
In the work the Eq.s are presented that describe the physical phenomenon and the calculation model, developed in a MatLab environment, through which the dynamic behaviour of the concentratorreceiverStirling engine system can be predicted to quantify the energy productivity. Two system solutions are compared: the first that uses the absorber with hot chamber and the second with simple absorber.
3.1 Absorber equipped with hot chamber
In order to assess the temperature reached by the absorber and the hot chamber, a model discretization in three walls was used (Figure 6): the outer surface of the absorber (wall 1), the inner surface of the hot chamber (wall 2) and the surface of the inlet hole of the hot chamber (wall 3).
Figure 6. Discretization in three walls of the absorber and hot chamber
Compared to the real model, a simplification was made to the shape of the absorber which was considered cylindrical rather than trunkconical in shape.
Referring to Figure 6, the following parameters were defined: D_{e} outer diameter of the chamber, d diameter of the inlet hole, D inner diameter of the chamber, D_{a} absorber diameter, H chamber height and h absorber height.
The analysis was carried out by running the energy balances on the different walls in the solar spectrum to short wavelength, and in the infrared spectrum at high wavelength.
Analysis in the solar spectrum. The radiance of the surfaces forming the cavity, in the solar spectrum, are made solely by the terms of the radiation reflected from the surfaces because they can not emit in this spectrum:
$\mathrm{J}_{\mathrm{j}}^{\mathrm{c}}=\rho_{\mathrm{j}}^{\mathrm{c}} \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{F}_{\mathrm{jk}} \mathrm{J}_{\mathrm{k}}^{\mathrm{c}}$ (3)
In Eq.(3), ρ_{j}^{c} is the reflection coefficient of the “j” surface and F_{jk} is the view factor between the surfaces “j” and “k”.
Solar radiation entering the chamber through the hole, for an observer within it, can be interpreted as the radiance of the same hole. It is known a priori and is equal to the incident flux on the receiver:
$\mathrm{J}_{\mathrm{f}}^{\mathrm{c}}=\frac{\mathrm{DNI} \cdot\left(\mathrm{A}_{\mathrm{p}}\mathrm{A}_{\mathrm{o}}\right) \cdot \cos (\mathrm{i}) \cdot \rho_{\mathrm{p}} \cdot \mathrm{F}}{\mathrm{A}_{\mathrm{h}}}$ (4)
In Eq.(4), DNI is the direct normal radiation to the ground, A_{p} and A_{o} represent, respectively, the total area of the concentrator and the area fraction which does not receive radiation due to the shadow projected on it from the hot chamber, i is the angle of incidence of solar radiation (to take into account a hypothetical error of the tracking system, an angle of incidence of solar radiation of 0.3° was hypothesized), ρ_{p} is the reflection coefficient of the parabola, F is the convergence coefficient and A_{h} is the area of the hole of the hot chamber.
The view factors are determined by the geometry of the system and are valued using the principle of reciprocity and the additive property [2].
The direct normal radiation to the ground was calculated by Eq.(5) according to the ASHRAE model [3] to estimate the radiation to the ground on a clear day:
$\mathrm{DNI}=A \cdot \exp \left(\frac{\mathrm{B}}{\sin \beta}\right)$ (5)
Where β is the angle of solar height, A the apparent solar radiation outside of the atmosphere and B is the atmospheric extinction coefficient. Their values, for the twentyfirst day of each month, are shown in Table 2.
Table 2. Values of the constants A and B for the ASHRAE model
Month 
A [W/m^{2}] 
B [] 
Jan. 
1 230 
0.142 
Feb. 
1 215 
0.144 
Mar. 
1 186 
0.156 
Apr. 
1 136 
0.180 
May 
1 104 
0.196 
June 
1 088 
0.205 
July 
1 085 
0.207 
Aug. 
1 107 
0.201 
Sept. 
1 151 
0.177 
Oct. 
1 192 
0.160 
Nov. 
1 221 
0.149 
Dec. 
1 233 
0.142 
After determining the radiance by the above Eq.s, the solar flux absorbed by each wall can be evaluated:
$\Phi_{\mathrm{ass}, j}^{\mathrm{c}}=\alpha_{\mathrm{j}}^{\mathrm{c}} \cdot \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{F}_{\mathrm{jk}} \cdot \mathrm{J}_{\mathrm{k}}^{\mathrm{c}}$ (6)
Where α_{j}^{c} is the absorption coefficient of jth surface in the solar spectrum, which is the complement to one of the corresponding reflection coefficients.
$\alpha_{j}^{c}=1\rho_{j}^{c}$ (7)
The flow $\Phi_{\mathrm{ass}, \mathrm{f}}$ is, in reality, a “fictitious absorbed flow”; in fact, it represents the fraction of energy that is again sent outside through the hole (the absorption coefficient of the hole is unitary).
Analysis in the infrared spectrum. The walls, after absorbing solar radiation and their temperature is increased, reemit energy in the infrared spectrum. In this spectrum, the radiance contains both the emitted and the reflected component. For the jth surface radiance is written:
$\mathrm{J}_{\mathrm{j}}^{1}=\varepsilon_{\mathrm{j}}^{1} \sigma \mathrm{T}_{\mathrm{j}}^{4}+\left(1\varepsilon_{\mathrm{j}}^{1}\right) \cdot \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{F}_{\mathrm{jk}} \mathrm{J}_{\mathrm{k}}^{1}$ (8)
Where $T_{a}$ is the infrared emissivity of jth surface and σ is the StefanBoltzmann constant.
The incoming radiance through the hole, since it is not provided with glass, is assumed equal to:
$\mathrm{J}_{f}^{1}=\sigma \cdot \mathrm{T}_{\mathrm{a}}^{4}$ (9)
Where T_{a } is the outside air temperature.
The flows absorbed in high wavelength are dependent on contributions from the energy incident on the surface under examination from the other surfaces of the cavity. Assuming that all the surfaces are grey, the following relationship holds:
$\Phi_{\mathrm{ass}, \mathrm{j}}^{1}=\alpha_{\mathrm{j}}^{1} \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{F}_{\mathrm{jk}} \mathrm{J}_{\mathrm{k}}^{1}=\varepsilon_{\mathrm{j}}^{1} \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{F}_{\mathrm{jk}} \mathrm{J}_{\mathrm{k}}^{1}$ (10)
Overall balance of the surface. In order to determine the temperatures reached by the absorber T_{ass} (wall 1) and the hot chamber T_{c} (wall 2), it is necessary to analyse the overall energy balance of the walls, which takes contributions in the two spectra into account.
Therefore the energy balance is the following:
$\left\{\begin{array}{l}\frac{\mathrm{Q}_{\mathrm{u}}}{\mathrm{A}_{1}}+\varepsilon_{1}^{1} \cdot \sigma \cdot \mathrm{T}_{\mathrm{ass}}^{4}\Phi_{\mathrm{ass}, 1}^{\mathrm{c}}\Phi_{\mathrm{ass}, 1}^{1}=0 \\ \frac{\mathrm{Q}_{\mathrm{p}}}{\mathrm{A}_{2}}+\varepsilon_{2}^{1} \cdot \sigma \cdot \mathrm{T}_{\mathrm{c}}^{4}\Phi_{\mathrm{ass}, 2}^{\mathrm{c}}\Phi_{\mathrm{ass}, 2}^{1}=0 \\ \mathrm{J}_{1}^{1}=\varepsilon_{1}^{1} \sigma \mathrm{T}_{\mathrm{ass}}^{4}+\left(1\varepsilon_{1}^{1}\right)\left[\mathrm{F}_{12} \mathrm{J}_{2}^{1}+\mathrm{F}_{13} \mathrm{J}_{3}^{1}\right] \\ \mathrm{J}_{2}^{1}=\varepsilon_{2}^{1} \sigma \mathrm{T}_{\mathrm{c}}^{4}+\left(1\varepsilon_{2}^{1}\right)\left[\mathrm{F}_{21} \mathrm{J}_{1}^{1}+\mathrm{F}_{22} \mathrm{J}_{2}^{1}+\mathrm{F}_{23} \mathrm{J}_{3}^{1}\right]\end{array}\right.$ (11)
The power Q_{p}, given by the hot chamber, is the sum of two contributions: power lost to the outside by convection and radiation (negligible because of the outer insulation of the chamber) and cooling power of the hot chamber walls Q_{w}, different from zero if the temperature reached by the absorber is greater than the maximum value allowed for the proper functioning of the Stirling engine.
The code set up allows performance of the analysis in the solar spectrum, necessary for the assessment of the flows absorbed at low wavelength from the two surfaces constituting the cavity ( $\Phi_{\mathrm{ass}, 1}$ , $\Phi_{\mathrm{ass}, 2}^{\mathrm{c}}$ ), and subsequently the analysis in the infrared spectrum, to assess the temperatures reached by absorber and hot chamber.
In order to ensure integrity and functionality of the engine, the hot chamber is provided with a cooling system. The function of this system is to intervene when the temperature reached by the absorber exceeds the maximum allowed. Drawing appropriate power Q_{w} through cooling of the chamber surfaces, the temperature of the absorber is always kept at the maximum value and the system can provide the nominal values of electrical power. In this case, the Eq.s to be solved are the same as those described by the Eq. system (11), in which, however, the temperature T_{ass} (set equal to 565 °C) is no longer unknown but the power Q_{w} included in Q_{p}.
In addition, the control system used provides the partial defocusing of the parabola which should not be able to maintain the temperature of the absorber lower than 565 °C, despite the cooling of the chamber surfaces.
3.2 Absorber without hot chamber
For the calculation of the temperature reached by the absorber in the absence of a hot chamber, it must satisfy the Eq. of energy balance, Eq.(12), in which the power absorbed by the receiver must equal the useful power supplied by the same, that is, the power absorbed by the Stirling engine, Eq.(2), and the power from it lost by convection and radiation.
$\mathrm{P}_{\mathrm{a}_{} \mathrm{ric}}=\mathrm{P}_{\mathrm{p}_{} \mathrm{con}}+\mathrm{P}_{\mathrm{p}_{}} \operatorname{irr}+\mathrm{Q}_{\mathrm{u}}$ (12)
The power absorbed by the receiver, which represents a rate of solar energy incident on the parabola, and the losses due to convection and radiation of the same, can be expressed through the relationship:
$\mathrm{P}_{\mathrm{a}_{} \mathrm{ic}}=\mathrm{DNI} \cdot\left(\mathrm{A}_{\mathrm{p}}\mathrm{A}_{0}\right) \cdot \cos (\mathrm{i}) \cdot \rho_{\mathrm{p}} \cdot \mathrm{F} \cdot \alpha_{1}^{\mathrm{c}}$ (13)
$P_{p_{} c o n}=\left(A_{f}+A_{l}\right) \cdot h_{c} \cdot\left(T_{a s s}T_{a}\right)$ (14)
$P_{p_{} \text {irr }}=\left(A_{f}+A_{1}\right) \cdot \varepsilon_{1}^{1} \cdot \sigma \cdot\left(T_{\text {ass }}^{4}T_{a}^{4}\right)$ (15)
In which A_{f }and A_{l }indicate, respectively, the front and the side area of the absorber, while h_{c} is the convective heat transfer coefficient, assumed at 20 Wm^{2}K^{1}. In accordance with the numbering shown in Figure 6, the subscript 1 was used for the emissivity and for the absorptivity of the absorber (in this case there is no wall 2).
3.3 The storage tank
In order to meet better the user requirements, the solar system is usually accompanied by a storage tank. The temperature of the tank is calculated by solving the following energy balance:
$P_{\text {ter }}Q_{los s}=\frac{\rho_{a} V_{s} c_{p}}{\Delta t}\left(T_{s}^{t}T_{s}^{t\Delta t}\right)$ (16)
In Eq.(16), ρ_{a} is the density of water, V_{s} the volume of the tank, \Delta t the number of seconds between a time instant and the previous one, while T_{s} is the tank temperature.
The power lost from the tank, Q_{loss}, is calculated by the following Eq.:
$\mathrm{Q}_{ \mathrm{loss}}=\mathrm{H}_{\mathrm{s}} \cdot \mathrm{S}_{\mathrm{s}} \cdot\left(\mathrm{T}_{\mathrm{s}}^{\mathrm{t}}\mathrm{T}_{\mathrm{a}}\right)$ (17)
In Eq.(17), H_{s} and S_{s} are, respectively, the transmittance and the heat exchange surface of the tank. In the simulations a 1000litre storage tank was used. The water temperature in the storage tank, at starting up of the system, was set at 20 °C.
The total thermal power P_{ter} is sum of the power cooling of the chamber surfaces Q_{w} (in the ranges where it is cooled), and the cooling power of the engine P_{t_m}.
The latter is calculated by Eq.(18).
$\mathrm{P}_{\mathrm{t}_{} \mathrm{m}}=\mathrm{Q}_{\mathrm{u}}\mathrm{P}_{\mathrm{loss}}\mathrm{P}_{\mathrm{el}} $ (18)
In Eq.(18) the power loss from the engine P_{loss} is a data provided by the manufacturer and it is equal to 300 W.
3.4 Factors characterizing the system performances
Once determined the temperature of the absorber, the electrical power produced by the engine and the total thermal power consumption by applying Eqs. (1) and (2) can be calculated.
The incident power on the parabola P_{i_par}, the incident power on the receiver P_{i_ric}, and the related efficiencies η_{par} and η_{ric}, are evaluated with following Eq.s:
$P_{i_{} \text {par }}=D N I \cdot\left(A_{p}A_{0}\right) \cdot \cos (i) $ (19)
$P_{1_{} \operatorname{icc}}=\operatorname{DNI} \cdot\left(A_{p}A_{0}\right) \cdot \cos (i) \cdot \rho_{p} \cdot F $ (20)
$\eta_{\mathrm{par}}=\frac{P_{i_{} \mathrm{ric}}}{P_{i_{} p a r}}$ (21)
$\eta_{\mathrm{ric}}=\frac{Q_{\mathrm{u}}}{P_{\mathrm{i}_{} \mathrm{ric}}}$ (22)
To define the system performance in both configurations (absorber with or without hot chamber), reference is made to dimensionless parameters that characterize the electrical and thermal production. These parameters are the electrical η_{el}, thermal η_{ter} and total η_{g} efficiency (according with first and second thermodynamics laws), evaluated at the system or engine level.
For the system:
$\eta_{\mathrm{el}}=\frac{\mathrm{P}_{\mathrm{el}}}{\mathrm{P}_{\mathrm{i}_{\mathrm{par}}}} $ (23)
$\eta_{\mathrm{ter}}=\frac{P_{\mathrm{ter}}}{P_{\mathrm{i}_{} \mathrm{par}}} $ (24)
$\eta_{\mathrm{g}, \mathrm{IP}}=\frac{P_{\mathrm{ter}}+P_{\mathrm{el}}}{P_{\mathrm{i}_{} \mathrm{par}}}$ (25)
$\eta_{\mathrm{g}, \mathrm{IIP}}=\frac{P_{\mathrm{ter}} \cdot \tau_{1}+P_{\mathrm{el}}}{\mathrm{P}_{\mathrm{ipar}}}$ (26)
For the engine:
$\eta_{\mathrm{el}, \mathrm{m}}=\frac{\mathrm{P}_{\mathrm{el}}}{\mathrm{Q}_{\mathrm{u}}} $ (27)
$\eta_{\mathrm{ter}, \mathrm{m}}=\frac{\mathrm{P}_{\mathrm{t}_{} \mathrm{m}}}{\mathrm{Q}_{\mathrm{u}}}$ (28)
$\eta_{g, m, I P}=\frac{P_{t_{} m}+P_{e l}}{Q_{u}}$ (29)
$\eta_{\mathrm{g}, \mathrm{m}, \mathrm{IIP}}=\frac{\mathrm{P}_{\mathrm{t} \mathrm{m}} \cdot \tau_{1}+\mathrm{P}_{\mathrm{el}}}{\mathrm{Q}_{\mathrm{u}}}$ (30)
The Carnot factor τ_{1} or dimensionless exergetic temperature [4], is calculated between the maximum allowable temperature of the engine and the ambient temperature.
In Figures 7 and 8 the graphical interfaces of the calculation models, implemented in MatLab, respectively for the system with a hot chamber and for the system with simple absorber are reported.
Cosenza was chosen as reference location (L = 39.3°, l = 16.15 °E). The simulations were performed for a full year of system operation.
The characteristic geometry data of the system are reported in Table 3. The lateral surface of the absorber (in the absence of chamber) and the hot chamber are insulated with 5 cm of insulating material with a thermal conductivity of 0.04 Wm^{2}K^{1}. They were considered two different types of absorber in relation to the material used: absorber in sandblasted stainless steel (Ass_Inox) and absorber in Silicon Carbide (Ass_SiC). In both cases the Alanod was used for the hot chamber as characterized by high values of reflectivity.
Table 4 reports the absorption coefficient, in the solar spectrum, and the emittance, in the infrared spectrum, of the materials used in the simulations.
Figure 7. Graphical interface of the computer code for the system with hot chamber
Figure 8. Graphical interface of the computer code for the system without hot chamber
Table 3. Geometric data for absorber and hot chamber
D_{a} [m] 
0.2 
h [m] 
0.08 
H [m] 
0.18 
D [m] 
0.24 
d [m] 
0.15 
D_{e} [m] 
0.3 
Table 4. Optical characteristics of the materials used
α^{c} 
Absorber 
0.78  Stainless steel oxidized (sandblasted) 0.90  Silicon carbide (SiC) 
Hot chamber 
0.20  Alanod 

Hole 
1.00 

ε^{l} 
Absorber 
0.60  Stainless steel oxidized (sandblasted) 0.90  Silicon carbide (SiC) 
Hot chamber 
0.80  Alanod 

Hole 
1.00 
The simulation results obtained for the absorber in stainless steel, are shown in Tables 5 and 6. In the latter, in particular, the various efficiencies assessed at the level of the overall system are reported.
Table 7 shows the average annual efficiency of the engine in the case of stainless steel absorber. The efficiency of receiver is equal to 62% if it is provided with hot chamber and to 55.3% in the contrary case.
In Figures 917, for the absorber in SiC, with and without hot chamber, the trend of the absorber temperature T_{ass}, of the absorbed power of the same P_{a_ric}, of the power absorbed by the engine Q_{u}, of the electric power of the motor P_{el}, of thermal power P_{ter}, of thermal efficiency η_{ter}, of electrical efficiency η_{el}, of the total efficiency of the first η_{g,IP }and second law η_{g,IIP}, of the efficiency of the absorber η_{ric}, evaluated for the system, are presented.
Table 5. Values of T_{ass}, P_{a_ric}, Q_{u}, P_{el}, P_{ter} (Ass_Inox)
Month 
Model 
T_{ass} [°C] 
P_{a_ric }[W] 
Q_{u } [W] 
P_{el} [W] 
P_{ter} [W] 
Jan. 
Chamber 
551.23 
6 386.13 
4 419.89 
1 046.78 
4 533.32 
No chamber 
496.70 
5 418.33 
3 860.43 
890.54 
2 669.89 

Feb. 
Chamber 
564.63 
7 009.17 
4 561.72 
1 085.15 
5 189.66 
No chamber 
531.78 
5 946.95 
4 196.33 
991.05 
2 905.28 

Mar. 
Chamber 
565.00 
7 226.39 
4 566.12 
1 086.23 
5 453.76 
No chamber 
542.88 
6 131.25 
4 313.94 
1 022.86 
2 991.08 

Apr. 
Chamber 
565.00 
7 020.34 
4 566.12 
1 086.23 
5 197.20 
No chamber 
533.34 
5 956.42 
4 204.12 
995.52 
2 908.60 

May 
Chamber 
565.00 
6 856.31 
4 566.12 
1 086.23 
4 994.34 
No chamber 
525.51 
5 817.25 
4 116.13 
973.07 
2 843.06 

June 
Chamber 
565.00 
6 741.73 
4 566.12 
1 086.23 
4 853.04 
No chamber 
519.92 
5 720.03 
4 054.40 
957.06 
2 797.34 

July 
Chamber 
565.00 
6 681.24 
4 566.12 
1 086.23 
4 778.58 
No chamber 
516.91 
5 668.71 
4 021.70 
948.44 
2 773.26 

Aug. 
Chamber 
565.00 
6 734.57 
4 566.12 
1 086.23 
4 844.41 
No chamber 
519.46 
5 713.96 
4 050.35 
955.77 
2 794.59 

Sept. 
Chamber 
565.00 
6 940.25 
4 566.12 
1 086.23 
5 098.62 
No chamber 
529.33 
5 888.47 
4 160.79 
984.04 
2 876.75 

Oct. 
Chamber 
564.82 
6 860.11 
4 564.05 
1 085.72 
5 002.54 
No chamber 
524.81 
5 820.47 
4 116.69 
971.09 
2 845.60 

Nov. 
Chamber 
555.38 
6 444.10 
4 460.82 
1 058.65 
4 571.60 
No chamber 
501.27 
5 467.51 
3 891.30 
903.63 
2 687.67 

Dec. 
Chamber 
540.11 
6 115.28 
4 322.72 
1 014.92 
4 281.25 
No chamber 
479.29 
5 188.52 
3 730.52 
840.66 
2 589.86 

Mean values 
Chamber 
560.93 
6 751.30 
4 524.34 
1 074.57 
4 899.86 
No chamber 
518.43 
5 728.16 
4 059.73 
952.81 
2 806.92 
Table 6. Values of η_{ter}, η_{el}, η_{g,IP}, η_{g,IIP } (Ass_Inox)
Month 
Model 
η_{ter} 
η_{el} 
η_{g,IP} 
η_{g,IIP} 
Jan. 
Chamber 
0.572 
0.132 
0.705 
0.504 
No chamber 
0.335 
0.112 
0.447 
0.330 

Feb. 
Chamber 
0.597 
0.125 
0.722 
0.513 
No chamber 
0.332 
0.113 
0.446 
0.329 

Mar. 
Chamber 
0.609 
0.121 
0.730 
0.517 
No chamber 
0.332 
0.113 
0.445 
0.329 

Apr. 
Chamber 
0.597 
0.125 
0.722 
0.513 
No chamber 
0.332 
0.114 
0.446 
0.330 

May 
Chamber 
0.587 
0.128 
0.715 
0.510 
No chamber 
0.332 
0.114 
0.446 
0.330 

June 
Chamber 
0.580 
0.130 
0.710 
0.507 
No chamber 
0.333 
0.114 
0.447 
0.330 

July 
Chamber 
0.577 
0.131 
0.708 
0.506 
No chamber 
0.333 
0.114 
0.447 
0.330 

Aug. 
Chamber 
0.580 
0.130 
0.710 
0.507 
No chamber 
0.333 
0.114 
0.447 
0.330 

Sept. 
Chamber 
0.592 
0.126 
0.719 
0.511 
No chamber 
0.332 
0.114 
0.446 
0.330 

Oct. 
Chamber 
0.588 
0.128 
0.716 
0.510 
No chamber 
0.333 
0.114 
0.446 
0.330 

Nov. 
Chamber 
0.572 
0.132 
0.716 
0.504 
No chamber 
0.334 
0.112 
0.447 
0.330 

Dec. 
Chamber 
0.564 
0.134 
0.698 
0.501 
No chamber 
0.340 
0.110 
0.450 
0.331 

Mean values 
Chamber 
0.585 
0.128 
0.714 
0.509 
No chamber 
0.333 
0.113 
0.447 
0.330 
Table 7. Mean values of η_{ter,m}, η_{el,m}, η_{g,m,IP}, η_{g,m,IIP }(Ass_Inox)
η_{ter,m} 
η_{el,m} 
η_{g,m,IP} 
η_{g,m,IIP} 

Mean values 
With chamber 
0.696 
0.237 
0.934 
0.690 
Without chamber 
0.691 
0.235 
0.926 
0.684 
Tables 8 and 9 show the average annual values of parameters obtained using the absorber in SiC.
Table 10 reports the values of the average annual efficiency of the engine in the case of SiC absorber.
Table 11 shows the percentage differences, for the two absorbers, among the average values of the variables obtained for the system with hot chamber and those obtained for the system without hot chamber.
Figure 9. Absorber temperature (Ass_SiC)
Figure 10. Power absorbed from absorber (Ass_SiC)
Figure 11. Power absorbed from engine (Ass_SiC)
Figure 12. Electrical power of engine (Ass_SiC)
Figure 13. Total thermal power of the system (Ass_SiC)
Figure 14. Thermal efficiency of the system (Ass_SiC)
Figure 15. Electrical efficiency of the system (Ass_SiC)
Figure 16. Total efficiency of the system (Ass_SiC)
Figure 17. Efficiency of the absorber (Ass_SiC)
Table 8. Mean values of T_{ass}, P_{a_ric}, Q_{u}, P_{el}, P_{ter} (Ass_SiC)
Model 
T_{ass} [°C] 
P_{a_ric }[W] 
Q_{u} [W] 
P_{el } [W] 
P_{ter} [W] 
With hot chamber 
561.65 
6881.62 
4531.46 
1076.62 
5044.77 
Without hot chamber 
539.05 
6609.41 
4286.18 
1011.87 
2974.31 
Table 9. Mean values of η_{ter}, η_{el}, η_{g,IP}, η_{g,IIP}, η_{ric} (Ass_SiC)
Model 
η_{ter} 
η_{el} 
η_{g,IP} 
η_{g,IP} 
η_{ric} 
With hot chamber 
0.602 
0.129 
0.731 
0.520 
0.621 
Without hot chamber 
0.353 
0.120 
0.474 
0.350 
0.584 
Table 10. Mean values of η_{ter,m}, η_{el,m}, η_{g,m,IP}, η_{g,m,IIP }(Ass_SiC)
η_{ter,m} 
η_{el,m} 
η_{g,m,IP} 
η_{g,m,IIP} 

Mean values 
With hot chamber 
0.696 
0.238 
0.934 
0.690 
Without hot chamber 
0.694 
0.236 
0.930 
0.687 
While at the level of the engine, the presence of the hot chamber seems not to bring significant benefits in that it causes differences on efficiencies less than 1% (Tables 7 and 10), this is no longer true at the level of the overall system. For the latter, in fact, the use of a hot chamber with absorber
in stainless steel involves an increase of 14% on electrical efficiency, of 75% on thermal efficiency and of 54% on the total efficiency of second law of thermodynamics, compared to the same plant with simple absorber.
Table 11. Percentage differences between the two plant solutions.

Percentage differences 

Ass_Inox 
Ass_SiC 

T_{ass} 
8% 
4% 
P_{a_ric} 
18% 
4% 
Q_{u} 
11% 
6% 
P_{el} 
13% 
6% 
P_{ter} 
75% 
70% 
η_{ter} 
75% 
70% 
η_{el} 
14% 
7% 
η_{g,IP} 
60% 
54% 
η_{g,IIP} 
54% 
49% 
η_{ric} 
12% 
6% 
With the use, instead, of an absorber made of silicon carbide, the increments are, respectively, 7%, 70% and 49%.
Minor offsets are justified by the fact that the SiC, allowing a greater absorption of solar energy than
sandblasted stainless steel, involves absorber temperatures almost similar in the two solutions.
Obviously, the efficiency of the parabola is not influenced by the plant solution adopted, and it is 87%.
This paper analyses the performances of a DishStirling concentrating solar system using the Stirling engine for the production of electrical and thermal energy. In particular, with focus on the receiver, its performance was evaluated considering two different system solutions: the first using the absorber with hot chamber and the second an absorber without hot chamber.
The results derived from simulations revealed that the use of the absorber provided with hot chamber entails a considerable increase in performance of the system, especially from a thermal point of view, owing to the further removal of the thermal power resulting from the cooling of the walls of the hot chamber. This system solution enables the temperature of the absorber to be kept always close to the maximum allowed value so that the engine can provide the nominal values of thermal and electric power.
With temperature control the possible irreversible deformations of the engine and the continuous misalignments of the parabola are averted.
In particular, for a system with a parabola of 10 m^{2} area, absorber in stainless steel and a Stirling engine of 1 kWe, located in Cosenza (Italy), the presence of the hot chamber entailed for the system an increase of 14% in the electrical efficiency, of 75% in thermal efficiency and of 54% in the total efficiency of the second law of thermodynamics, compared to the same plant with simple absorber.
The use of an absorber made of silicon carbide and hot chamber involves, however, an increase of 7% in electrical performance, of 70% in thermal efficiency and of 49% in the total efficiency of the second law of thermodynamics.
1. S. Cucumo, A. Muzaka, L. Laino, E. Pastorelli, “Analisi delle prestazioni di un sistema solare termico a concentrazione (csp) con stima della producibilità,” Atti del 7° Congresso Nazionale AIGE, Rende (CS), 1011 Giugno 2013. Edizioni TEOMEDIA.
2. M.F. Modest, Radiative Heat Transfer, McGrawHill, New York, 1993.
3. ASHRAE HandbookFundamentals, New York, 1989.
4. M.A. Cucumo, D. Kaliakatsos, V. Marinelli, Energetica, Pitagora Editrice, Bologna, 2006.