Power generation for off‐grid building with a small segments parabolic dish concentrator and ORC unit: Numerical investigation

In this research, the small segments parabolic dish concentrator (SSPDC) with a modified cavity was optically and thermally investigated. The SSPDC consisted of small mirrors that were tracking the sun individually. The SSPDC allows using different concentration ratios and aperture areas. Oil, pure water, and water + perypolen glycol (PG) were evaluated as working fluids. Different structural characteristics of the solar system were investigated, including dish focal distance, cavity outer diameter, and cavity aperture area. Then the investigated solar system was explored as a heat source of an organic Rankine cycle (ORC) unit for providing the power for a house. Finally, some environmental parameters of the investigated ORC units, such as carbon dioxide emission and carbon dioxide credits, were evaluated. The results reveal that the investigated solar unit had a dish depth of 0.14 m, a focal distance of 1 m, a cavity aperture outer diameter of 0.1 m, and a cavity aperture inner diameter of 0.08 m for a 10‐mrad optical error and a 1° tracking error. Usage of pure water is recommended for low‐temperature application, water + PG for medium‐temperature application, and oil for high‐temperature application. It was concluded that two units of the proposed ORC could provide energy to the house with solar radiation of more than 800 W/m2 and the number of units should be increased for achieving the required power with decreasing solar radiation.


| INTRODUCTION
Consumption of fossil fuels generates many environmental problems, such as global warming, acid rain, depletion of ozone layers, and so forth. 1 Nowadays, clean energies are identified as an appropriate option for fossil fuels, including geothermal, wind, solar energy, hydropower, and so forth. 2,3Solar source of energy is introduced as a globally clean source of energy for generating power or heat. 4Solar collectors can be used to transform energy from the sun into heat. 5Two sets of solar collectors exist: stationary and tracking solar collectors. 6A solar dish concentrator is introduced as a tracking solar collector. 7The dish concentrator is proper for high-temperature applications with the lowest heat losses.The solar dish concentrators use different types of absorbers, including volume, external, and cavity receivers. 8The cavity receivers have consisted of a long small tube for flowing working fluid and absorbing solar energy.The cavity tube has been shaped as a cavity structure for reducing heat losses and absorbing radiation and reradiation of the incoming solar radiation. 9umerous studies worked on the optimization of the cavity receivers. 10,11The cavity receivers have to be designed in such a way for increasing optical performance and reducing thermal heat losses. 12In the literature review, the shape design and dimensions of the cavity receivers are studied to achieve the highest thermal and optical efficiency. 13In addition, optimal design requires a fairly constant temperature pattern to reduce the heat flux and temperature peaks. 14Different cavity shapes have been examined in the literature, such as rectangular, conical, hemispherical, and cylindrical cavity receivers. 15,16Venkatachalam and Cheralathan 17 carried out an experimental study related to the thermal performance of a parabolic solar dish concentrator with a conic shape cavity receiver.It is found that the temperature of the receiver surface was reduced as the aspect ratio increased.Nevertheless, the thermal output reduction is observed.Therefore the receiver aspect ratio has a major effect on the thermal efficiency.Li et al. introduced a central cavity receiver with a spiral tube.They developed detailed numerical models for the thermal behaviors of the conical cavity receiver and validated them with experimental data.They suggested the operational volume flow rates to the cavity receiver using water and therminol.They stated that The optimal conical angle of 100°has a minimum loss of heat which results in maximum thermal efficiency. 18A numerical simulation of the inverted conical cavity has been done by Awasthi and Khan and validated with their own experiments and compared the simulation of cylindrical receiver cavities.It has been noticed that the inverted conical cavity at its outer surface undergoing constant heat flux with the inner surface being insulated is superior.Their results indicated that the conical cavity is always better used in the inverted position. 19ome other researchers have done studies related to the performance of cavity receivers numerically.Bellos et al. 20 studied five different cavity receivers and chose the most appropriate designs under different operating temperature conditions.They indicated that the innovative one with a cylindrical-conical shape is the best design, whereas the conical and spherical options are the next.The cylindrical-conical model has a thermal efficiency of 67.95%, an exergy efficiency of 35.73%, and an optical efficiency of 85.42% for operation at 300°C.Daabo et al. 21studied both the flux distribution and the optical efficiency of three different geometries (cylindrical, conical, and spherical).Their results showed that the flux propagation on the inner surfaces of the cavity and their optical quality is associated.The optical performance for the conical, cylindrical, and triangular shapes was 75.3%, 71.5%, and 70.1%, respectively.Si-Quan et al. 22 created a three-dimensional (3D) model to examine the spherical cavity receiver's optical and thermodynamic efficiency.They found that the distribution of radiation flux is more consistent the sphericalshape cavity receiver drifts away from the focal point in a positive or negative direction.On the basis of the simulation performance, the receiver's thermal efficiency ranged from 81.9% to 84.4%, and the optimum opening size (cavity aperture diameter) was about 1.0-1.5.Yang et al. 23 suggested a new design of a 2-stage dish concentrator cavity receiver.For cavity design and its performance analysis, both thermal and optical simulations are used.They found that the proposed model demonstrated higher performance compared with the traditional one.Li et al. 24 presented an analytic method to estimate the efficiency of a parabolic dish concentrator with a flat receiver or cavity receiver.They found that a nonwindow cavity receiver is favored if the optical error is less than 4 mrad.On the basis of the reported researches, cavity receivers have shown higher performance compared with traditional receivers.On the other hand, conical-, cylindrical-, and spherical-shape cavity receivers have resulted in appropriate optical and thermal performance compared with other cavity shapes.
Some studies have evaluated the performance of cavity receivers based on numerical and experimental studies.Soltani et al. 25 experimentally and theoretically studied a cylindrically baffled cavity receiver in a solar collector system.They used an innovative hybrid approach for the thermal and optical simulation of the solar collector system and studied the influence of certain geometric and structural parameters such as the length of the aperture size of the receiver to the focal point ratio, the aspect ratio of the receiver, and the geometric concentration ratio of the system.Their results showed that the optimum configuration of the above parameters can increase the system's thermal efficiency by up to 65%.A thermally insulated down receiver has been constructed by Azzouzi et al. 26 They experimentally and analytically studied different characteristics of a solar dish collector with a cylindrical cavity receiver.Optimum parameters of cavity receivers for achieving the highest performance were reported by the researchers based on numerical and experimental studies.
Influence of different cavity parameters was investigated on the performance of cavity receivers by many researchers.A numerical 3D examination is carried out by Wu et al. 27 to determine the cavity receiver's total heat loss under different receiver positions and slopes.Results showed that the amount of Nusselt is more sensitive to the angle of tilt and width of the aperture.Bahrehmand and Ameri 28 and Ngo et al. 29 explored numerical modeling and optimizing for the reduction of natural heat loss from convection in a cavity receiver with panel fins.They noticed that a significant decrease in natural heat loss from convection can be achieved using the panel fins in the cavity receiver.Li et al. 30 systematically analyzed the effect of the cavity receiver's geometric parameters and surface properties.Their analysis indicated that the optical performance improves with a greater height ratio it drops.Moreover, optical performance curves are decreased by the diameter ratio monotonically.Zhang et al. 31 to study the thermal efficiency of the 3D molten salt cavity designs in the steady state, suggested a modified combined computational method.They stated that the low thermal efficiency of a receiver would result from a very low or very high height.They noticed that if the height of the backside walls compared with the side walls increase, the thermal efficiency decreases first and then improves with the depth decreasing.It was concluded that the title angle and aperture area of cavity receivers have an effective influence on thermal heat losses.Also, it was found the application of the panel fins in the cavity receiver and a greater height ratio can show a positive effect on the performance of the cavity receiver.Related to optimum cavity height, researchers found that very low or very high heights have a negative effect on the performance of cavity receivers.
Also, some studies have been done related to environmental analyses of solar collectors. 32,33A growing world population trend has driven modern societies to search for more effective, environmentally friendly power plants.To achieve this goal, the coupled heating, cooling, and power generation plant may benefit modern society.Over the past decades, sustainable combined cooling, heat and power (CCHP) systems have gained more interest.Not only can solar energy run zeroemission CCHP plants, but it is also safe and simple to use.There are many publications on the role of CCHP systems in improving efficiency and reducing emissions. 34Lamrani et al. 35 analyzed the environmental effects of the use of solar energy in dryer applications.Results showed that the incorporation of the solar dish concentrator into the solar dryer system results in a decrease in the energy consumption of the heating system and an annual avoidance of about 34% of CO 2 emissions and expressed the fundamental modeling equations that are highly suitable for simulations based on optimization methods.Ahmadi et al. 36 studied the trigeneration systems' environmental impact assessment.They found a gas turbine-based trigeneration unit for generating cooling with a specific (Li/Br water absorption) chiller.Their Results indicated that emissions from a single generation to trigeneration were reduced by about 40%.
As seen in the mentioned literature review, there is no analysis of the optimization investigation of the small segments parabolic dish concentrator (SSPDC) with cavity receivers.Consequently, in the current research, an SSPDC with a hemispherical cavity receiver was explored and investigated based on optical and energy analyses.The SSPDC consisted of numerous small mirrors that were tracking the sun individually.The new suggested structure of the SSPDC allows using different concentration ratios and different aperture areas.Different parameters of the solar dish concentrator were optically investigated, such as dish depth, and dish focal distance as new subject.Also, various fluids were investigated as solar working fluids, including oil, water, and a combination of water + perypolen glycol (PG).In the next stage, the investigated solar unit with pure water was utilized as a heat source of an organic Rankine cycle (ORC) unit for power generation.The suggested solar ORC system with the investigated cavity receiver was investigated for providing the energy of an off-grid building or removing houses in different situations such as earthquakes as a new and interesting subject.For the building's power generation, the effect of sun radiation and the number of the proposed solar ORC unit were examined.The suggested solar ORC system for the power generation of a building was evaluated basis of environmental analyses.Different parameters of the cavity receiver were evaluated, including the cavity outer diameter and cavity aperture area.Finally, this investigation will be used to further our research related to building and conducted some experimental tests of the investigated solar unit in the current study.Finally, novelties of the current research compared with other published paper by Loni et al. can be summarized as: In this research, a new structure consisting of small segments of the mirror with cavity receivers was designed and investigated.On the other hand, the suggested solar ORC unit was considered as a main power provider for a building.Also, environmental analyses were conducted for the suggested power generation system, including CO 2 mitigated per annum and carbon credit.

| MODELING AND METHODOLOGY
In this research, a new structure of a dish concentrator with small segments of a mirror will be introduced.A redesigned cavity receiver was investigated as an absorber.The solar parabolic dish collector with the redesigned cavity receiver was optically and thermally investigated for determining the optimum amounts of cavity aperture diameter, dish focal length, dish aperture area, and dish rim angle.Afterward, the solar dish collector with optimum structure will be evaluated using different volume fractions of water + PG as a solar operating fluid.In the next step, the investigated solar unit with pure water will be used as a heat source of an ORC unit for power generation.The power generated by the solar ORC unit will be assumed as a power source for a building.Finally, the investigated solar unit as the power source of the building will be investigated based on environmental analyses, such as CO 2 emission and CO 2 credits.A solar ORC unit schematic is shown in Figure 1.Also, a summary table of the analysis process in this research is presented in Figure 2.

| Solar dish concentrator
In the current research, a new structure consisting of small segments of the mirror with cavity receivers was designed and investigated.A depiction of the solar unit under investigation is shown in Figure 3.It must be noted that in this work a redesigned cavity receiver has been investigated optically and thermally.The main advantage of the proposed dish concentrator is the variable structure specifications of the dish concentrator.The parabolic dish concentrator's component variables can be summarized as the focal length of the dish (f), the aperture diameter of the dish (D), the dish rim angle (φ), the area of the receiver (A), and the concentration ratio (C).A schematic of the dish concentrator parameters, including the focal length of the dish, the aperture diameter of the dish, and the dish rim angle, is depicted in Figure 3.
In the first step, the optical study of the solar parabolic concentrator with a cavity was done by SolTrace software.This must be noted that SolTrace programming is used as an accurate and free software for optical analysis of the dish concentrator.Some assumptions were taken into account during optical modeling, including sun-shape was assumed as a pillbox, half-angle width was considered as 4.65 mrad, and number of ray intersections was assumed as 10,000.For the optimization of dish structure, different dish depths were investigated from 0.5 to 0.023 m.Optical analyses were conducted for different tracking errors, including 1°and 2°, and different optical errors, including 5, 10, 15, 20, and 35 mrad.Also, the outer diameter of the modified cavity receiver was investigated between 0.06 and 0.5 m.Finally, the cavity aperture area of the modified cavity receiver was optically and thermally investigated for various amounts of outer-to-inner diameters ratios, including 1, 0.8, 0.6, 0.4, and 0.2.
In the next step, the thermal optimization of the suggested parabolic concentrator with the modified cavity receiver is presented.The thermal modeling of the solar unit was conducted in Maple software based on energy balance equations.In general, the redesigned cavity receiver has three types of heat losses, including internal convection, internal radiation, and conduction.Mineral wool insulation lined the external sides of the improved cavity receiver with a thickness of 2 cm, average conductivity of 0.062 W/m K. 37 Figure 4 displays the schematic view of the heat transfer from the modified cavity receiver.It should be mentioned that external convection heat losses from the cavity receiver with the conduction heat losses were assumed as the conduction heat loss in Figure 4. Also, the main dimensions of the examined solar thermal collector are presented in Table 1.
In the receiver tube, the net heat transfer rate (Q ̇net ) is expressed as where Q * (W) is the solar heat flux to the cavity receiver, η optical and η refl are described as the optical efficiency and the dish reflectivity efficiency, respectively.η refl is presumed to be equal to 0.84 in this study, Q ̇solar (W) is the total solar heat flux received by the concentrator, I sun | 965 F I G U R E 1 Schematic of the solar ORC system as a power source of a building.ORC, organic Rankine cycle.
is the solar beam radiation equal to 800 (W/m 2 ), D conc is the diameter of dish aperture equal to 1.5 m.Also, Q ̇loss cond , (W), Q ̇loss rad , (W), and Q ̇loss conv , (W) are the conduction heat loss, radiation heat loss, and convection heat loss measured in the following subsections, respectively.On the basis of the following equations, amounts of conductive heat loss, radiation heat loss, and convection heat loss were calculated: loss conv conv rec s , (6)   Using these equations, conductive heat loss of the cavity outside (Q ̇loss cond , ) was calculated using resistance method using Equation ( 4), radiation heat loss of the inner space of the cavity receiver (Q ̇loss rad , ) was estimated using Equation ( 5), and convection heat loss of the inner space of the cavity receiver (Q ̇loss conv , ) was calculated based on Equation ( 6).Related to the presented Equations ( 4) and ( 5) the following equations can be used: (9) On the basis of Equations ( 7) and ( 8), the convection heat coefficient (h outer ) was calculated for the condition that there are natural convection (Nu natural ) and forced convection (Nu forced ) outside of the cavity receiver.The following equation is related to calculation of radiation heat coefficient from inside space of the cavity receiver (h rad ) based on Reddy and Sendhil Kumar 38 : | 967 Some parameters of these equations can be calculated based on the following equations 38 : On the other side, the convection heat loss coefficient (h conv ) from inside space of the cavity receiver can be calculated based on the following equations 38 : ) .
Finally, the cavity tube was divided into a smaller length, whereas each smaller length was considered as a separate element.The temperature of the receiver surface (T s n , ) and efficient heat transfer rate (Q ̇net n , ) are assumed as two unknown parameters for the different elements of the cavity pipe.The receiver surface temperature (T s n , ) and efficient heat transfer rate (Q ̇net n , ) at the various elements of the tube were determined with defining two the following equations based on external energy balance equation and internal energy balance equation: Pure water and three separate fractions of the PG volume (25%, 50%, and 55%) in water were evaluated as the solar operating fluid.A flow rate of the working fluids was considered 100 mL/s.

| Organic Rankine cycle
The ORCs are known as an interesting technology for generating of energy form different sources of heat, such as solar energy, waste heat, and so forth.A low boiling point organic fluid is used in the ORCs as a working fluid.The phase of the organic fluids will change to saturated or super-saturation gas with the absorption of low amount of heat in an evaporator.The saturated or super-saturation gas has enough potential for rotation in a turbine to power generation.The ORC unit has been consisted of an evaporator for absorbing heat at constant pressure condition, a turbine for power generation at isentropic condition, a condenser for ejecting heat at constant pressure, and a pump for pressurized the ORC working fluid at constant pressure.The ORC unit's schematic view is depicted in the previous paragraphs.Air was utilized as the second operating fluid of the condenser for cooling the ORC operating fluid.The ORC unit was considered under the condenser temperature of 311 K and constant evaporator pressure of 3 MPa.In this research, R113 was chosen as the ORC operating fluid based on the optimization study by Shahverdi et al. 39 The output of the ORC unit and the total output of the solar ORC unit are calculated as below: In these equations, W ̇net (W) is the amount of net power generation by the ORC unit, Q ̇evp (W) is the absorbed heat by the ORC unit in the evaporator, I beam (W/m 2 ) is the solar beam radiation, and A ap Dish , is the aperture area of the dish concentrator.It should be mentioned that the amount of Q ̇evp was assumed equal to the absorbed heat by the solar collector.On the other side, the amount of W ̇net can be determined as 40 where W ̇T (W) is the generated power by the turbine, W ̇P (W) is the consumption power by the pump, h* 4 (kJ/ kg) and h* 3 (kJ/kg) are the enthalpy of the ORC operating fluid at outlet and inlet of the evaporator, and h* 2 (kJ/kg) and h* 1 (kJ/kg) are the enthalpy of the ORC working fluid at outlet and inlet of the pump, respectively.It should be mentioned that the mechanical efficiency of the system assumed as 100% during the analyses.On the other side, ṁO RC (kg/s) is the organic fluid mass flow rate and that can be determined as 40

| Providing required power of a building
In this research, the suggested solar ORC unit was considered as the main power provider for a building.A schematic view of the investigated building is displayed in the previous paragraphs.The goal of this investigation is providing the required power to help people without the support of remote infrastructures, such as an electrical grid.This technology can be assumed as an off-the-grid technology.A list of used devices in the investigated building is presented in Table 2 as a case study.

| Environmental analyses
Today, the importance of the environmental influence of different sources of energy for providing the required energy has increased.This matter has become more important due to appear some environmental problems, such as depletion of the ozone layer, global warming, and so forth, with fossil fuel consumption.Consequently, the application of renewable energy has been introduced as a suitable alternative instead of fossil fuel.Related to this subject, environmental analyses, including CO 2 mitigated per annum, and carbon credit with the usage of the suggested solar ORC unit were determined as below 42 : T A B L E 2 A list of used devices in the investigated building. 41vice Number where φ CO 2 (ton) is the amount of the CO 2 emission per annum, ψ CO 2 (kg CO 2 /kWh) is the average CO 2 producing for power generation from coal that was assumed equal to 2.04, E en ann , (kWh) is the power generation by the solar ORC units during a year, whereas each year was considered 2500 h, Z CO 2 ($) is the carbon credit per annum, z CO 2 ($/ton) is the carbon credit which was assumed equal to 14.5, and φ CO 2 (ton) is the CO 2 emission per annum. 42

| Verification and validation
In this section, verification will be presented between the calculated thermal efficiency in the current study and reported data by Loni et al. 14 In Loni et al., 14 a dish concentrator with a hemispherical cavity receiver was explored, whereas water was used as working fluid.It should be mentioned that all assumptions by Loni et al. 14 were assumed for verification of the current research.Figure 5A presents a correlation between the results measured in the current study and the results recorded by Loni et al. 14 As seen, a strong agreement between the estimated results of this study and the results stated by Loni et al. 14 was observed.Also, a validation between the calculated results in the current study with reported data by Hogan et al. 43 was conducted.Water was used as the working fluid in the current study and Hogan et al. 43 Figure 5B shows validation between the calculated results in the current study and reported experimental data by Hogan et al. 43 As seen, a good agreement can be seen between the results of the current study and the reported data by Hogan et al. 43 3 | RESULTS AND DISCUSSION

| Dish depth investigation
In this section, the depth of the SSPDC was investigated based on the optical analysis.In this analysis, the dish aperture diameter was assumed as a constant amount of 1.5 m.The dish depth was investigated from 0.5 to 0.023 m.The focal distance of the dish concentrator was calculated from the below equation: Consequently, the focal distance of the SSPDC was varied from 0.25 to 6 m.As mentioned, optical analyses in this section were conducted by the SolTrace software.Figure 6A shows the variation of solar heat flux versus the variation of depth of the SSPDC for different tracking errors, including 1°and 2°.In these results, the optical error of the SSPDC was assumed equal to 5 mrad.As seen in Figure 6A, there is an optimum dish depth for receiving the highest amount of solar heat flux for both investigated tracking errors.This is due to decreasing focal distance of the dish collector with increasing dish depth amount at a constant value of the dish aperture diameter.Conversely, values of focal distance increased with decreasing dish depth at constant dish aperture diameter (see Equation 26).Consequently, an optimum amount of focal distance and dish depth can be calculated for achieving the highest amount of absorbed solar heat on the cavity wall.Figure 7A-C presents solar heat flux distribution for h = 0.56 m and f = 0.25 m, h = 0.09 and f = 1.5 m, and h = 0.03 and f = 5 m, at a constant aperture diameter of 1.5 m, consequently.As seen in Figure 7, absorbed solar heat flux decreased at lower or higher amounts of the optimum dish depth.Optimum amounts of the dish depth for tracking error of 1°and 2°were calculated as 0.09 and 0.18 m,

(A) (B)
F I G U R E 5 (A) Verification between the calculated thermal efficiency in the current study and reported data by Loni et al. 14 and (B) validation results of the current study and reported experimental data by Hogan et al. 43 respectively.Optimum amounts of the focal distance for achieving the highest amounts of the solar heat flux on the cavity receiver as 1679.21 and 1399.21W were calculated as 1.5 and 0.75 m for tracking errors of 1°and 2°, respectively.Also, it can be found that the amounts of the solar heat flux reduced with an increasing tracking error of the solar unit.On the other side, optimum amounts of the dish depth increased with an increasing tracking error of the solar unit to achieve the highest quantities of the solar heat flux.
On the other side, the solar heat flux variation versus a change of dish depth is depicted in Figure 7B for different optical errors, including 5, 10, 15, 20, and 35 mrad.This analysis was done at tracking error of 1°.As concluded from Figure 7B, there is an optimum dish depth for receiving the highest amount of solar heat flux for all of the investigated optical errors.The reason of this is similar reason that was presented in the previous paragraph.The highest amounts of the solar heat flux in the receiver were calculated equal to 1679.21, 1581.71,1535.68,1469.32, and 1163.19W, for optical errors of 5, 10, 15, 20, and 35 mrad, respectively.Optimum amounts of the dish depth were calculated as 0.09, 0.14, 0.19, 0.19, and 0.19 m, for optical errors of 5, 10, 15, 20, and 35 mrad, respectively.Also, optimum amounts of the dish focal distance were calculated as 1.5, 1, 0.75, 0.75, and 0.75 m, for optical errors of 5, 10, 15, 20, and 35 mrad, respectively.As seen, the highest amounts of solar heat flux decreased with the increasing optical error.Similar results were presented by other researchers. 10,12,44Related to optimum structural parameters of the dish concentrator, for achieving the highest optical performance with the increasing optical error of the solar unit, higher dish depth with lower focal distance needs to be assumed.
Variation of optical efficiency versus change of the depth of SSPDC for different tracking errors has been presented in Figure 8A.In this study, optical error was assumed to be equal to 5 mrad.It can be seen that optical performance data show a similar pattern relative to the measured solar heat flux with a variation in the depth of the dish concentrator.The highest amounts of optical efficiency were estimated equal to 95.07% and 79.22% for tracking errors of 1°and 2°, respectively.Optimum values of the dish depth were calculated as 0.09 and 0.18 m for tracking errors of 1°and 2°, respectively.Also, optimum amounts of the focal distance were calculated as 1.5 and 0.75 m for tracking errors of 1°and 2°, respectively.As seen, optical efficiency decreased with increasing tracking errors, and optimum amounts of focal distance decreased with increasing tracking errors.Similar results were presented by other studies. 10,12,44It should be mentioned that calculated optimum values of the focal distance have a similar trend of heat flux distribution with variation of depth dish for different tracking errors.Consequently, the reason for this is presented in the previous paragraphs.
On the other side, the solar system optical efficiency versus variation of dish depth has been presented in Figure 8B for different optical errors at tracking error of 1°.Different optical errors were investigated, including 5, 10, 15, 20, and 35 mrad.As seen, the trend of optical efficiency data is similar to the calculated solar heat flux with a variation of depth of SSPDC for different optical errors.The highest amounts of optical efficiency were estimated equal to 95.07%, 89.55%, 86.95%, 83.19%, and 65.86% for the optical error of 5, 10, 15, 20, and 35 mrad, respectively.Optimum amounts of the dish depth were calculated as 0.09, 0.14, 0.19, 0.19, and 0.19 m for the optical errors of 5, 10, 15, 20, and 35 mrad, respectively.Also, optimum amounts of the focal distance were calculated as 1.5, 1, 0.75, 0.75, and 0.75 m for the optical errors of 5, 10, 15, 20, and 35 mrad, respectively.As seen, optical efficiency decreased with increasing optical error, and optimum amounts of focal distance decreased with increasing optical errors.As mentioned that defining optimum values of the focal distance is due to a similar trend of heat flux distribution with variation of dish depth for different optical errors.In other words, the reason for this issue has been presented in the previous paragraphs.It should be mentioned that similar results were reported by other studies. 10,12,44eat flux distribution on cavity aperture is presented in Figures 9 and 10 for optical error of 5 mrad and tracking error of 1°.Heat flux distribution of different amounts of dish depth was presented, including 0.56, 0.19, 0.14, 0.07, 0.05, 0.04, 0.03, and 0.02 m.It can be seen that the heat flux intensity increased with decreasing dish depth until an optimum value.It is a similar result compared with the concluded results in the previous sections.

| Cavity outer diameter investigation
In this section, the hemispherical cavity receiver's outer diameter will be investigated optically and thermally.The dish concentrator with an aperture diameter of 1.5 m, a 10mrad optical error, and a 1°tracking error was investigated in this part.It should be mentioned that based on the calculated results of Section 3.1, the investigated dish depth and the focal length of the SSPDC equal to 0.14 and 1 m were used, respectively.Figure 11  diameter variation.Different cavity outer diameters were investigated between 0.06 and 0.5 m.As seen, solar heat flux and optical efficiency have similar trends.In other words, solar heat flux and optical efficiency increased with increasing cavity outer diameter until D out,cavity = 0.1 m, after that optical performance of the solar dish unit remained almost constant with increasing cavity outer diameter.This is because of the increasing optical performance of the solar dish system with increasing cavity aperture until D out,cavity = 0.1 m, after that the dish concentrator received the highest constant possible thermal performance as seen in Figure 11.The maximum solar heat flux and optical efficiency of the solar unit were calculated equal to 1571.07 W and 88.95% for D out,cavity = 0.1 m, respectively.Similar results were presented by other researchers. 10,12,44igure 12 depicts the variation of heat flux distribution at the cavity aperture area with the change of cavity outer diameter, including 0.06, 0.1, 0.2, 0.4, and 0.5 m.These analyses were done for the dish aperture diameter of 1.5 m, and investigated the focal length of 1 m for a 10mrad optical error and a 1°tracking error.It can be seen that the heat flux intensity increased with decreasing cavity outer diameter until an optimum value, then the heat flux intensity remained almost at constant amounts.Similar results were presented by other researchers. 10,12,44It is a similar result compared with the concluded results in the previous paragraph.
Figure 13 shows the cavity-absorbed energy variation and solar unit thermal efficiency versus different diameters of the cavity between 0.06 and 0.5 m for a 10-mrad optical error and a 1°tracking error.It should be mentioned that the small segments parabolic dish collector with an aperture diameter of 1.5 m, investigated dish depth of 0.14 m, and a focal length of 1 m was investigated.As concluded from Figure 13, the cavity-absorbed energy has resulted in a similar trend in comparison with the thermal efficiency of the solar unit.In other words, the energy absorbed by a cavity, and thermal efficiency resulted in the maximum amounts equal to 1290.06 W, and 86.95% at D out,cavity = 0.1 m, respectively.As seen, the thermal performance of the SSPDC increased with increasing cavity outer diameter until the optimum cavity outer diameter of 0.1 m, then the thermal performance reduced with increasing cavity outer diameter.This is because of the optical and thermal performances of the cavity receiver have reverse relation with increasing cavity diameter aperture.In other words, optical performance improved with increasing cavity outer diameter, whereas thermal heat losses of the cavity increased with decreasing cavity outer diameter.Similar results were presented by other researchers. 10,12,44Consequently, there is an optimum cavity outer diameter of 0.1 m for achieving the highest thermal performance.

| Cavity aperture investigation
In this section, to achieve the highest efficiency, the cavity aperture area was investigated optically and thermally.It should be mentioned that the small segments parabolic dish collector with an aperture diameter of 1.5 m, investigated dish depth of 0.14 m, and a focal length of 1 m was investigated.The hemispherical cavity receiver with the investigated outer diameter of 0.1 m was studied in this section.The optical and tracking errors of the solar unit were assumed equal to 10 mrad and 1°, respectively.In this research, "C" was assumed as the outer-to-inner diameters ratio of the cavity aperture.Five levels of C were investigated, including 1, 0.8, 0.6, 0.4, and 0.2.The total heat loss variation of the cavity versus different amounts of the outer-to-inner diameters ratio of the cavity aperture is depicted in Figure 14.As seen, total heat losses increased with increasing the outer-to-inner diameters ratio of the cavity aperture.This is because of increasing internal convection and heat losses from radiation with increasing the outer-to-inner diameters ratio.In other words, the lowest internal heat losses have happened for the lowest amount of the external-to-internal diameters ratio of the cavity aperture equal to 0.2.
Figure 15A,B shows the variation of the absorbing heat, and the cavity receiver thermal efficiency versus the variation of the outer-to-inner diameters ratio of the cavity aperture.The small segments parabolic dish collector with an aperture diameter of 1.5 m, an investigated dish depth of 0.14 m, and a focal length of 1 m, was evaluated.The hemisphere cavity with an investigated external diameter of 0.1 m was examined as the solar system receiver.The optical error of 10 mrad and the tracking error of 1°were used for the investigated solar unit.The outer-to-inner diameters ratio of the cavity aperture was investigated, including 1, 0.8, 0.6, 0.4, and 0.2.As seen, the cavity receiver's thermal efficiency is optimum at C = 0.8.This is because of the increasing the cavity receiver optical performance with the increasing amount of outer-to-inner diameters ratio of the cavity aperture, and increasing heat losses with increasing amount of outer-to-inner diameters ratio of the cavity aperture.Consequently, the outer-to-inner diameters ratio of the cavity aperture equal to 0.8 has resulted in the highest thermal performance of the investigated solar unit.

| Solar unit performance
Figures 16A,B displayed the variation of surface temperature and absorbed net heat along the cavity tube using different working fluids, respectively.The influence of various working fluids, including oil, pure water, water + 0.25PG, water + 0.5PG, and water + 0.55PG, was investigated.It should be mentioned that the investigated solar collector with the modified receiver was studied in this section, including the dish focal distance of 1 m, the collector aperture diameter of 1.5 m, the cavity outer diameter of 0.1 m, and the inner diameter of cavity aperture as 0.08 m.These reported investigated data were calculated for a 10-mrad optical error and a 1°tracking error.As seen in Figure 16, the modified cavity receiver surface temperature resulted in higher amounts using the application of oil as operating fluid compared with water and combinations of water with PG.Also, it could be understood that the lowest surface temperature of the modified cavity receiver was calculated for water.On the other side, using oil as a working fluid, the lowest cavity heat gain along the cavity tube was determined.Also, for all of the examined working fluids maximum values of the surface temperature and cavity heat gain were found in the sixth round of the cavity tube.This is due to the sixth round of the cavity tube, based on the optical analysis, received the largest amount of solar radiation.Similar results were presented by other researchers. 10,12,44ariation of absorbed energy and thermal efficiency of the modified cavity receiver has been depicted in Figure 17A,B, respectively.Different working fluids were investigated, including oil, pure water, water + 0.25PG, water + 0.5PG, and water + 0.55PG.As mentioned in the previous paragraph, these results are related to the investigated solar dish collector with a dish focal distance of 1 m, a dish aperture diameter of 1.5 m, a cavity outer diameter of 0.1 m, and the inner diameter of a cavity aperture as 0.08 m.The solar dish unit was investigated with a 10-mrad optical error and a 1°tracking error.As seen in Figure 17A,B, pure water and oil as operating fluid resulted in the highest and lowest thermal performance of the solar unit, respectively.Amounts of the absorbed energy by the cavity receiver and thermal efficiency were calculated equal to 1261.70 W and 66.70% with the application of pure water, and 1218.02W and 64.65% with the use of oil as operating fluid, respectively.Also, it can be concluded that the application of PG had a negative effect on the thermal performance of the solar unit.Consequently, it can be recommended usage of pure water for low-temperature use, water + PG for medium-temperature application, and oil for hightemperature application.

| Solar ORC unit performance
Variation of absorbed energy and thermal performance of the modified receiver versus the change of solar radiation between 500 and 1000 W/m 2 has been  presented in Figure 18.As the solar working fluid, pure water was used.This should be noted that the investigated solar dish collector with the modified cavity was studied as a heat source of an ORC unit in this section.As mentioned, the investigated dimensions of the solar unit were including the dish focal distance of 1 m, the dish aperture diameter of 1.5 m, the cavity outer diameter of 0.1 m, and the inner diameter of the cavity aperture of 0.08 m.Also, R113 under constant evaporator pressure of 3 MPa and condenser temperature of 311 K was used as the operating fluid of the ORC unit.As resulted in Figure 18A, the cavity heat intake and solar system thermal efficiency improved as the solar radiation increased.The cavity heat gain had been changed between 800 and 1600 W with solar radiation differences from 500 to 1000 W/m 2 .Also, the thermal efficiency of the solar unit had been varied from 66.7% to 67.05%, with solar radiation differences from 500 to 1000 W/m 2 .
On the other hand, Figure 18B presents the ORC network variation and the solar ORC unit total efficiency versus the of solar radiation using water as an operating fluid.The solar radiation ranged from 500 to 1000 W/m 2 .As seen, network values and total solar ORC efficiency increased with increasing amounts of solar radiation.It can be concluded that the variation in the ORC network and total solar ORC unit efficiency indicated similar trends compared with the cavity heat intake variation, and the solar unit thermal efficiency with solar radiation variation, respectively.The solar ORC unit network was varied between 200 and 400 W with the change of solar radiation between 500 and 1000 W/m 2 .Also, the total efficiency of the solar ORC unit varied from 22.46% to 22.58%, with the solar radiation variation between 500 and 1000 W/m 2 .
The ORC network variation versus solar radiation variation for various numbers of the suggested solar ORC unit has been reported in Table 3.The investigated solar dish collector with the modified cavity receiver has been used as the ORC heat source.Water and R113 have also been used as the solar unit's operating fluid and the ORC technique.As mentioned in 2.2.3, the proposed solar ORC unit has been developed for providing the required power for a house.As stated, the required power of the house with five light bulbs, one television (TV), and one refrigerator was estimated as 3800 Wh/day.As seen in Table 3, two units of the proposed solar ORC unit with a F I U R E 16 Variation of (A) surface temperature and (B) absorbed net heat along the cavity tube using different working fluids.

(A) (B)
F I G U R E 17 Variation of (A) absorbed energy and (B) thermal efficiency of the modified cavity receiver using different working fluids.solar beam radiation of more than 800 W/m 2 can provide this required energy.As seen, for locations with lower amounts of solar radiation, more units need to be used for providing the required power.For example, three units of the solar ORC unit need to be used for providing power to the house with solar radiation of more than 600 W/m 2 .

| Environmental analyses
Finally, environmental analyses with the variation of solar radiation for different numbers of the suggested solar ORC unit have been presented in Table 4. Amounts of CO 2 mitigated per annum, and carbon credit with the usage of the proposed solar ORC unit  | 979 are shown in Table 4.This should be noted that these variables are calculated for the solar unit and the solar ORC unit separately.In other words, the energy intake of the solar unit and the electricity generated by the solar ORC system are assumed on the basis of the solar unit and solar ORC unit environmental analyses, respectively.From Table 4 this can be found that the application of the suggested solar ORC unit can be recommended for power generation due to its effective positive influences on the environment.It can be seen from Table 4 that amounts of CO 2 mitigated per annum changed between 4.01 and 8.05 ton CO 2 with variation of solar radiation between 500 and 1000 W/m 2 for the dish concentrator in one unit.Also, amounts of CO 2 mitigated per annum changed between 2.66 and 5.35 ton CO 2 with a variation of solar radiation between 500 and 1000 W/m 2 for the ORC system in one unit.On the basis of the calculated analyses in a condition with solar radiation of 500 W/m 2 , we need at least four units of the designed setup for providing the required power that this setup generates 16.02 ton CO 2 for the dish concentrator and 10.65 ton CO 2 for the ORC system.It can be concluded from Table 4, amounts of CO 2 mitigated per annum, and carbon credit increased with increasing solar radiation and a number of units for power generation.Also, related to some places with solar radiation of more than 800 W/ m 2 , the results of the analyses were shown in Table 4.

| CONCLUSIONS
In the current research, an SSPDC was optically and thermally investigated using a modified cavity receiver.Various structural characteristics of the solar unit were investigated, including dish focal distance, cavity outer diameter, and cavity aperture area.Also, the influence of different working fluids, including oil, water, and water + PG, was investigated.In the second stage, the investigated solar unit was investigated as a source of heat for an ORC unit for providing required power for a house.Finally, some environmental analyzes have been carried out of the proposed solar ORC system for the house.A summary of the main achievements of this study can be presented below: • It was concluded that there is an optimum dish depth for receiving the highest amount of solar heat flux, and optical efficiency for various investigated tracking errors, and optical errors.
• The optimum amount of the dish depth was calculated as 0.14 m, with an absorbed solar energy of 1581.71W, and an optical efficiency of 89.55%, for a 10-mrad optical error and a 1°tracking error.Also, the optimum amount of the dish focal distance was calculated 1 m, for a 10-mrad optical error and a 1°t racking error.• The optimal outer diameter of the cavity is 0.1 m to achieve maximum thermal performance for a 10-mrad optical error and a 1°tracking error.• It was concluded that the optimum outer and inner diameter of the cavity aperture for to achieve maximum thermal performance were calculated as 0.1, and 0.08 m for a 10-mrad optical error and a 1°tracking error, respectively.

F
I G U R E 2 A summary of the analysis process in this research.ORC, organic Rankine cycle.F I G U R E 3 A schematic of the dish concentrator parameters.HOSSEINZADEH ET AL.

F I G U R E 4
Schematic view of heat losses from the modified cavity receiver.T A B L E 1The main dimensions of the examined solar thermal collector.

6
Variation of solar heat flux versus variation of dish depth of dish concentrator for (A) different tracking errors at the optical error of 5 mrad and (B) different optical errors at tracking error of 1°.
depicts solar heat flux variation and solar system optical efficiency versus cavity F I G U R E 7 Solar heat flux distribution for (A) h = 0.56 m and f = 0.25 m, (B) h = 0.09 and f = 1.5 m, and (C) h = 0.03 and f = 5 m, at a constant aperture diameter of 1.5 m.

8
Variation of optical efficiency versus variation of dish depth of dish concentrator for (A) different tracking errors at the optical error of 5 mrad and (B) different optical errors at tracking error of 1°.

F I G U R E 9
Heat flux distribution on cavity aperture area with a variation of dish depth for (A) h = 0.56 m, (B) 0.19 m, (C) 0.14 m, (D) 0.07 m, (E) 0.05 m, (F) 0.04 m, (G) 0.03 m, and (H) 0.02 m.

F
I G U R E 10 Heat flux distribution on cavity aperture area with a variation of dish depth for (A) h = 0.56 m, (B) 0.19 m, (C) 0.14 m, (D) 0.07 m, (E) 0.05 m, (F) 0.04 m, (G) 0.03 m, and (H) 0.02 m.

F
I G U R E 11 Solar heat flux variation and solar system optical efficiency versus cavity diameters for a 10-mrad optical error and a 1°tracking error, dish aperture diameter of 1.5 m, and focal length of 1 m.F I G U R E 12 Variation of heat flux distribution of the cavity receiver with variation of cavity diameter, including (A) D out,cavity = 0.06 m, (B) D out,cavity = 0.1 m, (C) D out,cavity = 0.2 m, (D) D out,cavity = 0.4 m, and (E) D out,cavity = 0.5 m for a 10-mrad optical error and a 1°tracking error, dish aperture diameter of 1.5 m, and focal length of 1 m.

F
I G U R E Variation of cavity-absorbed thermal efficiency of the solar unit versus cavity diameter for a 10-mrad optical error and a 1°tracking error, a dish aperture diameter of 1. 5 m, and a focal length of 1 m.I G U E 14 Variation of total cavity heat loss versus variation of cavity aperture area for investigated cavity diameter of 0.1 m, investigated focal length of 1 m, for a 10-mrad optical error and a 1°t racking error, and 1.5 m diameter of the dish aperture.
R 15 Variation of (A) absorbed heat by the cavity receiver, and (B) thermal efficiency versus variation of cavity aperture area for investigated cavity diameter of 0.1 m, investigated focal length of 1 m, for a 10-mrad optical error and a 1°tracking error, and dish aperture diameter of 1.5 m.

F
I G U R E 18 Variation of (A) absorbed energy and thermal efficiency and (B) ORC network and total efficiency versus solar variation using water as the operating fluid.ORC, organic Rankine cycle.T A B L E 3 ORC network variation versus solar radiation variation for different numbers of the proposed solar ORC unit.W net,ORC (Wh) I sun (W/m 2 ) Environmental analyses with the variation of solar radiation for different numbers of the suggested solar ORC unit.
Abbreviation: ORC, organic Rankine cycle.T A B L E 4 Abbreviation: ORC, organic Rankine cycle.a Amounts of CO 2 mitigated per annum.b Carbon credit.HOSSEINZADEH ET AL.
• The ORC network varied between 200 and 400 W, and total solar ORC efficiency rose from 22.46% to 22.58% with variations in solar radiation from 500 to 1000 W/ m 2 , respectively.•It was concluded that two units of the suggested solar ORC unit with solar radiation of more than 800 W/m 2 could provide the required energy of a house with five light bulbs, one TV, and one refrigerator.