Utilizing thermoelectric generator as cavity temperature controller for temperature management in dish-Stirling engine

Journal Pre-proofs Utilizing Thermoelectric Generator as Cavity Temperature Controller for Temperature Management in Dish-Stirling Engine Ali Mohammadnia, Behrooz M. Ziapour, Farzad Sedaghati, Lasse Rosendahl, Alireza Rezania PII: DOI: Reference:

S1359-4311(19)33274-0 https://doi.org/10.1016/j.applthermaleng.2019.114568 ATE 114568

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

13 May 2019 19 September 2019 19 October 2019

Please cite this article as: A. Mohammadnia, B.M. Ziapour, F. Sedaghati, L. Rosendahl, A. Rezania, Utilizing Thermoelectric Generator as Cavity Temperature Controller for Temperature Management in Dish-Stirling Engine, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/j.applthermaleng.2019.114568

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© 2019 Published by Elsevier Ltd.

Utilizing Thermoelectric Generator as Cavity Temperature Controller for Temperature Management in Dish-Stirling Engine

Ali Mohammadniaa, Behrooz M. Ziapoura,*, Farzad Sedaghatib, Lasse Rosendahlc, Alireza Rezania c, a Department

b

c

of Mechanical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

Department of Electrical and Computer Engineering, Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran

Department of Energy Technology, Aalborg University, Pontoppidanstraede 111, Aalborg DK-9220, Aalborg, Denmark

Abstract Harvesting energy from sustainable and accessible resources such as solar energy is one of the most interesting research areas in the last decades. This study proposes a novel application of thermoelectric generator (TEG) energy harvester in a dish-Stirling system to protect the system from thermal overloading and also to improve the overall energy conversion performance. Using the TEG as an energy harvester in the cavity makes it possible to have a larger solar concentration over the system. In the middle of the day, temperature of the cavity increases due to increasing of the intensity of the solar radiation. The cavity temperature controller protects the Stirling engine from increasing its hot-side temperature over the critical temperature defined for the system. Moreover, Control of the cavity temperature by the TEG leads to generate more electrical power by the Stirling engine in the beginning and ending hours of the day. Performance of the system is investigated by a coupled analytical model developed in this study. The results illustrate the proposed dish-Stirling engine generates 14.1 kW at solar noon. Furthermore, the proposed cavity temperature control strategy improves overall performance of the system 20- 30 % at the beginning and ending hours of a day.

Keywords: Solar energy; Stirling engine; Cavity temperature control; Energy harvesting; Performance improvement.



Corresponding authors E-mail address: [email protected] (B.M. Ziapour), [email protected] (A. Rezania)

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Nomenclature area, m2 𝐴 𝑎𝑒𝑙 thermoelectric element cross section, m2 interval between regenerator wires, m 𝑏 c mass specific heat, J kg-1 K-1 𝑐𝑝 constant pressure mass specific heat, J kg-1 K-1 𝑐𝑣 constant volume mass specific heat, J kg-1 K-1 diameter, m 𝐷 diameter of regenerator wire screen, m 𝑑 Grashof number 𝐺𝑟 heat transfer coefficient, W m-2 K-1 ℎ ℎ𝑒𝑙 thermoelectric element height, m 𝐼𝑑 direct solar radiation, Wm-2 𝐼𝑐𝑖𝑟 electrical current of TEG circuit, A intercept factor 𝐼𝑛𝑡 thermal conductivity, W m-1 K-1 𝑘 mass, kg 𝑚 number of N or P element of the TEG 𝑛 𝑁𝑀,𝑇𝐸𝐺 number of TEG modules 𝑁𝑠 number of regenerator screens Nusselt number 𝑁𝑢 𝑛𝑟 engine rotation speed, rpm power, W 𝑃 pressure, pa 𝑝 Prandtl number 𝑃𝑟 heat transfer or heat loss, W 𝑄 gas constant, J kg-1 K-1 𝑅 𝑅𝐿 external load resistance,  Reflectivity 𝑅𝑒𝑓 𝑅𝑚 Electrical resistance of TEG module,  stroke of pistons, m 𝑆 shading factor 𝑆ℎ𝑎 temperature, K 𝑇 speed, ms-1 𝑣 𝑣𝑔 working gas kinematic viscosity, m2s-1 piston speed, ms-1 𝑤 𝑤𝑆,𝐿 sound speed, ms-1 𝑋1 optimistic regenerative loss 𝑋2 pessimistic regenerative loss adjusting coefficient 𝑦

adjusting coefficient 𝑧′ Greek symbol 𝛼𝑐𝑎𝑣 cavity absorbance 𝛼𝑒𝑓𝑓 effective absorbance 𝛼𝑚 Seebeck coefficient of TEG module, VK-1 emissivity 𝜀 𝜀𝑣 volumetric ratio specific heat ratio 𝛾 𝜃𝑐𝑎𝑣 cavity tilt angle,  𝜂𝐶 Carnot efficiency 𝜂𝑔𝑒𝑛 generator efficiency 𝜂𝐼𝐼,𝛥𝑝 pressure loss 𝜂𝐼𝐼,𝑋 incomplete regeneration loss 𝜂𝑆𝑦𝑠 system efficiency 𝜂𝑇𝐸𝐺 TEG conversion efficiency Stefan–Boltzmann constant, W m-2 K-4 𝜎 ratio of gas extreme temperatures 𝜏 Subscript and Superscript initial state of Stirling cycle 1 𝑎𝑚𝑏 Ambient 𝑎𝑝𝑒𝑟 Aperture cold or cold-side 𝑐 cavity 𝑐𝑎𝑣 𝑐𝑜𝑛𝑐 concentrator 𝑐𝑜𝑛𝑣 convection Forced heat transfer 𝑓𝑜𝑟 gas 𝑔 hot or hot-side ℎ input 𝑖𝑛 𝑙𝑜𝑠𝑠 heat loss module for TEG and mean for Stirling 𝑚 engine Natural heat transfer 𝑛𝑎𝑡 regenerator 𝑅 radiation 𝑟𝑎𝑑 𝑆𝑡𝑖𝑟𝑙𝑖𝑛𝑔 Stirling engine 𝑇𝐸𝐺 thermoelectric generator wind 𝑤𝑖𝑛

1. Introduction High-efficient electricity production from renewable energies, such as solar energy, is concern of many researchers. Solar dish-Stirling engine is one of the most efficient systems that can convert the solar energy into electricity [1]. Since the Stirling engines needs high temperature to operate efficiently, this type of engine has been integrated with the solar concentrators, and many researches had focused on solar dish concentrators for solar applications. For example, Malali et al. [2] investigated the optical performance of a DishStirling engine affected by circumsolar radiation. Their results indicated that increasing the circumsolar radiation from 0.02 to 0.2 in a parabolic concentrator with rim angle of 60ᵒ and

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low mirror optical error reduces the optimal concentration ratio and maximum overall efficiency by about 18 % and 13 %, respectively. Under the same conditions, using a parabolic concentrator with high mirror optical errors reduced the optimal concentration ratio and maximum overall efficiency by about 11 % and 10 %, respectively. Ruelas et al. [3] studied performance of solar concentrator with offset parabolic satellite dishes (OPSDs) theoretically. They found that OPSD concentrator has the lowest cost compared to the high-temperature concentrator, parabolic dish solar collectors, Scheffler concentrator and Scheffler–type solar concentrator. Yan et al. [4] proposed a novel discrete dish concentrator for uniform distribution of heat flux on solar cavity. They improved the non-uniformity factor of the absorber surface and optimized the optical efficiency of the parabolic concentrator. Asselineau et al. [5] analyzed exergy impact of optical parameters of a concentrator. They showed that the slope error has the most substantial impact on performance of the concentrator. Therefore, there are many studies showing focus of researchers on field of solar concentrators. In spherical concentrated solar application, solar cavities are typically used as an absorber for reduction of the radiation heat loss. Hence solar cavities have often been studied to improve their absorption by using phase change materials [6] or nanofluids [7]. Masaddak et al. [8] assessed the thermal heat loss in the cavity receiver numerically. They investigated the cavity aspect ratio, operating temperature, surface emissivity and tilt angle, and found center of the absorber has the maximum heat loss and the cavity tilt angle strongly effects on the convection heat loss. Si-Quan et al. [9] numerically investigated thermodynamic and optical performance of a 3D spherical cavity model. Based on their results, spherical cavity receiver has higher optical efficiency than other shapes, where conversion efficiency of the cavity receiver varies from 81.9 % to 84.4 %. Al-Nimr et al. [10] proposed an integration of a cavity collector with TEG. Effects of TEG, solar intensity irradiance, the mass flow rate and wind speed on the system performance were investigated. TEGs are interesting mechanism of energy harvesting compatible with thermal systems. TEGs are used in various energy harvesting applications such as solar pond power plant [11], diesel engines [12], desalination systems [13] and hybrid solar energy conversion systems [14] due to the direct energy conversion from heat into electricity, having no moving parts, a large lifespan, no scale effect, shape conformability and noiseless operations. Kwan et al. [15] investigated application of TEGs to control of fuel cell temperature. In their system, thermoelectric modules harvested energy from the fuel cells whenever the device was temperature self-sustaining. When the system needed heating or cooling, the modules provided a suitable operating temperature for the fuel cell system. Shittu et al. [16] investigated a numerical model of segmented annular TEG. They found that the efficiency of the TEG is 21.7 %, which was 82.9 % greater than that of annular TEG at 200 K temperature difference. Mirhoseini et al. [17] investigated conversion efficiency and matched power output of TEGs as an energy harvester in a cement rotary kiln. Their results showed that the optimum leg length for maximum pick power is longer than the leg corresponding to maximum cost performance at a fix fill factor. Thermoelectric materials with both high figure of merit and high operating temperature are desirable for energy harvesting in concentrated solar energy systems. Design of a high performance TEG system is an interdisciplinary work across physics, chemistry and materials science and engineering. Therefore, interaction between critical parameters in the process and fundamental material properties of the module design needs to be evaluated [18]. Fu et al. [19]

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report a prototype of TEG with a high figure of merit with conversion efficiency of 6.2% and power density of 2.2 [W/cm2] at temperature difference of 665 K. Mahmoudinezhad et al. [20] investigated the transient behavior of the oxide TEGs in a concentrated solar power generation system. Their results show that the efficiency and power generation of the TEG escalate significantly in high solar concentrations. Furthermore, the use of graphite absorber sheet leads to enhance the power generation by increasing absorption of the solar radiation. High-efficient conversion of thermal energy into mechanical shaft work makes the Stirling cycle an interesting area of study to integrate with many applications [21]. Hou et al. [22] proposed a new technology based on a thermoacoustic Stirling engine that can recover liquefied natural gas cold exergy in small-scale applications. The maximum electrical power of 12.4 [kW] was obtained by their proposed system. Qiu et al. [23] developed a free-piston Stirling engine for a micro CHP application. They chose a tubular heat exchanger for hot-side and an extruded fin heat exchanger for the cold-side of Stirling engine. Their results pointed out that the considered system produced 1 kW of electricity, with efficiency of 38.3%, and 1.1 kW thermal energy. Güven et al. [24] applied a Stirling engine as a waste-heat recover from a heavy-duty engine. Their calculations showed that waste heat recovery with Alpha and Gamma-type Stirling engine is less efficient than Beta-type due to lower power density. The system provided more than 1.3% of the engine power and decreased fuel consumption of approximately 1%. The introduced studies indicated that Stirling engines are a suitable waste heat recovery technology in heavy internal combustion engines. Ahmadi et al. investigated Stirling engines to maximize the power generation [25], thermo-economic optimization of solar Stirling engine [26], multiple criteria designing of a solar Stirling heat engine [27], thermodynamic-based optimization of Stirling engine’s output power by implementing an evolutionary algorithm [28] and a new model based on finite-time thermodynamic [29]. Their results show a high potential of using Stirling engine for industrial applications especially for solar applications. For solar energy applications, a multi-objective optimization by Caballero et al. [1] illustrated an overall efficiency of 21% for dish-Stirling system. The dish-Stirling system was optimized for the concentrator, insulation, receiver, appropriate selection of cavity rim and tilt angle. Since Stirling engines usually work at high temperatures, these engines are used with spherical concentrators for solar energy applications. Design of concentrator must provide long operation for the Stirling engine during a day. In other words, increasing of the concentrator diameter results entering more energy into the cavity and, therefore, the Stirling engine starts operating sooner. The solar irradiance is higher around the solar noon; so that the operating temperature can cause damage to the hot-side of the Stirling engine due to overheating. In this study, a novel method is proposed to control the temperature and harvesting the energy in a cavity by utilizing TEGs in the hot-side of Stirling engine. In this hybrid system, for the first time, by controlling the external load resistance and current in the TEGs, the coldside temperature of the TEGs increases at low solar irradiance to provide higher temperature for the hot-side of the Stirling engine. Approaching the solar noon, the TEG cold-side temperature reaches to the upper limit of the Stirling engine by variation of load resistance. At this time, the variation of load resistance of the TEG circuit is adapted to reduce the cold-side temperature of the TEGs and to prevent the Stirling engine from overheating. The proposed method helps to give a clear vision to enhance the power generation of a dish-Stirling system

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without changing the scale of the engine. In this study, an analytical model is developed to investigate the thermal and power generation behaviors of the Stirling engine and TEG also the cavity heat loss during a day. Daily performance of the hybrid system is compared with performance of the original system. 2. Solar dish-Stirling-TEG system description The proposed system consists of a spherical concentrator, a cavity located in the concentrator focal point, TEGs mounted behind the cavity and hot-side tubes of the Stirling engine located behind the TEGs. Working fluid of the Stirling engine sweeps across the coldside of the TEGs through the pipes. A schematic view of the system is shown in Fig. 1 a), and an exploded-view from the proposed cavity temperature controller is shown in Fig. 1 b). Stirling engine Cavity

Concentrator

θ Cavity

a)

Spring clamps

Cold side heat exchanger Regenerator Piston

b) Cavity

Stirling hot side tube TEG modules

Fig.1 a) A Schematic view of the solar dish-Stirling-TEG system b) An exploded-view from proposed cavity temperature controller system Reflected solar radiation from the concentrator enters in the cavity and strikes the hot-side of the TEGs. A fraction of the absorbed energy in the cavity wastes through different heat loss modes such as radiation, natural convection and forced convection. The TEGs generate power from the absorbed heat in the cavity. The Stirling engine absorbs the output heat from the coldside of the TEGs and converts it to the mechanical shaft power. Water removes the rejected heat from Stirling engine at the ambient temperature. The energy flow of the system is shown in Fig. 2. As can be seen, using the cavity temperature control increases the generated power of the system. Since the system has operated in the worse tilt angle at 8:00 AM, the thermal

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loss of the cavity has a significant amount. Besides, the hot-side temperature of the Stirling engine is low at this time. Therefore, the low efficiency of the Stirling engine causes increasing of rejected heat.

Stirling inlet energy 25.4 kW

TEG inlet energy 26.2kW

Cavity inlet energy 45.2 kW

Power of Stirling engine with cavity temperature control 5.5 kW

`

Inlet solar radiation to the concentrator 61.8 kW

Rejected heat by the Stirling 21.3 kW

Power of Stirling engine 4.1 kW Power of TEG Without cavity 0.8 kW temperature control

Concentrator optical losses 16.6 kW

Cavity thermal heat losses 18.9 kW

Fig. 2. The energy flow through the dish-Stirling-TEG system with and without cavity temperature control at 8:00 AM In order to simplify the mathematical model developed in this work, following assumptions are made:      

The temperature of the cold heat reservoir of the Stirling engine is kept at the ambient temperature. The conduction heat loss from the cavity and the Stirling engine for the insulations is negligible. The radiation and convection heat loss inside the TEG module is neglected, and heat flow across the TEGs passes only through the thermoelectric material. Thermoelectric properties change with temperature changes according to [30]. The effect of thermal contact resistance on the cold and hot sides of the TEG modules is neglected. The hot-side of the Stirling engine has an ultimate temperature reported by the manufacturer. The commercial STM 4-120 Stirling engine is chosen in this model. This critical temperature was reported 800 ᵒC for the hot-side tube of STM 4-120 Stirling engine [31].

In the proposed system, the target is to manage the cavity temperature to achieve the optimal system performance by variation of load resistance of TEGs. With the sunrise, the solar radiation is directed to the cavity by the concentrator, which leads to increase temperature of the cavity. At the beginning hours of the day, the temperature does not reach the ultimate temperature of the Stirling engine. Since the conversion efficiency of the Stirling engine is higher than the TEG, it is better to generate more power by contribution of the Stirling engine. Hence, by adapting the external load resistance in the TEG system, the cold-side temperature of the TEGs can reach to the highest possible level. Around the solar noon, the cavity's temperature reaches the ultimate temperature of the Stirling engine. At this moment, the load resistance is changed to reduce the cold-side temperature of the TEGs and, consequently, to

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prevent any damages in the Stirling engine. The cold-side temperature of the TEGs is kept, as high as possible, around the ultimate temperature of the Stirling engine. 3. Mathematical model of solar dish-Stirling-TEG system The governing equations of the system consist of energy balance of each system’s component. The mathematical model was solved by Engineering Equation Solver (EES). The inlet energy into the concentrator aperture can be calculated using the following equation, which is used to calculate the first low efficiency of the system: (1)

𝑄𝑐𝑜𝑛𝑐,𝑖𝑛 = 𝐴𝑐𝑜𝑛𝑐,𝑎𝑝𝑒𝑟 ∙ 𝐼𝑑

where 𝐴𝑐𝑜𝑛𝑐,𝑎𝑝𝑒𝑟 is the concentrator aperture area, and 𝐼𝑑 is direct solar irradiance. An intercept, shading, and reflecting factor were considered for the concentrator as a coefficient with respect to the ideal condition. Based on Reinalter et al., [32] these coefficients are assumed as 0.85, 0.93, and 0.925, respectively. Thus, the incoming solar radiation into the cavity aperture can be calculated as follows: (2)

𝑄𝑐𝑎𝑣,𝑖𝑛 = 𝑄𝑐𝑜𝑛𝑐,𝑖𝑛 ∙ 𝐼𝑛𝑡𝑐𝑜𝑛𝑐 ∙ 𝑆ℎ𝑎𝑐𝑜𝑛𝑐 ∙ 𝑅𝑒𝑓𝑐𝑜𝑛𝑐

The reflected photons from the concentrator trapped into the cavity and are absorbed by the TEG absorber. High solar radiation into the cavity causes a cavity temperature increment. Hence the radiation and convection heat loss affected the absorbed heat on the hot-side of the TEGs. The absorbed heat can be calculated as: (3)

𝑄𝑇𝐸𝐺,𝑖𝑛 = 𝑄𝑐𝑎𝑣,𝑖𝑛 ― 𝑄𝑐𝑎𝑣,𝑙𝑜𝑠𝑠

With calculation of the cavity heat loss, the useful heat into the TEG absorber is determined. The cavity heat loss is the sum of the radiation and convection heat losses through the cavity aperture, as follow: (4)

𝑄𝑐𝑎𝑣,𝑙𝑜𝑠𝑠 = 𝑄𝑐𝑎𝑣,𝑟𝑎𝑑 + 𝑄𝑐𝑎𝑣,𝑐𝑜𝑛𝑣

Since the cavity and the hot-side of the Stirling engine are insulated, the effect of the conduction heat loss is neglected. The emitted and reflected radiation from the cavity aperture constitute the radiation heat loss as [1,33,34]: 𝑄𝑐𝑎𝑣,𝑟𝑎𝑑 = 𝜀𝑐𝑎𝑣 ∙ 𝜎 ∙ 𝐴𝑐𝑎𝑣,𝑎𝑝𝑒𝑟(𝑇4𝑐𝑎𝑣 ― 𝑇4𝑎𝑚𝑏) + (1 ― 𝛼𝑒𝑓𝑓)𝑄𝑇𝐸𝐺,𝑖𝑛

(5)

In the Eq. (5) 𝐴𝑐𝑎𝑣,𝑎𝑝𝑒𝑟, 𝑇𝑐𝑎𝑣, 𝑇𝑎𝑚𝑏, are the area of the cavity aperture, the cavity temperature, and the ambient temperature, respectively. Moreover, 𝜀𝑐𝑎𝑣 and 𝜎 are the cavity emissivity and the Stefan–Boltzmann constant, respectively. 𝛼𝑒𝑓𝑓 is the effective absorption of the cavity given as:

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𝛼𝑐𝑎𝑣

𝛼𝑒𝑓𝑓 =

(

𝛼𝑐𝑎𝑣 + (1 ― 𝛼𝑐𝑎𝑣)

)

𝐴𝑐𝑎𝑣,𝑎𝑝𝑒𝑟 𝐴𝑐𝑎𝑣,𝑖𝑛

(6)

where 𝐴𝑐𝑎𝑣,𝑖𝑛 and 𝛼𝑐𝑎𝑣 are the internal area of the cavity and cavity absorbance, respectively. Furthermore, the cavity convective heat loss, incorporated from the natural and forced convection, can be calculated by the following equation: 𝑄𝑐𝑎𝑣,𝑐𝑜𝑛𝑣 = (ℎ𝑐𝑎𝑣,𝑛𝑎𝑡 + ℎ𝑐𝑎𝑣,𝑓𝑜𝑟)𝐴𝑐𝑎𝑣,𝑖𝑛(𝑇𝑐𝑎𝑣 ― 𝑇𝑎𝑚𝑏)

(7)

Natural and forced heat transfer coefficients of the cavity are determined as [1]: ℎ𝑐𝑜𝑛𝑣,𝑓𝑜𝑟 = [0.1634 + 0.7498𝑠𝑖𝑛(𝜃𝑐𝑎𝑣) ― 0.5026𝑠𝑖𝑛(2𝜃𝑐𝑎𝑣) + 0.3278𝑠𝑖𝑛(3𝜃𝑐𝑎𝑣)]𝑣1.104 𝑤 ℎ𝑐𝑜𝑛𝑣,𝑛𝑎𝑡 =

𝑁𝑢 ∙ 𝑘𝑐𝑎𝑣

(9)

𝐷𝑐𝑎𝑣

where 𝜃𝑐𝑎𝑣, 𝑣𝑤, 𝑘𝑐𝑎𝑣 and 𝐷𝑐𝑎𝑣 are the tilt angle of the cavity, wind speed, thermal conductivity of the cavity, and cavity diameter, respectively. 𝑁𝑢 is Nusselt number in the cylindrical cavity that can be calculated as: 1 3

𝑁𝑢 = 0.088 ∙ 𝐺𝑟

0.18

( ) 𝑇𝑐𝑎𝑣

𝑇𝑎𝑚𝑏

(8)

(

(𝑐𝑜𝑠(𝜃𝑐𝑎𝑣))2.47

)

𝐷𝑐𝑎𝑣,𝑎𝑝𝑒𝑟 𝐷𝑐𝑎𝑣

(

1.12 ― 0.982

)

𝐷𝑐𝑎𝑣,𝑎𝑝𝑒𝑟 𝐷𝑐𝑎𝑣

(10)

In the Eq. (10) 𝐷𝑐𝑎𝑣,𝑎𝑝𝑒𝑟 is the diameter of the cavity aperture, and 𝐺𝑟 is the Grashof number that is the ratio of buoyancy force to the restraining force due to the viscosity of the air. Power generation by the TEGs can be calculated by the energy balance on its hot and cold sides. It is assumed that the entered energy into the cavity equally divided among the TEG modules. Hence [35,36]: 𝑄𝑇𝐸𝐺,𝑖𝑛 = 𝑁𝑀,𝑇𝐸𝐺(𝛼𝑚 ∙ 𝑇ℎ,𝑇𝐸𝐺 ∙ 𝐼𝑐𝑖𝑟 + 𝑘𝑚(𝑇𝑇𝐸𝐺,ℎ ― 𝑇𝑇𝐸𝐺,𝑐) ― 0.5 ∙ 𝑅𝑚 ∙ 𝐼2𝑐𝑖𝑟)

(11)

𝑄𝑇𝐸𝐺,𝑜𝑢𝑡 = 𝑁𝑀,𝑇𝐸𝐺(𝛼𝑚 ∙ 𝑇𝑇𝐸𝐺,𝑐 ∙ 𝐼𝑐𝑖𝑟 + 𝑘𝑚(𝑇𝑇𝐸𝐺,ℎ ― 𝑇𝑇𝐸𝐺,𝑐) + 0.5 ∙ 𝑅𝑚 ∙ 𝐼2𝑐𝑖𝑟)

(12)

𝑃𝑇𝐸𝐺 = 𝑁𝑀,𝑇𝐸𝐺(𝛼𝑚 ∙ 𝐼𝑐𝑖𝑟(𝑇𝑇𝐸𝐺,ℎ ― 𝑇𝑇𝐸𝐺,𝑐) ― 𝑅𝑚 ∙ 𝐼2𝑐𝑖𝑟)

(13)

In the Eqs. (11-13) 𝑁𝑀,𝑇𝐸𝐺 is the number of TEG modules, 𝛼𝑚, 𝑅𝑚 and 𝑘𝑚 are the Seebeck coefficient, electrical resistance and thermal conductivity of the TEG module, respectively. Furthermore, 𝑇𝑇𝐸𝐺,ℎ, 𝑇𝑇𝐸𝐺,𝑐, 𝐼𝑐𝑖𝑟, 𝑄𝑇𝐸𝐺,𝑖𝑛, 𝑄𝑇𝐸𝐺,𝑜𝑢𝑡, and 𝑃𝑇𝐸𝐺 are hot-side temperature, cold-side temperature, electrical circuit current, inlet heat, outlet heat and the generated power by the TEG modules, respectively. Properties of the thermoelectric materials are temperature dependent. Properties variations of Yb14MnSb11 thermoelectric couples as a function of temperature are shown in Fig. 3 as reported by [30]. The conversion efficiency of the TEG is as follows:

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𝜂𝑇𝐸𝐺 =

𝑃𝑇𝐸𝐺

(14)

𝑄𝑇𝐸𝐺,𝑖𝑛

Fig.3 Variation of TEG material properties as a function of temperature The passed heat across the TEG absorbs by the working fluid of the Stirling engine. The generated power by the Stirling engine with considering thermal and pressure drop irreversibilities is given as [37–39]:

( )

𝑃𝑆𝑡𝑖𝑟𝑙𝑖𝑛𝑔 = 𝜂𝐶 ∙ 𝜂𝐼𝐼,𝑋 ∙ 𝜂𝐼𝐼,𝛥𝑝 ∙ 𝑧′ ∙ 𝑚𝑔 ∙ 𝑅 ∙ 𝑇ℎ,𝑔 ∙ 𝑙𝑛𝜀𝑣

𝑤 ∙ 𝜂𝑔𝑒𝑛 2𝑆

(15)

where 𝜂𝐶, 𝜂𝑔𝑒𝑛,𝑚𝑔, 𝑅, 𝑇ℎ,𝑔, 𝜀𝑣, 𝑤, and 𝑆 are Carnot efficiency, generator efficiency, the mass of gas, gas constant, temperature of gas in the hot-side of the Stirling engine, volumetric ratio, piston speed, and stork of pistons, respectively. Moreover, 𝑧′ is adjusting coefficient that is set to 0.45 in this work according to experimental data of several Stirling engines [31,39]. The incomplete regeneration is the most crucial term in the irreversibility of the Stirling engine, which can be calculated as [37,39]: 1

𝜂𝐼𝐼,𝑋 = 1+

(𝑋1 ∙ 𝑦 + 𝑋2 ∙ (1 ― 𝑦)) ∙ 𝑐𝑣,𝑔 𝑅 ∙ 𝑙𝑛𝜀𝑣

(

1―

𝑇𝑐,𝑔

)

(16)

𝑇ℎ,𝑔

where 𝑋1 and 𝑋2 are the optimistic and pessimistic regenerative loss that can be adjusted with 𝑦. The best fit, by comparing the analytical and experimental results, occurs when 𝑦 is set to 0.27 according to [37,39]. Furthermore, 𝑐𝑣,𝑔 and 𝑇𝑐,𝑔 are constant volume specific heat of working gas and temperature of the gas in the cold-side of the Stirling engine. 𝑋1 and 𝑋2 in Eq. (16) are given as [37,39]:

9

1+2∙

―

𝑚𝑔 ∙ 𝑐𝑣,𝑔

𝑋1 =

+𝑒

𝑚𝑅 ∙ 𝑐𝑅

(

2 1+

𝑚𝑔 ∙ 𝑐𝑣,𝑔 𝑋2 =

𝑚𝑅 ∙ 𝑐𝑅

―

+𝑒

((

1+

((

1+

)

)

𝑚𝑔 ∙ 𝑐𝑣,𝑔 ℎ ∙ 𝐴𝑅

𝑆 ∙ 𝑚𝑅 ∙ 𝑐𝑅 𝑚𝑔 ∙ 𝑐𝑣,𝑔 𝑤

(17)

)

𝑚𝑔 ∙ 𝑐𝑣,𝑔 𝑚𝑅 ∙ 𝑐𝑅

)

𝑚𝑔 ∙ 𝑐𝑣,𝑔 ℎ ∙ 𝐴𝑅

)

𝑆 ∙ 𝑚𝑅 ∙ 𝑐𝑅 𝑚𝑔 ∙ 𝑐𝑣,𝑔 𝑤

(18) 1+

𝑚𝑔 ∙ 𝑐𝑣,𝑔 𝑚 𝑅 ∙ 𝑐𝑅

where 𝑚𝑅, 𝑐𝑅, and 𝐴𝑅 are regenerator screens mass, mass specific heat of regenerator material, and regenerator wires surface area, respectively. In addition, ℎ is the heat transfer coefficient that is defined as: 0.395(4𝑝𝑚 𝑅𝑇𝑐,𝑔) ∙ 𝑤0.424 ∙ 𝑐𝑝,𝑔(𝑇𝑚) ∙ 𝑣𝑔(𝑇𝑚)0.576 ℎ=

[

(1 + 𝜏) 1 ―

𝜋

]]

4[(𝑏 𝑑) + 1

(19)

23

𝐷0.576 ∙ 𝑃𝑟 𝑅

where 𝑝𝑚, 𝑐𝑝,𝑔, 𝑇𝑚, 𝑣𝑔, 𝑏, 𝑑, 𝐷𝑅, and 𝑃𝑟 are mean pressure of the Stirling engine, constant pressure mass specific heat of working gas, mean temperature of regenerator, kinematic viscosity of working gas, interval between regenerator wires, diameter of regenerator wire screen, diameter of regenerator, and Prandtl number, respectively, and 𝜏 is 𝑇ℎ,𝑔 𝑇𝑐,𝑔. The pressure drop irreversibility of the Stirling engine can be calculated as [37,39]: 𝑤 2 𝑤 12 ∙ 𝛾(1 + 𝜏 ) ∙ 𝑙𝑛𝜀𝑣 + 5 𝑁𝑆 𝑤𝑆,𝐿 𝑤𝑆,𝐿

( )

𝜂𝐼𝐼,𝛥𝑝 = 1 ―

𝜏 ∙ 𝜂𝐶 ∙ 𝜂𝐼𝐼,𝑋 ∙ 𝑙𝑛𝜀𝑣

―

3(0.94 + 0.045𝑤)105 4𝑝1

(20)

𝜏 ∙ 𝜂𝐶 ∙ 𝜂𝐼𝐼,𝑋 ∙ 𝑙𝑛𝜀𝑣

where 𝑤𝑆,𝐿, 𝛾, 𝑁𝑆, and 𝑝1 are the speed of the sound at heat sink temperature, specific heat ratio, number of regenerator screens, and working gas pressure at compression process. The system efficiency is determined by the ratio of generated power over the inlet solar radiation into the concentrator as follows: 𝜂𝑠𝑦𝑠 =

𝑃𝑆𝑡𝑖𝑟𝑙𝑖𝑛𝑔 + 𝑃𝑇𝐸𝐺

(21)

𝑄𝑐𝑜𝑛𝑐,𝑖𝑛

4. Validation of the mathematical model Since such a hybrid system, as proposed in this paper has not been studied yet, validation of the system has been carried out for the dish-Stirling system and the TEG individually. Table 1 presents a comparison of the results in the current study and a report by Reinalter et al. [32] on a dish-Stirling engine. As shown, there is a difference in cavity temperature between the

10

published literature and the results current study at 68 ᵒC. Increasing the cavity temperature leads to increasing the power generation in the Stirling engine and heat loss in the cavity. Thus, the power generation by the Stirling engine is compensated by increasing the cavity heat loss. Consequently, there is a good agreement between the results of the current study and previous published literature with the maximum deviation less than 20 % under similar conditions as reported by [32]. The used TEG oxide module for validation of current results is shown in Fig 4.a. CMO25-42s is a high-temperature module with 100 thermoelectric elements and size of 42 mm ×42 mm [40]. The TEG module is tested under heat reservoirs temperatures of 800 and 20 ᵒC. The operating conditions of the tested module are shown in Table 2. As indicated in Fig 4.b, there is a good agreement between the I-V and P-V curve of the current analytical study and the experimental data under the same boundary conditions. Table 1. Comparison of the system components results in the current study and reported data by in the literature

Dish-Stirling engine

Parameter Direct normal solar irradiance Power from dish Power into the cavity Cavity heat losses Power into the Stirling Engine Stirling shaft power Thermal power out Cavity temperature

Unit

Current study

(W/m2) (kW) (kW) (kW) (kW) (kW) (kW) (K)

906 44.2 37.59 7.23 30.36 13.45 16.91 1191

Eurodish [32] Value Error % 906 44.4 37.75 6.12 31.63 12.25 18.53 1123

0.0 0.4 0.4 18.1 4.0 9.8 8.7 6.0

Table 2. Parameter characterization of a CMO-25-42S TEG module at heater temperature of 800ᵒ C Theater [C]

Vopen circuit [V]

Ishort circuit [A]

Thot-side [°C]

Tcold-side [°C]

800

3.0255

2.1761

626

186

11

Fig 4. a) The used oxide TEG (CMO-25-42s) for validation of analytical code b) Comparison between analytical and experimental results of oxide TEG module 5. Results and discussion As the place where the research of this paper is carried out, location of Aalborg University, Denmark (57° 04' N and 9° 94' E) is considered as the sample location in this study. The concentrator has 2-axis tracking system and the weather condition is assumed sunny with clear sky in June. Fig. 5 shows monthly average of daily solar irradiance and ambient temperature in the selected city [41]. These values are used for daily thermal analysis of the system. The reference values used in the simulation are shown in Table 3.

12

Fig 5. Monthly average of daily solar irradiance and ambient temperature Table 3. The system reference values Components Solar dish

Stirling engine

Symbol

𝐷𝑐𝑜𝑛𝑐 𝐼𝑛𝑡𝑐𝑜𝑛𝑐 𝑆ℎ𝑎𝑐𝑜𝑛𝑐 𝑅𝑒𝑓𝑐𝑜𝑛𝑐 𝑛𝑟 -

TEG

𝜂𝑔𝑒𝑛 𝑛 𝑁𝑀,𝑇𝐸𝐺 𝑎𝑒𝑙 ℎ𝑒𝑙 -

𝑅𝐿 Other parameters

-

𝑣𝑤

Description

Value

Concentrator diameter

8.9 [m]

Intercept factor Shading factor Concentrator reflectance

0.85 0.93 0.925

Engine rotation speed Working fluid Engine type Generator efficiency Number of TEG couples Number of TEG Modules Element cross section Element height Material External Load resistance Solar Time Wind speed

1800 [rpm] H2 STM 4-120 0.925 50 100 3.5×3.5 [mm2] 1.2 [mm] Yb14MnSb11

𝑛 × 𝑅𝑚 12:00 1 [m/s]

Fig. 6 illustrates variations of the cold-side and hot-side temperature of the TEG and the temperature difference across the modules for different circuit currents. Analytical results show that the cold-side temperature correspondingly increases with the TEG circuit current. The lowest possible temperature of the cold-side TEG can be achieved when it is in the open circuit condition. Whereas in the short circuit condition, the cold-side has the highest possible temperature as shown by [42]. Decreasing the TEG current leads to increasing the temperature difference. Variation of the load resistance and, therefore, the current not only affect the power generation, it also change the temperature balance at the cold and hot-side of the TEGs.

Fig. 6 TEG temperature variations via circuit current

13

Fig. 7 shows power generation variations of the hybrid system versus the circuit current. This figure demonstrates effect of the external load variation of the TEG circuit on power generation of the system at solar noon. At an optimal current, the power generation by the TEG is maximum. However, further increment in the circuit current leads to increasing the cold-side temperature of the TEG. It, therefore, enhances the power generation of the Stirling engine. As can be seen, the effect of the external load variation on the power generation is due to the variation of thermal balance in the cavity.

Fig. 7 Power generation variations of the system components The power of the system reaches its maximum value by 14.1 kW at the current equal to 10.4 A, which is the current between the corresponding current for maximum power generation by the Stirling engine and the TEGs. Daily variation of the power generation by the TEG versus the circuit current is demonstrated in Fig. 8 without temperature controlling scenario. The maximum power generation is 1.48 kW at the solar noon. It can be seen that the high temperature of the cavity, which occurs at the solar noon, affects the maximum power point of the TEG power generation. Since the Seebeck coefficient of the considered TEG material in this study decreases after a specific temperature (~1300 K), increasing of the power generation is stopped at the solar noon.

14

Fig. 8 Daily power generation of the TEG with variation of the circuit current

For investigation of cavity temperature controlling system by TEGs, the system is investigated in both with and without load changing scenario. In without load changing (WIO L CH) scenario, the external load resistance is kept constant equivalent to the internal resistance of TEG modules during the day. In with load changing (W L CH) scenario, the external load changes during the day. At beginning and ending hours of the day, the TEG operates under short circuit to enable the temperature difference of the TEG reaching its minimum value, as shown in Fig. 6. This change increases the hot-side temperature of the Stirling engine and improves the power generation of the system. Over the time, increment in the solar irradiance boosts the temperature of the cavity. The temperature increment continues until the hot-side of Stirling engine reaches its ultimate temperature. At this time, the load resistance applied on the TEG circuit to decrease the electrical current. Consequently, decreasing of the TEG current leads increasing of the TEG temperature difference, while the hot-side temperature of Stirling engine is kept in the highest allowable temperature. During the ending hours of the day and decreasing of the cavity temperature, reduction of the load resistance causes higher hot-side temperature of the Stirling engine and enhances its performance. Fig. 9 shows the power generation of the system components with and without the cavity temperature controlling strategy by the TEGs. As shown, the power generation of the system enhances at the beginning and ending hours of the day by controlling of the cavity temperature. The TEG circuit switches to the short circuit mode and thermal balance in the thermoelectric materials increases the hot-side temperature of the Stirling engine. Since the power generated by the TEG in this mode is zero, power generation of the system is only from the Stirling engine power. During the middle of the day, the cavity temperature controller keeps the cold-side temperature of the TEGs at 800 ℃, by applying load resistance on the TEG circuit. It causes that the power generation by the TEG increases while the power generation by the system reduces due to reduction of the power generation of the Stirling engine. By calculating underthe-curve area of the generated power of the system, the results show that the daily power

15

generation of the system enhances by 73 kJ (1.25%) with cavity temperature control strategy. Furthermore, the hot-side temperature of the Stirling engine is limited at 800 ℃. The Percentage of the changes in the power generation of the system with cavity temperature controller in comparison with the system without cavity temperature control during a day is shown in Fig 10. It is seen that, during the beginning and ending hours of the day, the Stirling engine performance is enhanced that results in the enhancement of the system performance. Furthermore, since the power generation by the TEG is zero in the short circuit mode, percentage of the power variation of the TEG power is negative.

Fig. 9 Power generation of the system with and without the temperature of the cavity controlling strategy At the solar noon, the performance of the TEG increases, but due to decreasing the performance of the Stirling engine and its impact on the system power, the overall system power generation is negative in comparison with the system without the control strategy. As can be seen, the TEG power generation reaches its maximum two times during the day and it is decreases at the solar noon. This phenomenon occurs to keep the hot-side temperature of the Stirling engine under the critical defined temperature for the system.

16

Fig. 10 System power change with cavity temperature controller during a day Since the cavity temperature control is done by changing the TEGs load resistance, deviation from the optimum load resistance leads to reduction of the TEGs power generation. It is known that the highest power generation by the TEGs is achieved by the load resistance equal to the internal electrical resistance of the TEGs. The optimum circuit current for maximum power generation in the TEGs is shown in Fig 7. Fig. 11 shows the cold-side and hot-side temperatures and the TEG temperature difference with and without the cavity temperature controlling strategy. During the beginning and ending hours of the day, the TEG cold-side temperature with cavity temperature controlling has a higher level compare to the case without controlling of the cavity temperature. The coldside temperature of the TEG during the mid-hours of the day is fixed in 800 ℃.

Fig. 11 TEG temperature and the temperature difference variation with and without cavity temperature controlling during the day Furthermore, the temperature difference across the TEGs during the beginning and ending hours of the day has a lower level when the cavity temperature is controlled. This is while during the mid-hours of the day, when the cavity temperature increases, the load resistance is applied on the TEG circuit. Therefore, the TEG temperature difference across the TEG rises suddenly. It can be seen that hot-side of the TEG has a higher temperature when the cavity temperature is controlled. As a result, heat losses in the cavity increases at the beginning and ending hours of the day. Variation of the heat loss during the day is shown in Fig 12. At the mid-hours of the day, the convective heat loss in the cavity decreases due to its tilt angle. The cavity tilt angle is approximately 60° at these hours for the considered geographical location in this study. As can be seen, at the beginning and ending hours of the day the cavity heat loss is increased due to its higher temperature. This condition for the system with cavity temperature control is similar

17

to the traditional model because there is approximately the same temperature of cavity in both situations at the mid-hours of the day.

Fig. 12 The cavity heat loss and tilt angle variation during a day

6. Conclusions In this study, the use of TEG in a cavity of a dish-Stirling engine is theoretically investigated as a temperature controller of the system. Using the TEG as an energy harvester in the system makes it possible to use a larger concentrator in the system to utilize more solar radiation and to prevent the Stirling engine from thermal overloading. In the proposed system, the cavity temperature is controlled by variation of the external electrical load resistance on the TEGs. The temperature control system can harvest approximately 1.2 kW at mid-hours of the day. The results show that, the power generation by the Stirling engine during the beginning and ending hours of the day was enhanced by 20- 30%. Moreover, the hot-side of the Stirling engine was protected from thermal overloading caused by high solar irradiance at the solar noon. Due to better energy management of the cavity by this novel energy harvester technique, the hybrid dish-Stirling-TEG system generated 1.25 % more electrical energy during the day. Consequently, the dish-Stirling system with concentrator diameter around 9 m generates 14.1 kW at mid-hours of a day in June. The performance improvement of the system by the TEGs in the cavity improves the performance of the system at low irradiance hours (beginning and ending hours of a day). While June is one of the high irradiance months during a year, it is possible that the system performance improves further in cold season of a year by this novel energy harvesting method.

References [1]

G.E. Carrillo Caballero, L.S. Mendoza, A.M. Martinez, E.E. Silva, V.R. Melian, O.J. Venturini, O.A. del Olmo, Optimization of a Dish Stirling system working with DIRtype receiver using multi-objective techniques, Appl. Energy. 204 (2017) 271–286.

18

doi:10.1016/J.APENERGY.2017.07.053. [2]

P.D. Malali, S.K. Chaturvedi, R. Agarwala, Effects of circumsolar radiation on the optimal performance of a Stirling heat engine coupled with a parabolic dish solar collector, Appl. Therm. Eng. 159 (2019) 113961. doi:10.1016/J.APPLTHERMALENG.2019.113961.

[3]

J. Ruelas, D. Sauceda, J. Vargas, R. García, Thermal and concentration performance for a wide range of available offset dish solar concentrators, Appl. Therm. Eng. 144 (2018) 13–20. doi:10.1016/J.APPLTHERMALENG.2018.08.028.

[4]

J. Yan, Y. Peng, Z. Cheng, Optimization of a discrete dish concentrator for uniform flux distribution on the cavity receiver of solar concentrator system, Renew. Energy. 129 (2018) 431–445. doi:10.1016/J.RENENE.2018.06.025.

[5]

C.-A. Asselineau, J. Coventry, J. Pye, Exergy analysis of the focal-plane flux distribution of solar-thermal concentrators, Appl. Energy. 222 (2018) 1023–1032. doi:10.1016/J.APENERGY.2018.04.027.

[6]

M.A. Bashir, A. Giovannelli, Design optimization of the phase change material integrated solar receiver: A numerical parametric study, Appl. Therm. Eng. 160 (2019) 114008. doi:10.1016/J.APPLTHERMALENG.2019.114008.

[7]

R. Loni, E.A. Asli-Ardeh, B. Ghobadian, A. Kasaeian, Experimental study of carbon nano tube/oil nanofluid in dish concentrator using a cylindrical cavity receiver: Outdoor tests, Energy Convers. Manag. 165 (2018) 593–601. doi:10.1016/J.ENCONMAN.2018.03.079.

[8]

A. Msaddak, E. Sediki, M. Ben Salah, Assessment of thermal heat loss from solar cavity receiver with Lattice Boltzmann method, Sol. Energy. 173 (2018) 1115–1125. doi:10.1016/J.SOLENER.2018.08.059.

[9]

Z. Si-Quan, L. Xin-Feng, D. Liu, M. Qing-Song, A numerical study on optical and thermodynamic characteristics of a spherical cavity receiver, Appl. Therm. Eng. 149 (2019) 11–21. doi:10.1016/J.APPLTHERMALENG.2018.10.030.

[10]

M.A. Al-Nimr, I.A. Al-Darawsheh, L.A. AL-Khalayleh, A novel hybrid cavity solar thermal collector, Renew. Energy. 115 (2018) 299–307. doi:10.1016/J.RENENE.2017.08.048.

[11]

B.M. Ziapour, M. Saadat, V. Palideh, S. Afzal, Power generation enhancement in a salinity-gradient solar pond power plant using thermoelectric generator, Energy Convers. Manag. 136 (2017) 283–293. doi:10.1016/J.ENCONMAN.2017.01.031.

[12]

E.S. Mohamed, Development and performance analysis of a TEG system using exhaust recovery for a light diesel vehicle with assessment of fuel economy and emissions, Appl. Therm. Eng. 147 (2019) 661–674. doi:10.1016/J.APPLTHERMALENG.2018.10.100.

[13]

M.J. Aberuee, E. Baniasadi, M. Ziaei-Rad, Performance analysis of an integrated solar based thermo-electric and desalination system, Appl. Therm. Eng. 110 (2017) 399–411. doi:10.1016/J.APPLTHERMALENG.2016.08.199.

[14]

S. Mahmoudinezhad, A. Rezania, D.T. Cotfas, P.A. Cotfas, L.A. Rosendahl, Experimental and numerical investigation of hybrid concentrated photovoltaic – Thermoelectric module under low solar concentration, Energy. 159 (2018) 1123–1131. doi:10.1016/J.ENERGY.2018.06.181.

19

[15]

T.H. Kwan, X. Wu, Q. Yao, Bidirectional operation of the thermoelectric device for active temperature control of fuel cells, Appl. Energy. 222 (2018) 410–422. doi:10.1016/J.APENERGY.2018.04.016.

[16]

S. Shittu, G. Li, X. Zhao, X. Ma, Y.G. Akhlaghi, E. Ayodele, High performance and thermal stress analysis of a segmented annular thermoelectric generator, Energy Convers. Manag. 184 (2019) 180–193. doi:10.1016/J.ENCONMAN.2019.01.064.

[17]

M. Mirhosseini, A. Rezania, L. Rosendahl, Harvesting waste heat from cement kiln shell by thermoelectric system, Energy. 168 (2019) 358–369. doi:10.1016/J.ENERGY.2018.11.109.

[18]

M. Karami Rad, A. Rezania, M. Omid, A. Rajabipour, L. Rosendahl, Study on material properties effect for maximization of thermoelectric power generation, Renew. Energy. 138 (2019) 236–242. doi:10.1016/J.RENENE.2019.01.104.

[19]

C. Fu, S. Bai, Y. Liu, Y. Tang, L. Chen, X. Zhao, T. Zhu, Realizing high figure of merit in heavy-band p-type half-Heusler thermoelectric materials, Nat. Commun. 6 (2015) 8144. doi:10.1038/ncomms9144.

[20]

S. Mahmoudinezhad, A. Rezania, P.A. Cotfas, D.T. Cotfas, L.A. Rosendahl, Transient behavior of concentrated solar oxide thermoelectric generator, Energy. 168 (2019) 823– 832. doi:10.1016/J.ENERGY.2018.12.001.

[21]

M.H. Ahmadi, M.-A. Ahmadi, F. Pourfayaz, Thermal models for analysis of performance of Stirling engine: A review, Renew. Sustain. Energy Rev. 68 (2017) 168– 184. doi:10.1016/J.RSER.2016.09.033.

[22]

M. Hou, Z. Wu, G. Yu, J. Hu, E. Luo, A thermoacoustic Stirling electrical generator for cold exergy recovery of liquefied nature gas, Appl. Energy. 226 (2018) 389–396. doi:10.1016/J.APENERGY.2018.05.120.

[23]

S. Qiu, Y. Gao, G. Rinker, K. Yanaga, Development of an advanced free-piston Stirling engine for micro combined heating and power application, Appl. Energy. 235 (2019) 987–1000. doi:10.1016/J.APENERGY.2018.11.036.

[24]

M. Güven, H. Bedir, G. Anlaş, Optimization and application of Stirling engine for waste heat recovery from a heavy-duty truck engine, Energy Convers. Manag. 180 (2019) 411– 424. doi:10.1016/J.ENCONMAN.2018.10.096.

[25]

M.H. Ahmadi, H. Hosseinzade, H. Sayyaadi, A.H. Mohammadi, F. Kimiaghalam, Application of the multi-objective optimization method for designing a powered Stirling heat engine: Design with maximized power, thermal efficiency and minimized pressure loss, Renew. Energy. 60 (2013) 313–322. doi:10.1016/J.RENENE.2013.05.005.

[26]

M.H. Ahmadi, H. Sayyaadi, A.H. Mohammadi, M.A. Barranco-Jimenez, Thermoeconomic multi-objective optimization of solar dish-Stirling engine by implementing evolutionary algorithm, Energy Convers. Manag. 73 (2013) 370–380. doi:10.1016/J.ENCONMAN.2013.05.031.

[27]

M.H. Ahmadi, H. Sayyaadi, S. Dehghani, H. Hosseinzade, Designing a solar powered Stirling heat engine based on multiple criteria: Maximized thermal efficiency and power, Energy Convers. Manag. 75 (2013) 282–291. doi:10.1016/J.ENCONMAN.2013.06.025.

[28]

M.H. Ahmadi, A.H. Mohammadi, S. Dehghani, M.A. Barranco-Jiménez, Multi-

20

objective thermodynamic-based optimization of output power of Solar Dish-Stirling engine by implementing an evolutionary algorithm, Energy Convers. Manag. 75 (2013) 438–445. doi:10.1016/J.ENCONMAN.2013.06.030. [29]

M.H. Ahmadi, M.A. Ahmadi, A. Mellit, F. Pourfayaz, M. Feidt, Thermodynamic analysis and multi objective optimization of performance of solar dish Stirling engine by the centrality of entransy and entropy generation, Int. J. Electr. Power Energy Syst. 78 (2016) 88–95. doi:10.1016/J.IJEPES.2015.11.042.

[30]

J.-A. Paik, E. Brandon, T. Caillat, R. Ewell, J.-P. Fleurial, Life testing of Yb14MnSb11 for high performance thermoelectric couples, (2011). https://trs.jpl.nasa.gov/handle/2014/41871 (accessed September 6, 2019).

[31]

W.B. Stine, R.B. Diver, A compendium of solar dish/Stirling technology, Albuquerque, NM, and Livermore, CA (United States), 1994. doi:10.2172/10130410.

[32]

W. Reinalter, S. Ulmer, P. Heller, T. Rauch, J.-M. Gineste, A. Ferriere, F. Nepveu, Detailed Performance Analysis of a 10 kW Dish∕Stirling System, J. Sol. Energy Eng. 130 (2008) 011013. doi:10.1115/1.2807191.

[33]

L.S. Mendoza Castellanos, G.E. Carrillo Caballero, V.R. Melian Cobas, E.E. Silva Lora, A.M. Martinez Reyes, Mathematical modeling of the geometrical sizing and thermal performance of a Dish/Stirling system for power generation, Renew. Energy. 107 (2017) 23–35. doi:10.1016/J.RENENE.2017.01.020.

[34]

R.Y. Ma, R.Y., Wind effects on convective heat loss from a cavity receiver for a parabolic concentrating solar collector, Albuquerque, NM, and Livermore, CA (United States), 1993. doi:10.2172/10192244.

[35]

J. Gao, Q. Du, M. Chen, B. Li, D. Zhang, Assessing the accuracy of mathematical models used in thermoelectric simulation: Thermal influence of insulated air zone and radiation heat, Appl. Therm. Eng. 82 (2015) 162–169. doi:10.1016/J.APPLTHERMALENG.2015.02.072.

[36]

G. Li, G. Zhang, W. He, J. Ji, S. Lv, X. Chen, H. Chen, Performance analysis on a solar concentrating thermoelectric generator using the micro-channel heat pipe array, Energy Convers. Manag. 112 (2016) 191–198. doi:10.1016/J.ENCONMAN.2016.01.025.

[37]

M. Costea, S. Petrescu, C. Harman, The effect of irreversibilities on solar Stirling engine cycle performance, Energy Convers. Manag. 40 (1999) 1723–1731. doi:10.1016/S01968904(99)00065-5.

[38]

L. Jehring, Bejan, A., Advanced Engineering Thermodynamics. New York etc., John Wiley & Sons 1988. XXIII, 758 pp. ISBN 0-471-83043-7, ZAMM - J. Appl. Math. Mech. / Zeitschrift Für Angew. Math. Und Mech. 72 (1992) 320–320. doi:10.1002/zamm.19920720803.

[39]

S. Petrescu, C. Petre, M. Costea, O. Malancioiu, N. Boriaru, A. Dobrovicescu, M. Feidt, C. Harman, A methodology of computation, design and optimization of solar Stirling power plant using hydrogen/oxygen fuel cells, Energy. 35 (2010) 729–739. doi:10.1016/J.ENERGY.2009.10.036.

[40]

CMO-25-42S - Thermoelectric Generator, (n.d.). generator.com/product/cmo-25-42s/ (accessed July 19, 2019).

[41]

PV

potential

estimation

21

https://thermoelectric-

utility,

(n.d.).

https://re.jrc.ec.europa.eu/pvgis/apps4/pvest.php?lang=en&map=europe (accessed July 19, 2019). [42]

M.C. Torrecilla, A. Montecucco, J. Siviter, A. Strain, A.R. Knox, Transient response of a thermoelectric generator to load steps under constant heat flux, Appl. Energy. 212 (2018) 293–303. doi:10.1016/J.APENERGY.2017.12.010.

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Highlights

 A novel energy harvester is evaluated in the solar dish-Stirling system.  The thermoelectric generator is used as a temperature controller in the cavity.  The TEG temperature controller protects the Stirling engine from overheating.

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