Experimental and numerical performance analyses of Dish-Stirling cavity receivers: Radiative property study and design

Accepted Manuscript Experimental and numerical performance analyses of Dish-Stirling cavity receivers: Radiative property study and design Jorge Garrido, Lukas Aichmayer, Abdallah Abou-Taouk, Björn Laumert PII:

S0360-5442(18)32399-5

DOI:

https://doi.org/10.1016/j.energy.2018.12.033

Reference:

EGY 14286

To appear in:

Energy

Received Date: 26 October 2018 Revised Date:

5 December 2018

Accepted Date: 6 December 2018

Please cite this article as: Garrido J, Aichmayer L, Abou-Taouk A, Laumert Bjö, Experimental and numerical performance analyses of Dish-Stirling cavity receivers: Radiative property study and design, Energy (2019), doi: https://doi.org/10.1016/j.energy.2018.12.033. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Experimental and numerical performance analyses of Dish-Stirling cavity receivers: radiative property study and design

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Authors: Jorge Garridoa, Lukas Aichmayera, Abdallah Abou-Taouk b, Björn Laumerta

Department of Energy Technology, Royal Institute of Technology, SE-100 44 Stockholm

b

Azelio, Regnbågsgatan 6, 417 55 Gothenburg, Sweden

Contact Details:

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Jorge Garrido: [email protected]

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a

Lukas Aichmayer: [email protected]

Abdallah Abou-Taouk: [email protected]

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Björn Laumert: [email protected]

Corresponding Author: Jorge Garrido, +46 (0) 8 790 7467

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design

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Key words: Solar simulator; Experimental measurements; Coatings; System modelling; Receiver

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Abstract The solar receiver performance has a direct impact on the CSP power plant performance and, thereby, its levelized cost of electricity. Improved receiver designs supported by new advanced

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numerical tools and experimental validation campaigns directly help to make CSP technology more competitive. This paper presents an experimental and numerical investigation of the

influence of the cavity receiver radiative properties and the thermal power input on the Dish-

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Stirling performance. Three cavity coatings are experimentally investigated: the original cavity material (Fiberfrax 140), Pyromark 2500 and Pyro-paint 634-ZO. Moreover, simulations

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validated with the experimental measurements are utilized to define a higher performance cavity receiver for the Eurodish system. The results indicate that the absorptivity of the cavity should be as low as possible to increase the receiver efficiency whereas the optimum emissivity depends on the operating temperatures. If the cavity temperature is lower than the absorber temperature, low

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emissivities are recommended and vice-versa. All material/coatings analyzed for the cavity provide similar receiver efficiencies, being Fiberfrax 140 slightly more efficient. Finally, a total receiver efficiency of 91.5 % is reached by the proposed Eurodish cavity receiver when

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operating under the most favorable external conditions.

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1 Introduction The growing environmental concern, new policies and the price reduction of renewable energies have initiated a major transition from fossil fuel-based technologies to renewables [1]. Among the renewable

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technologies, Concentrating Solar Power (CSP) is considered a strong candidate since it can produce dispatchable electricity. In CSP technologies, cavity receivers are widely utilized since they offer high efficiencies at high temperatures. Cavity receivers consist of an open enclosure with an active zone

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collecting the thermal energy (absorber) and a non-active zone to increase the efficiency (cavity). The active zone comprises the working fluid passages whilst the non-active does not. Cavity receivers are

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especially important for parabolic dishes since the concentration ratio is the highest and narrow apertures can be utilized. Among parabolic dish technologies, Dish-Stirling Systems (DSS) have proven high potential [2] but with a need of further development to improve its competitiveness. In these systems, the cavity receiver consists of a Stirling heater (absorber) and an insulating material (cavity). A proper design accounting for the interactions among these two parts, the dish and the engine is crucial to increase the

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system efficiency and lifetime, thus reducing the technology Levelized Cost of Electricity (LCoE). Multiple experiments of cavity receivers for parabolic dishes have been previously conducted. However, many of them just study the thermal efficiency of different cavity receiver concepts, i.e. [3] and [4] for

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pressurized-air receivers and [5] and [6] for non-Stirling tubular receivers. [7], [8] and [9] additionally include measurements of the absorber temperatures. [10] and [11] also show a comparison of different

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cavity receiver configurations and [12] proposes a variable aperture mechanism. For Dish-Stirling systems, most of the literature presents general measurements of the electric generation under different Direct Normal Irradiances (DNIs), such as [13] and [14]. [15] shows further results of the flux distribution and thermal loss breakdown calculation but with limited information of the cavity receiver performance. Finally, [16] presents for the first time temperature measurements inside a Dish-Stirling (DS) cavity receiver and conducts a parametric experimental study of various cavity apertures and shapes. However,

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this work analyzes neither the cavity receiver radiative properties nor different thermal power inputs. Consequently, there is still a lack of experimental data in this regard. In 1982, [17] identified the critical cavity receiver design parameters leading to multiple studies after it.

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Most of the studies performed during the last years focus on the analysis and optimization of the cavity receiver geometry (shape and aperture diameter). Some of them approach it from optical point of view, i.e. [18] and [19], missing a proper thermal analysis. Others, such as [20] and [21], concentrate on

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modelling the thermal analysis missing the study of the system optics. A third group of studies couples more efficiently the thermal and optical models towards the system optimization, for example [22], [23],

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[24] and [25]. However, the studies analyzing the radiative properties of the receiver (i.e [26] and [27]) have been performed with simplified thermal models and further studies are needed to obtain more representative results. Moreover, none of the papers mentioned above analyzes the influence of the radiative properties of a non-active part (cavity).

To fill this gap, the first goal of this paper is to present experimental measurements of various DSS cavity

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receivers varying the cavity radiative properties, the thermal power input and the operating conditions. It provides a broad set of experimental data available to validate thermal simulations using electric powers and temperatures along the cavity and the receiver at multiple operating conditions. The second goal

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consists of analyzing the receiver efficiency sensitivity to changes in the cavity and absorber coatings in order to find the most efficient material. Finally, a higher-efficiency DSS cavity receiver is designed for

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the Eurodish system [15] accounting for: system working temperatures, cavity receiver radiative properties, DNI, cavity receiver aperture and cavity receiver shape (considering design restrictions from the active/non-active zones). The Eurodish system was chosen since it is a high performance dish with extensive data available.

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2 System description This section gathers an overview of the simulations and experiments included in this paper. More detailed explanations are presented in Sections 3 and 4. Figure 1 shows a schematic of the integration of the

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numerical models and the experimental measurements. The system components are drawn in solid black lines (dish/lamps, cavity receiver, Stirling engine and generator), the numerical models in dash-dot blue boxes (ray-tracing and thermal model) and the measurements in green (flux, temperature and electric

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in red (radiation ra, convection cv and conduction cd).

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power). The irradiance from the dish or solar simulator is shown in yellow and the heat transfer processes

Figure 1: Coupling of numerical models and experiments3 Experimental

setup

The experimental campaign was conducted in the solar simulator at the Royal Institute of Technology

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(KTH) powering a first generation Cleanergy C11S Solar Module [28]. It consists of an alpha type

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Stirling engine operating at 1500 rpm coupled with an 11-kWe generator. The C11S Module was positioned to have the peak flux in the center of cavity receiver aperture. The layout during operation is presented in Figure 2, which shows the C11S Module and the solar simulator lamps when the solar laboratory is idle (left) and in operation (right).

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Figure 2: KTH solar simulator: idle (left) and in operation (right)

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To perform the parametric experimental study of the cavity radiative properties, three cavities with the same dimensions and different radiative properties (Figure 3) were tested. The figure shows the cavity assembly (left) and one quarter of each cavity type (right). Fiberfrax 140 is the ceramic material of the cavities (SiO2+Al2O3), and it was coated with Pyromark 2500 and Pyro-paint 634-ZO (ZrO). Both the internal and external parts of the cavity were coated as shown on the left of Figure 3. The cavity has an

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aperture diameter of 170±3 mm, length of 150±1 mm and absorber diameter of 280±3 mm.

Figure 3: Cavity assembly (left) and cavity coatings (right)

All the experiments were conducted maintaining the simulator indoor temperature constant at 20°C. The cavities were tested with six, nine and twelve lamps on in order to vary the total thermal power delivered into the cavity receiver. The flux from the lamps was distributed as even as possible for each combination

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of lamps. However, six lamps did not suffice to reach the targeted absorber temperatures. The total power into the cavity receivers is calculated from the experimental characterization of the solar simulator [29], obtaining a thermal power of 17.2±0.5 kWth within an aperture of 300 mm diameter at the focal plane

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when all lamps are operating. Each cavity was tested in steady-state conditions under three receiver reference operating temperatures (670°C, 710°C and 750°C). The receiver reference temperature is the maximum temperature on the absorber (Tmax,abs). The receiver reference temperature is adjusted by the

receiver reference temperature is too high and vice versa.

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engine control system regulating the pressure of the working fluid (He), increasing the pressure when the

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During the experiments, multiple temperature measurements were taken along the cavity receiver. As depicted in Figure 4, twenty K-type thermocouples (TCs) were installed on the back of the absorber (red dots) and three on the cavity surface (green) every 90° circumferentially. Five extra thermocouples were installed on the external case of the cavity to assess conduction losses. The total generated electric power

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was measured by a power meter Sineaux M603.

Figure 4: Thermocouple positions and reference system

4 Simulation methodology

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This paper utilizes the same models presented in [16], where a more detailed explanation can be found. The two models gathered in Figure 1 (in blue) are coupled to analyze the system performance. A Monte Carlo Ray-Tracing (MCRT) model sets the flux boundary conditions (BCs) and the thermal model

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calculates the heat transfer inside the cavity receiver, the system efficiencies and the final electric output. The absorber tubes are made of Inconel 625® with a Pyromark 2500® coating and the cavity is made of Rigidform Fiberfrax 140®, coated in different experiments with Pyromark and Pyro-paint 634-ZO. The

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material temperature-dependent thermal properties were provided by the manufacturers. After many experiments, degradation on the absorber Pyromark was visible so its spectral radiative properties were

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obtained combining the results from [30] and [31] as if it had suffered a 10-hour aging at 850°C. The spectral radiative properties of the cavity were characterized by the Centre National de la Recherche Scientifique (CRNS) at room temperature and around 400°C (maximum feasible characterization temperature for insulating materials). The characterization results are shown in Figure 5. Since there is no existing procedure to characterize reflectance at high temperatures and low wavelengths, the values were

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extrapolated from the measurements at room temperature (dotted lines). During the characterization campaign, it was observed that the radiative properties strongly depend on the sample temperature during the test, the coating thickness, the curing temperature and the order in which the curing and coating are

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applied. For Figure 5, the coating is first applied with a thickness of 25-50 µm; then, the sample is cured as recommended by the manufacturer; and finally, the sample is heated to the average cavity temperature

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found in the experiments.

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Figure 5: Spectral hemispherical reflectance

The radiation analysis is divided into three parts, having each material a different reflectivity in each of

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them. The first one deals with the external irradiance (laboratory or sun), and the second and third parts solve the other thermal radiations from 0.3-4 µm and 4-1000 µm, respectively. The radiative properties

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are weighted for each part as recommended in [32] (Equation 1),

ρ i ,1 =

∑ λ ρ (λ )G λ (λ )∆λ ∑ λ G λ (λ )∆λ k

1

1

k

k

k

(1)

k

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where λ is the wavelength and ρi,1 is the spectral reflectance of the surface i for the spectral irradiance Gλ in the spectral range λ1. For part one, the reflectance is weighted with either the spectral irradiance from the laboratory or the sun (ASTM G173-03 AM1.5 standard). For parts two and three, the spectral black body radiation at the surface temperature is used. As clarification, absorptivity (α) will refer to (1-ρ1) for part one and emissivity (ɛ) to (1- ρ2-3) for the weighted combination of components two and three. All

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cavity receiver materials showed purely diffuse reflectance and no transmittance. When necessary, the reflectance values were corrected with an incidence angle factor as presented in [30].

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4.1 Ray tracing model The RT model consists of a 3D MC simulation in MATLAB. For the solar simulator, three lamps of the KTH solar simulator are modelled and rotation matrixes are applied. More detailed explanation of the

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model was presented in [33].

To model the dish, two ray deviation sources were considered: sun shape and beam quality of the dish.

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The solar sun shape spread was modelled as a pill-box distribution with 4.65 mrad of maximum deviation whereas the beam quality deviation was modelled with a Probability Density Function (PDF) of the surface normal deviation defined by Equation 2, as measured in [34],

dPe θ −θ 2 / 2σ BQ2 = 2 e dθ σ BQ

(2)

quality.

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4.2 Thermal model

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where dPe/dθ is the probability per unit of angular deviation, θ the angular deviation and σBQ the beam

The thermal model consists of an EES (Engineering Equation Solver) model that calculates the thermal

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power collection of the receiver and the system efficiencies. The model discretizes the absorber in 4 axissymmetrical concentric rings and the cavity in 3 radial subdivisions, 4 angular and 3 axial. Each node fulfils the thermal power balance of Equation 3,

Q& cv ,i + Q& ra ,i + Q& cd ,i + Q& cvWF ,i = 0

(3)

where Q̇ refers to power, cv convection, ra radiation, cd conduction, WF working fluid (only applicable to the absorber) and the sub-index i the node denotation. The radiation sub-index includes the analysis of the external irradiance source, the radiative emissions and the reflections.

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4.2.1 Conduction

cd ,i

∑

cd ,i → j

(4)

(5)

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Q& cd ,i → j

2 ⋅ π ⋅ k (T ) ⋅ L ⋅ (T j − Ti )   ∑ ln( ri r j ) cylinder = A ⋅ k (T ) ⋅ (T j − Ti )  ∑ ij  plane ∆x ij Q& = Q&

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Cylindrical or planar wall conduction is applied depending on the local geometry (Equations 4 and 5),

where k(T) is the temperature-dependent thermal conductivity, r the radius, A the contact area, L the axial

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length of contact, T the temperature, ∆x the distance between node centers and the sub-index j each node adjacent to i. As mentioned before, the temperature measurements from five thermocouples set the external temperature BCs for the conduction analysis.

4.2.2 Radiation

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The radiation heat transfer is solved, as explained in [35], with the equation system 6-8, (6) (7) (8)

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Q& ra,i→ j = Ai ⋅ Fij ⋅ ( J i − J j )  σTi 4 − J i  &  Qra,i = (1 − ε i ) ε i ⋅ Ai  & &  Qra,i + Qirr ,i = ∑ Q& ra,i→ j

where F is the view factor, ɛ the weighted emissivity in the analyzed spectral range, J the radiosity, σ the

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Stefan-Boltzmann constant, and the sub-index irr refers to the integrated direct irradiance on the surface from the dish or solar simulator. The radiative and the reflection losses are calculated with equations 9 and 10,

Q& ra = ∑ Q& ra ,i →amb

(9)

Q& refl = ∑ Q& ra ,i →amb

(10)

λ2 − 3

λ1

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where λ1, λ2 and λ3 are the spectral ranges defined in the beginning of section 4 and amb the ambient. The reflection loss (Q̇ refl) is the solar power into the cavity receiver that is reflected back to the ambient without being absorbed whereas the radiative loss (Q̇ ra) is the power emitted by the cavity receiver walls

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that leaks to the ambient.

4.2.3 Convection

The analysis accounts for two convection sources: convection losses on the surfaces of the cavity receiver

13 are used [16],

hi = hi , ref

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Q& cv ,i = Ai ⋅ hi ⋅ (Ti − Tamb )

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(Q̇ cv,i) and convection to the WF (Q̇ WF,i). To calculate the convection losses on each surface, Equations 11-

b1

 D ap ⋅ D  ref

hav , ref =

    ∑ Ai i

T ⋅  CR T  ref ⋅ hi , ref

   

(11)

0.51

∑A

(12)

(13)

i

i

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where D is the diameter and hi,ref and b1 are constant values determined by two cavity experiments and later validated with the others. The sub-index CR refers to the cavity receiver surfaces, ref a reference value, av the average and ap the aperture. Equation 12 defines the convection coefficient as a constant value times two correction factors dependent on the cavity receiver average temperature and the aperture

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diameter. Equation 13 is proposed to define a reference convection coefficient to calculate the convection losses, thereby simplifying the influence of the wind direction, wind velocity and cavity receiver

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inclination. The total convection losses (Q̇ cv) are defined analogously to equation 5. When Dref and Tref were set to 170 mm and 1070 K, respectively, the validation process obtained b1=0.32 and hav,ref=9 W/m2K for the solar laboratory. The convection to the WF was analyzed similarly with equations 14 and 15 [16], being the PWF the WF pressure. The best fit with the experiments is obtained with b3=0.95 for Pref=150 bar.

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b3

P  hWF = hWF , ref ⋅  WF  P   ref  & QWF ,i = Ai ⋅ hWF ⋅ (Ti − TWF )

(14) (15)

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4.2.4 Efficiency calculation In this section, the efficiency definitions utilized in this paper are presented. Figure 6 depicts a sketch of

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these efficiencies.

Figure 6: Power flows and efficiencies

The total system efficiency (ηt,sys in Equation 16) is the multiplication of the total receiver efficiency

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(ηt,rec), the thermal efficiency of the engine (ηst), the mechanical efficiency (ηme) and the generator efficiency (ηge). The mechanical and generator efficiencies were provided by the system manufacturer.

η t , sys = η t ,recη stη meη ge

(16)

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The total receiver efficiency (ηt,rec) is the product of the interception (ηinter) and receiver (ηrec) efficiencies (Equation 17). The interception efficiency is defined as the ratio between the total power supplied within

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the aperture (Q̇inter) and the total power supplied to the cavity receiver (Q̇irr) whereas the receiver efficiency is the amount of thermal power collected by the working fluid (Q̇WF) divided by Q̇inter.

,      

     

(17)

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The thermal efficiency of the Stirling engine (ηst) was calculated with equation 18 [16], where C is the Stirling cooler and H the Stirling heater (absorber). From the validation, B2=0.47, B3=0.838 and b4=1.1 when Tref is set to 838 K. b4

(18)

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4.2.5 Receiver considerations for the dish

   

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 TH 1 − TC T H  η st = B 2 1 + B3 (1 − TC TH )  Tref

In this paper, the cavity receiver is modelled for both the solar laboratory lamps and the Eurodish. This

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sub-section gathers the considerations utilized while simulating the cavity receiver coupled with the Eurodish dish. The absorber diameter is fixed to 280 mm due to Stirling engine design restrictions whereas the cavity depth is set to 150 mm owing to maximum allowable peak flux constrains. cavity receiver simulations analyzing the external coating for the dish obtained that it has very little influence on the total receiver efficiency (less than 0.1 %) for interception efficiencies close to 99 %. Consequently, no

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external coating is applied. The cavity shape is always reverse-conical as recommended in [16]. The cavity is made of Fiberfrax without coatings and the absorber is coated with Pyromark. The radiative properties are assumed to be as described in the beginning of section 4 for both Pyromark and Fiberfrax.

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The system operates to have a maximum absorber temperature of 770°C (1043K) in order to limit the damage/degradation of the absorber materials (both Inconel 625 and Pyromark 2500). The cavity

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thickness was increased to 130 mm to reduce the conduction losses at higher temperatures. Finally, as the convection influence presents very high variability due to the wind speed, angle of incidence and cavity inclination, the analysis was simplified fixing an average reference convection coefficient (hav,ref in Equation 13). Thus, only the influence of the cavity receiver temperature and aperture size was included, as presented in Equation 12. The typical value assumed for hav,ref is 7 W/m2K, which is congruent with the experiments conducted in the KTH High-Flux Solar Simulator (HFSS) and multiple convection studies, such as [36] and [37].

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5. Validation In order to prove the representativeness of the models, the validation of the models is presented in this

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section. The RT model of KTH HFSS was validated against the experimental flux measurements

presented in [29] and the dish RT against the dish flux measurements taken in [38]. The receiver thermal model was validated against the experimental data (temperatures and electric power) measured for this

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paper.

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5.1 Ray tracing

The solar simulator RT validation is already presented in [33], finding a good agreement with the experimental results.

For the dish, different beam quality errors were analyzed to match the experimental flux data from [38], obtaining an accurate fitting for a total dish beam quality (σBQ) of 4.2 mrad (similar to a slope error of 2.1

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mrad) with a pill-box sun-shape spread of 4.65 mrad. Figure 7 depicts the comparison of the experimental and simulated values. The maximum error is 6 %, the mean error 3 % and the standard deviation 3 %. The

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power delivered by the dish is 42 kWth for a DNI of 850 W/m2.

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Figure 7: Dish ray-tracing validation

5.2 Thermal Model

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In previous work [16], a validation of the same thermal model was presented analyzing the model for different aperture diameters and operating temperatures. In this paper, the thermal model is additionally validated for three different cavity properties with two thermal power inputs at three different operating

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temperatures. The validation is performed against the cavity temperatures and the electric power output. Figure 8 shows the cavity temperatures for the experiments (crosses) and simulations (solid lines) for

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each cavity coating (colors) at a receiver reference operating temperature of 1020K. The x-axis of the figure refers to the thermocouple position at different depths (z) and angles (β) as defined in Figure 4. The error margins of the experiments are only shown for Fiberfrax for the shake of clarity. A good agreement is observed between experiments and simulations. The experimental values of Pyromark are consistently lower than the simulations results since Pyromark (due to its high absorptivity) is more sensitive to uneven irradiances from the KTH HFSS.

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Figure 8: Cavity temperature validation for Tmax,abs=1020 K

Figure 9 and 10 depict the electric power output comparison for three operating conditions defined by the

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maximum temperature of the absorber (Tmax,abs). Figure 9 correspond to the HFSS operating at full power (17.2 kWth within a diameter of 300 mm) whereas, in Figure 10, nine out of twelve lamps were utilized for the measurements. The lamps were selected to keep a flux distribution as homogeneous as possible.

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The figures show that the simulation results lay within the error margins of the experiments (2 % F.S. or ±40 W). It is observed that all coatings provided very similar electric outputs. This happens due to having

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the external surface coated (see Figure 3) in combination with relatively low interception efficiencies (around 85 %). This is further discussed in the result section.

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Figure 9: System electric output validation (17.2 kWth)

Figure 10: System electric output validation (13 kWth)

The thermal model was then validated against multiple parametric experiments studying the receiver operating temperature, thermal power input, cavity shape, aperture and coating.

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6. Results

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This section is divided into two sub-sections: laboratory results and cavity receiver design for the

Eurodish. In the first sub-section, the results of the parametric studies varying the cavity coating, thermal power input and operating temperature are presented. The second sub-section aims at applying the

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validated model to design a higher performance cavity receiver analyzing the cavity shape, aperture

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diameter, radiative properties, thermal power input (DNI) and cavity receiver operating conditions.

6.1 Solar simulator

This section presents the temperature distribution in the cavity receiver (Figure 11) and thermal power breakdown (Figure 12) of the cavities tested in the KTH HFSS. Figure 11 depicts the average cavity temperatures while varying the thermal power input, receiver reference temperature and cavity coating. It

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is observed that the absorber mean temperature is very similar in all the cases since the Stirling engine regulates its working conditions. As the solar laboratory mainly emits between 0.3 and 2 µm, the absorptance below 2 µm is identified as the primary factor increasing the cavity temperature. Finally,

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increasing the thermal power approximately 4 kWth leads to an increase of the average cavity temperature of 20-45°C, depending on the coating. This increase is not only caused by higher direct irradiances on the

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cavity, but also the reflected irradiance from the absorber.

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Figure 11: Cavity receiver temperatures

Figure 12: Thermal power breakdown for each coating with Tmax,abs=1020K and 17.2 kWth

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The thermal power breakdown is obtained from the simulations based on the experimental results. Figure 12 depicts the power breakdown for each coating at a receiver reference temperature of 1020 K and a thermal power of 17.2 kWth. Even if the Pyromark coating has larger thermal losses, the thermal power

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transferred to the engine is very similar due to the extra thermal power collected at the external part of the cavity. This effect only appears when the interception factor is relatively low (85% for the case of study). As mentioned in section 4.2.5, the external coating has very little influence in the real cavity receiver

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design due to the high interception efficiency. Comparing the thermal losses of the cavities, convection and radiation for the same coating have similar contributions; conduction increases quickly with the

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temperature owing to the increasing conductivity of the insulating materials at higher temperatures; and reflection losses highly increase for lower cavity absorptivities. The change of absorptance with the incidence angle was found to be a critical parameter to calculate the cavity receiver temperatures and the reflection losses. Thereby, cavity receiver designs can benefit from this effect improving its performance

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by lowering the absorption of direct irradiance on the cavity walls.

6.2 Receiver operating temperatures

The simulation was applied to find a high efficiency cavity receiver for the Eurodish BC. Instead of

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presenting an optimized solution, this paper provides efficiency maps to show the sensitivity of each variable and to determine the potential efficiency improvement that new materials/analyses could

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introduce. The main results focus on the receiver efficiency as a function of the cavity receiver radiative properties, the DNI and the convection coefficient.

6.2.1 Radiative properties

Figures 13 and 14 show the receiver efficiency dependent on the cavity emissivity and absorptivity for a cavity aperture diameter of 150 mm. The crosses represent the material properties, weighting the emissivity with the black body spectrum at the specified temperature. As explained before, the

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absorptivity is weighted with the solar spectral irradiance distribution from ASTM G173-03 (direct plus circumsolar AM 1.5). Black is related to the absorber temperature whilst red to the cavity average temperature. The main difference between both figures is the DNI and the convection conditions, leading

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to cavity temperatures higher or lower than the absorber temperatures. The green arrows represent

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increasing receiver efficiency.

Figure 13: Simulated receiver efficiency dependent on the cavity radiative properties for DNI 850 W/m2 and hav,ref=7

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W/m2K

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In Figure 13, the receiver efficiencies are quite similar for materials with similar emissivity (ɛ) and absorptivity (α). Thereby, the ratio ɛ/α mainly determines the receiver efficiency, increasing the efficiency the higher the ratio is. Among the coatings tested, Fiberfrax leads to slightly higher receiver efficiency. Using Fiberfrax as reference, the receiver efficiency has a potential improvement of around 0.6% for materials with higher ɛ/α ratio. It is also observed that the emissivity of ZrO and Fiberfrax decrease with the temperature, which has a negative effect on the receiver efficiency.

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Figure 14: Simulated receiver efficiency dependent on the cavity radiative properties for DNI 500 W/m2 and hav,ref=20 W/m2K

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On the other hand, Figure 14 depicts a different behavior for lower thermal power input and higher thermal losses. In this case, the average cavity temperature can be lower than the absorber temperature (region below the green dashed line). When this happens, the net radiative flux goes from the absorber to the cavity and lower emissivities are recommended to hinder the radiative heat transfer.

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Considering Figures 13 and 14, it can be concluded that the optimum material for the cavity depends on

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the relative temperature cavity-absorber, which is a function of the direct irradiance, reflected irradiance and thermal losses. Thus, the optimum cavity material depends on the specific meteorological conditions of the location and the cavity receiver design. However, under typical meteorological conditions and cavity receiver designs, the cavity temperature is expected to be higher than the absorber temperature, so Figure 13 would apply.

Figure 15 depicts the receiver efficiency as a function of the absorber emissivity and absorptivity, evaluating the emissivity at 1050K. The cavity material utilized for this figure is Fiberfrax, the aperture

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diameter 150 mm, the DNI 850 W/m2 and hav,ref 7 W/m2K. Unlike other receiver concepts, higher absorber emissivities increase the receiver efficiency due to the radiation from the cavity walls. The figure also shows a comparison of the receiver efficiency for some typical materials/coatings used in receivers.

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“Pyromark deteriorated” refers to a Pyromark whose absorptance has dropped due to its lamination at high temperatures. It is observed that the use of Pyromark can increase the receiver efficiency around 2.5

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% compared to the analyzed oxides but it would decrease 1.2 % if the Pyromark got deteriorated.

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Figure 15: Simulated receiver efficiency dependent on the absorber radiative properties * These values have been obtained from a material characterization at ambient temperature performed by the Italian

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Energy Agency for new Technologies (ENEA) and may vary depending on, among others, the degree of oxidation and the temperature of the sample during the characterization

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6.2.2 DNI and convection As explained before, this paper aims at studying the influence of some cavity receiver design parameters instead of finding an optimum configuration for a specific case of study. This section analyzes the impact

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of the DNI and convection towards finding a higher efficiency cavity receiver. Figure 16 shows the total cavity receiver efficiency as a function of the DNI and the aperture diameter for an average reference convection coefficient of 7 W/m2K. The black crosses represent the aperture

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diameter that provides the maximum total receiver efficiency for each DNI level. The optimum aperture diameter depends on the DNI but it is quite constant for high DNIs, which are more important because

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they deliver more thermal power. Then, the optimum aperture diameter could be set to 148±2 mm

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depending on the venue, having a low sensitivity of the total receiver efficiency at that aperture range.

Figure 16: Simulated total receiver efficiency as a function of the DNI and the aperture diameter

Figure 17 depicts the total cavity receiver efficiency dependent on the average reference convection coefficient and the aperture diameter for a DNI of 850 W/m2. The black crosses refer to the maximum

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total receiver efficiency for each reference convection coefficient. According to the figure, convection has negligible influence to find an optimum aperture. However, the convection approach (Equation 12) utilized in this paper is based on natural convection formulas only validated for three aperture diameters

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horizontally positioned [16], so this result cannot be generalized and further experimental studies should

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be performed.

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Figure 17: Simulated total receiver efficiency as a function of the convection coefficient and the aperture diameter

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Utilizing all previous results, a high total receiver efficiency cavity receiver is proposed for the Eurodish dish. Its specifications are gathered in Table 1. As final result, the performance map of the proposed cavity receiver is shown in Figure 18. The total receiver efficiency reaches 90.5 % at optimum BCs (maximum DNI and minimum convection losses). At DNI 850 W/m2 and hav,ref 7 W/m2K, the total receiver efficiency is 88.7 % with the following loss breakdown: 1.8 % interception, 2.4 % convection, 0.5 % conduction, 3.6 % reflection and 3% radiation. The maximum total receiver efficiency would be improved to 91.5 % if the Pyromark on the absorber is maintained in a “non-deteriorated” state.

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Figure 18: Simulated total receiver efficiency as a function of the DNI and hav,ref: performance map Table 1: Proposed cavity receiver specifications for the Eurodish

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7. Conclusions

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Investigated Aperture diameter 150 mm Shape Reverse-conical Operating temperature 770°C Cavity material Fiberfrax Cavity thickness 130 mm Cavity coating None Pre-fixed Cavity depth 150 mm Absorber diameter 280 mm

An extensive experimental campaign was conducted in the KTH HFSS focused on analyzing various material coatings for cavity receivers and on increasing the available experimental data for simulation validation. These experimental data were utilized to validate a coupled RT-thermal model to enhance a Dish-Stirling cavity receiver design. Sensitivity analyses are presented to show the sensitivity of the critical design parameter on the total receiver efficiency, which includes interception and receiver efficiencies.

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The cavity radiative properties analysis indicates that, when the cavity temperature is higher than the absorber temperature, cavities with higher ɛ/α ratio provide higher efficiencies. When the cavity temperature is lower, both ɛ and α should be as low as possible. Comparing the three

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coatings at typical operating conditions, they all present quite similar efficiencies, being

Fiberfrax slightly more efficient than ZrO and Pyromark (0.2 and 0.6 %, respectively). A

material/coating with a high ɛ/α ratio could further increase the receiver performance up to 0.6%.

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Regarding the absorber radiative properties, 0.03 reduction of the absorber absorptivity reduces approximately 1 % the receiver efficiency. The receiver emissivity should be as high as possible

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when the cavity temperatures are higher than the absorber ones, but the receiver efficiency is very little sensitive to the absorber emissivity.

Using the models presented in this paper, the optimal aperture size of the system presents quite low sensitivity to DNI and convection variations. However, more specific convection

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experiments should be performed to verify this initial result.

Finally, a cavity design is proposed for the Eurodish system with a peak total receiver efficiency

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(which includes the interception efficiency) of 91.5 % for an absorber operating at 770°C.

Acknowledgements

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We would like to acknowledge the financial support from the “Strategic Innovation Program of Metallic Materials”, a joint venture of Vinnova, Formas and the Swedish Energy Agency with the project number 2016-02836. This work was also supported by the French "Investments for the future" programme managed by the National Agency for Research under contract ANR-10EQPX-49-SOCRATE.

[m2] [-] [-] [m] [-] [W/m3] [W/m2] [W/m2] [W/m-K] [m] [Pa] [-] [W/m2] [W] [m] [K] [m]

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Symbols A area constant value (exponent) bi Bi constant value D diameter F view factor Gλ spectral irradiance h convection coefficient J radiosity k thermal conductivity L length P Pressure Pe probability q̇ flux ̇Q power r radius T temperature x position

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Nomenclature Abbreviations BC Boundary Condition CNRS Centre National de la Recherche Scientifique CSP Concentrating Solar Power DNI Direct Normal Irradiance DS Dish-Stirling DSS Dish-Stirling System EES Engineering Equation Solver ENEA Italian National Agency for new Technologies HFSS High Flux Solar Simulator KTH Royal Institute of Technology LCoE Levelized Cost of Electricity MC Monte Carlo PDF Probability Density Function RT Ray-Tracing TC ThermoCouple WF Working Fluid

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Subscripts amb ambient abs absorber ap aperture av average C cooler cd conduction CR cavity receiver surfaces cv convection ge generator H heater i,j node denotation inter interception irr direct irradiance max maximum me mechanical ra rediation rec receiver ref reference refl reflection st Stirling sys system t total w cavity receiver wall WF working fluid

[-] [-] [-] [%] [mrad] [µm] [-] [W/m2K4] [mrad]

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Greek symbols α absorptance/absorptivity ∆ increment ε emittance/emissivity η efficiency θ angular deviation λ wavelength ρ reflectance/reflectivity σ Stefan-Boltzmann constant beam quality σBQ

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Table Captions Proposed cavity receiver specifications for the Eurodish

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Table 1:

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Figure Captions Coupling of numerical models and experiments

Figure 2:

KTH solar simulator: idle (left) and in operation (right)

Figure 3:

Cavity assembly (left) and cavity coatings (right)

Figure 4:

Thermocouple positions and reference system

Figure 5:

Spectral hemispherical reflectance

Figure 6:

Power flows and efficiencies

Figure 7:

Dish ray-tracing validation

Figure 8:

Cavity temperature validation for Tmax,abs=1020 K

Figure 9:

System electric output validation (17.2 kWth)

Figure 10:

System electric output validation (13 kWth)

Figure 11:

Cavity receiver temperatures

Figure 12:

Thermal power breakdown for each coating with Tmax,abs=1020K and 17.2 kWth

Figure 13:

Simulated receiver efficiency dependent on the cavity radiative properties for DNI

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Figure 1:

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850 W/m2 and hav,ref=7 W/m2K

Simulated receiver efficiency dependent on the cavity radiative properties for DNI

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500 W/m2 and hav,ref=20 W/m2K Figure 15:

Simulated receiver efficiency dependent on the absorber radiative properties

Comment on Figure 15: * These values have been obtained from a material characterization at ambient temperature performed by the Italian Energy Agency for new Technologies (ENEA) and may vary depending on, among others, the degree of oxidation and the temperature of the sample during the characterization

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Figure 16:

Simulated total receiver efficiency as a function of the DNI and the aperture

diameter Figure 17:

Simulated total receiver efficiency as a function of the convection coefficient and

Figure 18:

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the aperture diameter

Simulated total receiver efficiency as a function of the DNI and hav,ref: performance

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map

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Investigated Aperture diameter 150 mm Shape Reverse-conical Operating temperature 770°C Cavity material Fiberfrax Cavity thickness 130 mm Cavity coating None Pre-fixed Cavity depth 150 mm Absorber diameter 280 mm

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Performed a parametric experimental study of cavity coatings and thermal powers Large set of experimental data collected capturing detailed performance parameters System simulations validated against multiple parameters and operating conditions Sensitivity studies of the influence of coatings on the cavity receiver efficiency Higher efficiency cavity receiver designed maximizing the total electric production

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• • • • •