Experimental and numerical study on a novel energy efficient variable aperture mechanism for a solar receiver

Solar Energy 197 (2020) 396–410

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Solar Energy journal homepage: www.elsevier.com/locate/solener

Experimental and numerical study on a novel energy efficient variable aperture mechanism for a solar receiver Mostafa Abuseadaa, Nesrin Ozalpb, a b

T

⁎

Department of Mechanical and Aerospace Engineering, University of California Los Angeles, 90095 CA, USA Department of Mechanical and Civil Engineering, Purdue University Northwest, 46323 IN, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Variable aperture mechanism Solar receiver Monte Carlo ray tracing Radiation heat transfer Solar simulator

A novel energy efficient variable aperture mechanism for a cavity-type solar receiver is presented. A 10 kWe solar simulator was used to experimentally test the receiver with and without the aperture mechanism and while the mechanism’s blades were uncooled and water-cooled. An in-house model of the system was developed by coupling a Monte Carlo ray tracing to a two-dimensional heat transfer analysis, which was then experimentally validated at three different solar simulator power levels, four different feedstock gas flow rates, and eight different aperture sizes. Using the validated model, it was determined that approximately 60% of the receiver’s input power is lost through radiation, which was mitigated by optimizing the receiver’s fixed aperture size. It was observed that the receiver’s temperature non-uniformity decreases as the aperture size reduces and its temperatures peak at a certain optimum aperture size, which decreases as the input power level increases. As for the aperture mechanism, water-cooling the aperture mechanism had no apparent impact on the receiver’s temperature distribution. Furthermore, the aperture mechanism did not demonstrate the same desirable behaviors as varying the receiver’s fixed aperture size, such as obtaining peak temperatures at certain smaller sizes. Nevertheless, the aperture mechanism was shown to be a very promising technique to regulate a solar receiver’s temperature and compensate for intermittent solar irradiance since the results showed that the aperture mechanism can regulate the average temperature within the range of 475–800 °C and while capturing and recovering 54% of any surplus power it intercepts.

1. Introduction Solar energy is a promising source to meet considerable amount of the expanding global energy demand. Approximately 75,000 Terawatts of solar power from the sun reaches the Earth’s surface (Camacho and Berenguel, 2012). However, this power is very intermittent and diffuse. Therefore, it is essential to develop new technologies to efficiently capture intermittent solar energy. Out of the main types of concentrating solar power (CSP) technologies, central receivers and parabolic dishes stand out with their ability to reach very high temperatures and accommodate solar thermochemical production of fuels and commodities that are traditionally obtained through combustion of fossil fuels. These applications include the production of hydrogen, syngas, and/or carbon (Ozalp and Shilapuram, 2010; Baniasadi, 2017; Furler and Steinfeld, 2015), zinc (Kräupl and Steinfeld, 2005; Muller et al., 2006), and other products, such as lime (Koepf et al., 2017). Through solar thermochemical processes, the carbon footprint is greatly reduced where the solar alternatives have potential solar to fuel efficiencies

⁎

exceeding 50% (Hathaway and Davidson, 2017). A common type of solar central receivers is a cavity-type receiver, where a comprehensive review of different solar receivers developed at Paul Scherrer Institute can be found in (Koepf et al., 2017). A cavitytype receiver is one with an aperture that aims for maximizing irradiation captured from the solar source, while minimizing re-radiation lost within its cavity. As the receiver’s aperture size increases, both the captured irradiation and lost re-radiation increase. Therefore, this type of receivers has an optimum aperture size that results from a compromise between the two aforementioned phenomena for a maximized temperature or efficiency. The optimum aperture size depends on several factors, most importantly being the cavity’s temperature, as shown in (Steinfeld and Schubnell, 1993), and the power distribution from the solar source. Its size is pre-determined through numerical analyses at nominal operating conditions and the aperture is then remained fixed for all operating conditions. However, since solar power is intermittent and the sun’s direct normal irradiance (DNI) is fluctuating throughout a given day, having a fixed aperture size does not allow for optimizing the

Corresponding author. E-mail address: [email protected] (N. Ozalp).

https://doi.org/10.1016/j.solener.2020.01.020 Received 22 September 2019; Received in revised form 29 November 2019; Accepted 8 January 2020 0038-092X/ © 2020 International Solar Energy Society. Published by Elsevier Ltd. All rights reserved.

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Nomenclature

ρ ϱ σ θ

Latin variables

A C cp CF D d f h I k L m ṁ N Q̇ R r T t V V̇

Area (m2) Constant Specific heat capacity (J/kg·K) Correlation factor Distribution factor Diameter (m) Focal point Convection heat transfer coefficient (W/m2·K) Input current (A) Thermal conductivity (W/m·K) Length (m) Mass (kg) Mass flow rate (kg/s) Number or counter Power (W) Random number Radius (m) Temperature (K) Time (s) or thickness (m) Volume (m3) Volumetric flow rate (m3/s)

Subscripts and superscripts

avg arc b bp c cap cond conv emit f ff in ins int m out prim qp rad rec sc sec w ∞

Greek variables

β Δ ε η ϕ

Density (kg/m3) Reflectivity Stefan-Boltzmann constant (W/m2·K4) Zenith/Polar angle (rad)

Polar angle (rad) Increment Emissivity Efficiency Azimuth angle (rad)

Average Xenon arc Back Back plate Cavity or center Captured Conduction Convection Emitted Front or fixed Front flange Inner Insulation Intercepted Middle or index Outer Primary Quartz plate Radiation Recovered Shell cover Secondary Window Ambient

models of the system is necessary for several applications. First, a numerical model can be used as a tool for designing solar receivers and optimizing their performance (Steinfeld and Schubnell, 1993; Li et al., 2016). Furthermore, the model can be used to assess the different forms of heat transfer and hence the overall process efficiency (Furler and Steinfeld, 2015; Guene Lougou et al., 2017). In addition, the model can be used to simulate the transient and steady state responses of the system. This can be used for offline system identification and control applications to maintain semi-constant temperatures within a solar receiver (Gallego et al., 2013; Saade et al., 2014; Abedini Najafabadi and Ozalp, 2018), which can save significant time and cost associated with tuning controllers. Therefore, to develop accurate system models, several analyses need to be coupled to obtain a full representation of the process’s behavior. These include an optical analysis for the radiative heat transfer and input solar power, heat transfer analysis for the flow of energy within the receiver’s walls and components, and a fluid dynamics analysis to monitor the feedstock and its effect on the convection heat transfer. In the case of reacting flows, additional analyses are implemented to further govern the process at hand. In this paper, a new experimental setup at the High Flux Gas Dynamics Laboratory is presented, which includes a cavity-type solar receiver and a novel variable aperture mechanism. The aperture mechanism is designed to allow for continuous adjustment of the aperture size, which provides a superior performance to a set of fixed varying sizes (Abedini et al., 2019). The current work improves on previous variable aperture designs by (1) having a more compact mechanism with its thickness reduced by 33% relative to that in (Abedini et al., 2019) and (2) coupling the mechanism’s blades to flow channels to capture surplus input solar power intercepted in the process of temperature regulation within a solar receiver. Unlike previous work on

performance of a receiver or regulating its temperature at all times. Therefore, this motivated proposing variable aperture mechanisms to allow for continuous optimization of solar receivers by regulating the cavity’s temperature (Ophoff and Ozalp, 2017; Rajan et al., 2016; Ophoff et al., 2018). In applications that require semi-constant operating conditions for maximized process efficiencies (Zhu et al., 2016; Lei et al., 2019) or have process temperature limitations (Roeb et al., 2011), the variable aperture mechanism can directly affect the power distribution inside the receiver. This method of control can be superior to other control methods currently being implemented, such as heliostats and Venetian-blind shutters control (Ophoff and Ozalp, 2017). Variable aperture concepts are implemented in a great number of fields for different purposes. Fields of applications include medicine, as in radiosurgery (Echner et al., 2009), optics, as in focus regulation (Ren et al., 2012), and others, as in irrigation (Sobenko et al., 2018). A variable aperture mechanism consists of a number of blades, usually not less than four, that move together in a translational or rotational type of motion to vary the mechanism’s opening. In general, there is no preference for a specific type of motion unless connections exist to or from the blades, where a translational motion is preferred. In addition, the blades can either be aligned to overlap for a more compact design, as in (Ren et al., 2012), or slide across one another, as in (Tanabe and Ito, 2014). The number and shape of the blades depend on the desired shape of the varying aperture. In most applications, including CSP applications, it is usually more desirable to have a circular aperture over a polygonal shaped one by having the blades’ edges curved. However, variable aperture mechanisms tend to have a closer approximation of a circular opening as the number of blades increases at the expense of the mechanism’s added size and weight (Syms et al., 2004). For a solar receiver system, developing accurate validated dynamic 397

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variable apertures that was performed using a 7 kWe high flux solar simulator (HFSS), the current experimental testing of the new solar receiver system with and without the variable aperture mechanism is performed using a 10 kWe HFSS to characterize the system at significantly much higher operating temperatures. This allows testing the system’s performance under operating temperatures similar to that required for solar thermochemical processes and at which radiation heat transfer dominates. Additionally, the effect of the flow channels on the temperature distribution within the solar receiver is experimentally tested. Furthermore, a numerical model of the system is developed by coupling an optical analysis for radiation heat transfer performed via the Monte Carlo ray tracing (MCRT) method to a two-dimensional heat transfer analysis in order to effectively simulate the temperature distribution within the receiver. The model is validated against experimental results and then used in a parametric study to simulate different test scenarios, such as design changes and scaling up of the solar energy source.

(Hirsch, 2003). The exit port of the receiver is located off-center at the front side of the cavity and is equipped with an exhaust cleaning mechanism for experiments involving carbon particles flow. The receiver also has four additional inlet tangential ports at the front side with diameters of 0.23 cm that are directed towards the window to cool it down and maintain it in a clean condition in carbon particles flow experiments. However, these experiments are outside the scope of this paper. Furthermore, there are 10 thermocouple probes connected around the receiver’s cavity and two additional probes at the back plate. Thermocouple probes around the cavity provide a better estimate of temperature at each axial position and a measure of temperature symmetry within the solar receiver. At the back plate, one thermocouple is located at the center of the plate, while the other is located vertically above the first thermocouple to provide an estimate of the radial power distribution at the back plate. A color coded model of the solar receiver with its main components and connections is shown in Fig. 3. Finally, the receiver is insulated with approximately 12.2 cm thickness of Calcium-Magnesium-Silicate wool (known as Superwool plus blanket) and is housed in the external shell that mounts to the front flange as shown in Fig. 3.

2. Experimental setup and procedure 2.1. High flux solar simulator

2.3. Variable aperture mechanism

A 10 kWe xenon arc HFSS has been used in the experimental testing of the present work. The HFSS consists of a lamp house, a single 10 kWe xenon arc, intake and exhaust fans, and an ellipsoidal reflector. The ellipsoidal reflector has its two focal points located at 7.5 and 90 cm from the ellipsoid’s vertex and has truncated diameters of 9.1 and 39 cm. The power output from the HFSS can be controlled through adjusting the current supply in the range of 80–200 A. Upon experimentally characterizing the HFSS, the heat flux distribution obtained at the focal plane and maximum current supply closely resembles a Lorentzian distribution with a peak flux density of 6.99 ± 0.22 MW/ m2 and total power of 3.49 ± 0.11 kW on a 10 × 10 cm2 target. A twodimensional plot of the relatively symmetric heat flux distributions at different supply current values ranging from 120 to 200 A w.r.t. the radial position from the center of a target placed at the focal plane is shown in Fig. 1. The peak flux density and total power were found to correlate linearly with the current supplied I to the HFSS, where their aforementioned maximum values are multiplied with a correlation factor CF as stated in Eq. (1). Additional information on the HFSS, its experimental characterization, and numerical modeling can be found in (Abuseada et al., 2019; Abuseada and Ozalp, 2019).

CF =

45.039I − 2128.1 6879.7

2.3.1. Design of variable aperture The variable aperture mechanism was fully fabricated out of stainless steel 316 and designed to have several characteristics of interest in its application for cavity-type solar receivers. The fabricated and fully assembled mechanism at the maximum aperture size is shown in Fig. 4(a) for its front and rear views. As can be seen in Fig. 4(a), the blades of the variable aperture mechanism have curved edges to better approximate a circular aperture and provide a perfectly circular aperture when fully opened. The mechanism can vary the aperture from 2 to 8.75 cm in diameter, where a circular aperture is preferred since the heat flux distribution on a solar receiver from a parabolic/ellipsoidal reflector is circular in nature. In addition, the mechanism consists of eight blades in total based on a compromise between the level of circular aperture resemblance and overall thickness, which gives an overall thickness of 4.0 cm. The eight blades of the mechanism are divided into two groups: primary and secondary blades. The primary and secondary blades alternate creating a fully circular aperture and blades of each type are allowed to overlap at smaller diameters by designing them like two-step stairs for a more compact design as can be seen in Fig. 5. Furthermore, the primary blades are designed with flow channels that cover most of their surface areas for a more efficient energy recovery system of the intercepted excess solar power, as shown in Fig. 4(b). As for the secondary blades, they do not have flow channels to allow for a much lower overall thickness of the mechanism, where the primary and secondary blades

(1)

2.2. Solar receiver The cavity-type solar receiver designed consists of five main components: a cylindrical body, back plate, front flange, and two additional plates at the front to hold the quartz window and ultimately seal the receiver. The front flange serves as a protection shield from any spilled irradiation (radiation not falling within the aperture size) and as a mean of connection to the quartz plates, receiver’s insulation outer shell, and variable aperture mechanism. The five components are made of stainless steel 316 and come together to form the cavity of the receiver. The configuration and dimensions of the solar receiver were partially based on findings in (Abedini and Ozalp, 2018) to improve the temperature uniformity within the receiver’s cavity and its optical efficiency. An overview of the solar receiver mounted in front of the HFSS is shown in Fig. 2, while the dimensions and materials of its components are summarized in Table 1. The solar receiver has four circumferentially distributed tangential inlet ports at the rear side of the cavity with diameters of 0.48 cm for entry of the main feedstock flow. These ports create a vortex-like flow and enhance convective heat transfer similar to that implemented in

Fig. 1. Two-dimensional plot of the heat flux distributions at supply current values ranging from 120 to 200 A 398

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Fig. 2. Illustration of solar receiver and connections before insulation

are approximately 1.25 and 0.45 cm in thickness. In addition, the secondary blades only cover up a relatively small surface area of the overall mechanism’s front view when fully opened and are completely shadowed at smaller aperture sizes, as shown in Fig. 5. Therefore, power intercepted by them is less significant as compared to the primary blades. 2.3.2. Motion of variable aperture The motion of the blades was designed to be in a translational manner to avoid any jamming issues between the flow connections of the primary blades. The translational motion of the blades was achieved using a mounting/guiding plate in addition to a guiding gear, as shown in Fig. 4(a), that are 0.45 and 0.85 cm in thickness. The function of the guiding plate is to attach the mechanism to the solar receiver while constraining the blades in a single axial motion. On the other hand, the guiding gear is the component that forces the blades to translate in a synchronized motion. By rotating the guiding gear through a driving chain and stepper motor, the arc paths within the gear shown in Fig. 6 force the blades to follow those paths, while still adhering to the constrained paths set by the guiding plate. To be able to control the variable aperture, the relationship between the gear’s rotation and blades’ motion needs to be obtained. The schematic of the guiding gear is shown in Fig. 6, where O represents the origin, c represents the center of the arc, and x f represent a point with a fixed x-coordinate. By considering a path within the guiding gear, the position of the blade’s support can be obtained by starting with the equation of a circle presented in Eq. (2). 2 (x − x c )2 + (y − yc )2 = Rcircle

Fig. 3. Color coded model of the solar receiver and its components

values of x c and yc change and are functions of the polar angle θ , as shown in Eq. (3), where R c = 3.992 + 3.162 = 5.09 cm.

x c = R c cos(θ + β ) and yc = R c sin(θ + β )

(3)

Substituting Eq. (3) into Eq. (2) and solving for r gives Eq. (4).

(2)

where R circle = 8.26 cm, x = x f = −1.10 cm, and the initial values of x c and yc are 3.99 and 3.16 cm. In addition, vertical position of the arc path, y , is related to the blade’s curved edge through y = r + 5.21, where r is the aperture’s radius. With the initial values of x c and yc , the initial polar angle β that the path creates with the x-axis when the aperture is fully opened is 38.3°. When the guiding gear rotates, the

r = 5.09 −0.43cos(βθ ) + sin2 (βθ ) + 1.58 + 5.09sin(βθ ) − 5.21

120.4)/ π °

(4)

where βθ = (πθ + . Eq. (4) then provides the relationship between the radius of the aperture and rotation angle of the guiding gear in θ°, starting from the fully opened position. With this relationship in mind, the variable aperture is controlled by rotating the guiding gear

Table 1 Components of solar receiver, their materials, and dimensions. Component

Material

Dimensions (cm)

Main Cylinder Back Plate

Stainless Steel 316 Stainless Steel 316

dc, in = 10.2, tc = 1.52, Lc = 29.3 dbp = 13.2, tbp = 1.52

Front Flange

Stainless Steel 316

dff , in = 10.2, dff , out = 42.7, t ff = 0.64

Quartz Plates

Stainless Steel 316

dqp, in = 8.89, dqp, out = 19.7, tqp = 1.27

Window Insulation Shell Cover

Fused Quartz Calcium-Magnesium-Silicate Wool Aluminum 6061

dw = 10.2, tw = 0.74 tins≈ 12.2 dsc, in = 37.6, tsc = 0.25, Lsc = 42.3

399

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Fig. 4. (a) Illustration of the variable aperture, in real view, for a maximum opening size of 8.75 cm in diameter, and (b) cross-sectional view of fabricated primary blade

control), two NI 9214 (for temperature monitoring), and one NI 9215 (for water flow rate measurements). In addition, a Voegtlin red-y smart series flow controller is used to control the feedstock’s volumetric flow rate and can control it within the range of 0–30 LPM with an accuracy of 1% full scale. Furthermore, OMEGA Inconel 600 type K thermocouple probes are used for temperature monitoring, where they have a temperature range up to 1250 °C and tolerance of the greater of 2.2 °C or 0.75%. Moreover, McMillan Company S-111 flow meter is used to measure the water flow rate and has a flow range from 0.1 to 1.0 L/min with an accuracy of 1%. Finally, a SureStep DC integrated stepper motor (model STP-MTRD-17038E) and SureGear precision planetary gearbox (model PGCN17-505 M) are used to control the variable aperture with a nominal output torque of 16 N·m, steps per revolution of 10,000 steps, and an external encoder.

Fig. 5. Front and rear views of fabricated variable aperture at opening diameters of 4 and 2 cm

2.5. Experimental procedure The complete working setup of the solar receiver is shown in Fig. 7 with the variable aperture mechanism coupled to it. The center of the receiver’s fixed aperture is first aligned at the second focal point of the

Fig. 6. Schematic of the guiding gear of the variable aperture mechanism, where measurements are in cm

through a driving chain, gearbox, and stepper motor based on the motor’s steps per revolution.

2.4. Data acquisition and instrumentation A data acquisition and control system using LabVIEW and hardware from National Instruments was implemented. The system consisted of cRIO 9030 equipped with four modules: one NI 9375 (for motor

Fig. 7. Complete working setup of the solar receiver with the variable aperture mechanism coupled to it 400

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HFSS’s ellipsoidal reflector. Then, to characterize the solar receiver without the variable aperture, experiments under different operating conditions were performed to determine the transient and steady state responses of the temperature distribution within its cavity. The steady state is treated as the point in time where the temperature gradients’ average value drops to approximately 0.05 °C/min, which is normally achieved after 6.5 h of operation when starting an experiment from room temperature. Experiments with different input currents to HFSS (power levels) of 160, 150, and 140 A (2.58, 2.35, and 2.12 kW) in addition to different nitrogen feedstock flow rates of 10, 7.5, 5, and 2.5 LPM were conducted. A maximum input current value of 160 A was chosen since it was the value at which a maximum temperature of approximately 1000 °C was observed per initial simulations and experimentation. Following that, the variable aperture mechanism was coupled to the solar receiver, and further characterization at different aperture sizes was performed with and without water flowing through the primary blades’ flow channels. This was performed to investigate the effect of water-cooling the mechanism’s blades on the temperature distribution within the receiver, since not water-cooling the blades could potentially provide higher cavity re-radiation savings and radiation emission into the receiver in addition to lower conduction losses. For water-cooled experiments, the primary blades are connected together and to the water supply inlet and outlet lines through stainless steel flexible tubing as shown in Fig. 7. Finally, to be able to quantify the amount of power recovered by the variable aperture mechanism, type K thermocouple probes are connected to the water supply inlet and outlet lines. 3. Numerical methodology and procedure 3.1. Optical analysis 3.1.1. High flux solar simulator The MCRT method has been previously implemented to model the HFSS in (Abuseada and Ozalp, 2019). The electrical power of the xenon arc is 10 kWe for an input current of 200 A and its electrical-to-radiative power conversion efficiency, ηarc , is 0.5. As for the ellipsoidal reflector, its reflectivity, ϱ, is 0.9 and its specular error was based on implementing a deviating zenith angle that has a Gaussian distribution with a mean value of zero and a standard deviation of 5 mrad. Then, the xenon arc is modeled as a gray isotropic emitting volume consisting of a hemisphere with a radius of 1 mm, centered at the focal plane, that is attached to a cylinder of 1 mm in radius and 10 mm in length with a power ratio between the two shapes of 0.23:0.77. Finally, the available ̇ , in Watts is calculated through electrical power at the xenon arc, Qarc the use of the correlation factor in Eq. (1). Further information and details can be found in (Abuseada and Ozalp, 2019).

Fig. 8. Flowchart illustration of the general MCRT algorithm used to model the solar receiver

components can be described as a cylinder and/or a disk. In the case of the receiver’s main cylinder, quartz plates, and front flange, the surfaces are described as in Eq. (5).

x 2 + y 2 − rin2 = 0 for z min < z ≤ z max

(5)

where z min and z max represent the starting and ending positions. However, in the case of the quartz window, quartz front plate, front flange, and back plate, the surfaces are described as in Eq. (6).

rin ≤ 3.1.2. Overview of the MCRT method The information presented in this paper only complements the methodology in (Abuseada and Ozalp, 2019). In addition, two types of rays are defined within the MCRT algorithm to distinguish between the sources contributing to radiation heat transfer as commonly performed in literature (Kräupl and Steinfeld, 2005; Hirsch, 2003). These are the primary rays that represent rays from the solar source (HFSS) and secondary rays that represent rays emitted by the receiver’s cavity. Starting with the assumptions that the analysis considers, all surfaces surrounding the solar receiver, such as the aluminum structure, are treated as non-participating. Hence, their re-radiation effects (if any) are neglected. Also, all surfaces are assumed to be diffuse gray and have constant surface properties that are independent of temperature. Furthermore, the feedstock flow (nitrogen) is treated as a non-participating medium. Finally, the quartz window is assumed to have a refractive index of one, and hence not affecting the direction of any incoming rays. When analytically describing the surfaces of the solar receiver, all

x 2 + y 2 < rout

for

z = z position

(6)

where rin = 0 for the back plate and z = 0 for the quartz front plate. As for the variable aperture, it is assumed to be circular at all sizes and hence can be described using Eq. (6) for different aperture radii and while having its front side at z = -0.04 and its rear side at z = -0.02. 3.1.3. MCRT algorithm The MCRT algorithm for quantifying the primary and secondary rays is shown in Fig. 8. The subscript i in the counter Nij can be dropped and substituted by “prim” for the primary rays, while the subscripts i and j correspond to surface indices for the secondary rays. The methodology starts with the primary rays approaching the solar receiver as obtained from the model in (Abuseada and Ozalp, 2019), where the first step would be to determine if and where intersection occurs. For that, receiver’s surface equations will be used to obtain the distance travelled by a ray up until the first intersection point. Then, whether a ray is absorbed or reflected by the solar receiver will depend on the surface properties, and will be determined probabilistically by generating a 401

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random number R ϱ between zero and one, which is then compared to the surface reflectivity. The ray is deemed to be reflected if R ϱ ≤ ρ , and absorbed otherwise. If absorbed, the corresponding surface counter is incremented by one and the ray’s history is terminated, where the algorithm moves to the next ray. If the ray is reflected, it is done in a diffusive manner and the reflection direction is evaluated through Eq. (7). Once the direction is obtained, the algorithm proceeds until the ray is determined to be absorbed by a surface or lost from the solar receiver. Finally, the power distribution of the primary rays is then computed once Nrays rays have been emitted from the xenon arc.

(θ , ϕ) = (sin−1 R θ , 2π R ϕ)

mcp

dT ̇ cond + Qin ̇ conv + Q̇rad, prim + Q̇rad, sec − Q̇rad, emit = Qin dt

(10)

The most critical location with most heat transfer modes occurring is the first layer within the cavity walls. Therefore, the derivation will only be shown for the group of elements that lie within the horizontal cylinder portion of the cavity. Starting from Eq. (10), the different terms of the equation for the discrete volumetric elements are shown in Eqs. (11)–(15). The discrete elements are presented by i and j based on their relative location within the solar receiver. For clarity, the subscripts i and j for the MCRT optical analysis are now substituted by m and n . Indices in the optical analysis represent the corresponding surface element rather than its location. Hence, being different from the subscripts i and j used in the heat transfer analysis. Additionally, the harmonic mean for the thermal conductivity and the fully implicit scheme are implemented due to their higher accuracies (Patankar, 1980).

(7)

For the secondary rays, a total number of itotal discrete surface elements are defined. For each element, a total number of Nrays rays are emitted to obtain the power distribution from surface i to surfaces j . The location of emission is determined using Eq. (8) or (9) for a cylindrical or disk-shaped section, respectively. Then, the direction of surface emission is determined through Eqn. (7) and the algorithm proceeds to emit all rays for all surfaces involved while incrementing the corresponding counters. Finally, the distribution factor Dij is computed, which represents the ratio of radiation emitted by surface i that is absorbed by j due to direct radiation and all possible reflections. The distribution factor simply becomes Dij = Nij / Nrays .

cond

̇ , i, j Qin

(2ki − 1, j ki, j )(2πrm, j Δr )

=

(Ti − 1, j − Ti, j ) +

(ki − 1, j + ki, j )Δz (Ti + 1, j − Ti, j ) +

(2ki, j + 1 ki, j )(2πr j + 1 Δz ) (ki, j + 1 + ki, j )Δr

conv

(r , ϕ, z ) = (rin, 2π R ϕ, (z max − z min ) R z + z min )

(8)

̇ , i, j = h (2πr j Δz )(Ti, j − 1 − Ti, j ) Qin

2 2 2 (r , ϕ, z ) = ( Rr (rmax − rmin ) + rmin , 2π R ϕ, z )

(9)

Qṅ

rad, prim

rad, emit

Qṅ ori, j

3.2. Heat transfer analysis The heat transfer analysis is performed using the finite volume method, which couples results of the MCRT method. All system components under consideration are centered around the z-axis and have geometries and properties that are axisymmetric, except the exhaust and insulation layer. Therefore, the system is assumed to be two-dimensional in the solid phase. Additionally, the system is assumed to be one-dimensional in the fluid phase to simplify the analysis since a detailed study on the fluid flow through the receiver is out of the scope of this paper. Based on this, the system is discretized in the form of annular elements throughout the solid phase having dimensions of Δz and Δr and disk-shaped elements throughout the fluid phase. In addition, it is assumed that the feedstock enters the receiver right by its back plate and then progresses throughout the cavity until the window. Furthermore, it is assumed that the variable aperture does not have an impact on the thermal distribution within the solar receiver through radiation emission or conduction from/to the aperture mechanism, and so its geometry can be neglected from the heat transfer analysis (but plays a critical role in the optical analysis). Finally, the room temperature surrounding the solar receiver is assumed to remain constant at 25 °C, which has been verified by constantly monitoring the temperature right next to the receiver’s shell using a thermocouple. A schematic for the heat transfer model showing the control volumes, flow path, and heat transfer mechanisms is shown in Fig. 9. For the solid phase, conservation of energy is used to determine the governing equation for each volumetric element, describing the transient heat transfer of the system. Each group of elements has a different governing equation depending on its location within the receiver. For example, the first layer within the receiver’s cavity will involve conduction, convection, and radiation heat transfer in addition to the power intercepted form the HFSS. On the other hand, exterior/outer elements have conduction, convection, and minor radiation heat transfer. The governing equation for the general case is shown in Eq. (10), where heat transfer due to conduction and convection is assumed to be entering the control volume.

rad, sec

Qṅ

̇ = = Nprim, n Qray

Nprim, n Nrays

= εi, j (2πr j Δz ) σTi4, j mtotal

=

∑ m=1

̇ rad, emit Dm, n Qm

(2ki + 1, j ki, j )(2πrm, j Δr ) (ki + 1, j + ki, j )Δz (Ti, j + 1 − Ti, j )

(11) (12)

̇ ηarc Qarc

(13) (14)

(15)

where ηarc = 0.5, r j = rc, in , rm = rc, in + Δr /2 , r j + 1 = rc, in + Δr , and the heat transfer coefficient h is approximately 7.2 W/m2·K following the work described in (Szekely and Carr, 1966). Then, the mass term in Eq. (10) becomes m = ρV = ρ (2πrm Δr )Δz . Just in a similar manner, several equations are obtained representing the heat transfer into different volumetric elements at the boundary surfaces of the receiver and the interior elements based on the heat transfer modes involved. For the fluid phase, the mass conservation states that mass entering is the same as that leaving the control volume, which is equal to ṁ . Also, based on conservation of energy, energy due to fluid flowing in and that of convection heat transfer must equal to that of the fluid flowing out. By applying the upwind scheme, the equation for the temperature at each location within the fluid phase is simplified and presented in Eq. (16), where A = 2πrin Δz .

Fig. 9. A schematic diagram demonstration of the heat transfer model of solar receiver 402

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Ti, j =

̇ p mc hA Ti + 1, j Ti, j + 1 + ̇ p + hA ̇ p + hA mc mc

fact that the insulation shell is not completely filled with Superwool Plus blanket, but also contained stainless steel components, and the insulating material was compressed inside the outer shell. Therefore, the insulation’s thermal conductivity was modified by adding a constant Ck = 0.3 W/m·K to obtain temperatures at the outer shell layer that are close to that monitored experimentally and the insulation’s density was modified by multiplying its density by a constant Cρ = 2 to obtain a transient response that accurately represents the system. Results from the numerical model were then obtained for the transient temperature response of the system up to 6.5 h. Fig. 11 shows the transient response of both the experimental and numerical results at five different locations and four operating conditions. The five locations represent the average temperature values across the front, middle, and back sections of the receiver in addition to the two positions at the back plate. The four operating conditions span the range of experimental measurements, where the feedstock flow rate and input current values were (a) 7.5 LPM and 160 A, (b) 7.5 LPM and 150 A, (c) 10 LPM and 160 A, and (d) 10 LPM and 140 A. As can be seen in Fig. 11, the numerical model accurately represents the temperature distribution within the actual system. It exhibits the same non-uniform distribution across the back plate with the peak temperature being at its center. The average error value for the steady

(16)

3.3. Variable aperture mechanism’s performance The useful power captured by the mechanism is easily obtained experimentally through Eq. (17).

̇ = mc ̇ p ΔT = V̇ cp (Tout − Tin)/60 Qcap

(17)

where V̇ represents the water flow rate in L/min, Tout and Tin represent the recorded thermocouple temperatures, and cp is assumed to be constant with a value of 4187 J/kg·K. The useful power captured provides a basis for the variable aperture’s efficiency calculations w.r.t. the amount of power actually intercepted by the variable aperture mechanism obtained from the primary rays’ optical analysis (at z = −0.04) and verified using the experimental intercepted power at the focal plane in (Abuseada et al., 2019). Once the intercepted power w.r.t. different aperture sizes was obtained, a fourth order polynomial function was fitted to the data and identified in Eq. (18), where d is the aperture diameter in cm. This polynomial provided a perfect fit to the data and is used to evaluate the power intercepted by all aperture blades.

̇ = 0.4186d4 − 10.993d3 + 118.49d 2 − 858.67d + 4158.2 Qint

(18)

4. Results and discussion 4.1. Solar receiver with fixed aperture 4.1.1. Optical analysis validation The first step in validating the numerical model is to ensure that the number of rays used for the MCRT analysis is sufficient for successful converge. The required number of rays depends heavily on the size of the discretized elements; when the elements are larger in size, Nrays decreases significantly. Throughout this paper, the solar receiver is discretized into a fine mesh with 462 × 213 elements in the axial and radial directions. The successful convergence of the optical analysis is demonstrated in Fig. 10, where the (a) normalized power values of primary rays, and (b) normalized distribution factors of secondary rays are plotted w.r.t. the number of rays emitted from the (a) HFSS, and (b) each surface element. As shown, all values converge smoothly to unity while the surface elements with lower power values (quartz plates) in Fig. 10(a) take longer to converge. This behavior is per expectation, which results in their convergence being less important than that of the cavity or back plate. In addition, Fig. 10 shows the significant decrease in the value of Nrays when moving from the simulation of primary rays to that of the secondary rays. The value of Nrays required for the primary rays is 20 times more than that of the secondary rays due to the nature of the power distribution coming from the HFSS, which have relatively higher gradients and loses a significant portion of power outside the receiver’s cavity. 4.1.2. Heat transfer analysis validation As a starting point, material properties of the receiver were initially evaluated from appropriate references and then tweaked to better represent the response of the experimental results. The material properties used in the numerical model are summarized in Table 2. Only three properties were modified, which are: stainless steel’s emissivity, insulation’s density, and insulation’s conductivity. The emissivity of stainless steel can significantly vary depending on the surface condition, and its value can have major effects on the overall temperature distribution inside the solar receiver and location of maximum temperature. Therefore, the final value of ε = 0.6 was the closest in resembling the temperature distribution inside the receiver. The two other tweaked parameters were the insulation’s properties due to the

Fig. 10. Convergence of MCRT analysis for different solar receiver’s components for (a) normalized power values of primary rays, and (b) normalized distribution factor values of secondary rays 403

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Table 2 Material properties used in the numerical model. Temperature, T , is in Kelvin. Material

ρ (kg/m3)

cp (J/kg·K)

Stainless Steel

8238

Quartz Insulation

2203 160Cρ

−1.78e−4 T2 + 4.16e−1 T + 3.62 700 1050

Aluminum Nitrogen

2770 1.056

875 1042

k (W/m·K) 1.55e

−2

Optical

T + 8.92

1.3 (1.61e−7 T2 – 4.56e−5 T + 2.65e−2) +Ck 237 2.75e−2

ε = 0.6 τ = 0.95, α = 2.7 m−1 – ε = 0.8 –

Ref. Cengel and Ghajar (2015) Beder et al. (1971) Sheet and Therm (2016) Cengel and Ghajar (2015) Cengel and Ghajar (2015)

Fig. 11. Solar receiver’s temperature transient response of experimental (dotted lines) and numerical (solid lines) results for feedstock flow rates and input currents of (a) 7.5 LPM & 160 A, (b) 7.5 LPM & 150 A, (c) 10 LPM & 160 A, and (d) 10 LPM & 140 A

4.1.3. Grid independence test The effect of the chosen mesh size on results of the heat transfer model was investigated for three different mesh sizes: (a) fine mesh with 462 × 213 elements, (b) medium mesh with 231 × 107 elements, and (c) coarse mesh with 154 × 71 elements, in the axial and radial directions. Fig. 12 shows the steady state temperature distribution along the receiver’s cylindrical cavity for an input current of 160 A and flow rate of 7.5 LPM for the three aforementioned mesh sizes. Based on the results shown in Fig. 12, it is clear that the course mesh had significantly different temperature values than that of the medium and fine meshes. However, it was still able to demonstrate the same trend in the temperature distribution, but with slightly lower temperature values by around 25 °C. The difference between the temperature distribution of the medium and fine meshes is very insignificant. It can be seen that towards the front region of the cavity that both mesh sizes provided identical results. Nevertheless, the fine mesh was the final chosen size in an attempt to capture more of the heat transfer dynamics.

state temperatures is 0.3% with a maximum relative error of 1.1%. However, the transient temperature errors at the beginning of the experimental runs are as large as 65% especially at the front and middle sections of the receiver’s cavity. This can be attributed to three factors. The first and most dominant one is due to the transient nature of the HFSS, where it starts at approximately 75% of its steady state power and takes approximately 10 min to reach the 95% mark (Abuseada et al., 2019). However, this transient behavior has not been incorporated in the model since further identification of the transient behavior was not performed and it does not play a critical role in the system’s overall response. The second factor is due to the additional components attached to the front of the receiver that are not well modeled, such as the exhaust cleaning mechanism. These components can significantly affect the heat transfer occurring at the front region. The final factor is due to the assumption of treating the fluid flow as one-dimensional. This assumption could have been a drive for the heat transfer from the backward sections of the receiver to the front ones, leading to higher transient temperature predictions. Nevertheless, the heat transfer model can now be treated as validated.

4.1.4. Heat transfer and power losses The heat transfer modes significantly change as temperature within 404

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and its highest achievable temperatures. There will be a point where radiation losses within the cavity start dominating over the amount of solar radiation entering the system, where blocking some of the input power saves relatively more of the radiation losses. The recovered radiation emission within the cavity will be referred to as Q̇Rec , which is quantified through evaluating the sum over Eq. (15). To determine the optimum aperture size of this solar receiver, all its dimensions were kept constant with the exception of the quartz plates’ inner diameter to solely examine the effect of varying the aperture size on the temperature inside the cavity. For this, dqp, in was varied between its highest possible value of dc, in to a value of 4 cm. As an initial investigation of the aperture’s effect, the numerical model was used to simulate the temperature distribution at a flow rate of 7.5 LPM and power level of 160 A. Fig. 14(a) shows the steady state maximum temperature, ̇ ) average temperature, and radiation power recovered and spilled (QSpill ̇ values for the solar receiver at different aperture diameters, where QSpill is the radiation power not falling within the aperture size. Based on results shown in Fig. 14(a), the average and maximum temperature values reach their peaks at certain diameter sizes. Given the conditions of this simulation, the optimum aperture sizes were determined to be 8.2 and 7.6 cm for the maximum and average temperatures. These optimum sizes did not coincide, since the temperature distribution within the receiver’s cavity changes with different aperture sizes. Therefore, it is not a proportional change across the cavity, as is

Fig. 12. Temperature distribution along receiver’s cylindrical cavity for an input current of 160 A and flow rate of 7.5 LPM using three different mesh sizes

the solar receiver increases. To inspect the different modes of heat transfer, system’s losses were evaluated at each time step and divided into three modes: radiation losses inside and outside of the receiver’s ̇ cavity (Q̇Rad ), convection losses outside of the receiver’s cavity (QConv ), and convection heat transfer to the feedstock flow (Q̇Flow ). These losses ̇ conv are evaluated based on Eq. (19), summation of Qout , i, j for the outer ̇ p ΔTFlow , where ΔTFlow represents the elements subject to T∞, and mc temperature difference between the feedstock inlet and outlet. ntotal

̇ QRad =

∑ n=1

rad, emit

Qṅ

rad, sec

− Qṅ

(19)

The power input to the receiver, Q̇In , is just the summation over rad, prim ̇ and the power consumed in bringing up the cavity to its temQn ̇ , is just the difference between Q̇In and the sum of the perature, QSystem three thermal loss modes, denoted as Q̇Loss . Fig. 13 shows the simulation results of the (a) receiver’s steady state temperature contour map, and (b) different modes of heat transfer through the transient response of the system operating under a feedstock flow rate and input current of 7.5 LPM and 160 A. Based on results in Fig. 13(b), the system reaches an approximate ̇ steady state after 6.5 h of operation as previously assumed, since QSystem drops from 2740 to 26 W. In addition, the numerical model is energy conservative, as Q̇Loss approaches and never exceeds Q̇In for any additional simulation time. Furthermore, it can be seen that after two hours of operation where the system reaches an average temperature of approximately 700 °C, radiation losses start to dominate the convection losses. At steady state, 60% of the input energy is lost through radiation, 36% is lost through convection, and only 4% is transferred to the feedstock flow. Therefore, attempts to increase the overall temperature inside the solar receiver should focus on reduction of the radiation losses. In addition, based on Fig. 13(a), it is clear that there is a significant hotspot region at the back plate. The temperature non-uniformity within the receiver is approximately 37%, which represents the relative difference between the highest (Tbp2 ) and lowest (≈ Tf ) temperatures w.r.t. the highest one in °C. Higher temperature non-uniformities within the cavity lead to lower receiver efficiencies since radiation losses are amplified at the hotspots, which results in higher overall radiation losses. 4.1.5. Optimum aperture A major parameter of design and performance optimization of a solar receiver is its fixed aperture. The aperture size can have a significant effect on temperature distribution inside the receiver’s cavity

Fig. 13. (a) Steady state temperature contour map, and (b) Modes of heat transfer through the transient response of the receiver to a feedstock flow rate of 7.5 LPM and input current of 160 A 405

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Fig. 15. Average and maximum temperature values within the solar receiver for different aperture sizes at a flow rate of 7.5 LPM and power level of 200 A

from the source increases since the receiver’s operating temperature and thus radiation losses increase. On the other hand, the optimum aperture should increase in size as the power distribution becomes more uniform. This behavior is one of the reasons behind proposing a variable aperture. Therefore, to quantify such a variation, the aperture size was varied w.r.t. different power levels from the HFSS to once again predict the optimum aperture sizes. Fig. 15 shows the variation of the average and maximum temperature values within the solar receiver for different aperture sizes at a flow rate of 7.5 LPM and power level of 200 A. Based on Fig. 14(a) and Fig. 15, the optimum aperture size is a function of the power level from the HFSS, which is representative to variation of the sun’s DNI. At a power value of 200 A, the optimum aperture sizes were 7.8 and 7.2 cm based on the maximum and average temperatures. The same simulation was duplicated for 180, 140, and 120 A, which showed optimum aperture sizes of 8.0, 8.4, and 8.6 cm based on the maximum temperature, and 7.4, 7.8, and 8.0 cm based on the average temperature. As can be concluded, the optimum aperture size decreases as the power level from the HFSS increases. Therefore, with a varying DNI, the solar receiver can be continuously optimized at any given time using predictive models to vary the aperture size accordingly and obtain maximum process efficiencies whether by maximizing the temperature or maintaining it at a semi-constant value.

Fig. 14. (a) Average temperature, maximum temperature, and radiation power recovered and spilled values, and (b) temperature values within the solar receiver for different aperture sizes at a flow rate of 7.5 LPM and power level of 160 A

shown in Fig. 14(b). Furthermore, the obtained optimum sizes do not coincide with the aperture size for the peak of Q̇Rec with a value of ̇ ) as a result of 7.4 cm, since the aperture blocks additional power (QSpill its reduced size which at this point does not compensate for the additional radiation recovered. Although the increase in the average temperature observed in Fig. 14(a) is only 29 °C, this effect can be much more significant in optimizing other receiver designs. To better observe the temperature distribution change within the cavity, the individual temperatures at the five different thermocouple locations w.r.t. the aperture’s diameter are shown in Fig. 14(b). As shown in Fig. 14(b), the temperature distribution within the solar receiver changes as a result of the different aperture sizes investigated. Therefore, the temperature profile at each individual thermocouple position might have its own unique aperture size at which it peaks. With the data shown in Fig. 14(b), Tb , Tbp1, and Tbp2 peak at an aperture size of 8.2 cm, while Tm peaks at 8 cm and Tf peaks at 6.8 cm. Hence, depending on the objective of optimizing the aperture size, the optimum size is expected to be different. In addition, as a result of decreasing the aperture size from 10.2 to 4 cm, the temperature nonuniformity dropped from 40.8 to 29.4%. However, at an aperture size of around 6.6 cm, the decrease in the non-uniformity starts to be insignificant. The non-uniformity values at the proposed optimum aperture sizes of 8.2 and 7.6 cm are 34.3 and 32.5%. Therefore, optimizing the aperture size also significantly improves the temperature distribution within the receiver’s cavity. The optimum aperture size is expected to vary w.r.t. characteristics of the power source, such as its distribution and power. As a general guideline, the optimum aperture size should decrease as the total power

4.2. Solar receiver with variable aperture 4.2.1. Uncooled vs. water-cooled variable aperture Steady state temperature values across the receiver were obtained experimentally for different aperture sizes ranging from 2 to 8.75 cm, while the variable aperture mechanism is uncooled and water-cooled. The rest of the experimental conditions were kept the same throughout, where the feedstock flow rate and power level were maintained at 7.5 LPM and 160 A, while the cooling water flow rate and temperature were approximately 0.35 L/min and 20 °C. The experimental temperature values at different positions within the receiver are shown in Fig. 16(a) w.r.t. the aperture’s diameter while the variable aperture was uncooled and water-cooled. For the uncooled experiments, the minimum aperture was only set to 4 cm in diameter to avoid the deterioration of the mechanism due to high radiation flux levels at lower sizes. Based on the results shown in Fig. 16(a), the steady state temperatures were not affected by water cooling the variable aperture mechanism. The two sets of temperatures at different positions were nearly identical at smaller aperture sizes and were slightly higher for the uncooled experiments at larger aperture sizes. However, the maximum difference between the two sets of temperatures was 406

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Fig. 16. (a) Steady state temperature distribution for uncooled and water-cooled variable aperture, and (b) temperature distribution of numerical model and watercooled experimental results with the variable aperture at different diameters for a feedstock flow rate of 7.5 LPM and power level of 160 A

higher steps of the primary blades become the only visible portion of the mechanism. In addition, the model slightly overestimates some of the temperatures at all positions with the exception of the front thermocouple position, which is due to the assumption of not considering the variable aperture in the heat transfer analysis. The model’s maximum relative temperature error at the front position within the receiver is approximately 8.5%, which also represents the maximum error across all locations. The rest of the relative error values are approximately 4% and below. Therefore, this further validates the numerical model. Based on the results in Fig. 16(b), it is clear that the variable aperture mechanism did not provide a peak in temperature values due to variation of the mechanism’s aperture size. This is due to the reason that power intercepted by the mechanism does not get transferred to the receiver and gets lost from the system. Hence, this no longer allows for a smaller aperture size to be an optimum one (within a variable aperture size range from 2 to 8.75 cm), since the additional cavity reradiation losses saved by a smaller aperture size do not compensate for sacrificing nearly all of the additional intercepted radiation. Therefore, the designed variable aperture mechanism failed in depicting a similar behavior to that expected from a fixed aperture.

approximately 4 °C or 0.45%. This difference is insignificant and can be attributed to changes in uncontrolled variables, such as a decrease in xenon arc’s output power over its operating hours since the uncooled experiments were performed first. Furthermore, the addition of the aperture mechanism created a significant drop in temperatures within the solar receiver, with its front side having the most significant decrease. The experimental steady state temperatures at Tbp2 , Tbp1, Tb , Tm , and Tf without the aperture mechanism were 984, 954, 926, 835, and 618 °C, while they were 956, 927, 898, 807, and 557 °C with the mechanism having an aperture diameter size of 8.75 cm. This shows a drop of approximately 28 °C at all thermocouple positions except the front thermocouple which decreased by 61 °C. This is due to the reason that the aperture mechanism intercepts power from the HFSS that was previously intercepted by the quartz front plate and receiver’s front section. This behavior in addition to the thickness of the variable aperture mechanism, which intercepts slightly more power, results in a decrease in temperature values across the rest of the cavity. This also led to an increase in temperature non-uniformity, where it increased from 37.2% to 41.9% with the variable aperture fully opened at 8.75 cm, and further increased to 45.5% with the variable aperture fully closed at 2 cm. The general trend shows an increase in temperature non-uniformity as the variable aperture mechanism closes, which opposes the previous trend exhibited by varying the fixed aperture size. Finally, based on the results discussed earlier, the power intercepted by the variable aperture seemed to not be transferred to the front side of the receiver. Therefore, the previously stated assumption of not including the mechanism in the heat transfer analysis is now justified.

4.2.3. Power captured by variable aperture mechanism With flow channels coupled to the variable aperture mechanism, power intercepted by the mechanism can be captured and converted into useful power. In the present work, power captured is used to increase the temperature of a water flow. The captured power is calculated using Eq. (17) for different water flow rates that range between 0.1 and 1.0 L/min with an inlet water temperature of approximately 20 °C at each different aperture size. The average captured power at each size is then calculated and the standard deviation of the experimental data was used to represent the uncertainty in the results. Fig. 17 shows both the intercepted and average captured experimental power values, where the ratio of the captured power to the intercepted one provides the efficiency of the mechanism. As can be seen in Fig. 17, the efficiency of the variable aperture mechanism remains relatively constant for different diameter sizes. Based on the uncertainty bars shown, it can be concluded that a flow rate within 0.1 and 1.0 L/min provides relatively the same efficiencies and captured powers. The efficiency of the mechanism was approximated to be 0.54, which is slightly less than the assumed emissivity value for stainless steel. Therefore, an assumed value of 0.6–0.8 should be reasonable. At a power level value of 160 A, a fully opened aperture intercepts 594 W with an efficiency of 0.54, while a fully closed aperture intercepts 2093 W with an efficiency of 0.56.

4.2.2. Numerical model validation Fig. 16(b) shows a comparison between the experimental and numerical steady state temperature values at different positions for aperture diameters ranging from 2 to 8.75 cm, while maintaining feedstock flow rate and power level at 7.5 LPM and 160 A. As can be seen, the model comprising the aperture mechanism and its assumptions provides a satisfactory representation of the experimentally obtained results. The model simulates the system more accurately at larger aperture sizes, where its results then diverge a little bit from the experimental ones at the rear side of the receiver for diameter sizes of 3 to 6 cm but then converges for diameter sizes of 3 cm and below. This is due to the assumption of treating the variable aperture as a single surface at the higher location of the primary blades, whereas in reality, the secondary blades and second step of the primary blades are at a position further away from the HFSS. Thus, this creates the biggest errors in the region of 3 to 6 cm since the variable aperture’s effect becomes much more significant for aperture sizes of 6 cm and below. The errors then decrease in the region of 3 cm and below because the 407

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temperature profile of both proposed improvements converges as the aperture’s diameter decreases in size, since the change in emissivity has a more prominent effect as the aperture closes but is also directly related to the temperature inside the receiver’s cavity. Hence, the difference peaks at an aperture diameter of 4.9 cm, where a compromise between both effects is achieved. On the other hand, the temperature increase due to the reduction in thickness decreases directly with decreasing diameter, since the amount of power saved by this improvement decreases in magnitude. Despite the fact that slight temperature peaks were observed in Fig. 19 for both proposed improvements, the behavior exhibited by varying the fixed aperture size was not yet observed. The temperatures peak at 8 cm by 0.9 °C for the reduced emissivity and at 8.3 cm by 0.6 °C for the reduced thickness, which is insignificant. The major issue that still remains is that the power intercepted by the aperture mechanism does not get transferred to the system. As long as this issue remains, the observation of temperature peaks at optimum aperture sizes will be difficult. Therefore, if the objective of the variable aperture is to achieve the highest possible temperature rather than regulating it, further work should be focused on integrating the variable aperture mechanism into the solar receiver’s design more effectively.

Fig. 17. Intercepted and captured power by the variable aperture mechanism at a power level of 160 A for different aperture sizes, with error bars representing the standard deviation of results

4.2.4. Characterization of the variable aperture coupled solar receiver To further characterize the effect of the variable aperture mechanism, the model was used to simulate the system for different operating conditions. Fig. 18 shows a contour map of the steady state maximum temperatures for varying power levels from the HFSS within the range of 100–200 A and for varying aperture diameters within the range of 2–8.75 cm for a fixed feedstock flow rate of 7.5 LPM. Based on results at a power level of 200 A shown in Fig. 18, the maximum temperature ranged from 752 to 1180 °C, where the maximum temperature always increased as the aperture’s diameter increased. Therefore, an optimum aperture size was still unobserved at higher power levels, which is still due to the same reason stated earlier. In a similar manner, the average temperature ranged from 563 to 970 °C at 200 A without observing a peak in its values. Therefore, the variable aperture mechanism failed in demonstrating its full expected potential and exhibiting a similar trend to that of varying the fixed aperture size even at higher power levels and thus operating temperatures. Nevertheless, the regions of isotherm in Fig. 18 demonstrates the promising desired capability of the variable aperture in maintaining a semi-constant temperature within a solar receiver undergoing significant changes to its input power level or DNI.

5. Conclusions In this paper, an experimentally validated numerical model coupling MCRT method to a heat transfer analysis for a new solar receiver system was presented. The numerical model was first used to study the different modes of heat transfer within the solar receiver, where approximately 60% of the receiver’s input power at steady state is lost through radiation. Thus, showing the significant contribution of radiation losses to the overall temperature state of the receiver and leading to the discussion on the optimum aperture size. It is then shown that the maximum or average temperature within the receiver peaks at a certain reduced fixed aperture size. Additionally, the temperature non-uniformity within the receiver’s cavity decreased as its fixed aperture size reduced, leading to a more uniform temperature distribution. Finally, the optimum aperture size is shown to depend on the power level from the HFSS (and thus DNI), where its size decreased as the power increased. Then, a novel variable aperture mechanism coupled to flow channels for the solar receiver was presented. Results showed that watercooling the aperture mechanism had no apparent impact on the temperature distribution within the receiver’s cavity. This was mainly concluded to be due to intercepted power by the mechanism completely

4.2.5. Future design recommendations Two design modifications were investigated for the variable aperture in an attempt to improve its performance. The first modification was changing the emissivity of the aperture blades’ rear surfaces from a value of 0.6 to 0.2. Hence, recovering more of the cavity re-radiation losses. This change could have been achieved by having a finer surface finish on the aperture blades and not allowing the mechanism to run uncooled to minimize its oxidation. The second was changing the thickness of the aperture mechanism from a value of 4 to 2 cm. Hence, intercepting less of the solar power irradiated by the HFSS to achieve higher temperatures within the solar receiver. This could have been achieved by decreasing the amount of clearance between the blades in addition to the wall thicknesses. These two design modifications should make the variable aperture mechanism exhibit a closer behavior to that obtained by varying the fixed aperture. With that being mentioned, Fig. 19 shows the average temperature within the solar receiver w.r.t the aperture’s diameter for the current aperture mechanism in addition to two aperture mechanisms with the proposed modifications. Based on the results shown in Fig. 19, it can be seen that the average temperature within the solar receiver slightly increased for each of the proposed modifications. However, this increase in temperature is insignificant, where the average temperature increased by a maximum of 3.8 °C upon decreasing the emissivity at an aperture diameter of 4.9 cm and increased by a maximum of 7.2 °C upon decreasing the mechanism’s thickness at an aperture diameter of 8.75 cm. The average

Fig. 18. Steady state maximum temperature contour w.r.t. power level and variable aperture's diameter at flow rate of 7.5 LPM 408

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Fig. 19. Receiver’s average temperature w.r.t. aperture’s diameter for different aperture mechanism modifications

lost and not transferred to the solar receiver. Therefore, the behavior of obtaining peak temperatures by varying the aperture size was not observed by using the aperture mechanism even at simulated higher power levels. Additionally, the temperature non-uniformity within the receiver’s cavity increased as the variable aperture reduced in size. On the other hand, results showed that an average of 54% of the intercepted energy by the mechanism’s blades was captured by its flow channels, and so can be used to recover any surplus solar power in the process of regulating a solar receiver’s temperature for maximum process efficiencies. Although the variable aperture mechanism did not exhibit the same behavior as varying the fixed aperture size, it can be used to regulate the solar receiver’s temperature in applications requiring semi-constant operating conditions for maximized efficiencies. These include processes with efficiencies that peak at specific temperatures or that have temperature limitations, such as two-step splitting thermochemical cycles for CO2 and H2O (Zhu et al., 2016; Roeb et al., 2011) and the non-catalytic cracking of ethane (Lei et al., 2019). As an example and for the water splitting cycle presented in (Roeb et al., 2011), the temperature of the cycle’s regeneration step is required to be maintained at 1200 °C, but cannot exceed 1250 °C to avoid the deactivation of the catalyst used. Therefore, the presented variable aperture mechanism is a promising alternative to heliostat field or shutter control for regulating the temperature under intermittent DNI in these applications due to its wide range of temperature control and promising ability to capture and recover any surplus solar radiation. The power recovered by the aperture mechanism can be either used to run a separate process for electricity generation or can be integrated into the main process in the solar receiver, such as by preheating the feedstock to achieve higher fluid temperatures and/or production rates as demonstrated in (Rodat et al., 2011). Based on the results presented in (Rodat et al., 2011) for methane thermal decomposition, the hydrogen and carbon production rates can increase by approximately 6.2% by preheating the methane feedstock to a temperature of 200 °C. On the other hand, for processes that would require maximized temperatures, the aperture mechanism should be integrated more effectively into the solar receiver to allow for intercepted radiation to be transferred to the system more efficiently and exhibit the same trend as varying the fixed aperture size. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgments This research has been funded by University of Minnesota Duluth. The corresponding author appreciates the diligent effort and support of 409

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