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Energy Procedía 49 (2014) 344 - 353

SolarPACES 2013

Design space exploration of a 5 MWth small particle solar receiver

P. Fernándezab, F. Millera*, M. McDowellc and A. Huntd

a Mechanical Engineering Department, San Diego State University, San Diego, CA 92182-1323, United States b Escuela de Ingenierías Industriales, Universidad de Valladolid, 47011 Valladolid, Spain c Aerojet Rocketdyne, Canoga Park, CA 91309, United States d Thermaphase Energy, El Cerrito, CA 94530, United States

Abstract

We present a design space exploration of a 5 MWth Small Particle Solar Receiver for solar tower power plants. This new solar receiver, developed under the support of the U.S. Department of Energy's SunShot Program, aims to volumetrically absorb concentrated solar irradiation using an air-particle mixture to drive a gas turbine or a combined cycle at much higher temperature than the state-of-the-art molten salt receivers. Among other advantages, the thermodynamic efficiency of the power block and the overall efficiency of the plant would considerably increase with this technology. The design space consists of the wall angle of the receiver, the geometry of the window (necessary to allow the solar irradiation to enter into the receiver) and the radiative properties of the walls. The constraints are based on material limits, ensuring the mechanical integrity of the quartz window, and other technical issues; though some of them are imposed via a penalty method. The design space is explored through parametric studies and a multidisciplinary approach is adopted. The aluminum oxide walls, the 45° spherical-cap window and the 45° wallangle receiver are preferred due to their best compromise between thermal efficiency and wall temperature.

© 2013 F. Miller. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selectionandpeerreview bythescientificconference committeeofSolarPACES2013underresponsibilityofPSEAG. Final manuscript published as received without editorial corrections.

Keywords: Concentrated solar power; CSP; Design optimization; Numerical-stochastic modeling; Small particle solar receiver

1. Introduction

While current commercial CSP plants utilize molten salts as heat transfer fluid and Rankine steam cycles in the power block, there is a goal to develop higher efficiency plants based on gas turbine (Brayton cycle) or combined

* Corresponding author. Tel.: +1 619-594-5791; fax: +1 619-594-3599. E-mail address: fmiller@mail.sdsu.edu

1876-6102 © 2013 F. Miller. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http:// creativecommons. org/licenses/by-nc-nd/ 3.0/).

Selection and peer review by the scientific conference committee of SolarPACES 2013 under responsibility of PSE AG.

Final manuscript published as received without editorial corrections.

doi:10.1016/j.egypro.2014.03.037

cycle operation. The advantages of this technology are apparent. For example, it would lead to higher thermodynamic cycle efficiency (due to the much higher temperatures) [1], and it would require much less cooling water. To accomplish this goal, new solar receivers are needed. One such receiver, first proposed by Hunt in 1979 [2], is the Small Particle Solar Receiver or Small Particle Heat Exchange Receiver (SPHER). This concept is based on employing carbon nanoparticles (~200 nm) in an air stream to volumetrically absorb concentrated solar irradiation and produce outlet temperatures in excess of 1300 K. Moreover, it produces much less pressure drop and is probably less costly to construct than current tubular receivers. The high incident flux levels (much higher than any existent commercial technology) and the intimate mixing between gas and particles offer many possibilities for solar chemistry as well [3]. A schematic of the preliminary design of the 5 MWth Small Particle Heat Exchange Receiver previously used in [4] is shown in Figure 1. The mixture of air and carbon nanoparticles enters the rear of the receiver (blue arrows), travels towards the front absorbing concentrated solar irradiation (which penetrates through the ellipsoidal window displayed in gleaming light gray, as illustrated with yellow arrows), and finally exits the receiver going backwards through the central outlet tube (red arrows).

Our previous work was focused on developing a robust multi-physics model of the receiver and optimizing the iterative solution procedure for the governing integro-partial differential equations. While simple parametric studies of the operating conditions have been performed and published previously [4,5], no effort had been made to optimize the design of the receiver. This is of great importance in the highly competitive energy market: For example, increasing one percent the overall efficiency of a 100 MWe CSP plant would translate into a profit increase of the order of several M$/year. Hence, in order to maximize the efficiency, reduce capital and O&M costs, increase the lifespan of the different components and, in turn, reduce the Levelized Cost of Energy (LCOE), the design of the Small Particle Solar Receiver needs to be optimized from a multidisciplinary point of view.

Fig. 1. Schematic of the preliminary design of the 5 MWth Small Particle Heat Exchange Receiver used in previous publications [4] (yellow arrows: solar irradiation; blue arrows: air-particle mixture inlet; red arrows: air-particle mixture outlet.)

Nomenclature

Latin Letters:

h Specific enthalpy, J kg-1.

'Spectral intensity, W m-2 ^m-1 sr-1.

Blackbody spectral intensity, W m-2 ^m-1 sr-1.

Spectral intensity on the inner surface of the window, W m-2 ^m-1 sr-1. Effective thermal conductivity of the air-particle mixture, W m-1 K-1. n Outward unit normal vector to the boundary of the solar receiver.

p Thermodynamic pressure, Pa.

qrj Radiative heat flux vector, W m-2.

r Ratio between principal axes of the ellipsoidal window.

5 Direction vector.

s' In-scattering direction vector.

T Thermodynamic temperature, K.

Tw Wall temperature, K.

U[ Reynolds-averaged part of the velocity vector, m s-1. Greek Letters:

a^ Hemispherical, spectral absorptivity.

e'x Spectral, directional emissivity.

6 Zenith angle, rad.

Kx Spectral absorption coefficient, m-1.

p Density of the air-particle mixture, kg m-3.

p'x Spectral, bidirectional reflection function, sr-1.

aSjx Spectral scattering coefficient, m-1.

Tyj Reynolds-averaged viscous stress tensor, Pa.

<t>x Spectral scattering phase function, sr-1.

ft Solid angle, sr.

2. Numerical-stochastic model

A three-dimensional fluid flow and radiative heat transfer model developed by Fernández [4,6] is employed to simulate the 5 MWth Small Particle Solar Receiver. Based on a coupled CFD solver and in-house Monte Carlo Ray Tracing (MCRT) method, it is possible to exactly model the concentrated solar irradiation that reaches the window^ and simulate any axisymmetric geometry for the solar receiver. Moreover, this software can accommodate flat, ellipsoidal and spherical cap windows. On account of their small size (~200 nm), the carbon nanoparticles are in thermal equilibrium with their environment [7] and move as part of the air flow. Therefore, the air-particle mixture is treated as a single phase for modeling purposes. The CFD solver and the MCRT code have been coupled together via User-Defined Functions (UDFs) and iterate alternatively until convergence. The adaptive solution procedure was optimized to prevent numerical oscillations and reduce the CPU time by two orders of magnitude compared to the two-dimensional version of the code. Particle oxidation is not included yet, but will be included in future publications. Physically, this corresponds with a nitrogen-driven receiver, which is an alternative for the closed-loop operation of the receiver. While the numerical model is briefly outlined in the following paragraphs, the interested reader is referred to [6] for a much more detailed description of our software.

2.1. CFD model:

The steady-state Reynolds-averaged Navier Stokes and energy equations (Eq. 1-3), together with the two equations of the SST K-ro turbulence model and the corresponding constitutive relations (the latter two not shown for simplicity), are solved numerically by the CFD package ANSYS Fluent. Note that the pressure work, kinetic energy, viscous dissipation and chemical reaction (oxidation) terms are negligible compared to the divergence of the radiative heat flux and are not included in the energy equation (Eq. 3).

^ The Monte Carlo method is coupled with a heliostat field model developed by Mecit [8], i.e. the spatial, directional and wavelength dependence of the concentrated solar irradiation at different times and days is exactly modeled by our software.

dpUi axi (1)

d dp dTji dx¡ Pu,ui dx¡ dx¡ '¿J ~PUW =° (2)

dx¡ p dx¡ dT dq] (3)

2.2. Radiative heat transfer model:

An in-house Monte Carlo Ray Tracing (MCRT) method [4,6] is employed for the radiative heat transfer due to the highly directional intensity distribution from the heliostat field [8,9] and the strong spectral dependence of the radiative properties of the particles [10], which cannot be easily modeled by conventional numerical techniques such as the Spherical Harmonics or the Discrete Ordinates methods. Equation 4 gives the integro-differential form of the quasi-steady Radiative Transfer Equation (RTE) solved statistically by the MCRT method, while Equations 5 show the boundary conditions used for the solution. Note also that Turbulence-Radiation Interactions (TRI) have been neglected since the optically thin fluctuation approximation (OTFA) applies.

s-^ks =KxiM - Kz + er^ ix s + ^ ix s' «D^ s,s' da' ( )

™ in

iA s = sxibix(Tw) + 2np% s',s ix s' cose'da' for sn> 0 and Vs'-n< 0 (5a)

1*3= W « for s n> 0 (5.b)

The absorption and scattering properties of the carbon particles are calculated through the Mie solution to Maxwell's equations. The gas phase is modeled as radiatively non-participating due to the negligible amount of CO2 generated in the receiver (&co-, ^ 0 vs. apart « 0.99 for the solar spectrum and the axial path length.)

3. Design optimization methodology

In PDE-constrained optimization problems, such as the design optimization of the 5 MWth Small Particle Solar Receiver, the objective functional depends on the simulation results (the velocity and temperature fields), which in turn depend on the design variables through the governing equations. Thus, the difficulty to use conventional gradient descent methods lies in computing the sensitivities of the flow field with respect to the design variables, which is computationally very expensive. Other strategies, such as adjoint methods^ or computing the sensitivities via finite differences are also either much beyond the scope of the project or would require an unaffordable CPU time. Therefore, we will explore the design space in a finite number of points (rather than finding the actual solution using descent methods), which leads to a NP-hard discrete optimization problem. Hence, the design space should be cleverly defined to avoid introducing irrelevant or insensitive variables. An informal formulation of the problem is presented below.

Design space: The design space consists of the wall angle of the receiver, the geometry of the window and the radiative properties of the walls.

Constraints: The constraints are based on material limits (for example, the maximum operating temperature of aluminium oxide is around 1560°C), ensuring the mechanical integrity of the quartz window, and other technical issues. Some of these constraints are imposed via a penalty method as they depend on the simulation results.

Objective function: A wide variety of objective functions can be defined, such as the receiver efficiency at a particular time, the thermal energy collected by the receiver throughout the day, or even throughout the year. For a more multidisciplinary approach, the generation cost of the electricity could be minimized, for which the cost of the

^ The adjoint operator of the RTE is such that L* = L X,— il . Hence, the in-house Monte Carlo Ray Tracing software [4,6] could, with

small modifications, be employed to solve the adjoint thermal radiation problem.

Table 1. Design parameters and operating conditions of the baseline design of the parametric study.

Design Parameter Value Design Parameter Value

Receiver: Walls:

- Shape Cylindrical (0° wall angle) - Radiative properties Aluminum oxide (Al2O3)

- Length 3 m - Thermal resistance 2 m2-K/W

- Front diameter 2 m (including the insulation)

- Tilt angle -26.5° Mass flow rate 4 kg/s

Window: - Material Fused quartz (HOQ-310 [8]) Inlet temperature 700 K

- Shape Spherical cap (45° cap angle) Solar irradiation:

- Diameter 1.7 m - Time 12.00 PM

- Thickness 2.54 cm - Day Spring equinox

- Temperature 800°C - 850°C - Solar input 4.25 MWth

Outlet tube: Operating pressure 5 bar

- Length 2.1 m Inlet particle mass loading 0.5 g/m3

- Diameter 0.6 m 200 nm

- Thickness 1 cm Particle diameter

different components and their expected life span need to be known. In this paper, we will employ the receiver efficiency at 12:00 PM on the Spring equinox as the objective function since the cost of the components and their expected lifespan cannot be accurately estimated yet. Objective functions that consider the weighted-average efficiency at different times and days would be more accurate to elucidate the best design, but would yield a prohibitive CPU time.

Optimization technique: The design space is explored via parametric studies. This way, it will be possible to identify important and sensitive variables, determine approximate design variable ranges to meet material limits, and obtain a first estimate of the optimum design and of the maximum efficiency that the 5 MWth Small Particle Solar Receiver can achieve. The design parameters and the operating conditions of the baseline design are based on preliminary results [6] and are collected in Table 1.

4. Numerical results

4.1. Wall properties optimization

The infinite degrees of freedom necessary to describe the spectral dependence of the radiative properties of the walls can be reduced essentially to four types of properties, denoted by PI, P2, P3 and P4:

• P1: High absorptivity in the solar spectrum and low emissivity at longer, infrared wavelengths (e.g. selective coatings of solar collectors.)

• P2: High absorptivity and emissivity in the whole spectrum (e.g. a blackbody).

• P3: Low absorptivity in the solar spectrum and high emissivity at infrared wavelengths (e.g. aluminum oxide).

• P4: Low absorptivity and emissivity in the whole spectrum.

An approximation of how the spectral absorptivity of these four types of radiative properties looks like is shown in Fig. 2. The directional behavior is assumed diffuse in all cases.

Table 2 shows a summary of the simulation results with the radiative properties P2, P3 and P4. The properties P1 are not simulated as they would lead to unacceptable wall temperatures over the blackbody case. From Table 2 we can infer that the radiative properties P3 (aluminum oxide) show the best compromise between wall temperature and thermal efficiency. Moreover, aluminum oxide walls would also serve as thermal insulation. It should be noted that the thermal efficiency is defined as the useful thermal output divided by the solar power that goes through the window and enters the receiver. Hence, the irradiation losses due to absorption and reflection in the window are not included in the definition of thermal efficiency, but rather they are accounted for by the so-called optical efficiency of the receiver (i.e. the transmissivity of the window.) It is important to note also that the low thermal efficiency and the high temperature of the lateral wall are mainly due to the reduced diameter and simple, right-cylindrical geometry of the baseline design. Optimized geometries will dramatically reduce the wall temperature and increase the thermal efficiency, as will be discussed later.

O-1-1-1-1-1

O 2 4 6 S 10

Wavelength, i. (|im)

Fig. 2. Schematic representation of the spectral absorptivity of the four types of surface radiative properties considered. Note that, under local thermodynamic equilibrium, the spectral emissivity equals the spectral absorptivity in diffuse surfaces.

Table 2. Summary of simulation results with the different types of surface radiative properties considered.

P2 P3 P4

Radiative properties employed to simulate this case «1 = 1 AI2O3 «1 = 0.1

Thermal efficiency of the receiver 77.46% 79.63% 80.46%

Outlet temperature 1414.5 K 1433.3 K 1440.4 K

Maximum temperature:

- Walls ~1725 K ~1600 K ~1750K

- Outlet tube ~1600 K ~1450 K ~1500K

Pressure drop 163.6 Pa 165.0 Pa 165.5 Pa

4.2. Window geometry optimization

A curved window is required to withstand the mechanical loading due to the pressurized environment inside the receiver (5 bar). The material selected for the window is fused quartz, or fused silica, due to its selective optical behavior (high transmissivity in the solar spectrum and low transmissivity at infrared wavelengths) and very high compressive strength (around 1100 MPa). Hence, a fused quartz window will perform well as long as only small tensile stresses are allowed to develop (thereby the curved geometry.) Moreover, its extremely low coefficient of thermal expansion accounts for its remarkable ability to undergo large, rapid temperature changes, such as during cloudy transient periods, without cracking. In particular, HOQ-310 is employed in this analysis.

Regarding its shape, spherical-cap and ellipsoidal windows are considered and will be compared here (Fig. 3). The latter is simply a prolate spheroid with ratio between principal axes r — 2. As for mechanical considerations, the ellipsoidal geometry would eliminate tensile stresses and the window would be entirely in compression [11]. Moreover, it may be preferable from a seal design perspective. Spherical windows, however, are much easier to fabricate and polish than ellipsoidal shapes as they are a portion of a sphere. Previous studies conducted by Mecit [8] showed that the optical efficiency of spherical-cap windows has only one local and global minimum at 45° cap angle and then increases in both directions (towards 0° and towards 90°). The optical efficiency of the ellipsoidal window equals the one of a 70° cap angle window. These results only account for the transmittance of concentrated solar irradiation from the heliostat field to the inside of the receiver; while the transmission of radiation from the inside to the outside of the receiver constitutes the main loss mechanism [4] and needs to be considered as well.

Thus, the optimum window geometry would be a compromise between both effects; not to mention that the efficiency is only one of the many aspects to be considered in this multidisciplinary decision-making process.

The ellipsoidal window (r — 2) and the 45° spherical-cap window have been compared in the preliminary design optimization presented in this paper. A summary of the simulation results with both window geometries is shown in Table 3. The optical efficiency is, as expected [8], greater with the ellipsoidal window, but the overall receiver efficiency (optical + thermal) is higher with the 45° spherical-cap geometry. This result is mainly because the ellipsoidal window penetrates deeper into the solar receiver than the 45° spherical-cap window and the radiative losses are thereby higher. The maximum wall and outlet tube temperature is independent of the window geometry. Regarding the pressure drop, it is kept constant as the position of the outlet tube was chosen in both cases to maintain a distance to the window of 0.5 m. Finally, from Table 3, the total radiation absorbed by the ellipsoidal window is 8% greater than with the 45° spherical-cap window. However, the absorption per unit area is smaller with the ellipsoidal window due to its higher surface.

45° spherical-cap window 1.7 m

Ellipsoidal window

Fig. 3. 45° spherical-cap window (top) and ellipsoidal window (bottom).

The optimum window geometry should be a compromise between efficiency, mechanical behavior, manufacturing issues and economic aspects. Hence, the 45° spherical-cap window is likely preferred over the ellipsoidal window as it provides higher efficiency, and is less expensive and easier to manufacture. Further stress [12] and thermal [13] analyses of the two geometries are currently under study.

Table 3. Summary of simulation results with the ellipsoidal and the 45° spherical-cap window.

45° Spherical-Cap Window

Ellipsoidal Window

Efficiency of the receiver:

- Optical (transmissivity of the window)

- Thermal (useful power vs. solar power that enters the receiver)

- Overall (optical + thermal)

Outlet temperature

Maximum temperature:

- Walls

- Outlet tube

Radiation absorbed by the window:

- From the heliostat field

- From the solar receiver

92.14% 79.63%

73.37% 1433.3 K

~1600 K ~1450 K

274.4 kW 33.0 kW 241.4 kW

93.08% 76.03%

70.77% 1407.1 K

~1600K ~1450K

288.0 kW 33.2 kW 254.8 kW

Pressure drop

165.0 Pa

165.6 Pa

Fig. 4. Temperature field (K) in horizontal section on the left and vertical section on the right. The first row corresponds with the 0° wall angle and the second row with the 45° wall angle. The color scale varies between both designs. Note also that the second design is at a smaller scale than the first one for an easier visualization of the temperature field. In reality, both designs are the same length (3 m).

4.3. Receiver geometry optimization

To simplify the analysis, only the angle between the front wall and the initial part of the lateral wall -or, equivalently, between the inlet surface and the end of the lateral wall- is varied (see Fig. 4 for greater clarity.) The length and the front diameter of the receiver are kept constant (3 m and 2 m, respectively) in all the designs. This way, the continuous function to describe the generatrix of the solar receiver (infinite degrees of freedom) is reduced to only one design variable (one degree of freedom). In particular, the two geometries illustrated in Fig. 4 were simulated, which correspond with the cases of 0° and 45° wall angle. The choice of these designs is based on preliminary studies of the distribution of solar irradiation on the walls for different receiver geometries [6].

The main simulation outputs for the two geometries analyzed are collected in Table 4, while Fig. 4 shows the temperature field inside the receiver. The 45° wall-angle design maximizes the thermal efficiency and minimizes the temperature of the walls, which is now acceptable unlike in previous sections. This result is expected since the optical thickness provided by this geometry in different directions approximates the directional distribution of the radiation intensity coming from the heliostat field. The 45° wall-angle receiver also considerably reduces the radiation absorbed by the window, mainly due to the lower temperature level (Fig. 4) and view factor from the walls to the window. This is important to keep the window cool and, in turn, ensure the integrity of the quartz, reduce the thermal losses and maybe allow to use an anti-reflective coating. The pressure drop is limited to 173.3 Pa, which is well below tubular receivers and does not diminish the thermodynamic efficiency of the gas turbine due to the additional pressure drop between the compressor and the turbine caused by the receiver. Note also that the outlet tube temperature is not a concern as it can be easily reduced just by distancing it from the window.

The extremely high temperature in some fluid regions of the receiver is due to the lack of particle oxidation in the current model. In reality, these high temperature zones cannot exist as particles would immediately oxidize and no absorption would occur. This, in turn, would increase the thermal efficiency of the receiver since the radiative

losses due to emission from the air-particle mixture, which is the main losses mechanism in all the designs analyzed in this paper, would dramatically diminish. Actually, the outlet temperature of the 5 MWth Small Particle Solar Receiver will probably be limited by the temperature at which the particles fully oxidize; although the efficiency could be raised by increasing the mass flow rate [4,6] even if premature oxidation occurred. Note, however, that this strategy would reduce the solar share since the natural gas consumption would be increased due to both higher carbon particle requirements (to maintain the mass loading) and a higher fuel demand in the combustor (to achieve the turbine inlet temperature desired.) We are currently adding oxidation to the model to quantify this effect and the results will be included in future publications.

Table 4. Summary of simulation results with the two geometries of the solar receiver considered here.

0° Wall Angle 45° Wall Angle

Thermal efficiency 79.63% 85.47%

Outlet temperature 1433.3 K 1485.8 K

Maximum temperature:

- Walls ~1600 K ~ 1325 K

- Outlet tube ~1450 K ~1500 K

Radiation absorbed by the window: 274.4 kW 215.4 kW

- From the heliostat field 33.0 kW 33.0 kW

- From the solar receiver 241.4 kW 182.4 kW

Pressure drop 165.0 Pa 173.3 Pa

The 45° geometry is suggested for the 5 MWth Small Particle Solar Receiver to be constructed and tested at the National Solar Thermal Test Facility (Albuquerque, USA). This geometry has, however, greater cross sectional area than the cylindrical design, which would increase the residence time of the particles, could lead to premature oxidation and could limit the outlet temperature.

It is important to note that the window temperature is not calculated by the model; instead, it is imposed as a boundary condition of 850°C if r < 0.3 m or 800°C if r > 0.3 m. For this window temperature, the radiative source term in the window turns out to be positive, i.e. the temperature is actually greater than 800-850°C. This implies that in reality more radiation will be emitted by the window, more useful power will be collected by the receiver and the thermal efficiency will be higher. Therefore, the values of the thermal efficiency presented in this paper are only to be understood as relative values between different designs, but not as absolute values. For example, it is expected that the actual thermal efficiency of the 45° wall-angle design is around 90% instead of the predicted 85%. It should also be noted that the spectral absorption coefficient of H0Q-310 used in this paper is greater than the actual one (new and more accurate data are available); which implies that the overall efficiency of the receiver (thermal + optical) will be further increased. This way, the overall efficiency of the Small Particle Solar Receiver would be above the 83% that is expected to be achieved with a 650°C molten salt tubular receiver [14], even though the former produces much higher outlet temperatures (and also much less pressure drop).

5. Conclusions

A multidisciplinary design optimization of a 5 MWth Small Particle Solar Receiver for solar tower power plants was presented. This new solar receiver, currently being developed under the U.S. DOE SunShot Program, aims to heat air to temperatures in excess of 1300 K in order to drive a gas turbine or a combined cycle. The design space was explored through parametric studies and consisted of the wall angle of the receiver, the geometry of the window and the radiative properties of the walls. The aluminum oxide (Al2O3) walls, which would also serve as thermal insulation, showed the best compromise between wall temperature and thermal efficiency compared to the other three main types of radiative properties that can be employed. As for the window geometry, the receiver efficiency is higher with a 45° spherical-cap window than with an ellipsoidal window; while the wall temperature and pressure drop are virtually independent of its shape. In addition, the 45° spherical-cap window is less expensive and easier to

manufacture. Finally, the 45° wall-angle receiver was the best geometry analyzed as it maximizes the thermal efficiency and minimizes the wall temperature.

Although interactions between design variables are not properly captured by parametric studies, it is thought that they are small in our design space and the conclusions inferred for each variable are of general validity. At any rate, using Al2Ü3 walls, the 45° wall-angle receiver and the 45° spherical-cap window, the wall temperature can be kept below 1350 K and the thermal efficiency above 85%. It is important to note that the thermal efficiency is expected to be higher (around 90%) when the window temperature is calculated, instead of being imposed as a boundary condition of 800-850°C as in the current model. This way, the overall efficiency of the Small Particle Solar Receiver (thermal + optical) would be above the 83% that could be achieved with a 650°C molten salt tubular receiver [14], even though the former produces much higher outlet temperatures (and also much less pressure drop). Possible future work to improve the Small Particle Solar Receiver include the use a high-temperature anti-reflective coating on the window, a further design space exploration (more points and new degrees of freedom), and the use of the cocurrent flow direction (fluid flow vs. solar irradiation). In short, the small particle receiver, in combination with a Brayton cycle, a supercritical Rankine cycle or a combined cycle, is expected to increase the overall efficiency of CSP plants in comparison with the state-of-the-art molten salt tubular receivers and subcritical Rankine cycles; mainly due to the considerably higher thermodynamic efficiency that can be achieved with the high outlet temperatures of this proposed technology [1].

Acknowledgements

The authors gratefully acknowledge the U.S. Department of Energy for providing funding for this research through the SunShot Initiative under the Award #DE-EE0005800. We would also like to thank Aerojet Rocketdyne, Solar Turbines and Thermaphase Energy for their collaboration in the project.

References

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[2] Hunt, A. "A New Solar Thermal Receiver Utilizing Small Particles", Proceedings of the International Solar Energy Society Conference, Atlanta, GA, 1362-1366, 1979.

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[4] Fernández, P., Miller, F. and Crocker, A. "Three-Dimensional Fluid Dynamics and Radiative Heat Transfer Modeling of a Small Particle Solar Receiver", ASME 2013 7th International Conference on Energy Sustainability, Minneapolis, MN, USA, July 14th-19th, 2013.

[5] Crocker, A. and Miller, F. "Coupled Fluid Flow and Radiation Modeling of a Cylindrical Small Particle Solar Receiver", ASME 2012 6th International Conference on Energy Sustainability, San Diego, CA, July 23th-26th, 2012.

[6] Fernández, P. "Numerical-Stochastic Modeling, Simulation and Design Optimization of Small Particle Solar Receivers for Concentrated Solar Power Plants", Proyecto Fin de Carrera, University of Valladolid, Spain, 2013 (research conducted while visiting SDSU Combustion and Solar Energy Laboratory.)

[7] Yuen, W. W., Miller, F. J. and Hunt, A. J. "Heat Transfer Characteristics of a Gas-Particle Mixture under Direct Radiant Heating", International Communications in Heat and Mass Transfer, Vol. 13, pp. 145-154, 1986.

[8] Mecit, A. M. "Optical Analysis and Modeling of a Window of the Small Particle Solar Receiver using the Monte Carlo Ray Trace Method", Master's Thesis, San Diego State University, Department of Mechanical Engineering, 2013.

[9] Mecit, A. M. and Miller, F. "Optical Analysis of a Window for Solar Receivers using the Monte Carlo Ray Trace method", ASME 2013 7th International Conference on Energy Sustainability, Minneapolis, MN, July 14th-19th, 2013.

[10] Ruther, S. "Radiation Heat Transfer Simulation of a Small Particle Solar Receiver using the Monte Carlo Method", Master's Thesis, San Diego State University, Department of Mechanical Engineering, 2010.

[11] Mande, O. K. "Window and Seal Design for a Small Particle Solar Receiver", Master's Thesis, San Diego State University, Department of Mechanical Engineering, 2011.

[12] Saung, E. "Dome Window and Mount Design for a 5 MWth Solar Receiver", SolarPACES Conference, Las Vegas, NV, USA, September 17-20, 2013.

[13] Mecit, A. M., Miller, F. and Whitmore, A. "Optical analysis and thermal modeling of a window for a small particle solar receiver", 19th SolarPACES Conference, Las Vegas, NV, USA, September 17-20, 2013.

[14] Kolb, G. J. "An Evaluation of Possible Next-Generation High-Temperature Molten-Salt Power Towers", Sandia National Laboratories Technical Report, SAND2011-9320, 2011.