Optimization of flat tubular molten salt receivers

Optimization of flat tubular molten salt receivers Meige Zeng, Jon Pye Researc Scool of Engineering, Australian National University, Canberra, Australia Abstract E-mail: meige.zeng@anu.edu.au, jon.pye@anu.edu.au Te receiver is an essential part of a concentrating solar power (CSP) system, and its performance is strongly constrained by material limits wic in turn limit te allowable flux on te receiver. Tis paper seeks to understand te benefits wic arise at te receiver as a result of adjusting te flux profile, comparing a simple Gaussian spot and wit a linear ramp pattern, wile respecting an upper limit on te allowable film temperature of te molten salt working fluid. Te ramp profile performed better, matcing material limits more closely over te receiver surface, ence permitting a smaller receiver wit lower losses. 1. Background and literature review Solar One and Solar Two [1] - [4] were te two pioneering central tower CSP systems, and operated in California between 1988 and 1999 respectively. Solar Two was a major re-vamp of Solar One wit te addition of a molten salt receiver. Solar Tres (ultimately renamed Gemasolar ) in Spain was te first commercial solar power plant built using tis molten salt receiver tecnology, about tree times te size of Solar Two, and commenced operation in April 2011 [5]. Nomenclature convection coefficient, J/kg T temperature, C Q eat rate, MW X exergy rate, MW W energy rate, MW α absorptivity, solar-weigted ε emissivity σ Stefan-Boltzmann constant n tubes No. of tubes per bank n banks No. of tube banks in te receiver n No. of flow segments G direct normal irradiance, W/m 2 C concentration ratio L lengt (along receiver tube), m W widt, m Nu Nusselt number k termal conductivity, W/(m K) Pr Prandtl number Re Reynolds number ρ density, kg/m 3 f friction factor η efficiency, % V flow velocity (bulk) Δp pressure drop troug receiver m mass flow rate, kg/s Subscripts spil spillage sun total energy inc incident refl reflected abs absorbed rad radiation due to termal emission ext external wall of receiver tube int internal wall of receiver tube slice for/in one flow segment only conv convective eat transfer lost lost troug leaving te system dest destroyed witin te system i Internal eat transfer to fluid I first law II second law t/termal termal rec receiver conditions pu pump conditions PR pump + receiver

Possible approaces to improve te efficiency of te receivers are reducing te surface temperature by varying te flux distribution, adopting te multi-diameter receivers and te multi-pass receivers. Boerema et al found tat suc tecniques could improve energy efficiency by 1-2% [6]. Corrosion and te termal stress are te two most critical constraints in design of molten salt receivers, and were used to determine allowable flux density by Sáncez-González et al [7]. Tis allowable flux density ten leads to te need for accurate aiming strategies for te eliostat field. In te optimization of concentrating solar systems, te second law of termodynamics plays a significant role as it allows us to quantify te amount of work tat can ultimately be extracted from a eat source (exergy), and deals wit eat-transfer-related irreversibilities tat act to reduce tis amount [8]. Exergy analysis as proven to be a valuable tool to investigate possible configurations of te optimized solar termal receivers, since it is able to present te types, causes and locations of termodynamic losses more clearly wen compared to energy analysis [9]. A review of exergy analysis on various types of solar collectors and applications of solar termal systems was presented by Kalogirou et al [10], empasising its importance in te design of sustainable energy systems. Te review includes exergetic analysis for various types of solar collectors including flat-plate collectors, ybrid PV/termal systems, parabolic troug and dis collectors as well as oter applications suc as pase cange materials. 2. Introduction An exergy analysis of a Gemasolar-style convex tubular receiver, as sown in Figure 1, wit different eat transfer fluids (HTF) was studied by Pye et al [11]. It was sown tat te performance of molten salt (wit properties as per [12]) is igly competitive in its standard temperature range, but oter fluids suc as liquid sodium perform better if te temperature and concentration ratio can be increased. Tat study, owever, considered only te case of uniform flux. Tis paper, as a furter development, examines ow non-uniform flux impacts te termal performance. Te working temperatures of te molten salt are controlled witin te range from 290 to 565. Te lower limit is to avoid freezing, and te upper limit is to avoid cemical degradation of te salt. Te present model is limited to flat/convex receivers. Te flow pat is separated into n sequential segments, wit banks of parallel tubes passing up and down te receiver surface, connected togeter in series, wit parallel tubes in eac bank. Te value of is calculated geometrically,. (1) Figure 1. Billboard receiver (Source: Univ Carlos III), and receiver pipe flow model numbering and layout.

3. Metodology Te net energy flow into a receiver from concentrated solar radiation will be balanced by energy outflows from te flow of HTF or oter energy conversion process, plus a range of energy losses, due to unwanted reflection, radiative emission, convective or conductive processes [13]. Te total energy loss is te sum of tese four contributions,. (2) First-law efficiency of termodynamics indicates ow well an energy transfer process is accomplised and provides a sound basis for studying te various forms of energy. Te overall first-law efficiency of te receiver as well as te receiver termal efficiency are [ ( ) ( )], and (3),were. (4) Te exergy losses and exergy destruction (internal irreversibilities) in te receiver can be accounted as follows: Te overall second-law efficiency of te receiver is te ratio of te net increase in working fluid flow exergy to te exergy of te solar radiation reflected by te eliostat field, (5) (6). (7) More detailed equations for energy and exergy balances are in te previous paper [11]. 4. Simulation and parametric studies 4.1. Gaussian flux distribution Te distribution of irradiance on te receiver, assumed ere to be flat, as been firstly approximated by a bivariate Gaussian distribution. A Gaussian spot is pysically based and arises naturally wen effects due to te sun-sape, eliostat slope errors and tracking errors are combined wit a single-point aiming strategy. Te Gaussian spot is represented by ( ) ( ( ) ), ( 8 ) were ( ) ( ) ( 9 ) and x and y are orizontal and vertical coordinates on te receiver of widt W and eigt L. For a given amount of (ere, 20 MW), te flux density map was set by te spot size (σ) and te geometry of te receiver. Spot size is affected by mirror quality, eliostat sape and te circumsolar ratio. Terefore, te parametric studies based on tese factors ave been presented in te following sub-sections. Firstly, te effect of varied spot size on te termodynamic efficiencies was studied. Te Gaussian distribution was incorporated into te model as described in Section 2. Te fraction

First-Law Efficiency(%) First Law Efficiency(%) Flux Fraction of solar flux incident on square targets of varying size, for varying, is sown in Figure 2. Smaller spots allow te solar flux to be collected wit a smaller aperture, as expected. 100% 80% 60% 40% 20% 0% 0 20 40 60 80 100 120 140 160 Aperture area (m 2 ) σ (m) 0.5 0.8 1 1.3 1.6 1.8 Figure 2. Flux distribution fraction vs. Aperture area of te receiver for different spot size, σ. Aperture is a square. Small spot area is capable of performing ig first-law efficiency due to te ig peak flux density and low effect of spillage, as sown in Figure 3. Te optimal spillage fraction ere is ~5 8%, sowing te strong trade-off between small area wit ig spillage versus a large area wit ig termal losses. 100% 80% 60% 40% 20% 0% 0 50 100 150 200 Aperture area of receiver(m 2 ) σ in (m) 0.5 0.8 1 1.3 1.6 1.8 0% 0% 10% 20% 30% Figure 3. Te effect of variable aperture areas and te spillage on te first law efficiencies Next, we studied te effect of te Gaussian spot size and te receiver aperture area on te peak film temperature (Table 1). For small spots, very large peak film temperatures are seen, rendering te results above infeasible. González et al., (2016) [15] indicates tat te igest allowable fluid temperature for molten salt sould be 630. Terefore, te best-case and values were selected to be to 1.9 m and 49 m 2 respectively for te remaining analysis. Table 1. Peak film temperature wit spot size and, (m 2 ), (m) (m 2 ) (m) ( ) ( ) 0.5 6.25-64 1326-2240 0.8 16-81 960-1460 1.0 4-62 796-1058 1.3 4-64 744-825 1.6 16-81 648-740 1.9 36-64 620-643 2.1 64-81 619-636 2.3 25-64 608-610 Detailed exergy and energy accounting for molten salt receiver wit variable σ and uniform (49 m 2 ) are presented in Figure 4 and Table 2. Te dominant exergy destruction occurs in te absorption step, due to te large step-down in temperature between te sun and te external walls of te receiver (from 5800 K to ~903.15 K ( i.e. 630 )), decreasing a little for te case of very small spots. Spot size σ as a strong effect on spillage, as well as internal convection and external radiation. External radiation is sensitive to small areas of ig external temperature, due to te effect. Internal convection losses arise from te large temperature difference between HTF and te inner wall (Figure 5). Te trade-offs between spillage, external termal radiation and internal convection lead to an optimal spot size wit maximised total net exergy to te working fluid. 100% 80% 60% 40% 20% Spillage(%) σ in (m) 0.5 0.8 1 1.3 1.6 1.8

σ = 2.3 m σ = 1.5 m σ = 0.5 m 0 2 4 6 8 10 12 14 16 18 20 X_net Figure 4. Exergy accounting wen te aperture area of te receiver and te total energy from te sun were uniform to 49 m 2 and 20 MW, respectively. Table 2. Effect of Gaussian spot size on receiver performance. 20 MW 5800 K 1 bar 20 W/m K 30 W/m 2 K 290 ºC 550 ºC 1000 W/m 2 49 m 2 7 cm 1 mm 20 m MW MW MW MW MW % % % 0.5 20 0.6484 1.121 7.90 10.33 51.6 51.6 31.9 2090.11 1 19.95 0.6478 1.133 3.20 15.00 75.1 75.0 46.4 985.77 1.5 19.23 0.6235 1.132 2.60 14.88 77.4 74.4 47.8 702.66 1.9 17.48 0.5668 1.127 2.44 13.35 76.4 66.8 47.2 628.00 2.3 15.22 0.4934 1.120 2.35 11.26 74.0 56.3 45.7 597.78 Te receiver temperature profiles (Figure 5) and te corresponding flux distributions (Figure 6) for tese cases sow tat, for tis particular flow configuration, te maximum inner wall temperature ( ) was 628, close to te allowable film temperature for molten salt, is reaced wen te spot size σ is set to 1.9 m. Te peak flux density in tat case is 0.87 MW/m 2. A larger value of σ, for example 2.3 m, results in excessive spillage. Figure 5 Receiver temperature profiles, for a range of spot sizes σ. Extracted detail is sown at top-rigt. Figure 6. Flux distributions on a square receiver (49m 2 ). Left: σ = 0.5 m; rigt: σ = 1.9 m.

4.2. Linear ramp flux distribution In te above study we found tat wit Gaussian distribution, te maximum allowable film temperature is reaced in only a small localised region, limiting te performance of te wole receiver. Terefore, it was proposed to examine weter a flux profile tailored to te rising fluid temperature could be sown to improve receiver performance. A simple linear ramp distribution in flux concentration was considered, wit flux reducing from te left (inlet) to te rigt of te receiver surface (outlet), wit te x-wise rate of reduction of flux (slope) being te variable parameter. Tis very simplified profile is similar to tose arising from more detailed studies [7]. A sinusoidal curve is applied at te edges of tis idealised flux profile, to mimic modest spillage losses. We adjusted te size of te aperture and te Concentration Ratio (CR) in order to matc te peak film temperature constraint. Te total flux and spillage are constant at 20 MW, 12% respectively. Slope ere is defined as te rate of cange of aperture irradiance ( ) in te negative x- wise direction across te receiver. For te flat portion of distribution, exclusive te sinusoid tails, ( ) (10) (a) Figure 7. Linear ramp flux profiles: (a) slope=+60 kw/m²/m, (b) slope=-60 kw/m²/m. Te possible values of slope are from 125 to 125 kw/m 2 /m wen te lowest flux from tat flat portion is set to be zero at te edge of te receiver. (b) slope = 120 slope =90 slope =60 slope =30 slope =0 slope =-30 slope =-60 Unit: kw/m 2 /m 0 2 4 6 8 10 12 14 16 18 20 X_net Figure 8 Exergy accounting wit variable slope (in kw/m²/m). were fixed at 630 by varying te size of aperture and te CR for te ramp flux profile study sow tat, for fixed aperture area, te negative slope (iger flux at outlet) cases perform worse tan positive slope cases (iger flux at inlet). Te negative slope cases (slope from -60 to -125 kw/m 2 /m) lead to te maximum film temperature constraint being broken. Wen positive slope cases are used, and te aperture area is adjusted until te peak film temperature equals maximum allowable value, smaller receivers wit iger efficiency result. Even toug te external surface temperatures are iger, te reduced area gives overall lower losses. Te best case found was wit a slope of

90 kw/m 2 /m, since it ad te smallest aperture of 13.9 m 2 wic resulted in lowest exergy destroyed in absorption step. 4.3. Effect of tube diameter We used Gaussian distribution as an example to study te effects of varying oter major parameters on te termodynamic efficiencies since te trends for tese efficiencies are te same in te cases of Gaussian distribution and Linear distribution. Te optimal spot size σ (1.9 m) was determined in Section 4.1. To start wit te tube inside diameter, decreasing tube diameter lowers te inner and outer wall temperatures, since a smaller tube gives iger fluid velocity, resulting in increased Reynolds number, and ence increased Nusselt number and improved internal eat transfer coefficient (Figure 10). Te result is reduced exergy destruction in internal convection and reduced external losses. for a Gaussian flux profile (Figure 9, Table 3). d_i = 15 cm d_i = 10 cm d_i = 7 cm d_i = 3 cm 0 5 10 15 20 Figure 9. Exergy accounting wit variable X_net (Gaussian Flux distribution) Tere is no optimal tube diameter identified by te model at tis stage, since te results sows tat te receiver efficiency keeps increasing as tube diameter decreases. Figure 10. Te trend of internal eat transfer coefficient ( ) and Nusselt Number. Table 3. Gaussian flux distribution wit variable. sig 20 MW 5800 K 1 bar 20 W/m K 30 W/m 2 K 290 ºC 550 ºC 1000 W/m 2 49 m 2 1 mm 1.9 m 20 cm MW MW MW MW MW % % % 3 17.48 0.57 1.040 1.969 13.91 79.5 69.5 49.1 566.6 7 17.48 0.57 1.127 2.437 13.35 76.4 66.8 47.2 626.37 10 17.48 0.57 1.192 2.855 12.87 73.6 64.3 45.5 685.93 15 17.48 0.57 1.297 3.677 11.94 68.3 59.7 42.1 771.56 Te Prandtl number Pr, a material parameter, is te ratio of diffusivities of momentum and temperature. If te is too small, Pr number would be out of its lower bound wic is 0.6 for for te Dittus-Boelter internal convection correlation used ere. Tis limits te smallest to

be 3 cm is tis case study. In addition, pressure drop ( ) is anoter restricted factor for te. 4.4. Effect of tube wall tickness Reducing te tube wall tickness as te expected effect of improving receiver performance by reducing te termal resistance of te wall and ence exergy destruction in te wall as well as lowering external temperatures and te corresponding termal losses. A secondary effect is tat tinner tube lengt allow an increase in te total pipe lengt, allowing a sligtly increase in per bank, even allowing non-integer values. are sown in Table 4. t = 10 mm t = 5 mm t = 2 mm t = 1 mm t = 0.5 mm 0 2 4 6 8 10 12 14 16 18 20 X_net Figure 11. Exergy accounting wit te cange in tube (Gaussian Distribution) Table 4 Gaussian flux distribution wit varying in tube sig 20 MW 5800 K 1 bar 20 W/m K 30 W/m 2 K 290 ºC 550 ºC 1000 W/m 2 49 m 2 7 cm 1.9 m 20 mm MW MW MW MW MW % % % 0.5 17.48 0.57 1.117 2.373 13.42 0.768 0.671 0.474 627.96 1 17.48 0.57 1.127 2.437 13.35 0.764 0.668 0.472 628.00 2 17.48 0.57 1.148 2.570 13.20 0.755 0.660 0.466 628.01 5 17.48 0.57 1.172 2.738 13.00 0.744 0.650 0.459 628.53 10 17.48 0.57 1.282 3.584 12.05 0.689 0.602 0.426 627.49 4.5. Effect of flow configuration Te flow configuration sown in Figure 1 allows varying degrees of flow in parallel or in series. By increasing, te flow pat lengtens and tere are less tubes in parallel. Te model excludes tube-end manifolds and minor losses, but te important effects of tube friction and eat transfer enancement, due to varying fluid velocities in te different configurations, are captured. below (Figure 12 and Table 5 for Gaussian profile; Figure 13 and Table 6 for linear profile) sow te effect of canging. Similar to te scenario of varying te tube diameter, a larger number of banks causes reduced external radiation and internal convection exergy destruction, resulting in iger overall efficiency, driven by improved internal convection. If were large, owever, te tube wall tickness would need to be increased to avoid excessive oop stress in te tubes (tis model requires a safety factor on oop stress of at least one compared to an allowable stress fixed constant at 100 MPa), but at tis stage was kept constant and were less tan 80. n_banks = 40 n_banks = 33 n_banks = 20 n_banks = 10 0 2 4 6 8 10 12 14 16 18 20 Figure 12. Exergy accounting wit te cange in (Gaussian distribution) X_net

Table 5. Receiver performace for Gaussian flux profile wit varying flow configuration 20 MW 5800 K 1 bar 20 W/m K 30 W/m 2 K 290 ºC 550 ºC 1000 W/m 2 49 m 2 7 cm 1 mm - MW MW MW MW MW % % % 10 17.48 0.57 1.240 3.200 12.49 71.38 62.45 44.08 734.84 20 17.48 0.57 1.127 2.437 13.35 76.37 66.75 47.16 626.37 33 17.48 0.57 2.152 2.152 13.62 78.22 68.11 48.30 586.37 40 17.48 0.57 2.076 2.076 13.79 78.83 68.97 48.68 576.65 80 17.48 0.57 1.03 1.91 13.97 80.17 70.47 49.51 558.88 From Table 5, we figured out tat te igest termodynamic efficiencies obtained wen is 80, among all of te parametric studies in Section (4.3-4.5). Terefore, te same parameter study but wit linear flux distribution is presented in Figure 13 and in Table 6, in order to figure out wat te igest efficiencies were in tis scenario. Te best-case was found wit a slope of 90 kw/m 2 /m in Section 4.2. Tus, it was selected to do te following study. n_banks = 80 n_banks = 40 n_banks = 33 n_banks = 20 n_banks = 10 0 2 4 6 8 10 12 14 16 18 20 Figure 13. Exergy accounting wit effect of variable (Linear distribution) Table 6. Receiver performance for Linear flux profile wit varying flow configuration 20 MW 5800 K 1 bar 20 W/m K 30 W/m 2 K 290 ºC 550 ºC 1000 W/m 2 13.9 m 2 7cm 1 mm - MW MW MW MW MW % % % 10 17.48 0.57 0.470 1.891 14.554 83.25 72.77 51.41 20 17.48 0.57 0.400 1.183 15.333 87.80 76.66 54.16 33 17.48 0.57 0.369 0.966 15.581 89.12 77.90 55.03 40 17.48 0.57 0.358 0.872 15.685 89.72 78.42 55.40 80 17.48 0.57 0.335 0.732 15.849 90.66 79.24 55.98 4.6. Discussion on pumping losses Te above studies suggest tat tubes wit a large number of banks wit very small tin tubes will be te most efficient, were it not for limits due to tube stresses and peraps limits on manufacturability. Bot decreased and increased owever will increase te receiver pressure drop, resulting in presumably muc increased pumping work. Terefore, a pump is implemented into te modelling to re-calculate te termodynamic efficiencies and exergy destruction. As molten salt is modelled ere as an incompressible fluid, and assuming

negligible temperature rise across te pump, we can relate te isentropic efficiency of te pump to te pump work (defined to be negative wen te pump is working on te fluid) using ( ). ( 11 ) Now, te termodynamic efficiencies of overall system (pump + receiver) are defined to be: [ ( ) ( )] ( 12 ) ( 13 ) ( 14 ) Using Gaussian flux distribution and as an example to discuss te effect of pump on tese efficiencies. A of 48.19 kw is required to supply a HTF wit pressure in 20.86 bar. Tis amount of energy required is negligible wen compared wit oter exergy losses and destructions. Tis was evident from termodynamic efficiency results listed in Table 7. Te large number of decimal place ere is used to sow te tiny difference in efficiencies. Table 7. Effect of variable (cont d Table 5) wen pump was implemented into te system - % % % % % % kw bar 10 71.3831778 62.4514368 44.0794377 71.3831739 62.4514334 44.0794377-0.107 0.05 20 76.3667190 66.7504135 47.1568038 76.3667000 66.7503970 47.1568038-0.872 0.38 30 78.2233910 68.1056911 48.3033236 78.2233361 68.1056433 48.3033236-3.72 1.57 40 78.8284852 68.9651584 48.6769850 78.8284019 68.9650855 48.6769850-6.59 2.75 80 80.1709025 70.4732210 49.5060568 80.1705483 70.4729097 49.5051090-48.19 19.86 5. Conclusion and discussion From tese case studies, te trends of termodynamics efficiencies for individual conditions ave been found. A comparison between best-case Gaussian and linear flux distributions is summarised in Table 8. sow tat te linear flux distribution is able to improve te efficiencies by ~ 10%, wen compare wit Gaussian distribution. It evidently sows te benefits of linear flux distribution, especially in te context of restriction in elevated temperatures and being able to tolerate iger flux densities. In addition to te effect of flux profile, effects of tube diameter, tickness and flow configuration were examined, and it was sown tat in te absence of more detailed models of material constraints, te most efficient molten salt receivers ave a large number of tin small-diameter pipes running mostly in series. Table 8. Summary comparison of best-case designs for Gaussian and Linear flux profiles 20 MW 5800 K 1 bar 20 W/m K 30 W/m 2 K 290 ºC 550 ºC 1000 W/m 2 7 cm 1 mm Flux W MW MW MW MW % Gaussian (from Table 5) 17.48 0.57 1.03 1.91 13.97 80.17 70.47 49.51 49 Linear (from Table 6) 17.48 0.57 0.335 0.732 15.85 90.66 79.24 55.98 13.9 e m 2

6. Future work Many areas for future work exist, including a more extensive optimisation process and more toroug consideration of material constraints on te receiver performance. will be generalised to te case of non-convex receivers, specifically bladed receivers. Tube expansion and minor losses will also be considered. More accurate flux profiles based on detailed raytracing will be integrated wit te model. References [1] ttp://wps.prenall.com/wps/media/objects/2513/2574258/pdfs/e21.6.pdf Extension 21.6: Solar One and Solar Two. Retrieved 11 November 2016 [2] C. E. Tyner, J. P. Suterland, W. R. Gould Solar Two: A Molten Salt Power Tower Demonstration [3] U.S. Department of Energy (DOE), Sun Lab (NREL) (2000) Solar Two Demonstrates Clean Power for te Future [4] M. Romero, R. Buck, J. E. Paceco (2002) An update on solar central receiver systems, projects and tecnologies In: Te American Society of Mecanical Engineers (ASME), 2002 [5] Gemasolar Termosolar Plant ttp://www.nrel.gov/csp/solarpaces/project_detail.cfm/projectid=40. Retrieved 11 November 2016. [6] N. Boerema, G. Morrison, R. Taylor, G. Rosengarten (2013). Hig temperature solar termal central-receiver billboard design. In: Solar Energy 97 (2013) pages 356-368 [7] A. Sáncez-González, M. Reyes Rodríguez Sáncez, D. Santana, 2015. Aiming strategy model based on allowable flux densities for molten salt central receivers. [8] Yunus A. Çengel, Micael A. Boles (2011) Termodynamics, an engineering approac London: McGraw-Hill Education Europe. [9] I. Dincer and T.A.H. Ratlamwala (2013) Importance of exergy for analysis, improvement, design, and assssment WIREs Energy Environ 2013, 2: 335 349 doi: 10.1002/wene.63. [10] Soteris A. Kalogirou, S. Karellas, V. Badescu, K. Braimakis (2015) Exergy analysis on solar termal systems: A better understanding of teir sustainability In: Renewable Energy. [11] Pye, J., Zeng, M., Zapata, J., Asselineau, C.-A., & Coventry, J. 2014. An exergy analysis of tubular solar-termal receivers wit different working fluids In: 20t Annual SolarPACES Conference. Beijing. [12] A. B. Zavoico (2001). 'Solar Power Tower Design Basis Document', Sandia National Laboratorie tecnical report SAND2001-2100, Nexant, San Francisco. [13] K. Lovegrove, J. Pye (2012). Losses from receivers. In Concentrating solar power tecnology, principles, developments and application (p. 37). Woodead Publising Limited. [14] ttps://en.wikipedia.org/wiki/normal_distribution, Te probability density of te normal distribution (2016). Retrieved 1 st November 2016 [15] Alberto Sáncez-González, María Reyes Rodríguez-Sáncez, Domingo Santana. Aiming strategy model based on allowable flux densities for molten salt central receivers. Solar Energy, 2016 Acknowledgements Funding from te Australian Renewable Energy Agency (project 1-UFA006) is gratefully acknowledged.