Resumen de Thermo-mechanical modelling to evaluate solar receiver damage
Seeking for renewable alternatives to decrease the dependence on fossil fuels, Solar power tower (SPT) technologies take advantage of the direct solar radiation to produce electricity. They are constituted by an array of mirrors, the heliostat field, that reflect the direct normal irradiance (DNI) onto the receiver subsystem. Such receiver is placed at the top of a tower and it behaves as a heat exchanger, with the heat transfer fluid (HTF) through it being eventually heated. Such thermal power transferred to the HTF is then converted into electricity in the power block. Additionally, these plants can equip thermal energy storage (TES) systems, decreasing the impact of the solar resource variability on the production. Depending on the HTF selected, such TES system can be directly or indirectly integrated; in the case of molten salt, its thermal properties and chemical stability make it an optimal option for the direct TES implementation, which highlights its appealing. The molten salt TES system is constituted by a cold salts tank, at a minimum salt temperature of 290 °C to prevent their freezing, and a hot one, at a maximum of 565 °C in order to avoid their decomposition, which would accelerate the corrosion of the piping and tank components.
Nevertheless, SPT facilities still have not reached their maturity yet, with room for improving their efficiencies and reducing their costs. Moreover, they face challenges associated with their demanding working conditions. In that sense, the receiver subsystem is one of the most critical components, being subjected to high non-uniform fluxes and working under a cyclic operation due to the diurnal cycles and cloud interruptions of the solar radiation. These heat fluxes cause great thermal gradients on the receiver tubes, leading to thermal stresses and deformations. The presence of great deformations would cause the contact of adjacent tubes, leading to the appearance of hot spots. Thus, the tubes are periodically guided with supports that aim to prevent their excessive bending; nevertheless, these supports introduce additional mechanical stresses. During hold times under high temperatures and stresses, the tubes are exposed to the creep damage, which manifests in form of the formation of voids in the material grain boundary. On the other hand, the cyclic operation leads to high strain cycles, favoring the appearance of fatigue damage; although its early effects are not observable at a macroscopic level, it eventually causes cracks that initiate at the components outer face. These two damage mechanisms can potentially lead to the receiver early failure and their effects are aggravated by their interaction, with the fatigue cracks growing rapidly through the creep voids. It should be considered, however, that a moderate creep is desirable since it leads to stress relaxation: a fraction of the elastic strain is turned into creep strain, decreasing the elastic stresses on the tubes. In order to guarantee the stress relaxation on the receiver tubes despite the cyclic nature of its operation, the stress reset limit must not be surpasses. For that end, the receiver aiming strategy should be watched during operation. Additionally, control on the aiming strategy should also focus on keeping the film temperature (temperature of the inner tube wall, in contact with the HTF) below the admissible limit set by the HTF employed and the tube material, avoiding corrosion problems that could aggravate the fracture mechanisms.
To study the behavior of the receiver during the mentioned extreme operation conditions, the placement of sensors is not a feasible alternative due to these high heat fluxes and the receiver large dimensions, and thus the use of simplified analytical and numerical models is required. Moreover, the numerical models typically entail a high computational cost that makes the study of the whole receiver not feasible, thus being the analytical models the best alternative. Hence, this thesis aims to study the creep and fatigue damages on the tubes of a central receiver of a SPT facility, using molten salt as heat transfer fluid (HTF), from an analytical point of view. The prior thermal and mechanical characterization required for that end is also covered in this dissertation, paying attention to the aiming strategy to safely operate with respect the film temperature and stress reset limits that set the allowable flux density on the receiver surface. The optical model employed throughout this dissertation to couple the heliostat field and receiver behavior allows selecting aiming strategies from an equatorial configuration (with the heliostats aiming at the receiver vertical center, providing greater optical efficiencies but higher heat fluxes that may compromise the receiver) to an open one (heliostats aiming to the receiver vertical ends, high optical losses that lower the receiver efficiency but lower peak fluxes); in such spectrum of strategies , a flat aiming, that maximizes the receiver efficiency while decreasing the peak flux as much as possible, can be found.
Consequently, the initial step is to thermally characterize the receiver, providing the temperature profile of the tubes and the HTF temperatures. It is achieved with the analytical bi-dimensional thermal model developed, which considers the multiple reflections and emissions that take place in the receiver tubes, discretized in axial and circumferential divisions. For a certain design point, the model also contemplates the calculation of the optimum tube thickness to minimize the losses through the tube wall while assuring its endurance to the pressure stresses and corrosive effects of the HTF. Then, the methodology to perform a high-resolution exergy analysis of the receiver is subsequently developed, considering it coupled to the heliostat field upstream; despite the two focal temperatures remaining constant (the sun temperature and the HTF outlet one) such exergy model is used to explore potential ways to improve the receiver exergy efficiency. The heliostat field provides the greatest exergy loss, which can only be modified by altering the aiming strategy, increasing the efficiency by selecting one as peak as possible but always keeping in mind the allowable flux limits. When disregarding the heliostat field and solely analyzing the receiver exergies under different aiming strategies, it is observed that the gains on certain exergy losses are counteracted by the descent on others, resulting in similar outcomes for the receiver regardless the aiming strategy chosen. Thus, it is a factor that only alters the exergy of the heliostat field. The greatest exergy destruction in the receiver is due to the emissions and reflections originated at the tubes. Thus, since these are coated to enhance their optical properties, the effects of the degradation of their coating paining over time is investigated, showing that repaint tasks are advised to avoid increasing the exergy losses and that the coating selection should be focused on providing an absorptivity as high as possible, while a low emissivity is preferred. Despite the exergy efficiency increases with the increment of the DNI of the site, the exergy of the receiver is found to depend greatly on the ambient temperature (the dead state); thus, locations with moderate DNI but low ambient temperatures are more efficient in terms of exergy than sites with extremely high DNI but accordingly greater temperatures.
Upon knowing the tubes temperatures, their elastic stresses and strains can be obtained. The analytical method proposed regards the temperature dependence of the material selected for the tubes manufacturing and its accuracy is tested against numerical results, showing a good agreement and with a considerably lower computational cost. The stress results obtained when considering the thermal and mechanical properties of the tubes constant are greatly deviated with respect the numerical -and analytical- ones; thus, the temperature dependance is found essential to accurately estimate these elastic stresses and strains, since it can potentially lead to major error during the damage assessment otherwise. Moreover, the supports guiding the tube greatly reduce their bending, which serves to avoid additional problems such as the contact of two adjacent tubes; again, the constant property case does not predict it as accurately as the temperature dependent one. In terms of stresses, the placement of a finite number of supports is found to be very similar to considering generalized plane strain conditions, which is equivalent to an infinite number of them. Thus, the generalized plane strain assumption is an accurate simplification approach in the stress calculation.
With the receiver characterized in thermal and mechanical terms, the dissertation then focuses on the damage calculation for the receiver tubes, which also leads to the receiver lifetime estimation. The methodology followed in that regard considers essential aspects such as the stress relaxation due to plastic strain accumulation. The first analysis focuses on selecting the most adequate alloy alternatives for the tubes manufacturing, considering the creep and fatigue damages they must endure during their regular operation, the thermal power they can produce- which differs due to their different thermal and mechanical characteristics, leading to deviations in the allowable flux density they can endure- and the costs associated with the replacement of damaged panels for a certain lifespan. The five alloy options examined are alloy 316H, a high carbon variant for the one used in the testing facility Solar Two (alloy 316), Incoloy 800H, with its regular variant (Incoloy 800) being used in Solar One, Inconel 625, Haynes 230 and Inconel 740H; the last three options exhibiting great mechanical properties and typically regarded as the most suitable ones in similar applications. The disparate allowable flux densities these alloys present leads them to yielding different thermal power at a certain time instant; the most unfavorable in this regard are Inconel 625 and, specially, alloy 316H. On the other hand, the low yield strength of alloys 316H and Incoloy 800H leads them to the appearance of stress reset, preventing them from the desirable stress relaxation over the daily cyclic operation. Hence, Incoloy 800H is highly penalized by the stress reset, being the worst alternative in endurance terms and, consequently, costs. The best alternative in terms of lifetime is Inconel 740H, the most expensive one and yielding the greatest thermal power, followed closely by Haynes 230, slightly cheaper and with a similar thermal power. These two show the suitability of high-nickel alloys for their use in solar central receiver components. The next one in the expected lifetime regard is alloy 316H, which is the most inexpensive alternative but the one yielding, by far, the lower thermal power. Then, Inconel 625 lives slightly lesser and is more expensive than alloy 316H, but provides considerably greater thermal power, although far from Inconel 740H and Haynes 230. The proposed levelized cost of alloy (LCOA) metric combines their endurance, cost, and thermal power, and leaves Inconel 740H yet again being the best option, followed also by Haynes 230; nevertheless, Inconel 625 overtakes alloy 316H due to its poor power production.
Then, the goal is to determine the most adequate time-step to perform the lifetime/damages study, with the receiver operation taking place during the required hours in order to fill the thermal energy storage tank, starting early in the morning. For that end, the lifetime assessment is performed for time steps of 60, 30, 15, 5 and 1 minute, showing that a 5-minute time resolution is suitable, with results that resemble the ones obtained with the finer resolution, the 1-minute time step, and computationally reasonable. Moreover, it is found that the usual approach of selecting just the solar noon as design point greatly overestimates the damage on the receiver, being its use inadvisable for an accurate endurance assessment of the receiver. Finer time resolutions allow for a more precise aiming strategy selection through the day, switching earlier to more open aiming strategies as the morning hours progress and the DNI increases and also capturing earlier the DNI descend during the afternoon hours. Then, the use of a set of representative days, equally spaced in solar altitude through the year, from the summer solstice to the winter one, is compared to the use of just the spring equinox as design day. In that case, the single design day also underestimates the whole receiver lifetime despite its strategic selection (for being the day in between the summer and winter solstices, the days with the greater and lower solar altitude). From the set of days, the least harmful is the summer solstice since its aggressive DNI requires the selection of more open (less peak) aiming strategies earlier than days with lower DNI, contributing to reduce the damage concentration at the most demanding receiver spots, but still allowing the fastest tank filling than any other day.
Lastly, the share of the creep and fatigue damages in the total is analyzed during transient operation due to cloud passages and hazy days, with the mass-flow rate and aiming strategy remaining as the clear-sky scheduled in advance for the day. Thus, the results of such transient days are also compared with their assigned clear-sky one. The transient DNI database of a whole year is used for that end. The days of such database are arranged according to already tested clustering days that classify them according to their DNI main features: the energy level (high, medium, low or null), its variability (high, medium or low) and its distribution through the day (morning, balanced or afternoon). Such clustering results in 6 day-type suitable for the SPT receiver operation. Additionally, three characteristic days are considered to be used as representative of the different year stages: the spring equinox, the summer solstice and the winter one. The transient DNI of each day serves to determine the hours of operation and number of start-ups occurring at each day, taking into account that a minimum heat flux is established to operate, that a certain time window of that favorable operation conditions is required to start-up the receiver, and that the preheating process regarded before each start-up also requires for a minimum average heat flux on the receiver and must last 20 minutes. With the results for a representative day of each day-type and season (18 cases in total), it is found that creep is the main damage mechanism, being highly dependent on the energy level of the day. Fatigue damage can only be major altered when including multiple start-ups during a day, being the strain cycles due to small cloud transients negligible. Thus, high energy days show a great creep and low fatigue; on the other hand, medium energy days, typically with high variability, barely increase their fatigue damage with respect to the high energy instances, with lower variability, but suffer a creep plummeting. For these same reasons, the clear-sky analysis over the same time periods than the transient one translates in more conservative results, with creep overestimated and fatigue virtually the same. Also, the balanced days turn out to be slightly more damaging in terms of creep than morning or afternoon centered days, and the damage is virtually the same between both receiver halves: the Eastern and Western ones. The whole year analysis shows the abundance of the balanced-high energy days, being more than half of the operation days. These are followed by the balanced-medium energy days, with the rest of the day-type being much less. The effect of these balanced-high days is observed in the damage share obtained through the year for the transient DNI, with creep just shy of the 75% in the most damaged panel, the northern one, increasing its share as progressing to the southern panels, and by the even damage observed in both receiver halves. The clear-sky assumption is even more conservative, again due to the higher creep damage assumed, diluting the fatigue damage share (the minimum creep rate is not over an 82% in the northern panel). Thus, the lifetime obtained for the transient DNI is around 45 years, while for the clear-sky it descends up to 27. These two cases constitute the greatest (clear-sky) and lower (transient) creep damage scenarios, with finer mas-flow rate control modes placing in-between these two due to the descend on the mass-flow rate with respect the transient case considered, increasing the tubes temperatures.
