The influence of atmospheric boundary layer turbulence on the design wind loads and cost of heliostats

Highlights

• Design wind loads more sensitive to terrain roughness with increasing heliostat size.

• Pedestal and torque tube dimensions increase with full-scale ABL turbulence.

• Foundation pile depth dependent on longitudinal and vertical turbulence components.

• Relative contribution of structural component costs increases with heliostat size.

• Total heliostat cost reduced by up to 13% in a low-roughness turbulence field.

Abstract

This paper investigated the influence of the turbulent wind fluctuations in the lowest 10 m of the atmospheric boundary layer (ABL), depending on the surface roughness of the terrain surrounding a heliostat field, on the required dimensions and material cost of the structural heliostat components to resist the combined bending and torsional stresses due to the design wind loads. Turbulence data in the lowest 10 m of the full-scale ABL from ESDU 85020 were correlated with peak wind load coefficients on model-scale heliostats in wind tunnel experiments to determine the design wind loads as a function of heliostat size and terrain roughness. The results highlight the large dependence of wind loads and cost on terrain roughness with increasing heliostat size. The increasing mass of steel per unit area in the pedestal, torque tube and support mass led to their relative contribution increasing from 18% of the total specific cost of a 25 m² heliostat to 34% of the total cost of a 150 m² heliostat. The effect of the increasing turbulence characteristics in a high-roughness terrain resulted in a 10% increase in the total cost of a 25 m² heliostat and a 13% increase in the total cost of a 150 m² heliostat. An improved understanding of the influence of ABL turbulence on the design wind loads on full-scale heliostats can therefore allow the dimensions of structural components and the respective material cost of manufacturing to be optimised for the local wind conditions and terrain at different sites.

Introduction

Concentrating solar thermal (CST) is emerging as a large-scale energy source for power generation and industrial process heat, with 6.43 GWe of installed capacity at the end of 2019 (He et al. 2020). Of the various CST technologies, power tower plants are projected to drive cost reduction, due to improved power cycle efficiencies through operation at high temperatures (Mehos et al. 2017). Energy is collected in the form of heat by a solar receiver at the top of a central tower by intercepting focused solar radiation reflected from a large array of heliostats that track the sun individually in two axes. The most common heliostat type in existing commercial power tower plants consists of an array of mirror facets supported by a steel pedestal-mounted frame with azimuth-elevation tracking (Téllez et al. 2014). The high-precision drive mechanisms of state-of-the-art heliostats have been developed to optimise the tracking accuracy for improved field efficiency. The levelized cost of electricity (LCOE) provides a measure of the capital and operating costs of different technologies with respect to their net power output over their project lifetime, which was estimated by International Renewable Energy Agency (IRENA) for commercial-scale power tower systems to have decreased from USD $0.25/kWh to $0.10/kWh between 2014 and 18 (IRENA 2019). Increasing competitiveness in supply chains and the availability of lower cost finance contributed to these cost reductions, and it is projected by IRENA that the LCOE will fall within the range USD $0.06–0.10/kWh over the next few years (IRENA 2019). A significant opportunity to reduce LCOE is by cost reduction of the heliostat field, as it contributes 40–50% of the total plant cost (Kolb et al., 2011, Pfahl et al., 2017). Current commercial heliostat costs are estimated by National Renewable Energy Laboratory (NREL) at around USD $140/m² (Turchi et al. 2019), and with 2030 DOE targets set at USD $50/m² (Department of Energy 2017), there is a clear expectation of dramatic cost reduction. The drive unit and structural heliostat components contribute within the ranges of 25–30% and 30–35%, respectively, to the total heliostat cost depending on the heliostat size (Coventry et al. 2016). Sizing of structural components relies on understanding how external loads due to wind and gravity influence deflections and mirror shape for optical performance, and survivability in the case of extreme loads. Wind loads are a major driver of structural cost (Téllez et al. 2014), and thus a strong understanding of wind loads in all operating conditions is vital to lowering the total heliostat cost and achieving LCOE reduction in power tower systems.

Spillage losses associated with beam misalignment due to wind-induced heliostat tracking errors can significantly affect the operational performance of power tower plants, particularly with increasing distance from the tower in large-scale projects (Arbes et al., 2017, Emes et al., 2019e). Furthermore, dynamic wind loading on the heliostat surface due to unsteady pressure distributions impacts the survivability of heliostats in stow position under extreme wind conditions (Vásquez-Arango, 2016, Emes et al., 2017, Emes et al., 2018, Pfahl, 2018, Jafari et al., 2019a, Jafari et al., 2019c). The maximum wind loads on the structural components of the heliostat are most sensitive to the turbulent fluctuations of the wind in the lowest 10 m of the atmospheric boundary layer (ABL) (Arjomandi et al., 2019, Emes et al., 2019a, Jafari et al., 2019b), depending on the surface roughness of the terrain surrounding a heliostat field. Hence, the current study aims to determine the influence of terrain roughness and ABL turbulence on the design wind loading and cost of heliostats. The first objective is to determine the effect of terrain roughness on the design wind loads on a typical range of heliostat sizes, through semi-empirical load-turbulence correlations developed in wind tunnel experiments and semi-empirical data measurements in the full-scale ABL. The second objective is to develop a correlation between the terrain roughness and the required dimensions of the structural components of the different heliostat sizes to resist the bending and torsional stresses induced by the design wind loads. Finally, the third objective is to determine the influence of terrain roughness and heliostat size on the material cost of the structural components and thus the direct capital cost of heliostats. A detailed understanding of the heliostat design wind loads and their dependence on the wind speed and turbulence profiles for a variety of terrains in the full-scale ABL can allow the dimensions of structural components and the respective material cost of manufacturing heliostats to be optimised for the local wind conditions at different sites.

Influence of terrain roughness and atmospheric boundary layer (ABL) turbulence on heliostat design wind loads: The temporal and spatial variations of turbulence in the lowest 10 m of the ABL have a major impact on the peak aerodynamic coefficients used in the design wind load calculations for subsequent dimensioning and cost estimates of the drive units, pedestal, torque tube and foundation of a conventional T-shaped heliostat (Pfahl et al. 2017). With increasing surface roughness of natural topography or constructed features of the terrain, the gradient of the wind profiles in the ABL increases such that there is an increase in the turbulence intensity $I_u={\sigma }_u/{\overline{U}}_H$, defined by the ratio of the root-mean-square fluctuating longitudinal velocity to the mean velocity, at heights closer to the ground. Based on full-scale ABL data (ESDU 85020 2001), the turbulence intensity increases from 13% in a low-roughness flat area, defined by a logarithmic surface roughness height $z_0=$ 0.003 m, to 35% in a high-roughness suburban area ($z_0=$ 0.3 m) at the 10-m reference height in design wind codes and standards (Holmes 2007). Mean and gust wind speed probability distributions of 10-minute averaged data show a large variation at different sites, such as gust wind speeds of 6 m/s in Phoenix (Blackmon, 2014, Emes et al., 2015, von Reeken et al., 2016a), 8 m/s in Redstone (von Reeken et al. 2016a) and 10 m/s in Alice Springs (Emes et al. 2015) with a 10% probability of being exceeded throughout a year. Furthermore, wind velocity measurements at automatic weather stations (Bureau of Meteorology, 2020, National Climatic Data Center, 2020) are not collected at the required frequency and resolution to calculate the turbulence intensities of the longitudinal and vertical velocity components for heliostat wind load considerations (Blackmon 2014). In most cases, local meteorological data are applied with conservative factors in design standards for buildings that neglect the dynamic response of smaller slender tubing geometries of the structural heliostat components and overpredict the peak wind loads in low-roughness desert areas with reduced turbulence intensities (Emes et al., 2019d). Wind tunnel studies on the aerodynamic loads on heliostats are commonly modelled with an “open country” terrain ($z_0=$ 0.03 m) to approximate the surface roughness of the upwind terrain surrounding a heliostat field. Peterka and Derickson (1992) reported the maximum load coefficients of the drag and lift forces, hinge, overturning and azimuth moments on a single model heliostat in a simulated ABL with ${\overline{U}}_H\approx$ 12.6 m/s and $I_u$ $=$ 18% at the elevation axis height ($H=$ 0.155 m) of the heliostat. Design wind loads on industrial-scale heliostats adopted a quasi-steady approximation using mean wind speeds and peak aerodynamic coefficients of the measured forces on single model heliostats in wind tunnel experiments (Peterka and Derickson 1992), however the variation of the unsteady components of turbulence in the lowest 10 m of the full-scale ABL were not considered. For example, in an open country terrain with $z_0=$ 0.03 m (ESDU 85020 2001), $I_u$ increases from 18.7% at a 6-m elevation axis height of a large heliostat ($A\ge$ 120 m²), as currently deployed by Abengoa Solar and Sener, to 20.4% at a 3-m elevation axis height of a small heliostat ($A\le$ 20 m²), as developed by eSolar and Brightsource Energy (Téllez et al. 2014). The longitudinal component of the turbulence in the ABL is closely correlated to the maximum operating load coefficients of a heliostat positioned perpendicular to the ground with elevation angle $\alpha =$ 90° (Yu et al. 2019). With increasing surface roughness in the full-scale ABL (ESDU 85020 2001) from flat areas ($z_0=$ 0.003 m), such as deserts or short grass with no obstructions, to open level country ($z_0=$ 0.03 m) with few hedges and isolated trees, increasing $I_u$ from 13% to 21% approximately doubles the magnitude of the drag force, overturning moment and azimuth moment coefficients in their respective maximum operating positions (Peterka et al. 1988). For the same increase in surface roughness, the vertical component of turbulence intensity $I_w$ increases from 8% to 13%, leading to a 28% increase in the peak lift force coefficient and a 54% increase in the peak hinge moment coefficient on a heliostat aligned horizontally in stow position (Pfahl et al. 2015). Hence, the current study aims to estimate the design operating and stow loads on heliostats of different sizes as a function of the level of terrain roughness with respect to the turbulence intensity profiles at the range of heliostat elevation axis heights in the full-scale ABL (ESDU 85020 2001).

Effect of the heliostat design wind loads on the sizing and dimensions of the structural heliostat components: Determination of the dimensions of the load-bearing structural components of a conventional heliostat requires the distribution of the loads over the mirror surface to be accurately estimated for the maximum loading cases corresponding to the operating and stowed positions of the heliostat. Design codes and standards, such as ASCE 7–02, 2002, AS/NZS 1170.2, 2011, outline directional procedures for predicting the static and dynamic wind effects on the aerodynamic shape factors for buildings. Some codes include wind load design procedures for buildings with enclosed and open structures, such as solid freestanding walls or billboards (EN 1991-1.4 2010), and building attachments, such as roof-mounted PV panels (ASCE/SEI 7-16 2016) and ground-mounted PV panels (Ginger et al. 2019), based on the tilt angle, aspect ratio and height above the surface corresponding to the maximum upward and downward pressures on the panel surfaces. The IEC 61400-1 (2005) standard for wind turbines provides aero-elastic structural load calculations based on the aerodynamic shapes of the turbine components and their dependence on the average and gust wind speeds, turbulence intensity and length scales across the rotor plane. The slender plate and cylinder geometries of the heliostat facets, trusses, torque tube, pedestal and foundation are inadequately defined in existing design standards for buildings, such that the maximum stresses and displacements for dimensioning of heliostat components must be determined from wind load measurements on heliostat models. Global wind effects considered in the current study include the bending and torsional loads at the hinge and base of the heliostat pylon resisted by the principal structural components of the torque tube, pedestal and foundation. Local wind effects, not considered in the current study, include reactions of local connections, beams and truss elements resulting from the torsional loads on the pylon and deformations of the mirror surface. As wind loads increase with heliostat area, the required diameter and thickness of the pedestal, torque tube and mirror support trusses increase to ensure the combined bending and torsional stresses remain below the ultimate tensile stress of the material within an acceptable limit of safety. Kolb et al. (2007) showed that the cost of the structural wind-dependent heliostat components of the 148 m² ATS heliostat scaled according to a three-halves power law with the heliostat area, based on material cost scaling of thin tubing with a constant maximum stress. Larger heliostats therefore require increasing mass of steel (per m² of surface area) and material cost to manufacture these structural components. Emes et al. (2015) found that an increase in heliostat design wind speed required increasing dimensions and thus cost of hollow cylindrical beams, representing the pedestal and support structure trusses of a 120 m² heliostat. Benammar and Tee (2019) developed relationships between the wind loads, combined bending and torsional stresses and the dimensions of the structural components of a 25 m² heliostat, such that the structural reliability of the heliostat was optimised by using a thick torque tube with small diameter at low wind speed sites and a thin torque tube with large diameters at high wind speed sites. However, the dependence of wind loads on the turbulence in the ABL implies that a change in terrain roughness affects the minimum required dimensions of the structural components of a fixed size heliostat with the same design wind speed specification. Hence, the second objective of this paper is to determine the relationship between the characteristic dimensions of the structural components with the height and surface roughness of the terrain for a range of heliostat sizes, based on the variation of turbulence characteristics and wind speed in the lowest 10 m of the ABL.

Effect of terrain roughness and heliostat size on the capital costs of a heliostat: The capital and operating expenditure of heliostat fields are conventionally reported as a specific cost in dollars per square metre of reflective area ($/m²). Whether there is an optimal heliostat size has long been debated, and is still an open question, even for plants of equivalent size and tower height. Evidence from built commercial systems is inconclusive. Large heliostats with area around 120 m² were deployed at the PS10 and PS20 plants (Abengoa Solar 2013), at the Gemasolar plant by Sener (Relloso and García 2015) and at Crescent Dunes by ACS Cobra (NREL 2016), with further increases to around 180 m² at the Noor III plant by Sener (Relloso and Gutiérrez 2017). Concurrent to the development of large heliostats, there has been commercial deployment of both mid-sized heliostats, such as the 50 m² Stellio heliostat at Hami (Keck et al. 2019), and small 15–20 m² heliostats at Ivanpah and Ashalim by Brightsource (Koretz 2013). Similarly, theoretical studies are split on the question of heliostat size. Parametric scaling analysis by Sandia indicated that heliostats should be at least 50 m², and preferably around 150 m² (Kolb et al. 2007). Blackmon (2013) found that the heliostat cost is sensitive to assumptions around the particular heliostat design, and the weighting of different categories of cost dependence on area. As an example, Blackmon (2013) showed that decreasing the relative cost contribution of the control and wiring (size independent) components from 10% to 5% resulted in a 16% reduction in the total heliostat cost, and the optimum heliostat area decreased from 60 m² to 38 m². The specific heliostat cost was reduced by 4% for 10 m² and 100 m² heliostats, with a maximum reduction of approximately 7% for 30–50 m² heliostats, by modelling the cost-area proportionality exponent $C\propto A^{0.5+{\alpha }_{\overline{U}}}$ for a power law velocity profile of an open country terrain with ${\alpha }_{\overline{U}}=$ 0.15 relative to a uniform velocity profile with ${\alpha }_{\overline{U}}=$ 1 (Blackmon 2013). Smaller heliostat sizes were also found by Emes et al. (2015) to be favourable for optimising the total specific heliostat cost to the maximum quasi-static wind loads on a 120 m² reference heliostat, such that the optimal heliostat area reduced from 50 m² to 25 m² with an increase in design wind speed for stowing the heliostat from 10 m/s to 20 m/s. A range of different mirror support truss designs of a 17 m² heliostat analysed by von Reeken et al. (2016b) showed that the relative contribution of the support structure varied from 17 to 28%, the drives from 37 to 50% and the foundation from 8 to 12%. Sensitivity analyses of three heliostat sizes of 17 m², 43 m² and 108 m² in a fixed capacity power tower plant indicated that the field of 43 m² heliostats was favourable for optimising optical performance (von Reeken et al., 2016b) and LCOE (Pidaparthi and Hoffmann 2017). In these studies, the heliostat cost of the wind-bearing structural components of conventional T-shaped heliostats were modelled to vary linearly with bending moment and thus with mirror area $A^{3/2}$. This scaling relationship from Kolb et al. (2007) was based on worst-case wind load coefficients from Peterka and Derickson (1992) in an open country terrain with a constant turbulence intensity $I_u=$ 18%, ratio of gust to mean wind speeds $G_u=$ 1.6, and design (gust) wind speeds of 22 m/s in operation and 40 m/s in stow. However, there is a significant variation of the turbulence characteristics at the reference hinge height of different heliostat sizes in the lowest 10 m of the full-scale ABL due to changes in terrain roughness. Hence, the current study aims to investigate the effect of heliostat size and ABL turbulence represented over a range of terrain roughness at different heliostat sites, on the wind-dependent structural heliostat costs. The dimensions and required mass of material, estimated through stress analysis of the design loads on the structural components, provide an insight into the effect of ABL turbulence on the total heliostat cost.