Scholarly article on topic 'Dynamic Effects of a Heliostat to Wind Loading'

Dynamic Effects of a Heliostat to Wind Loading Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — J.M. Terrés-Nícoli, C. Mans, J.P.C. King

Abstract This paper presents a methodology for evaluating dynamic wind load effects on a heliostat. A 1:50 scale pressure model of the heliostat is examined in a boundary layer wind tunnel. The model is instrumented with 58 pressure taps, with sufficient resolution to capture the abrupt spatial and temporal changes in wind forcing due to the turbulent nature of the wind. Time histories of generalized forces are generated from the wind tunnel data, in combination with structural modal analysis and a wind climate model of the site. Critical load effects are examined in order to develop pressure distributions for detailed stress analysis of selected structural elements. The analysis provides optimized loading distributions which are found to be considerably lower than Eurocode estimations for global uplift and drag forcing, with favorable and unfavorable implications in the design of individual structural components.

Academic research paper on topic "Dynamic Effects of a Heliostat to Wind Loading"

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Energy Procedía 49 (2014) 1728 - 1736

SolarPACES 2013

Dynamic effects of a heliostat to wind loading

J.M. Terres-Nicoliab'*, C. Mansb, J.P.C. Kingc

aUniversity of Granada, Structural Mechanics Department, Granada 18071, Spain bOritia & Boreas, C/Ojos del Salado 100, Granada 18008, Spain cAlan G. Davenport Wind Engineering Group, Western University, London N6A5B9, Canada

Abstract

This paper presents a methodology for evaluating dynamic wind load effects on a heliostat. A 1:50 scale pressure model of the heliostat is examined in a boundary layer wind tunnel. The model is instrumented with 58 pressure taps, with sufficient resolution to capture the abrupt spatial and temporal changes in wind forcing due to the turbulent nature of the wind. Time histories of generalized forces are generated from the wind tunnel data, in combination with structural modal analysis and a wind climate model of the site. Critical load effects are examined in order to develop pressure distributions for detailed stress analysis of selected structural elements. The analysis provides optimized loading distributions which are found to be considerably lower than Eurocode estimations for global uplift and drag forcing, with favorable and unfavorable implications in the design of individual structural components.

© 2013 J.M. Terrés-Nícoli. 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 andpeerreviewbythescientificconference committeeof SolarPACES2013underresponsibilityofPSEAG. Final manuscript published as received without editorial corrections. Keywords: Heliostat; wind loads; wind tunnel; dynamic loading

1. Introduction

Wind induced dynamic response of commercial heliostats remains an important factor, not only for ultimate limit design under extreme wind loading conditions, but also for vibration analysis during operational conditions. The latter is particularly important for large scale solar reflector parks where outer perimeter reflectors may be located far from the central receiver and micro-errors in targeting may considerably reduce the system energy efficiency.

* Corresponding author. Tel.: +34-958-109-494; fax: +34-958-715-529. E-mail address: terresnicoll@orltlayboreas.com

1876-6102 © 2013 J.M. Terrés-Nícoli. 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.2014.03.183

While active control systems can be used to auto-correct the instantaneous misalignment due to wind induced vibrations, a more cost effective solution may be to optimize the structural rigidity of the heliostat and reduce the size of the deflections to an acceptable bandwidth through efficient design. Any misalignment error is then limited to a defined threshold for regularly occurring wind conditions expected at the site and is only exceeded during strong wind events. Excessive stress cycles due to frequently occurring low intensity winds may also provoke failures related to fatigue due to repeated dynamic excitation. In these cases, the dynamic response of the structure is related just as much to the turbulent properties of the wind as the wind intensity at the site, while the fluid-structure interaction and aeroelastic phenomena such as vortex shedding and galloping may also contribute to repeated dynamic excitation.

Wind tunnel testing remains the only reliable method for evaluating the dynamic response of irregular shaped structures to the turbulent nature of the wind. Modern wind loading standards were originally developed in the 1980's to provide guidance on design wind loads on buildings and later extended to other isolated structures such as signposts, lattice towers and building attachments. As such, current standards do not contemplate the majority of structural geometries used in the solar energy industry (i.e. roof mount systems, two axis tracking heliostats or parabolic collectors) and what little published material that is available in the public domain [1] is only suitable for geometries resembling the tested structure, as extrapolation of aerodynamic coefficients to alternative geometries is no trivial task. Until standards are expanded to include these structural forms, boundary layer wind tunnel studies remain the most reliable method for predicting design wind loads and aerodynamic performance of structures. The dynamic response of the heliostat may be deduced from aerodynamic pressure coefficients measured on a scaled model in a boundary layer wind tunnel, in combination with the local climate model and the structural properties of the heliostat.

This paper presents the results of a dynamic analysis of a heliostat from simulations in a boundary layer wind tunnel. Critical load cases are defined for ultimate limit state design, including global forcing at the foundation and stresses within individual members, but the methodology is also valid for deflection and fatigue analysis. The corresponding dynamic forcing for each load case is presented as an equivalent static pressure distribution over the heliostat surface for stress analysis in a structural analysis software package.

2. Wind tunnel simulation

The experiments were performed in the high speed section of Boundary Layer Wind Tunnel II at Western University, Canada. The wind tunnel has a test section length of 39m, with cross section dimensions of 3.4m wide by 2.4m high at the measurement location. Measurements were performed on an isolated 1:50 scale heliostat in flow conditions matching the project site, defined as open country terrain, z0=0.03m, for all wind directions.

2.1. Heliostat model

In order to have adequate measurement resolution, particularly for determining load cases on individual structural elements with small tributary areas, a large number of pressure taps are required on both external surfaces of the heliostat panels. Therefore, the wind tunnel model is constructed at the largest possible scale, while still satisfying the constraint that the blockage of the wind tunnel test section does not exceed 5% [2]. In the case of the present study, a 1:50 scale pressure model was constructed of a fixed angle heliostat structure with panel dimensions of 13m length by 9.3m height and a 70° tilt angle from the horizontal, giving a maximum height of 9.66m above ground level. The model was instrumented with 58 pressure taps (48 taps on the external surface and 10 taps on the interior surface). Figure 1 presents the overall dimensions of the heliostat, along with the pressure tap distribution. Pressure taps are concentrated around the edge and corner zones of the heliostat exterior surface, where large pressure gradients, including flow separation and reattachment are expected to occur for certain wind directions. The microtubes are integrated within the interior of the panels and exit beneath the wind tunnel floor through the support column, thereby not exposing the tubing to the exterior of the panel to modify the local flow field surrounding the model during testing.

Fig. 1. Global dimensions and pressure tap layout on the 1:50 scale heliostat model

2.2. Atmospheric boundary layer simulation

Following accepted criteria for wind tunnel simulation on structures [2], special attention is given to correctly reproduce the mean velocity and turbulence intensity variation with height that corresponds to the site. Often, this includes modeling of the upstream terrain, surrounding topography and objects surrounding the heliostat which may interfere with the oncoming flow. In the present study, an isolated heliostat is considered as this is believed to represent the worst design wind loading condition. Figure 2(a) presents the measured and target (ESDU [3,4]) mean wind speed and longitudinal turbulence intensity profiles. The figure shows the simulated profiles are in good agreement with the theoretical profiles over the height of the heliostat. Note the mean wind speed profiles in the figure are normalized to the mean wind speed recorded at a height of 10m.

WAVE NUMBER, f/V(l/m)

Fig. 2 (a) Mean wind speed and longitudinal turbulence intensity profiles; (b) Longitudinal wind spectra measured at 4.88m height

Similarity of the simulation also requires matching of the integral length scale of the turbulence, such that the sizes of the simulated wind gusts are adequately represented with respect to the geometry of the model. For examp le,

large gusts may completely envelope an isolated heliostat which will control the overall response on the structure, while smaller gusts will govern local effects on individual panels. Figure 2(b) presents the longitudinal wind spectra measured at 4.88m height in the wind tunnel, along with the target ESDU spectra [4]. The figure suggests the simulated matches reasonably well with the target distribution and is comparable to accepted wind tunnel studies at similar geometric scales.

2.3. Data acquisition

Local pressure measurements were recorded at 10° intervals for the full 360° azimuth range, considering structural symmetry. Pressures were sampled essentially simultaneously for 240 seconds at a rate of 400 samples per second. This corresponds to a full-scale equivalent sampling rate of 25 samples per second for a period of one (1) hour.

The pressure time series measured in the wind tunnel are referenced to a mean dynamic pressure at a height above the model outside of the simulated boundary layer. Full-scale predictions of pressures and structural load effects, for various return periods, may then be derived through integration of a wind climate model of the site. The wind climate model is based on historical records of wind speed and direction recorded at an airport anemometer located near to the solar park and adjusted for upstream surface roughness variations for all wind directions. Figure 3 presents the relative importance factors of the wind directionality at the site according to return period. As shown in the figure, winds from the north-north-west present higher probability of occurrence for extreme wind events, while low intensity winds with short return period are more likely to occur from the west. Inclusion of the local wind climate directionality in this manner provides structural loads and responses on the heliostat that are optimized to local wind variations, for both ultimate limit state design and serviceability.

Fig. 3. Wind directionality of the local wind climate according to return period

As an example, 50 year return period net differential pressures, calculated as the pressure difference between the front and rear panel surfaces, are presented in Figure 4. This corresponds to the worst local pressures on the heliostat surface, irrespective of wind direction, valid for the design of local structural elements with small tributary area (i.e. connections of individual modules). Positive pressures are defined as inward acting and suctions are defined as outward acting loads. Note that the distribution is slightly biased towards the west side of the heliostat. This is due to the site-specific wind climate model and the tendency to experience strong winds from the north-west of the site. If the heliostat were to be sited at another location, different design load distributions could be developed in accordance with the updated wind climate model, without necessarily retesting the model in the wind tunnel if the upstream terrain conditions are consistent. Alternative load distributions would also be expected for heliostats within the interior of a solar park.

Fig. 4. Net differential pressures (kPa) for a 50 year return period. (a) Inward acting pressures; (b) Outward acting suctions

3. Dynamic analysis

3.1. Determination of aerodynamic forces and load effects

Different pressure distributions, either balanced or un-balanced, are expected to occur for different wind directions, which will in turn yield dominant load effects on critical structural members of the heliostat. Via the analysis of these critical load effects on selected structural members, pressure distributions are developed which may be applied for the design of all remaining elements in the structure. The selection of these structural members is key to the efficient design of the structure and is performed in close consultation with the promoter.

The overall structural loads and responses on the heliostat are derived by integrating the local differential pressure loads measured in the wind tunnel, in combination with the tributary area associated to the corresponding pressure tap, and weighted by the mode shapes in the first 3 fundamental modes. The process is repeated at each time instant, for each wind direction, to create new time histories of the generalized forcing in the first three modes. A total of nine (9) global load effects are investigated in the current study: Uplift, Drag, MX0, MXi, Mx2, MZ0, MZA, MZB, MX0+ MZ0, as defined in Figure 5. Bending moments along the edges of the heliostat panel are included in the analysis for identifying worst case un-balanced loading distributions.

From integration of the point pressures time series, P(t), the quasi-steady response of each load effect, R, may be determined from:

where Pi is the pressure measured at location i in the wind tunnel, Ai is the tributary area corresponding to Pi and ^ is the influence coefficient for response R, at location i.

Of interest is the peak response of R, which is the summation of a quasi-static and resonant dynamic component. For structures that are not expected to experience significant resonant motion, the response may be estimated by scaling the quasi-steady component by a safety index, derived from the relationship between the dynamic inertial loading due to resonant oscillations and the dynamic quasi-steady background loading of the overall structure.

Fig. 5. Sign convention of selected global load effects

However, the fluctuating component may be significant for light-weight structures like heliostats and parabolic collectors and a detailed analysis is recommended in most cases. For the present study, the resonant response is derived following the gust factor approach, which is the summation of the mean and fluctuating components :

R = R + g [a

where g is a time-varying peak factor with a value generally limited to between 3 and 4.

The fluctuating response is made up of a quasi-steady background component, aB, and a resonant component, aRe:

^Re = I Sr (f)Af

where aF is the rms generalized force, K is the generalized stiffness of the structure which may be estimated from the generalized mass, and Sr(f) is the power spectrum of the resonant response:

Sr (f ) = YL^mA (2f )2 h (f)Sf (f ) H \f\2nf )2 Wl 2 mt 2*t,

il i 2

where mt is the mass at location i, fa is the mode shape at location I, Sf(f) is the generalized force spectrum, and H(f) is the mechanical admittance function. Damping is assumed as 1% of critical of the structure.

The resulting structural load effects are combined with the directional wind climate model of the site to derive loads corresponding to a range of return periods. Table 1 provides a summary of predicted 50-year return period global structural load effects, as defined in Figure 5.

The present study focused on an isolated heliostat. For field studies not only the atmospheric turbulence structure is to be taken into account (Fig. 2) but also that originated by the heliostats upstream It is noted though that the formulation presented herein, in the frequency domain, would capture the fluctuating pressure of that nature and the corresponding energy that is fed into the resonant and background components of the force. It may be the case, however, for larger and more even flexible systems that there may be concern that aerodynamic instabilities may occur. In such case the dynamic flow structure interaction needs to be properly addressed and the pressure model approach could be no longer acceptable.

Table 1. Global structural load effects.

Structural load Positive Negative

Uplift force (kN) 25.8 27.7

Drag force (kN) 73.4 72.6

Xo Moment (kN-m) 69.4 43.5

Xi Moment (kN-m) 39.9 32.4

X2 Moment (kN-m) 42.4 32.0

Zo Moment (kN-m) 110.0 109.0

Za Moment (kN-m) 432.o 507.0

Zb Moment (kN-m) 520.0 550.0

Mxo + Mzo (kN-m) 150.0 107.0

3.2. Equivalent static load distributions

The pressure distribution corresponding to each of the derived load effects is necessary for evaluating individual structural components of the heliostat. These are derived following the load-response-correlation (LRC) method [5], which considers the relative contribution of the quasi-steady and resonant components to the load effect, as well as the relative contribution of different wind directions.

As an example, Figure 6 presents the design load distribution derived corresponding to the negative Mxo moment. Note the loading on the panel is biased to the western surface of the heliostat due to the contribution of the wind climate model in the analysis as extreme wind loads are more frequently observed from the west of the site.

Fig. 6. Equivalent static load distribution (N) fora 50 year return period forthe negative Mx moment load case (a) y direction; and (b) z direction 3.3. Structural analysis

Based on the loading distributions derived from the wind tunnel data and site-specific wind climate model, stress analysis was performed on selected structural members. For the current study, load cases corresponding to the global

loading on the structure (drag, lift and overturning moment) were used to determine the stress loading on principal members of the structure, including the base foundation and the steel support components above the central column.

The steel structure and concrete foundation were modeled separately, but linked through common boundary conditions. Initial checks of stability against base sliding and overturning were performed by calculating the overall ground reaction loads at the base of the foundation. The total axial load includes the wind load corresponding to each load case, the structural self-weight and the base weight. The soil properties of the site (sandy soil with a 30° angle of internal friction) are assumed for determining the resistive properties of the structure.

The advantage of the approach is apparent when viewing the derivation of global loading at the base of the structure. Typical design following the Eurocode implies a perceived conservative approach of simultaneously applying the global loading on the structure. In the present study, Eurocode recommended values for foundation design were calculated as a 9.16t axial load, 12.24t of shear and 34.28t.m of moment at the base.

In comparison, Table 2 provides a summary of the loading following the methodology in the present study, normalized with respect to the recommended code value. The Table shows the wind tunnel derived loads are significantly lower than Eurocode recommended values for some cases, but are higher in others. For example, the axial (vertical) load is less than half than the code recommendation. However, this is not necessarily to the benefit of the final design of certain elements of the structure. While this may alleviate the forcing on the panel rotating system, the reduced axial loading produced instability in the foundation due to overturning in some load cases.

Table 2. Foundation loads for selected load cases normalized to Eurocode recommended values.

Load Case Axial Nz Shear Vy Moment Mx

1 -0.14 0.31 -0.73

2 -0.31 0.64 -1.20

3 -0.16 0.34 -0.69

4 0.31 -0.63 0.98

5 -0.04 0.04 0.06

6 0.25 -0.51 0.82

7 -0.32 0.65 -1.18

8 0.29 -0.60 0.96

9 0.20 -0.42 0.75

4. Conclusions

This paper presents a methodology for dynamic analysis of a heliostat to wind loading through pressure model testing in a boundary layer wind tunnel. The procedure is routinely used in evaluating wind effects on tall buildings and singular structures, and is adapted to an isolated heliostat in the present study. In combination with instantaneous pressure distributions measured in the wind tunnel, the structural properties of the heliostat and the local climate of the site, the dynamic response of the structure is derived and presented at equivalent static pressure distributions for design. Analysis of load effects on governing structural members leads to optimized design of individual heliostats and potential further optimization by extending the wind tunnel study to include large scale studies of the entire solar park and the influence of surrounding heliostats on the dynamic loading.

Acknowledgements

This study was partially initiated and sponsored by Sacyr S.A.U. the co-operation and continued interest of various members ofthis organization is acknowledge and greatly appreciated. Notethat original location and wind speeds have been purposfully omited

References

[1] Peterka, J.A., Tan, Z., Bienkiewicz, B., Cermak, J.E. Wind loads on heliostats and parabolic dish collectors. SERI/TP-53-3668. Goldon, Colorado; Solar Energy Research Institute; 1988.

[2] ASCE. Wind tunnel model studies of buildings and structures. ASCE Manual and Reports on Engineering Practice No67. American Society of Civil Engineers. Reston, Virginia, USA; 1999.

[3] ESDU. Strong winds in the atmospheric boundary layer. Part 1: Hourly mean wind speeds. Engineering Science Data Unit. ESDU Data Item 82026; 1982.

[4] ESDU. Characteristics of atmospheric turbulence near the ground. Part 2: Single point data for strong winds (neutral atmosphere). Engineering Science Data Unit. ESDU Data Item 85020; 1985.

[5] Kasperski, M. Extreme wind load distributions for linear and nonlinear design. J Eng Structures 1992;14:27-34.