Chapter 5

Chapter 5, Technical Studies

Section 5.5: Characterization of Wind Loading

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5.5.1 INTRODUCTION

Understanding the role of wind in the design of a next generation telescope will be fundamental owing to two concerns: (1) the direct effects of wind-buffeting on the mechanical structure and other subsystems; and (2) the indirect effects on local seeing resulting from thermal effects and turbulence induced by air flow around structural elements. This chapter summarizes our efforts to understand these effects based on analysis and measurements of wind loading on current generation telescopes. Our studies represent first steps toward a deeper understanding of how to model the effects of wind on extremely large telescopes (ELTs), and how to mitigate these effects via appropriate choice of site, enclosure, structural design, and adaptive optics (AO).

The first concern is wind-buffeting. As air moves across the structure, the incident pressure causes structural deformations. These deformations affect both the primary mirror (M1) and the secondary mirror (M2). Because of the extremely tight tolerances required for operation in optical and near-infrared wavelengths, such deflections must be kept to a minimum. The problem is compounded by the nature of the loading. With the advent of AO, it is possible to correct slowly varying errors caused by gravity and changing temperature. Very high frequency disturbances are generally small enough to be ignored. However, wind loading presents a challenge because it is a dynamic load at a low enough frequency to produce significant displacements.

Telescope designers have traditionally provided wind protection for the telescope by enclosing it in a tightly enclosed dome. However, measurements made at the Multiple Mirror Telescope (MMT)1,2, the Anglo-Australian Telescope (AAT)3, and elsewhere showed that significant improvements in seeing were possible if local temperature effects could be reduced. During the design of the current generation of large telescopes, water and wind tunnel testing and computational fluid dynamics (CFD) were used to analyze the air flow in and around telescope enclosures, with the goal of developing designs with better ventilation to flush out warm air trapped in the enclosure. As a result, modern enclosures generally provide large, adjustable vent areas or active ventilation systems to address the local seeing issue, while still mostly shrouding the telescope structure. These designs have reached a balance between providing sufficient air flow to ensure good seeing and providing sufficient blockage to protect the structure from wind- buffeting under a variety of external wind loading conditions.

Many current proposals for ELTs are for telescopes of 30-m diameter and larger. Until now, primary mirror diameters of this size have usually been associated only with radio telescopes. In contrast to optical/infrared (O/IR) designs, large radio telescopes are generally operated in the open air, but have dramatically lower surface accuracy requirements. Even so, wind-buffeting is a concern for such telescopes both in the pointing accuracy and, for mm- and sub-mm-wave systems, the surface accuracy. Addressing the seeing and wind-buffeting problems for ELTs is particularly formidable. They have a considerably larger cross section to the incident wind, increasing the total loading and the quasi-static deflections. Very large structures also have lower natural frequencies, resulting in a larger dynamic response in the wind. At the same time, the potential for sharper images (because of the smaller diffraction-limited full width half-maximum (FWHM) reduces the tolerance for wind-induced image motion.

The other concern is local seeing, which is determined by variations in temperature between the telescope, the enclosure, and the surrounding air. This effect can be dramatically reduced by allowing air flow through the enclosure and across the telescope and mirror. Such air flow removes localized warm air layers and also aids in bringing the system to equilibrium with the outside air temperature.

Although it is understood that local seeing and wind-buffeting cause dynamic blurring and motion of the image, there are many unknowns in designing to address the problem. To actually design a successful ELT, there are several key wind characterization issues that must be understood.

5.5.1.1 The Seeing Problem

5.5.1.1.1 Ventilation of a Large Enclosure

As the size of an enclosure increases, the size of the ventilation openings must increase as well. Indeed, if an existing enclosure design is scaled proportionally, the ratio of vent area to the projected enclosure cross sectional area remains constant. However, the total vent area increases as the square of the structure size, while the volume contained within the dome increases as the cube. This suggests that for the same inlet wind velocity, an enclosure for a 30- m-class telescope could take four times longer to change the air than a similar enclosure for an 8- m version.

Although the actual requirements for either air flow rate or enclosure flushing rate are not well known, an understanding of this problem will be essential in scaling an enclosure design to accommodate an ELT. The extent to which AO systems can correct for local seeing, thus reducing ventilation requirements, must also be understood.

5.5.1.2 The Buffeting Problem

5.5.1.2.1 Characterization of Wind-Buffeting

In order to design an adequate telescope structure, one must be able to predict the amplitude, distribution, and frequency content of both the incident wind load and the response of the telescope structure. For such a large leap in scale, it is advantageous to base these predictions on direct measurements of wind-buffeting and structural response at large existing facilities. When combined with a finite-element analysis (FEA) of the structure, such tests allow the creation of a benchmark to show the level of prediction possible by CFD and FEA.

Most of the wind characterization data for proposed sites will be measurements of wind velocity. However, to predict the response of an ELT structure to wind-buffeting, it is necessary to quantify the incident forces applied by the wind. This suggests that it is necessary to measure the applied forcing on the telescope by direct measurement of pressures and by extraction from structural response data. These force measurements can then be compared with simultaneously measured local wind velocities to determine the conversions from wind velocity to drag force that are appropriate for dynamic wind loading in this type of structural environment.

An understanding of the wind input measured at existing facilities will demonstrate the predictability obtainable from modeling, and will bound the design problem in terms of required structural stiffness, range of actuator strokes in the active and adaptive optics systems, and the required bandwidths on the control systems.

5.5.1.2.2 How to Scale Measurements to ELTs

A critical component of applying the benchmark results will be determining how to scale those results to the larger scale of an ELT (for example, the 30-m GSMT point design). An understanding of such scaling must be obtained from a combination of measurements, simulations, and an understanding of fluid mechanics. The scaled wind loading will ultimately be the basis for the generation of dynamic load cases for structural analysis of an ELT.

5.5.1.3 Separating the Effects of Telescope Wind Loading

The deleterious effects of wind-buffeting are primarily caused by the dynamic portion of the wind loading. In order to optimize the design of the facility to limit wind-buffeting effects, it is necessary to understand the source of the dynamic content of the wind force. In general, this may be from (1) turbulence in the incoming wind arriving at the enclosure, (2) turbulence induced by passing through openings in the enclosure, and (3) turbulence generated by interaction of the wind with surfaces on the telescope structure itself. These are discussed below.

5.5.1.3.1 Local Topography

Turbulence in the wind arriving at the observatory is a combination of the dynamic content of the wind approaching the mountain and the turbulence generated by interactions with the local topography of the summit. This is a complex situation that depends not only on local wind direction, but also on the local thermal environment. It will be necessary to simulate the wind flows at proposed sites, as was done for many of the current generation of 8-m telescopes. Given the importance of the wind-buffeting problem, such modeling should be done fairly early in the site selection process (see Section 5.2).

The direct measurements of wind velocity described above should include measurements that can be used to calibrate CFD studies of the effects of local topography.

5.5.1.3.2 Enclosure Design

In addition to the ventilation issues for a large enclosure, it is important to understand the effects of the turbulence generated by the enclosure as the wind enters the slit and the vents. CFD simulations of different types of vents and enclosure geometries, combined with the analysis of in-situ measurements at existing facilities, will help guide the enclosure design.

5.5.1.3.3 Telescope Feature Shapes

Dynamic loading of telescope structures may be largely generated by turbulence induced by the interaction of the wind with the telescope structure itself. As a final mitigation against wind- buffeting, fairings might be used on parts of the telescope structure to reduce vortex generation caused by the flow around the structure. An understanding of such effects would likely not alter the fundamental design of the telescope structure, but could potentially reduce the dynamic variations of wind pressures on the system and thus reduce the requirements on the active/adaptive compensation systems.

5.5.2 SUMMARY OF PREVIOUS STUDIES

Each of the large telescope projects of the current generation has had to contend with local seeing and wind-buffeting effects, and a number of papers and reports have been written on wind loading of astronomical telescopes. Prior to considering what new studies are necessary to address the issues outlined in the previous section, it is worthwhile to review the results, information, and unresolved questions from previous studies of local seeing and wind loading on enclosures and telescopes. As we begin to design even larger telescopes, we need to learn everything we can from the 8-10-m class facilities.

5.5.2.1 Local Seeing Studies

During the design of the current generation of telescopes, many of the old paradigms concerning telescope enclosure design were challenged. Traditional, relatively expensive designs, with the telescope mounted in a tightly-closed, hemispherical dome on top of a multi-purpose observatory building, were found to provide inferior seeing compared with less expensive structures such as the lower, box-like design employed by the MMT.2,4 In spite of the larger opening and correspondingly greater exposure to wind, the MMT experience indicated that their best image sizes were obtained under a 10-20 mph wind.5 These realizations led to a revolution in enclosure design, in which ventilation of the dome was recognized as being as essential as wind protection.

To understand how to reduce enclosure-induced seeing, many groups performed experiments via scale model testing of flushing efficiency of different dome designs. A good example of this is the Gemini Observatory enclosure study conducted at the water tunnel facility at the University of Washington.6 In this test, the importance of ventilation was demonstrated dramatically (see Figure 1). Comparisons of flushing times with and without vents for the various designs revealed that improvements of a factor of 2-8 were possible. Additionally, a test of a cylindrical enclosure with a large slit opening but without cross-flow ventilation from side vents showed no improvement during side winds, confirming the notion that through flow is critical to exchanging the air and improving seeing.

Figure 1 Water tunnel test of an early model of a Gemini enclosure. In this case, the side vent
openings

 were closed and dye injected in the telescope chamber vented slowly, mostly through
the

 observing slit. (Reprinted from Reference 6.)

Since the revolution in enclosure design philosophy, existing telescopes have added active or passive ventilation systems to their enclosures, resulting in improved performance. It is clear that such an approach will also be necessary in the design of any enclosure for an ELT.

5.5.2.2 Site Wind Characterization

Previous contributions have also been made in the area of wind characterization, both in the site selection of telescopes and in the operation of existing facilities. Indeed, most observatories monitor the wind speed and direction as a standard operating procedure, and several make use of instruments capable of measuring the velocity spectrum out to moderate frequencies. Wind power spectra have been published for several sites 7,8 and vary in their behavior. While some results track the classical Davenport9 spectrum, others appear to have more energy in higher frequencies, in line with the Antoniou10 spectrum. An example of such data from Reference 8, taken from San Pedro Martir, is shown in Figure 2. The published results of such tests have frequently been limited to a single sensor at a single location, and often do not include enough time in the sample to allow for long averaging, resulting in a noisy appearance. However, they confirm that the usual design spectra generally bound the problem.

Figure 2 Power spectral density of wind velocity fluctuations measured on San Pedro Martir,
April 17, 1999. Average horizontal wind speed was 9.2 m/sec. The ultrasonic anemometer was
located on a mast 6.8 meters above the ground. (Reprinted from Reference 8.)

There have been many wind tunnel tests of proposed telescope and enclosure designs.11,12,13 These tests have generally been intended for calculation of survival condition loads on the enclosure or telescope, and for calculation of mean pressures on parts of the structure (e.g., the primary mirror). Such studies are helpful because they provide scale model measurements under controlled conditions and can provide information on the static component of the pressure distribution. It is worth noting that these studies cannot generally be used for investigating dynamic interactions between the structure and the flow, because it is difficult to achieve dynamic scaling and size scaling simultaneously. Flow visualization has also been performed in these tests, but is typically limited by what is visible.

To extend the wind tunnel results, it has become increasingly common to employ CFD analyses in predicting the behavior of wind flow within the environment of the enclosure and in the area around the site. This technique was employed extensively, for example, to investigate the effects of local topography at both Mauna Kea and at Cerro Pachon.14 The approach has the advantage of allowing visualization and recovery of the local conditions (velocities, pressure, etc.) at a large number of points, and it allows changing of flow conditions, such as wind speed and direction. Figure 3 shows the type of result available from this kind of analysis.

Figure 3 Magnitude of vorticity in a cross section of the atmosphere immediately above the
summit of Mauna Kea. Vorticity increases from zero (dark blue), or laminar flow, to the maximum
value shown as red. The free stream wind speed was 20 m/s, from the west. (Reprinted from
Reference 14.)

In this case, the analysis was used to confirm that upwind topographic features did not have a significant influence on performance, and that the proposed height of the telescope pier would put the primary mirror above the turbulent boundary layer for the majority of wind conditions at the site.14

5.5.2.3 Wind-Buffeting

The types of studies mentioned above did not produce data that are very useful for predicting dynamic wind loading on the telescope, particularly the primary mirror. Water tunnel tests provide visualization of flow patterns but can't give accurate quantitative information about the wind loading. Measurements of spectra made at observatory sites do not take into account the effects of the enclosure and telescope in increasing wind turbulence, but several studies4,15,16 have reported increased wind energy at higher frequencies inside telescope enclosures, particularly with the telescopes pointed close to the zenith rather than facing into the wind. CFD studies13,17,18 have been limited in the amount of detail they can model, and have usually been used to predict only average pressure variations (see Figure 4). Wind tunnel tests offer insights into average pressures at various points on telescope models (at the primary mirror, for example), but the several orders of magnitude difference in Reynolds number makes the accurate simulation of turbulent effects impossible, even when model features have been made intentionally rough. In addition, the pressure taps are normally recorded individually.

The problem is that both the spatial and temporal frequency of the wind loading on the telescope are crucial to determining the structural response. For example, most large telescope mirror support systems can handle uniform wind pressure on the primary mirror, because it is only a small fraction of the mirror weight. Similarly, telescopes with active optics systems, either large- mirror bending systems or segmented-mirror position control systems, can compensate for a quasi-static non-uniform wind pressure pattern, provided that the rate of change of the pattern is slow compared to the update cycle of the active system (slower than 0.1 Hz, for example). The problem comes from nonuniform pressure patterns that change with time, at rates faster than about 0.1 Hz. Therefore, to understand the effect of wind-buffeting on an ELT primary mirror, it is necessary to understand both the spatial and temporal variation of wind pressure.

Several studies have attempted to measure wind pressure simultaneously at several points on a telescope primary mirror. The Subaru Project made measurements at the Canada France Hawai'i Telescope,19 using differential pressure sensors to record the pressure difference between the front and back of the CFHT mirror cover. However, only five sensors were used, so the spatial information they obtained was limited. Similarly, Forbes and Gabor7 measured patterns of pressure at the MMT and at the United Kingdom Infrared Telescope (UKIRT), with differential pressure sensors recording pressure differences between the front and back of the mirror covers. They only used four sensors; again, the spatial information was limited.

The most important measurements of wind-buffeting prior to the recent tests at Gemini South (see 5.5.3.1) were those taken by ESO at La Silla.16 In these tests, 13 pressure taps were arranged on a 3.5-m plywood dummy mirror, as shown in Figure 5, and placed in an inflatable dome for some tests and in the New Technology Telescope (NTT) enclosure for others. In these tests, the 13 measurements were fit with eight Zernike polynomials in order to gain insight into the frequency response and pressure distribution on the mirror. In all cases, the data were normalized according to the measured mean wind velocity for the time record. While some power spectral density (PSD) data were published from this data set, it does not provide much information into the instantaneous pressure distribution across the mirror or the correlation of the pressure between points. Further, the dummy mirror was not part of a telescope structure and was not located in the position it would occupy in a dome. Even so, this was the best information available at the time of construction of the Gemini telescopes, and the data were used as part of the basis for their analysis.

Figure 4  Results from three-dimensional computational fluid dynamics analysis of flow past a
disk

 representing a telescope mirror cell, assuming steady-state incompressible flow. (Figures
reprinted

 from Reference 17.)

Figure 5 Distribution of the pressure sensors on the ESO 3.5-meter dummy mirror. Reprinted
from Reference 16.

A fairly recent measurement that is also relevant to the design of an ELT resulted from a series of tests performed at the Nobeyama 45-m mm-wave radio telescope, described in Appendix 5.5 A. These tests were primarily intended to investigate the pointing performance of the structure in wind, and combined on-sky pointing measurements with direct measurement of structural motion via a large number of accelerometers. Because the size of the structure (and thus its natural frequency) is comparable to many ELT concepts, the data provide useful information on the frequency and amplitude of structural response due to wind. For example, for a parked telescope in calm wind, the typical motions of an accelerometer near the periphery of the primary reflector, as shown in Figure 6, were on the order of a micron RMS (root mean square), and most of this was below the 2 Hz bending mode of the reflector.

By comparison, when the wind was blowing at about 6-8 m/s, the vibration of the structure increased by nearly a factor of ten (see Figure 7). Analysis of the corresponding deflections indicates that the motion will be greater than one micron RMS unless the errors are corrected to just over 4 Hz. While some of the low frequency increase is due to rigid body tilt, the higher frequency content results in additional modes contributing significantly to the motion of the surface. It is worth noting that for this case the response also exhibits a group of double-peaked narrowband responses at low frequency, which is characteristic of vortex shedding from different parts of the structure.

The Nobeyama results also indicate that motions of the M2 support are likely to be tens of microns.

A final useful lesson from the Nobeyama test is that the tracking of the telescope introduces almost as much vibration as the higher wind. Figure 8 shows the response of the same accelerometer during calm wind with the telescope tracking a source. The peak at 0.9 Hz was due to a feature within the controller. However, there is a broadband increase in the vibration disturbance to the structure. This demonstrates that tracking smoothness will be extremely important in the design of an ELT, and argues for hydrostatic azimuth bearings (as used on many optical telescopes), instead of the wheel-on-track design of the Nobeyama radio telescope.

Figure 6 PSD of structural response of Nobeyama radio telescope, with telescope parked and
calm

 wind. Reprinted from Appendix 5.5 A.

Figure 7 PSD of structural response of Nobeyama radio telescope, with telescope parked and
wind

 6-8 m/s. Reprinted from Appendix 5.5 A.

Figure 8 PSD of structural response of Nobeyama radio telescope, with telescope tracking and
wind

 6-8 m/s. Reprinted from Appendix 5.5 A.

5.5.3 SUMMARY OF GEMINI SOUTH STUDIES OF WIND-BUFFETING

During the integration of the Gemini South telescope on Cerro Pachón in 2000, there was an opportunity to make direct measurements of telescope wind loading. A series of measurements was taken by Gemini staff working in collaboration with faculty and students of the University of Massachusetts at Lowell and the University of Arizona, in a program designed to remedy some of the limitations of the previous wind studies cited above.

Because of the circumstances, Gemini South was the ideal instrument for this test. It is a large optical telescope and is located in an enclosure that has extremely large vent gates. This allows wind loading conditions from nearly fully protected to nearly fully exposed (see Figure 9). Perhaps even more importantly, Gemini South was an ideal choice because the telescope had reached a point in construction at which it was capable of controlled motion, but the primary mirror had not yet been installed. The "dummy" primary mirror provided a location for direct mounting of pressure transducers, while maintaining approximately the same mass and stiffness as the final mirror. The absence of the final optics also enabled a risk-free impact test of the structure to provide good modal characterization, which can ultimately be used to validate or improve finite- element models. Finally, the Gemini telescope design was subjected to an intensive modeling and testing effort during its design phase, so there is a substantial set of analytical and scale- model data that can be used to generate an analytical benchmark to be compared with the experimental results.

To take advantage of this testing opportunity, we conducted two sets of tests. In the first set, the telescope was instrumented with 24 pressure sensors, five anemometers (each capable of simultaneous measurement of three directions of wind speed), and 74 accelerometers. The second set of tests included only pressure and wind speed, but employed 32 pressure sensors and five anemometers (an additional anemometer was available for some tests).

Figure 9 The Gemini enclosures have large ventilation gates on their sides to allow natural
ventilation with ambient air.

5.5.3.1. Wind Pressure Tests: Group 1

In the first set of tests, there were two types: modal tests and operating tests. Modal data were taken at zenith pointing in maximally quiet conditions using an instrumented impact hammer to put a controlled input into the structure.20 The operating data were taken under a variety of telescope and enclosure configurations using the wind as the structural disturbance. Naturally, the response of the telescope varies widely with the wind loading conditions. Even the modal frequencies of the telescope vary somewhat with the elevation angle. As a result, it was impossible to cover the full testing parameter space in the time available for testing. Rather, as a practical matter the number of tests was reduced.

The operating data tests could not be taken at a single configuration, because the goal of the test was not only to determine the worst-case wind loading, but also to characterize the effects of the wind under a range of conditions. As a result, the following parameters were varied for the test:

  1. Wind azimuth angle of attack (AoA)
  2. Telescope elevation angle (El)
  3. Upwind vent gate position (UVG)
  4. Downwind vent gate position (DVG)

Additionally, one test was performed with the lower windscreen raised into position.

To illustrate the difficulty in fully covering the parameter space, consider varying the azimuth AoA from 0 (looking into the wind) to 180 (looking out of the wind) in 45-degree increments. This results in a total of five values. Varying the elevation angle to 30, 45, 60, and 75 degrees provides four distinct values. Finally, there were three vent gate positions of interest (open, half, and closed) for each of the vent gates. Covering the full combinations of this parameter space would result in 5*4*3*3 = 180 tests. Unfortunately, it would be impossible to obtain this many tests with anything resembling constant wind conditions. It is also worth noting that in the entire testing run, we were able to make fewer than 50 operating tests, so even this coarse sampling would not have been achievable.

Because it was impossible to provide full coverage of the parameter space, we elected instead to take a statistical approach to the test using standard design of experiments (DOE) approaches.21 In this way, we obtained better resolution in each of the parameters with many fewer tests. The main tests falling into this category were an L16 array and two L9 arrays. In the L16, the four parameters were varied to two values apiece, and all combinations were taken. Further, because not all of the tests could be taken on the same night, the tests were optimally "blocked" to reject any systematic differences between the nights. Although the L16 covered a comparatively small range of parameter space, it has the advantage that it provided information on interactions caused by varying parameters simultaneously. The two L9 measurements were taken on different days. Each one covered a larger area of parameter space than the L16; each parameter was varied to three different values. However, the tradeoff was that these tests could give no information on effects caused by changing two of the parameters simultaneously.

As stated above, for this test there was a total of 74 channels of accelerometers, located on the structure as shown in Figure 10. For most of the operating tests, however, only 62 of these were used to leave room in the acquisition system for the pressure transducers. (The twelve channels removed were four sets of triaxial accelerometers on the main weldment around the primary mirror cell.) There were 24 pressure transducers, and all were located on the primary mirror with the layout shown by the red dots in Figure 11. Finally, there were five ultrasonic anemometers, each measuring wind speed in three directions. Three were located at the outer edge of the main weldment (+X, -X, and -Y), one was located at M2, and the final one was installed on the top of the dome. For each test, time data was collected and stored directly to the hard drive for later processing. Each operating test was five minutes (300s) in length. The accelerometers and pressure transducers were sampled by one system with a sample rate of 200 Hz. The pressure transducers were also sampled (together with the anemometers) by a second acquisition system with a sample rate of 10 Hz.

Figure 10 Locations of accelerometers on the Gemini Telescope structure. Figure 11 Locations of pressure sensors on the dummy mirror. The 24 sensors shown in red
were

 used for the first set of tests; the eight sensors shown in blue were added for the second
set.

The modal tests were performed using all 74 accelerometers and an instrumented impact hammer. Because of the large accelerometer count, the hammer was used at only a few locations near the secondary. A modal characterization report was produced by the University of Massachusetts at Lowell Modal Analysis and Controls Laboratory.22

The operating data conditions covered a wide parameter range. A more complete description of the tests and layout is available at the NIO website.

5.5.3.2 Wind Pressure Tests: Group 2

To expand on the data taken in the first round of testing, eight additional pressure transducers were added, as shown by the blue dots in Figure 11. An additional anemometer was added at the +Y location on the primary mirror cell, but was removed again to serve as a replacement following failure of the dome sensor. As a result, most of this series of tests have velocity measurements at the same five locations as the Group 1 tests. In this series of tests, the opposite side of the structure was chosen as the "upwind" side in order to confirm symmetry of the results, and again a large number of configurations were tested. This additional coverage includes a set of measurements that are suitable for combination with the Group 1 tests to confirm the results.

5.5.3.3 Data Products

The tests produced a large volume of data. There were 116 operational test runs of five minutes each, with up to 114 channels of sensors. This wealth of data is both a great asset and a sizeable challenge. The New Initiatives Office (NIO) has already invested considerable effort in data reduction, as described in References 23, 24 and 25 for example, but further data analysis is ongoing.

Examples of the data products currently available for each of the 116 test cases include the following.

Wind velocity data:

Wind pressure data:

Figure 12 shows an example of maps of the average and RMS pressures.

Figure 12 Pressure maps for a case pointing into the wind, with both vent gates open. The map
on

 the left shows the average pressure pattern; the map on the right shows the RMS pressure
variation

 as a function of position. Black dots identify the locations of pressure sensors.

Animations of the pressure patterns, along with contour maps showing dynamic distortion of the mirror figure, are shown for three of the test cases in Appendix 5.5 B.

5.5.3.4 Evaluation of Results

5.5.3.4.1 L16 Experiment Group

Some interesting results from the first study can be seen in an analysis of the 16 configurations chosen to fill out the L16 experiment. This group of tests is of particular interest because it provides an estimate of the total random variability in the experiment. This makes it possible to identify those effects that are significant. For example, Figure 13 shows the average PSD of the (spatial) average pressure for the 16 tests, together with the average PSD for those cases with the upwind vent gate open and the average PSD for the cases with the upwind vent gate closed. Additionally, it shows the error bars per channel. From the figure, it is clear that the state of the upwind vent gate is significant, because the effect on the PSD is well outside the error bars. It can be seen that the effect of opening the upwind vent gate was, on average, to increase the pressure PSD by a factor of ten.

Figure 13 Comparison of the average pressure PSD for the 16 tests, with error bars, with the
average

 pressure PSD for those cases with the upwind vent gate open and the average PSD for
the

 cases with the upwind vent gate closed.

For the other parameters considered (see Figures 14-16), the results are less dramatic. On average, there is a difference between cases having 0 and 45 degrees of mean azimuth angle of attack. However, it is not much above the noise, and there is a similar small effect due to the position of the downwind vent gate. The surprising result was that there was no statistically significant change in the average PSD at the primary mirror due to changes in elevation angle of the telescope. While this is surprising, it is worth noting that this result is consistent with a result from the La Silla testing (Reference 16), in which the average pressure was found to depend on the elevation angle, but the pressure variations did not.

Another advantage of the L16 experiment is that it allows investigation into interactions between factors. For this data set, the most significant interaction is between the AoA and the UVG position. This is not surprising, as one would expect the position of the upwind gate to be more important for a strong crosswind component when compared with a nearly direct headwind.

Figure 14 Comparison of the average pressure PSD for the 16 tests, with error bars, with the
average

 pressure PSD for those cases with azimuth angle of attack 0 degrees, and the average
PSD

 for the cases with azimuth angle of attack 45 degrees.

Figure 15 Comparison of the average pressure PSD for the 16 tests, with error bars, with the
average

 pressure PSD for those cases with the downwind vent gate open and the average PSD
for

 the cases with the downwind vent gate closed.

Figure 16 Comparison of the average pressure PSD for the 16 tests, with error bars, with the
average

 pressure PSD for those cases with telescope elevation angle 30 degrees, and the
average

 PSD for the cases with telescope elevation angle 60 degrees.

5.5.3.4.2 L9 Experiment Group

The L9 experiments were performed to provide increased resolution in the testing. Specifically, by using the L9 experiment design (Reference 21) to sample four effects at three levels each, it has been employed here as a 'fully saturated' (i.e., maximally efficient) design. The advantage of this type of test is that it provided information about a wide parameter space. The main disadvantage is that it provides no estimate of the total random variability, so it is more difficult to say which effects, if any, are statistically significant. Additionally, it provides no information on the interaction between effects.

One of the most interesting results is evident from Figure 17. Even without error bars on the experiment, it is evident that there is essentially no change in the average pressure PSD when the upwind vent gate is changed from half to fully open. That is, for significant wind speed, the full excitation has been reached by the time the vent gate is half open.

Figure 17 Comparison of the pressure PSDs for those cases in the L9 set with upwind vent
gates

 open, half open, and closed.

5.5.3.5 Predicted Deformation of the Gemini Primary Mirror

Although the pressure on the Gemini primary mirror varies in a complex way with high spatial frequency content, the deformation of the primary mirror itself is simpler. This arises because the mass and stiffness of the primary makes it act as a "filter" to the incoming force. As a result, most of the deflections due to the complicated incident forcing distribution are manifest as piston, tip, tilt, focus, and astigmatism. After the removal of the rigid body modes, the remaining deflection pattern is essentially astigmatism (see Reference 23, included as Appendix 5.5.C). The higher spatial frequency components of the forcing are insignificant because the stiffness of the mirror against that mode of deformation is substantially higher. This is well illustrated by Figure 18.

Based on these analyses, it was concluded that, to meet the Gemini error budget, the allowable velocity at the primary mirror is approximately:

VM1 = 3.2 - 0.8 cos(q)

in meters per second, where q is the azimuth angle of attack of the incoming wind. Because this value is based on deformations of the solid 8-m mirror, a lower wind speed limit may be necessary on a larger telescope.

Figure 18 The surface map on the left shows the distribution of pressure on the surface of the
Gemini

 primary mirror at a single moment during a wind test, with the telescope pointing into the
wind,

 both vent gates open, and the telescope tilted 30 degrees from the Zenith. The scale is in
pascals.

 Notice that the areas with negative pressure are as large as those with positive
pressure.

 The surface map on the right shows the resulting mirror deformation calculated by
finite-element

 analysis, after removal of piston, tip, tilt, and focus. The remaining aberration is
almost

 entirely astigmatism. The scale is in microns.

5.5.3.5.1 Lessons Learned

Although we are still in the process of developing a full understanding of the fluid mechanics involved in telescope wind loading, several insights are apparent from an examination of the Gemini data. Some of these are listed below:

5.5.4 IDENTIFYING SOURCES OF PRESSURE VARIABILITY

One of the fundamental wind loading issues concerns the identification of the source of the pressure variation on the telescope. It could come from several sources, including: (1) the variability of wind velocity and direction in the free stream; (2) turbulence generated by the passage of the air through openings in the enclosure; or (3) the induced flow and vortices caused by the wind passing around the telescope structure itself. Separating these effects presents a challenge, as the measured flow around the telescope reflects a combination of these effects, but we can gain some insights by examining particular test cases .

Many of the plots of RMS pressure variation (for example, the plot on the right side of Figure 12) show the highest variation close to the edge of the mirror, implying that the turbulence is generated by air passing over the structure around the mirror. Upstream vortices would be expected to have a more uniform effect on the pressure variability across the mirror. Figure 20 illustrates the point-to-point difference in pressure variation.

Figure 19 Time history of (spatial) average pressure on mirror surface. The telescope was
pointing

 into the wind, 30 degrees from the Zenith, with both vent gates open. Note the long
period

 variation at frequencies down to 0.01 Hz. Figure 20 Pressure graphs for the test case shown in Figure 12. The graph on the left is a time
history

 from pressure sensor 12, located on the right side of the mirror. The graph on the right is
from

 sensor 13, located on the left side. Note the difference in magnitude of pressure fluctuation.

In the case shown in Figure 12, the air is flowing generally in the +Y direction over the mirror (the V component of wind velocity), and on the left side of the mirror the air is flowing generally towards the right (the U component). An area of higher pressure variation appears above and to the right of the central baffle, which may be caused by vortex shedding from the baffle structure. Similar features are seen in many other plots.

It is also possible to identify a number of cases in which the air flow is approximately parallel to the mirror surface. This condition occurs when the vent gates are open and the telescope is either zenith pointing or is pointed perpendicular to the wind in azimuth. Under these conditions, the air flow pattern is relatively simple, with the direction of air flow approximately the same over the entire surface. Twelve of the Gemini South test cases fit this criterion - Figure 21 and Table 1 show data from a typical case.

Figure 21 Data from test c09030oo, with the telescope oriented perpendicular to the wind
direction

 and tilted 30 degrees from the Zenith. Both vent gates were open, and the wind was
coming

 from the right. The color contour map on the left shows average pressures on the surface
of

 the 8-m diameter Gemini mirror - full scale is +/-5 pascals. The contour map on the right shows
the

 RMS amplitude of pressure variation as a function of position - the range of variation is 0-3
pascals

 RMS. Black dots identify the locations of pressure sensors.

Table 1 Wind velocity data for test case c09030oo.
Anemometer
Location
Velocity
X-component
(m/sec)
Velocity
Y-component
(m/sec)
Velocity
Z-component
(m/sec)
Resultant
Velocity
(m/sec)
RMS variation of
resultant velocity
(m/sec)
+X-9.01.32.49.50.9
-X-6.30.70.46.51.1
-Y-8.61.80.18.81.0
M2-1.6-1.0-0.42.41.0
Dome1.3-1.71.13.41.3

Similarities are apparent in all twelve of these cases. First, regardless of wind direction, the "incoming" side of the mirror is always characterized by negative pressures, and the "outgoing" side by positive pressures. For example, in the ten cases with telescope orientation perpendicular to the wind, all having average wind speeds above the mirror in the 4-10-m-per-second range, the average amplitude of moment about the Y-axis ranged from 120 to 304 N-m. Second, the areas that exhibit the highest RMS variation in pressure tend to be on the sides of the mirror surface, relative to the wind direction.

Because these effects occur whether the wind is from the front, right, or left of the enclosure, and occur whether the vent gates are fully or only half open, this indicates that the average pressure pattern on the mirror and the pattern of the amplitude of RMS pressure variation are strongly influenced by the telescope structure itself, at least in these high-air-flow cases. Consequently, we plan to put increased emphasis on understanding how turbulent wind-buffeting effects can be ameliorated by aerodynamic design of the telescope.

However, Reference 25, included as Appendix 5.5.D, evaluated the dynamic variation of pressure in four of these same cases and found that, over most of the mirror surface, the characteristic bandwidth of the pressure PSD and the correlation length exhibited by the structure function correlated with the size of opening in the enclosure in the manner predicted by Kolmogorov turbulence models. This implies that dynamic compensation requirements may be driven by the design of the enclosure.

This study also found that in certain localized areas, for example, directly behind the baffle at the center of the primary mirror, the bandwidth was shifted to higher frequencies, indicating local areas of increased vorticity apparently caused by the interaction of the wind with the telescope structure.

Clearly, the air flow environment around a telescope is complex. It appears that part of the pressure and velocity variations are caused by the enclosure, although much of the variation appears to be the result of air flow over the telescope structure itself. More measurements are planned to continue investigating this question.

5.5.5 NEXT STEPS

Although the previous studies and the on-going analyses have already provided information critical to the design of an ELT, additional work is required. NIO conducted a workshop November 26-27, 2001, in Tucson, Arizona to consider what additional tests and analyses are needed. Participants came from several institutions, as described below:

It was agreed that several tasks deserved particular attention: (1) to model air flow over a 30- meter segmented mirror; (2) to model air flow through enclosures of different geometries; (3) to conduct additional wind measurements to investigate the question of the origin of turbulence affecting the telescope; and (4) to continue analysis of existing wind data to investigate the same question. These initiatives are discussed briefly below.

5.5.5.1 CFD Modeling of 30-m Mirror

The consensus at the workshop was that a key source of the turbulence that produces fluctuating pressures on the telescope is the interaction of the wind with the telescope structure itself. Therefore, it was felt more productive to begin modeling details of proposed ELT designs rather than perform additional analyses to more thoroughly understand the measurements made on Gemini.

This analysis will start by modeling the 30-m primary mirror itself, and then proceed to further elaboration of the point design telescope structure. It will investigate turbulent shedding effects of air flow around a 30-m primary mirror under a range of wind speeds and directions, and will provide a first indication of likely pressure distributions and variations on the front and back surfaces of the mirror.

TSU has offered to conduct the CFD modeling of air flow over the 30-m mirror. Their proposal states, in part:26

"The research will focus on (a) understanding the flow mechanisms that affect the dynamic wind loading on the primary mirror of a 30-meter aperture giant segmented mirror telescope (GSMT), and (b) the development of efficient computational techniques that model the unsteady, turbulent flow field around the primary mirror.

The research group at TSU will adopt a mathematical and numerical formulation to analyze a flow field around a primary mirror of a 30-meter GSMT. Navier-Stokes equations will be solved in the entire flow field. Proper turbulence models will be used for modeling the separation. The dynamic response of the flow field to the incoming turbulence and harmonics will be studied.

The computational effort will focus on the extension of an existing, three-dimensional (3-D) Navier-Stokes solver to a GSMT primary mirror. In this approach, 3-D unsteady, compressible Navier-Stokes equations will be solved in the entire region on a body-fitted grid surrounding the primary mirror. The mirror leading edge under subjected air flow inevitably results in flow separation and turbulent shedding towards the mirror surface. Therefore, proper turbulence models for separated flow will be integrated into the solver. The ultimate goal of this modeling work is to study the effects of turbulent shedding due to mirror leading edge that is subject to the prescribed incoming wind with either steady or turbulence profile (buffeting effect) on the mirror dynamic wind loading."

5.5.5.2 CFD Modeling of ELT enclosures

AMEC has proposed to perform CFD analyses of air flow into and around different types of enclosures. This will allow comparison of results with the earlier CFD analyses on the Gemini enclosures to check current scaling assumptions, and it will provide first-pass information on the likely flushing rates and internal wind velocities for some enclosure types.

There is reason to have confidence in this modeling; the CFD studies performed by DeYoung18 modeling the patterns and velocities of air flow within the Gemini enclosure have been verified by the wind measurements made at Gemini South.

AMEC has agreed to share the results of their studies with the other collaborators.

5.5.5.3 Additional Wind Measurements

5.5.5.3.1 Velocity Measurements

Because the anemometers are still available at Gemini South, additional wind velocity measurements can be taken as needed. One measurement that will be made in the near future is intended to separate the effects of the variability of the free stream from the variability introduced by the passage of the flow through the dome. Identical anemometers will be placed on a weather tower outside the dome and on the telescope structure close to the primary mirror. Simultaneous measurements should allow identification of turbulent vortices that are traveling in the free air stream, and should provide a clear indication whether the level of velocity variation seen inside the enclosure is consistently higher than in the free air stream.

Although the comprehensive data measured at Gemini South is useful by itself, a separate experiment at another facility would be an excellent complement to the data set. If the test could be done at a facility with a markedly different enclosure, and if it could be designed to partially match the testing done at Gemini, the resulting data could be much more useful than the sum of the tests alone. NIO will explore collaborations with other institutions to implement such measurements on other enclosures.

5.5.5.3.2 Determine Forcing Input

Although the tests to date have measured wind velocities and structural response, the forcing distribution on the structure is still poorly known, except at the front surface of the primary mirror (where pressure transducers were mounted). The forcing input can be predicted via CFD analysis, but that approach is limited because of the extremely high cost in super computer time required to model complex detail. There are two other approaches that would help close this issue. The first approach is to use the existing modal data, together with a finite-element model of the Gemini telescope, to produce a corrected model, updated to reflect the behavior shown in the controlled testing. This corrected model can then be reduced to the degrees of freedom measured in the operating data testing, and the response inverted to back out the input forces. These input force histories could then be compared with the measured wind velocities in the vicinity of the accelerometers to determine effective drag and lift coefficients. The goal would be to be able to predict the dynamic loading on a telescope structure based on the air flow velocities and directions calculated by CFD analysis.

As an additional confirmation of local wind forcing, it would be worthwhile to purchase or develop a device to locally measure force (or perhaps pressure) on existing structures. This would provide a "ground truth" on the local forcing for comparison with either CFD predictions or extracted force profiles.

5.5.5.4 Working with the Current Data Set

A significant remaining task can be described as "mining" the currently available data from the Gemini South tests. Recent analyses by Likhatchev have already revealed valuable insights into the behavior of the flow over the primary mirror, and his work continues. It is worth noting that much of the analysis to date has focused on the cases with significant wind speed and open vent gates. This focus is due to the more interesting response that is obtained from higher excitation. However, it is perhaps more important in the design of an ELT to understand the environment under more protected conditions, because this will likely be the normal operating procedure. Therefore, NIO plans to focus more on the protected (i.e., closed-vent) test configurations.

Reduction of the operating data conditions and analysis of the structural results from the Group 1 data set via design of experiments techniques need to be performed. Further wind data reduction is also needed for wind pressures and wind velocities of all test configurations.

Finally, there are useful comparisons to be made with previous studies, including the measurements at La Silla and some of the wind tunnel and CFD studies.

5.5.6 ACKNOWLEDGMENTS

The studies summarized in this section are the result of a great deal of work by many people. The collection of the Gemini South data was accomplished by Myung Cho of the University of Arizona Optical Sciences Center, Gemini Observatory staff members, the testing team from Michigan Technical University Keweenaw Research Center, and the University of Massachusetts Lowell Modal Lab. Data reduction has been funded by Gemini, and was accomplished by Myung Cho, David Smith of Merlab, P.C., and Seongho Kim of the University of Arizona. Thanks are due to all participants in the NIO Wind Loading Workshop. Finally, the authors of previous and current work cited in this document provided the necessary technical foundation for this work to be performed.

5.5.7 REFERENCES

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October 2002