Computational fluid dynamics simulations and wind tunnel measurements of unsteady wind loads on a scaled model of a very large optical telescope: A comparative study

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Abstract

Thorough theoretical and experimental investigations were performed to analyze the main characteristics of unsteady flows past a 1:100-scale wind tunnel (WT) model of a very large optical telescope housed within a spherical enclosure. The investigations were focused on the prediction and measurements of unsteady pressures on the inner and outer surfaces of the enclosure and on the telescope primary mirror. The WT measurements were performed essentially to provide aerodynamic data on the telescope structure and also to build a database for correlation with numerical simulation of the flow using computational fluid dynamics (CFD). Unsteady viscous flow solutions were computed for different telescope orientations using the lattice Boltzmann method coupled with the RNG k-ε turbulence model. For WT testing, unsteady pressure measurements were performed in an open jet WT for different telescope orientations and wind speeds, using a number of pressure taps distributed around the inner and the outer surfaces of the enclosure and on the primary mirror surface. A smoke stream visualization technique was also used to study the flow behavior around and inside of the telescope enclosure. The flow solutions were computed using the WT flow conditions. Correlations were obtained between CFD and WT data in terms of the mean pressure coefficients on the enclosure and the primary mirror surfaces, and for their standard deviations. Power spectral density analyses were also carried out for a number of pressure signals collected on the primary mirror surface. Both CFD solutions and WT measurements demonstrated that the flow inside and outside the enclosure was unsteady and massively separated on the back of the enclosure. The mean values and standard deviations of the pressure coefficients on the enclosure and the primary mirror surfaces correlated well with the experimental data. Using the WT Mach number in the simulation, the shear layer over the enclosure opening and the resulting acoustic wave effects were well captured, and there was excellent agreement between the CFD results and the WT measurements.

Introduction

The incoming airflow over telescope enclosures leads automatically to the formation of a free shear layer across the enclosure opening. Under some flow conditions, the shear layer becomes unstable as it rolls up further into a series of strong vortices. As the vortices interact or impinge against the aft edge of the opening, acoustic waves are generated and propagate upstream. When these waves arrive near the leading edge of the opening, where the shear layer starts to build up, they excite and strengthen the newly formed vortices. This phenomenon can result in enclosure resonance when the acoustic waves arrive at the right time. A strong pressure fluctuation is thus induced inside the enclosure, which in turn contributes to significant dynamic loads on the telescope structure. As the size of a telescope increases, its natural frequency is shifted to lower frequencies where there is greater wind excitation, which collectively may impart significant structure displacements on the telescope mirror assemblies.

The astrophysics community is building larger and larger telescopes in order to study the universe at greater and greater detail. For such large structures, the unsteady wind loads will undoubtedly become an important factor in the telescope design. The wind flow around and inside a telescope enclosure can lead to many direct undesirable effects upon the “seeing” attributes of the mirror. An increase in “seeing” factor is generally associated with a degradation in the optical performance of the telescope. The induced unsteady wind loads on the telescope components lead to a dynamic structure deformation, causing wind buffeting that, owing to the large size of the telescope, directly affects the primary mirror and the secondary mirror assembly, where the later is usually exposed to high wind speeds near the enclosure opening. The induced flow turbulence near the enclosure opening and along the observation path as well as the thermally driven buoyancy-induced flow over the primary mirror are also responsible for the augmenting seeing factor.

The application of computational fluid dynamics (CFD) to predict flows and wind loads on telescope structures can provide critical data for the design of future large optical telescopes. Most of the mechanisms that affect the mirror seeing, such as the induced turbulence at the enclosure opening or inside the enclosure and induced thermal flows, can be addressed by CFD with an acceptable level of accuracy. De Young (1996) performed time-independent airflow simulations inside the Gemini telescope enclosure. The author found that for the telescope enclosure, venting (airflow through vents) was most effective for flow directions inside the enclosure, particularly near the vents and across the primary mirror surface. Turbulence was present for different wind conditions and orientations; however, it was worst when the enclosure opening was facing the wind and the flow was forced to negotiate its way around the opening. The author also identified a strong pressure gradient across the primary mirror for different wind conditions. Using CFD, Vogiatzis et al. (2004) estimated the effect of wind loading on the performance of extremely large telescopes. The computations were carried out for unsteady incompressible and isothermal flows. The effect of venting was studied for a given telescope orientation and wind speed. The CFD predictions were validated against wind tunnel (WT) measurements. The study showed the existence of an unstable shear layer over the opening that resulted in large pressure fluctuations inside the enclosure. The power spectral density of the normalized velocity signal, measured near the enclosure opening, showed the existence of different oscillatory mode frequencies, which agreed very well with experimental data. De Young and Vogiatzis (2004) also carried out some CFD simulations of airflow in very large optical telescope enclosures. Steady-state flow computations were performed and results were presented for an extremely large typical empty telescope enclosure, as well as for a more specific Gemini south telescope mounted on the summit of Mount Cerro Pachon. The authors presented only qualitative flow patterns to demonstrate the ability of CFD to simulate such complex flows inside and outside the telescope enclosure.

Angeli et al. (2002) experimentally studied the characteristics of wind loading on the Gemini telescope. The measurements were taken at different pressure taps incorporated on a dummy primary mirror surface. The wind velocity distribution on the primary mirror was estimated from measurements taken at the edge of the mirror where some velocity sensors were placed. The authors concluded that the wind flow experienced more turbulence when the telescope azimuth angle was increased. The pressure fluctuations on the primary mirror were extremely pronounced when the mirror was pointing into the wind with a small bandwidth of the wind load. Quattri et al. (2003) performed a full-scale CFD study of wind loading on the 100 m OWL telescope using a commercial CFD software. The study focused on the effect of the wind loads acting on the primary mirror caused by the presence of a building situated in front of the telescope. Pressure signals collected at different control pressure points on the mirror surface showed that the wind pressure at low frequencies was reduced by a building located upstream of the telescope; however, the high-frequency wind pressure components increased under these conditions. Cho et al. (2003) also reported on a similar wind loading study on the Gemini telescope. They concluded that the pressure fluctuations over the primary mirror were large; however, the average total wind force on the mirror was negligibly small. The average pressure on the primary mirror was mainly controlled by the airflow around the enclosure and the fluctuations were caused by the turbulence generated by the enclosure structures. Cho et al. (2001) considered wind-buffeting effects on the Gemini 8 m primary mirror. The measurements were conducted under actual mountaintop wind conditions. Pressure data were collected using various taps installed on the primary mirror surface and the wind velocity and direction were measured at several locations inside and outside the enclosure. The time history of the pressure data was used to calculate the primary mirror distortions using a finite-element method.

Riewaldt et al. (2004) carried out a very interesting and thorough WT investigation for an extremely large telescope with a 50 m primary mirror. The investigation was performed on a 1:200-scale model in the boundary layer WT at the National University in Galway, Ireland. Pressure signals were measured at different locations on the primary mirror and on the telescope enclosure. This particular study included a number of different telescope configurations including; an empty enclosure, a telescope unit on its own and an enclosure combined with a telescope. Aerodynamic forces and moments acting on the enclosure and on the primary mirror were also measured. They concluded that under nominal wind conditions (12 m/s), the wind produced high mean pressures and pressure fluctuations on the primary mirror surface. In addition to the above studies, Pottebaum and MacMynowski (2006) performed WT measurements of the flow inside an empty generic telescope enclosure with a rectangular opening. Smoke and tufts were used to visualize the flow patterns inside and around the enclosure. Digital particle image velocimetry data were collected on a vertical plane near the enclosure opening to estimate the mean flow velocity and the kinetic energy fluctuations. The experimental observations and measurements again revealed the existence of a strong shear layer that formed over the enclosure opening when it was pointing into the wind. Different oscillatory mode frequencies were detected owing to the formation of vortices along the shear layer. When the enclosure opening was pointing in the downstream direction, i.e. located in the separated flow region, the flow was driven inside the enclosure with less rigorous unsteady flow structures. Adding some vents around the enclosure tended to dampen considerably the amplitudes of the shear layer modes.

Previously at the National Research Council (NRC) of Canada—Institute for Aerospace Research (IAR), Cooper et al. (2004a) and Cooper and Fitzsimmons (2004) performed a number of WT measurements to estimate the wind loads on a very large optical telescope housed within a spherical enclosure. A 1:100-scale model of this very large optical telescope (VLOT) was considered and tested in the open jet WT at NRC–IAR. A number of pressure taps were instrumented on the inside and outside enclosure surfaces as well as on the primary mirror surface. The WT tests were performed for different wind speeds and VLOT orientations. The measurements revealed the existence of strong pressure fluctuations inside the enclosure. Owing to the formation of a shear layer across the opening, as many as four modal frequencies were identified. The number of modal frequencies decreased with the wind speed. The mean pressure inside the enclosure and on the primary mirror surface was roughly uniform. The effect of ventilating the enclosure by creating two rows of circular vents around the enclosure was also investigated by Cooper et al. (2004b) for the same WT VLOT model. The amplitude of the periodic pressure fluctuations that were measured in Cooper et al. (2004a) was considerably reduced. The multiple modes of the pressure fluctuations were also reduced to a single mode at low-pressure amplitudes.

Along with the aforementioned experimental studies, the NRC–IAR has also performed preliminary CFD-based studies to investigate unsteady wind loadings on a future VLOT for the NRC Herzberg Institute of Astrophysics (HIA). A number of different VLOT configurations at various azimuth and zenith orientations and wind speeds were considered. Mamou et al., 2004a, Mamou et al., 2004b investigated the wind loads on a full-scale 20 m very large optical telescope using the commercial PowerFLOW™ CFD software. The flow solutions obtained at different azimuth and zenith orientations were unsteady. Comparisons with WT measurements (Cooper et al., 2004a) showed good agreement for the mean pressure inside and outside the enclosure and on the primary mirror surface. However, some discrepancies between CFD and WT data were observed for the pressure fluctuations and the oscillatory modal frequencies. These discrepancies were attributed to several sources of error. First, scaling effects were present since the CFD solutions were obtained for a full-scale model that corresponded to a Reynolds number that was two orders of magnitude higher than the WT Reynolds number. Second, the viscous effects of the floor were neglected since an inviscid boundary condition was used in the simulations. Third, the VLOT structure roughness was also ignored; instead, a perfectly smooth model surface was assumed. Finally, the flow free stream conditions of Mount Mona Kea used in the CFD simulations were different from those existing in the WT. To reduce the magnitude of these sources of error, Mamou et al. (2004c) performed additional CFD simulations based on the WT model and using the same flow conditions reported in Cooper et al. (2004a). Non-slip conditions were considered for the floor to account for the formation of a shear layer that could affect the pressure distribution and the flow field near the enclosure base. However, the WT model roughness was not considered in the simulations since its effect was deemed negligible. Tahi et al. (2005a) also conducted a CFD analysis to predict the wind loading on the primary mirror surface for a 30 m VLOT telescope configuration at a given orientation and wind speed. A vented enclosure was considered. The results showed that the pressure fluctuations, when compared to the sealed enclosure case (Cooper et al., 2004a), decreased considerably, while the mean pressure on the primary mirror increased. Tahi et al. (2005b) also performed thorough comparisons between CFD and WT measurements for different VLOT configurations and wind conditions. The comparisons were focused mainly on the effect of the wind loads on the primary mirror of the telescope. Grid sensitivity and Mach number effects were reported for a given configuration. Overall, there was a good agreement between the CFD predicted and the WT measured mean pressure coefficients for a single row of pressure taps on the primary mirror surface.

The present paper contains CFD and WT results obtained using the 1:100-scale VLOT model for the following orientations: a zenith angle of 30° and an azimuth angle of 0° (VLOT-30-0), and a zenith angle and an azimuth angle of 30° (VLOT-30-30). The CFD simulations were performed using the Lattice Boltzmann method as implemented in the PowerFLOW™ solver (PowerFLOW™). Comparisons between the CFD predictions and measured WT data were made in terms of the mean pressure coefficients values and their standard deviations (root mean square) for a number of pressure taps around the inner and outer surfaces of the enclosure and on the primary mirror surface. Comparisons were also carried out for the power spectral density of the pressure signal recorded at one pressure tap on the primary mirror surface. The CFD analyses were performed to assess the capability and accuracy of the PowerFLOW™ CFD solver, to predict the flow behavior around and inside the VLOT enclosure, as it was a potential candidate for future aerodynamic analyses of the VLOT integrated model.

Section snippets

VLOT wind tunnel model

In order to furnish the astrophysics community with a more detailed and deeper capability for space exploration, the HIA of the National Research Council of Canada (NRC) had initiated a new project to build a VLOT, which consists of a primary mirror of 20 m diameter and a spherical enclosure of 51 m diameter. Owing to large dimensions of the telescope structure and the seeing factor requirements, HIA decided to consider the unsteady wind loads in the preliminary stage of design of the VLOT.

Wind tunnel measurements

The VLOT model was tested in an open-jet WT that was 1 m wide and 0.8 m high, see Fig. 3 and Cooper et al. (2004a). In this configuration, the WT test section has no walls, only the floor. The air flows from the upstream nozzle to the down stream collector. The pressure lines lengths were variable and each tube was calibrated for its frequency response to 200 Hz. The pressures were scanned at 400 Hz. Some scans were done at 800 Hz to show that no content was present above 200 Hz. Each pressure signal

VLOT CAD model

As shown in Fig. 4, the CAD geometry of the VLOT WT model was used in the CFD simulations without any simplification. As the WT Reynolds number, based on the enclosure diameter, was Re=4.59×105 and according to a study of flows past a rough sphere by Achenbach (1974), it appears that there is no significant difference in the drag coefficient of a sphere in the range 0⩽ks/D⩽25×10−5. Therefore, the WT model surface is treated as a smooth surface. The farfield, as shown in Fig. 5, was located 15D

Results and discussions

For the WT measurements (Cooper et al., 2004a), various wind speeds and telescope orientations were considered. The smoke visualization showed that the flow was massively separated on the back of the enclosure and a strong horseshoe vortex was formed on the floor around the front part of the enclosure. When the enclosure opening was fully or partially pointing into the wind, strong pressure fluctuations were captured in the enclosure displaying at least one to four periodic oscillatory modes,

Conclusions

CFD simulations and WT measurements were performed to investigate the unsteady wind loads on a 1:100-scale model of a very large optical telescope housed within a spherical enclosure. Unsteady flow solutions were computed using the commercial PowerFLOWTM software. Detailed comparisons between CFD predictions and WT measurements were performed.

In general, when the enclosure opening was facing the wind, both the CFD and the WT data revealed that the flow was highly unsteady inside and outside the

Acknowledgments

The authors are grateful to Dr. J. Sengupta and D. Hatfield from Exa Corporation for providing assistance, time, and support for the PowerFLOW™ code, and for running a simulation using the WT Mach number.

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