estudio de las condiciones locales meteorológicas y de seeing. El filo sur del Cordón Macón, en Salta, Argentina, ha sido estudiado por más de un a˜no, se han ...
Asociaci´ on Argentina de Astronom´ıa BAAA, Vol. 52, 2009 J.J. Clari´ a, E. Brandi, A.E. Piatti & F.A. Bareilles, eds.
´ MURAL PRESENTACION
Numerical simulation of winds behaviour in Mac´ on site E. Gonzalez1 , C. Sacco1 , R. Vrech2,3 , V. Renzi2 , D. Garc´ıa Lambas2 & P. Recabarren2,3 (1) Simularis, Simulation in Engineering and Science. (2) Instituto de Investigaciones Te´ oricas y Experimentales, CONICET UNCba. (3) Facultad de Ciencias Exactas, F´ısicas y Naturales, U.N.Cba. Abstract. The set up of a large telescope requires a previous comprehensive study of the local meteorological and seeing conditions. The south ridge of mount Mac´on, province of Salta, Argentina has been studied for more than a year and good seeing conditions have been found. However, strong wind conditions drastically affect the selection of the best place where a large telescope may be installed. In the present work, a CFD (Computed Flow Dynamic) study is performed to analyze the wind speed distribution and flow pattern over the site. A GPS based high resolution topographical model was developed. The numerical formulation is a large eddy simulation (LES) of the incompressible Navier-Stokes equations approximated using the finite element method and results are confirmed with the experimental measurements. Resumen. La instalaci´ on de grandes telescopios requiere de un acabado estudio de las condiciones locales meteorol´ ogicas y de seeing. El filo sur del Cord´on Mac´on, en Salta, Argentina, ha sido estudiado por m´ as de un a˜ no, se han encontrado buenos valores de seeing. Sin embargo, los fuertes vientos afectan dr´ asticamente las posibilidades de elecci´on de este sitio. En el presente trabajo, se expone un estudio computarizado din´ amico de flujo (CFD) con el objeto de evaluar y analizar los patrones de flujo sobre el sitio. Se cuenta con un modelo topogr´ afico basado en datos GPS. La formulaci´ on num´erica es una simulaci´ on a gran escala de las ecuaciones de Navier-Stokes son aproximadas usando el m´etodo de incrementos finitos. Los resultados fueron confirmados con mediciones experimentales. 1.
Introduction
The Instituto de Astronom´ıa Te´orica y Experimental (IATE) in collaboration with the European Southern Observatory (ESO) has been studying the south ridge of mount Mac´on. One year of measurements of the seeing quality through the Differential Image Motion Monitor (DIMM) and the atmospheric turbulence through Multi-Aperture Scintillation Sensor (MASS), three years of meteorological data and detailed studies of seismic activity has been collected. Besides, the essential parameters for construction and operation, as accessibility, water 277
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and power supply, etc., of an observatory facility were subject of analysis. The study shows that Mac´on site is a high quality place to install a telescope facility, but strong wind conditions prevail. The final objective of this work is to determine the ideal localization for a potential telescope facility within the Macon mount candidate area taking into account the wind speed distribution. Airflow pattern and wind speed distribution are calculated by CFD and compared to experimental measurements. IATE has two meteorological stations installed in Macon mount. The main station, named NewSite is at the main summit. The secondary station, named USite, is 380m east from the summit station.
2.
Mathematical Model
In this section we consider the flow problem for an incompressible fluid using the Navier-Stokes equations, δu 1 + u · ▽u − v∆u + ▽p = f δt ρ ▽·u=0
in
in
Ω × (0, tf )
Ω × (0, tf )
(1) (2)
where Ω = flow domain, t = time variable, (0, tf ) = time interval for the simulation, u = velocity field, ▽ = gradient operator, v = kinematic viscosity, ∆ = laplacian operator, p = pressure and , f = external body forces
The state of the airflows under consideration is generally turbulent. The standard Smagorinsky turbulence model is used (Smagorinsky 1963), being its expression, vT = c · h ·
√ ε:ε
(3)
where c = Smagorinsky constant(0.41), h = element size, ε = velocity stranin rate tensor
The near-wall strategy adopted here is based on the law of the wall. Since we are considering summit local aerodynamics and high wind conditions, we assume density constant and convective flow contributions negligible in this preliminary study. The energy equation is decoupled and not taken into account.
Numerical simulation of winds behaviour in Mac´on site
3.
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Numerical Model and Simulation
The set of partial differential equations is solved using the finite element method (Sacco 2008). The time-dependant fluid flow equations are solved by the fractional step (FS) method (Lohner 2001). The time integration uses the firstorder accurate backward Euler scheme. It is also necessary to use a stabilization method capable of dealing with all the instabilities that the standard Galerkin method presents. The stabilization technique used here is the Orthogonal Subscale Stabilization (OSS) (Bell 1989; Codina 2000; Soto 2001). The modeling of the ridge area was made by the combination of two sources of topographical information. A Differential Global Positioning System (DGPS) topographical survey of the summit carried out in 2008 by Geonorte (Geonorte 2008) was combined with a low resolution portion of the NASA Shuttle Radar Topographic Mission (SRTM) survey. A single computational domain is considered to solve the airflow around the Macon ridge. The zone of interest around the summit is 1 x 0.5 km at an elevation of 1km. Then the discretized domain covered a section of 9.2 x 10.6km of terrain and extends to an altitude of 9.8km to guarantee independance of local aerodynamics on the boundary conditions, these being, fixed velocity at inflow, pressure outlet and no slip at the terrain surface. The generated mesh for this domain was formed by 2.6 million tetrahedral elements and a boundary layer mesh was created on the ground. This boundary layer is formed by 7 elements in the surface normal direction and the first element is 0.5m high. The solution obtained is not stationary. In the computed flow pattern, multiple vortex shedding and flow separation were observed, especially behind the mountain range. However, the flow pattern within the summit zone is steady, only partially affected by the downward vortex. These results are summarized in following Figures.
Figure 1.
Velocity distribution and vectors. Weather station locations
The simulated evolution of the wind speed at the NewSite and USite is shown in the next figure.
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Figure 2.
4.
Simulated evolution of wind speed
Conclusions
The study was initially carried out at a higher than average wind speed in order to evaluate the high wind condition. The measured ratio between wind speed at NewSite (experimental 11 m/s and simulation 14 m/s) and USite (experimental 20 m/s and simulation 23 m/s) compares well with the simulation results. Given then stability of the wind speed and direction in different years, these one month results presented here are representatives. From the design point of view, this work shows that CFD is a powerful tool to decide, under stable wind conditions, which location is the best to place a new station to study the potential installation of a telescope facility. Although experimental measurements must be made to take into account meteorological variations and unstable characteristics that cannot be simulated, this kind of study may shorten the site testing time and save money. Future work may includes heat transfer addition and the modeling of the potential telescope buildings. References Instituto Geonorte, Cerro Macon Differential GPS Topographical Survey, Universidad Nacional de Salta, 2008. Lohner R., Applied CFD Techniques, John Willey and Sons (2001). Sacco C. and Gonzalez E., Finite element method solution of the Navier-Stokes equations, First Argentine Congress of Aeronautica Eng. CAIA I, La Plata, Arg., 2008. Smagorinsky J., General circulation experiments with the primitive equations. I. The basic experiment, Monthly Weather Rev. 91 (1963) 99 164. Bell J., Collela P. and Glaz H., A second order projection method for the Navier-Stokes equations, J. Comput. Phys. 85, 257-283 (1989). Codina R., Stabilization of incompressibility and convection through orthogonal subscales in finite element methods, Comput. Methods Appl. Eng. 190, 1579-1599 (2000). Soto O., Lohner R., An implicit monolithic time accurate finite element scheme for incompressible flow problems, AIAA 2616-2631 (2001).
