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Simulation of the Unsteady Flow Around the Stratospheric Observatory For Infrared Astronomy (SOFIA)

The operation of the flying observatory SOFIA (Stratospheric Observatory For Infrared Astronomy), which was designed to look at celestial bodies in the infrared range of the electromagnetic spectrum from the lower stratosphere above the obscuring water vapor, presents some challenging aerodynamic and aero-acoustic problems. Once the door that closes the large cavity in the rear fuselage of the highly modified Boeing 747SP is opened to clear the view of the 2.5m Cassegrain telescope to the sky (see Figure 1), the cavity is exposed to transonic flow conditions of an aircraft flying with a speed of about 900km/h (Mach number of 0.85) at altitudes above 13km.

Simulation of the Unsteady Flow Around the Stratospheric Observatory For Infrared AstronomySOFIA during an open door test flight over the Mojave desert in California
Copyright: © NASA

Due to the door opening during flight, the oncoming boundary layer detaches at the cavity leading edge and evolves in a highly unsteady shear layer that is responsible for large pressure fluctuations within the cavity that can potentially be amplified by acoustic resonances. The aerodynamic loads on the telescope and the cavity aero-acoustics are responsible for structural excitations that can degrade the telescope´s pointing stability in particular if the frequencies are close to structural telescope modes.

In order to understand the highly complex cavity flow mentioned above and to describe the aerodynamic excitations of the telescope during flight, Computational Fluid Dynamics (CFD) simulations of the SOFIA configuration with open door have been performed at the Deutsches SOFIA Institut (DSI) of the University of Stuttgart in cooperation with the Institute of Aerodynamics and Gas Dynamics (IAG). The major challenge for the CFD simulations was to capture the turbulent scale sizes that are getting smaller and smaller with higher Reynolds numbers (ratio of inertial forces to viscous forces). For the CFD simulation of SOFIA that is operating at a Reynolds number of about 5 million, the Detached Eddy Simulation (DES) approach turned out to be the best compromise between accuracy and efficiency. DES is characterized by a hybrid length scale that splits the physical space in a Reynolds-Averaged Navier-Stokes (RANS) and a Large Eddy Simulation (LES) domain. The idea is to entrust the calculation of the attached boundary to RANS where turbulence is only modeled statistically and the shear layer zone and wall distant regions to LES that resolves large turbulent structures directly in space and time down to a spatial filter width. Smaller scales are captured by a sub-grid scale model. For meaningful LES however, 80% of the turbulent spectrum should be resolved requiring a very fine spatial discretization of the shear layer over the cavity. This leads to significant mesh sizes of more than 50 million cell elements that can only be calculated on supercomputers such as SuperMUC of the Leibniz Supercomputing Centre (LRZ) in Garching.

Thanks to the performed CFD simulations, a detailed prediction of the flow field in space and time around the SOFIA telescope was possible. The instantaneous Mach number plot in Figure 2 shows that the unsteady shear layer (indicated by the black dashed lines in Figure 2) impinges on the so-called aperture ramp, a passive flow control device situated at the cavity trailing edge that stabilizes the shear layer and provides at the same time a smooth mass-flow balance into and out of the cavity.

Simulation of the Unsteady Flow Around the Stratospheric Observatory For Infrared AstronomyInstantaneous Mach number plot in a cut plane through the cavity at 40° telescope elevation with the telescope model
Copyright: © DSI

The inflow in the cavity was discovered to have an asymmetric character and to impinge on the telescope structure which can be recognized by the red zone in the left picture of Figure 3. The CFD simulations revealed that the inflow impingement is responsible for high aerodynamic loads and hence, it might be one potential reason for image jitter seen during flight. In the framework of passive flow control concept studies it was shown that devices such as a porous fence, vortex generators or spoilers installed upstream of the cavity in the attached aircraft boundary layer are capable of reducing the aerodynamic loading by mitigating the inflow impingement on the telescope. The comparison shown in Figure 3, for instance, depicts that a spoiler installed upstream of the cavity in the attached aircraft boundary layer leads to a significant reduction of the pressure amplitude over the entire telescope surface.

Simulation of the Unsteady Flow Around the Stratospheric Observatory For Infrared AstronomyComparison of the pressure amplitude by means of the Sound Pressure Level (SPL) plotted over the telescope surface without a spoiler (left) and with a spoiler installed upstream of the cavity (right) in the attached boundary layer
Copyright: © DSI

Next to the characterization of the pressure fluctuations inside the cavity and on the telescope surface, the CFD simulation also provided a description of the aero-optical properties of the observatory, more precisely the aberrations an observed signal (wavefront) suffers while passing the local flow field induced by the aircraft. Figure 4 for instance shows by means of the Optical Path Difference (OPD), a parameter to quantify the aero-optical error, that the inviscid flow region, which is the zone outside of the shear layer and the cavity in the near field of the aircraft, imposes a static tilt effect to the passing wavefront.

Simulation of the Unsteady Flow Around the Stratospheric Observatory For Infrared AstronomyAero-optical error in the inviscid flow region outside of the shear layer and the cavity shown by means of the Optical Path Difference (OPD) plotted over the primary mirror surface
Copyright: © DSI

Acknowledgements

SOFIA, the "Stratospheric Observatory for Infrared Astronomy“, is a joint project of the Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR; German Aerospace Centre, grant: 50OK0901) and the National Aeronautics and Space Administration (NASA). It is funded on behalf of DLR by the Federal Ministry of Economics and Technology based on legislation by the German Parliament, the state of Baden-Württemberg, and the Universität Stuttgart. Scientific operation for Germany is coordinated by the German SOFIA-Institute (DSI) of the Universität Stuttgart, in the USA by the Universities Space Research Association (USRA).

Dipl.-Ing. Christian Engfer
Telescope Aeroacoustics
Deutsches SOFIA Institut (DSI)
Institute of Aerodynamics and Gasdynamics (IAG), University of Stuttgart
Pfaffenwaldring 29, D-70569 Stuttgart/Germany
e-mail: engfer@dsi.uni-stuttgart.de

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