APPLICATION OF EN0 SCHEMES TO ROTARY AIAA-95-1892-CP Nathan Hariharan' School of Aerospace Engineering Georgia Instituteof Technology, Atlanta GA-30332 L N. Sankaf' School of Aerospace Engineering Georgia Instituteof Technology, Atlanta GA-30332 ABSTRACT Three dimensional, first-principles based Euleri Navier-Stokes simulation results are presented for two different rotors in hover. A second order temporally accurate, fifth order spatially accurate, implicit finite volume scheme is used. The captured tip vortex structure due to one of the rotor, is compared between the fifth order EN0 scheme and a third order MUSCL scheme. Integrated aerodynamic loads are also presented and compared with experiments. A comparison of the measured velocity profiles across a tip vortex from a wing, with the lower and the higher order schemes is also presented. It is concluded that higher order schemes can significantly improve the prediction of sensitive quantities such as vorticity, drag and toque. INTRODUCTION Research efforts towards solving the aerodynamics of the rotor-flows has progressed significantly during the past decade. Several researchers (e.g. Wake and Sankar[l,2], McCroskey[3,4], Srinivasan[3,4,5], Duque[6], Strawn[7,8], and Barth[9] ) have used various approaches to tackle this problem. The current trend towards computing the rotor flow field is to predict the wake structure without resort to any external empirical input. To have an adequate resolution of the wake vortex system it is clear that a large number of grid points are required. A very fine grid is needed in the vicinity of the vortex to prevent it from being diffused by numerical viscosity. This problem has been addressed both by the use of structured [3,4], and unstructured [8,9] * Graduate Research Assistant, AlAA Student Member " Professor, AlAA Senior Member Copyright O 1995 by Hariharan and Sankar. Published by A I M , Inc., with permission. meshes. With structured grids one either resorts to grid adaptation to resolve the wake structure or the use of embedded grids as has been done by Duque and Srinhrasan[G]. The unstructured grid approach allows superior grid refinement procedures as illustrated by Strawn[7,8]. An approach now receiving much attention is the use of higher order stencils to effect enhanced resolution. Workers in Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of Turbulence [lo] have used high order stencils with spectral like accuracy. Existing work on high resolution schemes, by researchers like Harten, Chakravarthy, Osher, Rai 118-221, indicate the possibility of using higher order schemes with enhanced efficiency for practical problems. In this paper we ask the question: Can higher order schemes be used to solve rotary- wing problems efficiently? The ability of these schemes to accurately predict the vorticity in the flowfield is critical to the success of first- principles based methodologies. If the tip vortex can be sufficiently well resolved, then these schemes can be effectively used to solve complex problems such as rotor-blade vortex interaction ( BVI ), rotor-airframe interaction, and main rotor - tail rotor interaction. The present authors have recently been studying the application of Essentially Non- Oscillatory (EN0 ) schemes to rotary-wing problems. A higher order EN0 scheme developed earlier [I 21, demonstrated the ability to correctly predict the surface loads on a simple untwisted rotor. This work is extended here, to study the tip vortex structure from the simple blade and also a realistic, twisted rotor blade. It should be remembered that unsteady rotary wing problems are a time-space phenomenon. Hence for a more accurate simulation, it is not adequate to just increase the spatial resolution. Temporal accuracy should also Downloaded by GEORGIA INST OF TECHNOLOGY on December 5, 2014 | http://arc.aiaa.org | DOI: 10.2514/6.1995-1892