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Innovative Method for Determining the Vorticity Confinement Term for Rotorcraft Computational Fluid Dynamics (CFD) Computations


OBJECTIVE: Develop a rigorous algorithm to define the vorticity confinement terms for rotorcraft Computational Fluid Dynamics computations, damping the numerical diffusion of vorticity. DESCRIPTION: The accurate representation of the rotor wake, especially the tip vortex structure, is crucial to the accurate prediction of blade loading and rotor performance. The vortex structures predicted by conventional CFD, however, diffuse much more than given by real viscous diffusion. This problem has generally attracted much attention in the past. High order solvers and/or grid refinement in the vortex regions have been explored (e.g., [1]). Certain level of success has been achieved, but not without significant computational resources (for more than 2~3 rotor revolutions). Another strategy involves the coupling of Navier-Stokes solver with a separate wake model or vorticity transport equation (e.g., [2-3]). Practical applications have been demonstrated with this approach, which is necessarily more algorithmically complex. A practical compromise for minimizing numerical diffusion of vorticity in rotorcraft CFD is the vorticity confinement method (e.g., [4]). It artificially introduces extra terms to the Navier-Stokes equations as a source to control the diffusion. Many conventional implementations of this method use an adjustable coefficient in the confinement term, reducing its robustness. As a first step, the development of a rigorous algorithm for defining the vorticity confinement terms for inviscid computations is needed. Adjustable coefficients are not encouraged and the confinement terms should ideally be automatically adjusted to achieve the accurate prediction of the vortex structures. PHASE I: Develop a rigorous algorithm that will define the vorticity confinement terms without an adjustable coefficient, and demonstrate feasibility analytically. PHASE II: Further develop the algorithm into a usable tool that can be coupled with CFD computations. Perform initial verification and validation of the methodology. PHASE III: Perform rigorous correlation with test data to provide validation and verification (V/V). Transition the technology to commercial and military applications. PRIVATE SECTOR COMMERCIAL POTENTIAL/DUAL-USE APPLICATIONS: The developed algorithm can be implemented in Helios, a helicopter simulation tool in DoD or private sector helicopter simulators. REFERENCES: 1. Wissink, Katz, A. , Chan, A., & Meakin, R. (2009). Validation of the Strand Grid Approach. AIAA-2009-3792. 2. Khanna, H. & Baeder, J. (1996). Coupled Free-wake/CFD Solutions for Rotors in Hover Using a Field Velocity Approach. American Helicopter Society 52nd Annual Forum, Washington, D.C. 3. Brown, R. & Line, A. (2005). Efficient High-resolution Wake Modeling Using the Vorticity Transport Equation. AIAA Journal, Vol. 43, p. 1434-1443. 4. Steinhoff, J. & Raviprakash, G. (1995). Navier-Stokes Computation of Blade-vortex Interaction Using Vorticity Confinement, AIAA-1995-0161. 5. Lorber, P., Stauter, R., Pollack, M., & Landgrebe, A. (1991). A Comprehensive Hover Test of the Airloads and Airflow of an Extensively Instrumented Model Helicopter Rotor, Vol. 1-5, USAAVSCOM TR-D-16 (A-E).
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