Incorporation of Morphing Theory to Aerodynamic Flows
Publication: Journal of Engineering Mechanics
Volume 146, Issue 8
Abstract
The research reported herein makes use of finite-volume simulations of morphing continuum theory (MCT) to reproduce critical relations of thin-airfoil theory for the simple configuration of a flat plate for supersonic and subsonic flows. With a small mesh size of elements, simulations confirm that inviscid flows simulated by MCT match analytic relations for lift and pressure coefficients derived from classical fluid mechanics, a result confirmed by the inviscid MCT equations. Initial success of MCTHyperFOAM version 1.0 for the flat plate indicates that the solver can be extended to more complex aerodynamic flows.
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Acknowledgments
The authors wish to thank the Air Force, the Air Force Institute of Technology (AFIT), and the Oak Ridge Institute for Science and Education (ORISE) for supporting and funding this work. This research was also made possible by collaboration with Dr. James Chen and Mohamad Ibrahim Cheikh at the University of Buffalo and with Mohamed Mohsen Ahmed of the University of Maryland.
References
Ahmed, M. M., and J. Chen. 2019. “Verification and validation of a morphing continuum approach to hypersonic flow simulations.” In Proc., AIAA Scitech 2019 Forum, 0891. Reston, VA: American Institute of Aeronautics and Astronautics.
Anderson, J. D., Jr. 2010. Fundamentals of aerodynamics. New York: Tata McGraw-Hill Education.
Cheikh, M. I., L. B. Wonnell, and J. Chen. 2018. “Morphing continuum analysis of energy transfer in compressible turbulence.” Phys. Rev. Fluids 3 (2): 024604. https://doi.org/10.1103/PhysRevFluids.3.024604.
Chen, J. 2017. “Morphing continuum theory for turbulence: Theory, computation, and visualization.” Phys. Rev. E 96 (4): 043108. https://doi.org/10.1103/PhysRevE.96.043108.
Chen, J., C. Liang, and J. D. Lee. 2012. “Numerical simulation for unsteady compressible micropolar fluid flow.” Comput. Fluids 66 (Aug): 1–9. https://doi.org/10.1016/j.compfluid.2012.05.015.
Cockburn, B., and C.-W. Shu. 1998. “The Runge–Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems.” J. Comput. Phys. 141 (2): 199–224. https://doi.org/10.1006/jcph.1998.5892.
Colella, P., and P. R. Woodward. 1984. “The piecewise parabolic method (PPM) for gas-dynamical simulations.” J. Comput. Phys. 54 (1): 174–201. https://doi.org/10.1016/0021-9991(84)90143-8.
Darwish, M., A. Abdul Aziz, and F. Moukalled. 2015. “A coupled pressure-based finite-volume solver for incompressible two-phase flow.” Numer. Heat Transfer, Part B Fundam. 67 (1): 47–74. https://doi.org/10.1080/10407790.2014.949500.
Eringen, A. C. 1964. “Simple microfluids.” Int. J. Eng. Sci. 2 (2): 205–217. https://doi.org/10.1016/0020-7225(64)90005-9.
Eringen, A. C. 1966. “Theory of micropolar fluids.” J. Math. Mech. 16 (1): 1–18. https://doi.org/10.1512/iumj.1967.16.16001.
Eringen, A. C. 1999. Microcontinuum field theories: I. Foundations and solids. New York: Springer.
Eringen, A. C. 2001. Microcontinuum field theories: II. Fluent media. New York: Springer.
Eringen, A. C., and E. S. Suhubi. 1964. “Nonlinear theory of simple micro-elastic solids—I.” Int. J. Eng. Sci. 2 (2): 189–203.
Glauert, H. 1928. “The effect of compressibility on the lift of an aerofoil.” Proc. R. Soc. Lond. A 118 (779): 113–119. https://doi.org/10.1098/rspa.1928.0039.
Haller, G. 2005. “An objective definition of a vortex.” J. Fluid Mech. 525 (Feb): 1–26. https://doi.org/10.1017/S0022112004002526.
Harten, A., B. Engquist, S. Osher, and S. R. Chakravarthy. 1987. “Uniformly high order accurate essentially non-oscillatory schemes, III.” J. Comput. Phys. 71 (2): 231–303. https://doi.org/10.1016/0021-9991(87)90031-3.
Hunt, J. C. R., A. A. Wray, and P. Moin. 1988. “Eddies, streams, and convergence zones in turbulent flows.”, 193. Washington, DC: Center for Turbulence Research, National Aeronautics and Space Administration.
Jeong, J., and F. Hussain. 1995. “On the identification of a vortex.” J. Fluid Mech. 285 (Feb): 69–94. https://doi.org/10.1017/S0022112095000462.
Kurganov, A., S. Noelle, and G. Petrova. 2001. “Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations.” SIAM J. Sci. Comput. 23 (3): 707–740. https://doi.org/10.1137/S1064827500373413.
Liu, X.-D., S. Osher, and T. Chan. 1994. “Weighted essentially non-oscillatory schemes.” J. Comput. Phys. 115 (1): 200–212. https://doi.org/10.1006/jcph.1994.1187.
Shu, C.-W., and S. Osher. 1988. “Efficient implementation of essentially non-oscillatory shock-capturing schemes.” J. Comput. Phys. 77 (2): 439–471. https://doi.org/10.1016/0021-9991(88)90177-5.
Van Albada, G. D., B. Van Leer, and W. Roberts. 1997. “A comparative study of computational methods in cosmic gas dynamics.” In Upwind and high-resolution schemes, 95–103. New York: Springer.
Wonnell, L. B., M. I. Cheikh, and J. Chen. 2018. “Morphing continuum simulation of transonic flow over an axisymmetric hill.” AIAA J. 56 (11): 4321–4330. https://doi.org/10.2514/1.J057064.
Wonnell, L. B., and J. Chen. 2016. “A morphing continuum approach to compressible flows: Shock wave-turbulent boundary layer interaction.” In Proc., 46th AIAA Fluid Dynamics Conf., 4279. Reston, VA: American Institute of Aeronautics and Astronautics.
Wonnell, L. B., and J. Chen. 2017. “Morphing continuum theory: Incorporating the physics of microstructures to capture the transition to turbulence within a boundary layer.” J. Fluids Eng. 139 (1): 011205. https://doi.org/10.1115/1.4034354.
Zhong, Q., Q. Chen, M. Qi, and X. Wang. 2015. “Comparison of vortex identification criteria for planar velocity fields in wall turbulence.” Phys. Fluids 27 (8): 085101. https://doi.org/10.1063/1.4927647.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Oct 14, 2019
Accepted: Mar 4, 2020
Published online: May 28, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 28, 2020
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