Abstract
A unified methodology for the analysis of potential and viscous flows is reviewed. The viscous-flow formulation is based on the decomposition of the velocity field into two terms: the first (vortical velocity) is due to the vorticity in the field, whereas the second is irrotational. The specific decomposition used is characterized by the fact that the vortical velocity vanishes in a region 𝓥 0, which comprises most of the irrotational region. As a consequence, the additional field sources in the equation for the potential also vanish in 𝓥0, even for unsteady compressible flows. This is a major advantage for boundary integral formulations. In addition, it is shown how in the limit, as the thickness of the vortical region goes to zero, the viscous-flow formulation reduces continuously to the potential-flow formulation. Also, the methodology is general in that it is applicable for the solution of unsteady compressible flows around complex configurations. The extent of the validation of the numerical implementation is reported : the validation for the potential-flow formulation is extensive (recent applications include unsteady transonic three-dimensional flows around isolated wings and subsonic flows around isolated helicopter rotors in forward flight), whereas the validation of the viscous-flow formulation is limited in the impulsive start of airfoils in two-dimensional incompressible flows.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Morino, L., A General Theory of Unsteady Compressible Potential Aerodynamics, NASA CR-2464, 1974.
Morino, L., Helmholtz and Poincaré Vorticity-Potential Decompositions for the Analysis of Unsteady Compressible Viscous Flows, Boundary Element Methods in Nonlinear Fluid Dynamics, Edited by P. K. Banerjee and L. Morino, Elsevier Applied Science Publishers, Barking, England, pp. 1–54, 1990.
Morino, L., Bharadvaj, B. K., Freedman, M. I., and Tseng, K., Boundary Integral Equation for Wave Equation with Moving Boundary and Applications to Compressible Potential Aerodynamics of Airplanes and Helicopters, Computational Mechanics, Vol. 4, pp. 231–243, 1989.
Morino, L., and Tseng, K., A General Theory of Unsteady Compressible Potential Flows with Applications to Airplane and Rotors, Boundary Element Methods in Nonlinear Fluid Dynamics, Edited by P. K. Banerjee and L. Morino, Elsevier Applied Science Publishers, Barking, England, pp. 183–246, 1990.
Hess, J., Panel Methods in Computational Fluid Dynamics, Annual Review of Fluid Mechanics, Vol. 22, pp. 255–274, 1990.
Gennaretti, M., and Morino, L., A Boundary Element Method for the Potential, Compressible Aerodynamics of Bodies in Arbitrary Motion, Aeronautical Journal, Vol. 96, pp. 15–19, 1992.
Wu, J. C., Fundamental Solutions and Numerical Methods for Flow Problems, International Journal for Numerical Methods in Fluids, Vol. 4, pp. 185–201, 1984.
Morino, L., Helmholtz Decomposition Revisited: Vor ticity Generation and Trailing Edge Condition, Part 1: Incompressible Flows, Computational Mechanics, Vol. 1, pp. 65–90, 1986.
Piva, R., and Morino, L., A Boundary Integral Formulation in Primitive Variables for Unsteady Viscous Flows, Boundary Element Methods in Nonlinear Fluid Dynamics, Edited by P. K. Banerjee and L. Morino, Elsevier Applied Science Publishers, Barking, England, pp. 117–150, 1990.
Morino, L., and Kuo, C. C., Subsonic Potential Aerodynamics for Complex Configurations: A General Theory, AIAA Journal, Vol. 12, pp. 191–197, 1974.
Morino, L., Chen, L. T., and Suciu, E. O., Steady and Oscillatory Subsonic and Supersonic Aerodynamics Around Complex Configurations, AIAA Journal, Vol. 13, pp. 368–374, 1975.
Morino, L., and Chen, L. T., Indicial Compressible Potential Aerodynamics Around Complex Aircraft Configurations, Aerodynamic Analyses Requiring Advanced Computers, NASA SP-347, pp. 1067–1110, 1975.
Morino, L., and Tseng, K., Time-Domain Green’s Function Method for Three-Dimensional Nonlinear Subsonic Flows, AIAA Paper 78–1204, 1978.
Tseng, K., and Morino, L., Nonlinear Green’s Function Method for Unsteady Transonic Flows, Transonic Aerodynamics, Edited by D. Nixon, Progress in Aeronautics and Astronautics, American Institute of Aeronautics and Astronautics, New York, New York, Vol. 81, pp. 565–603, 1982.
Tseng, K., Nonlinear Green’s Function Method for Transonic Potential Flow, PhD Thesis, Boston University, 1983.
Tseng, K., Application of the Green’s Function Method for Two- and Three-Dimensional Steady Transonic Flows, AIAA Paper 84–0425, 1984.
Iemma, U., Mastroddi, F., Morino, L., and Pecora, M., A Boundary Integral Formulation for Unsteady Transonic Potential Flows, Paper No. 7, AG ARD Specialists Meeting on Transonic Unsteady Aerodynamics and Aeroelasticity, San Diego, California, 1991.
Morino, L., and Soohoo, P., Green’s Function Method for Compressible Unsteady Potential Aerodynamic Analysis of Rotor-Fuselage Interaction, 4th European Rotorcraft and Powered-Lift Aircraft Forum, Stresa, Italy, 1978.
Preuss, R. D., Suciu, E. O., and Morino, L., Unsteady Potential Aerodynamics of Rotors with Applications to Horizontal-Axis Windmills, AIAA Journal, Vol. 18, pp. 385–393, 1980.
Morino, L., Kaprielian, Z. Jr., and Sipcic, S. R., Free-Wake Analysis of Helicopter Rotors, Vertica, Vol. 9, pp. 127–140, 1985.
Morino, L., and Bharadvaj, B., A Unified Approach for Potential and Viscous Free-Wake Analysis of Helicopter Rotors, Vertica, Vol. 12, pp. 147–154, 1988.
Suciu, E. O., and Morino, L., Nonlinear Steady Incompressible Lifting-Surface Analysis with Wake Roll-Up, AIAA Journal, Vol. 15, pp. 54–58, 1977.
Morino, L., Freedman, M. I., Deutsch, D. J., and Sipcic, S. R., An Integral Equation Method for Compressible Potential Flows in an Arbitrary Frame of Reference, Computational Methods in Potential Aerodynamics, Edited by L. Morino, Computational Mechanics Publications, Southampton, England, pp. 728–733, 1985.
Morino, L., Freedman, M. I., and Tseng, K., Unsteady Three-Dimensional Compressible Potential Aerodynamics of Helicopter Rotors in Hover and Forward Flight: A Boundary Element Formulation, American Helicopter Society National Specialist Meeting on Aerodynamics and Aeroacoustics, Arlington, Texas, 1987.
Gennaretti, M., Metodo delle Equazioni Integrali al Contornoper Analisi Aero-dinamica e Aeroacustica di Rotori in Flussi Potenziali, Compressibili, Nonstazion-ari, Tesi di Laurea, University of Rome “La Sapienza,” 1989.
Gennaretti, M., Macina, O., and Morino, L., A New Integral Equation for Potential Compressible Aerodynamics of Rotors in Forward Flight, Proceedings of the International Specialist Meeting on Rotorcraft Basic Research, Atlanta, Georgia, 1991.
Morino, L., Gennaretti, M., and Petrocchi, P., A General Theory of Potential Aerodynamics with Applications to Helicopter Rotor-Fuselage Interaction, 1991 Conference of the International Association for Boundary Element Methods, Kyoto, Japan, 1991.
Beauchamp, P. P., A Potential-Vorticity Decomposition for the Boundary Integral Equation Analysis of Viscous Flows, PhD Thesis, Boston University, 1990.
Beauchamp, P. P., and Morino, L., Viscous Flow Analysis Using the Poincaré Decomposition, Boundary Integral Methods: Theory and Applications, Edited by L. Morino and R. Piva, Springer-Verlag, Berlin, Germany, pp. 95–104, 1991.
Morino, L., Gennaretti, M., and Shen, S. F., Lighthill Transpiration Velocity Revisited: An Exact Formulation Based on Poincaré Decomposition, Proceedings of the 6th Italian Congress on Computational Mechanics, Brescia, Italy, 1991.
Lighthill, M. J., On Displacement Thickness, Journal of Fluid Mechanics, Vol. 4, pp. 383–392, 1958.
Batchelor, G. K., An Introduction tc Fluid Dynamics, Cambridge University Press, Cambridge, England, 1967.
Lighthill, M. J., Introduction to Boundary Layer Theory, Laminar Boundary Layers, Edited by L. Rosenhead, Oxford University Press, Oxford, England, Part 2, pp. 46–113, 1963.
Morino, L.Boundary Integral Equations in Aerodynamics, Applied Mechanics Reviews, Vol. 46, pp. 445–466, 1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Morino, L. (1994). Toward a Unification of Potential and Viscous Aerodynamics: Boundary Integral Formulation. In: Miele, A., Salvetti, A. (eds) Applied Mathematics in Aerospace Science and Engineering. Mathematical Concepts and Methods in Science and Engineering, vol 44. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9259-1_5
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9259-1_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9261-4
Online ISBN: 978-1-4757-9259-1
eBook Packages: Springer Book Archive