### On the Rotational Behaviour of the Euler Equations at High Angles of Attack

^{(*)}

*Corresponding author*

**DOI's assignment:**

*the author of the article can submit here a request for assignment of a DOI number to this resource!*

**Cost of the service: euros 10,00 (for a DOI)**

#### Abstract

This study investigates the Euler equations behavior at high angles of attack for a NACA 0012 airfoil. It was shown that the Euler equations could successfully predict the separation behavior under certain conditions. For this purpose, a logical analogy between the physical and numerical viscosities should be established. The produced vortices on the upper side of airfoil were clearly captured due to the fact that the Euler equations could admit rotational solutions. This fact is justifiable also by the Crocco’s theorem which relates the entropy change to the flow parameters. For flux treatment a novel pressure-based method was applied which has currently been developed for incompressible flows resulted in a wider stability and faster convergence. For marching in time, a fifth-order Runge-Kutta scheme has been used. The obtained results are compared with available data in the technical literature. *Copyright © 2013 Praise Worthy Prize - All rights reserved.*

#### Keywords

#### Full Text:

PDF#### References

J. D. Jr. Anderson, Modern Compressible Flow, (2nd edition, McGraw-Hill, 1990)

R. M. Cummings, J. R. Forsythe, S. A. Morton, K. D. Squires, Computational Challenges in High Angle of Attack Flow Prediction, Progress Aero. Sci., Vol. 39, pp. 369-384, 2003.

P. S. Murthy, V. S. Holla, H. Kamath, Unsteady Navier-Stokes Solutions for NACA 0012 airfoil, Comput. Meth. Applied Mechanics Eng., Vol. 186, pp. 85-99, 2000.

C. L. Rumsey, A Computational Analysis of Flow Over Five Different Airfoil Geometries at High Angles-of-Attack, AIAA-188, NASA Langley Research Center, Hampton, VA, 1987.

S. N. Chakrabartty, Numerical Solution of Navier-Stokes Equations for Two-Dimensional Viscous Compressible Flows, AIAA J., Vol. 27, n. 7, pp. 843-849, 1989.

V. A. Aleksin, S. N. Kazeikin, Three-Dimensional Boundary Layers of Complex-Shaped Bodies at Angles of Attack, J. Applied Math. Mech., Vol. 59, n. 1, pp. 99-109, 1995.

A. Jameson, W. Schmidit, E. Turkel, Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping, AIAA 14th fluid and plasma dynamics conference, Palo Alto, California, 23-25 June 1981.

P. L Roe, Characteristic-Based Schemes for the Euler Equations, Annual Review of Fluid Mechanics, Palo Alto, CA, Vol. 18, pp: 337-365. 1986.

S. E. Razavi, K. Zamzamian, A. Farzadi, Genuinely Multidimensional Characteristic-Based Schemes for Incompressible Flows, Int. J. Numer. Meth. Fluids, Vol. 57, pp. 929-949, 2008.

S. E .Razavi, J. Ghasemi, A. Farzadi, Flux Modeling in the Finite-Volume Lattice Boltzmann Approach, Int. J. Comput. Fluid Dyn., Vol. 23,n. 1, pp. 69-77, 2009.

A. Jameson, D. Mavriplis, Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh, AIAA 23rd Aerospace sciences meeting, Reno, Nevada, 14-17 January 1985.

S. E. Razavi, Analysis of External Compressible Flows Using the New Far-Field Conditions, J. Faculty Eng., Vol. 33, n. 2, pp. 27-39, 2006.

R. C. Lock, Test Case for Numerical Methods in Two-Dimensional Transonic Flows, AGARD REPORT NO.575, 1970.

### Refbacks

- There are currently no refbacks.

Please send any question about this web site to info@praiseworthyprize.com**Copyright © 2005-2024**** Praise Worthy Prize**