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Comparison of Euler and Navier-Stokes solutions for vortex flow over a delta wing

Published online by Cambridge University Press:  04 July 2016

A. Rizzi  and
B. Müller
A. Rizzi
Affiliation:
FFA, The Aeronautical Research Institute of Sweden, Bromma, and, KTH, Royal Institute of Technology, Stockholm, Sweden
B. Müller
Affiliation:
FFA, The Aeronautical Research Institute of Sweden, Bromma, Sweden
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Summary

A numerical method has been developed recently to solve the Navier-Stokes equations for laminar compressible flow around delta wings. A large-scale Navier-Stokes solution on a mesh of 129 × 49 × 65 points for transonic flow Mx = 0·85, α = 10° and Rex = 2·38 × 106 around a 65° swept delta wing with round leading edge is presented and compared with a correspondingly large-scale Euler solution. The viscous results reveal the presence of primary, secondary, and even tertiary vortices. The starting location of the primary vortex is seen to be quite different in the two solutions. In the viscous solution it starts at the wing apex, but in the Euler results it starts about one quarter chord downstream. The secondary reparations are also different, due to the up-lifting of the boundary layer in the viscous results, but to a cross-flow shock in the Euler computation. Comparison with experiment shows that the interaction between the primary and secondary vortices in the Navier-Stokes computation is obtained correctly and that these results are a more realistic simulation than the one given by the Euler equations.

Type
Research Article
Information
The Aeronautical Journal , Volume 92 , Issue 914 , April 1988 , pp. 145 - 153
Copyright
Copyright © Royal Aeronautical Society 1988 

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Footnotes

*

Current address: DFVLR-AVA, D-3400, Göttingen, FRG

References

1. Smith, J. H. B. Vortex Flows in Aerodynamics. Ann Rev Fluid Mech, 1986, 18, 221–242.Google Scholar
2. Newsome, R. W. and Kandil, O. A. Vortical Flow Aerodynamics — Physical Aspects and Numerical Simulation. AIAA Paper 87-0205, Jan. 1987.Google Scholar
3. Rizzi, A. and Purcell, C. J. On the Computation of Transonic Leading-Edge Vortices Using the Euler Equations. J Fluid Mech, 1987, 181, 163–195.Google Scholar
4. Elsenaar, A. and Eriksson, G. (eds), Proc Int Vortex Flow Experiment on Euler Code Validation, FFA TN, Stockholm, 1986.Google Scholar
5. Müller, B. and Rizzi, A. Navier-Stokes Computation of Transonic Vortices Over a Round Leading Edge Delta Wing. AIAA Paper No 87-1227, 1987.Google Scholar
6. Müller, B. and Rizzi, A. Runge-Kutta Finite-Volume Simulation of Laminar Transonic Flow over a NACA 0012 Airfoil Using the Navier-Stokes Equations. FFA TN 1986-60, 1986.Google Scholar
7. Müller, B. and Rizzi, A. Navier-Stokes Simulation of Laminar Flow over the 65° Round Leading Edge Delta Wing at Mx = 0.85 and α = 10°. In Ref. 4, 269–280.Google Scholar
8. Rizzi, A. and Eriksson, L.-E. Computation of Flow Around Wings Based on the Euler Equations. J Fluid Mech, 1984, 148, 45–71.Google Scholar
9. Rizzi, A. and Inouye, M. Time Split Finite-Volume Method for Three-Dimensional Blunt-Body Flow. AIAA J, 1973, 11 (11), 1478–1485.Google Scholar
10. Eriksson, L.-E. Generation of Boundary Conforming Grids Around Wing-Body Configurations Using Transfinite Interpolation. AIAA J, Oct 1982, 20. (10), 1313–1320.Google Scholar
11. Rizzi, A. Vector Coding the Finite-Volume Procedure for the CYBER 205. Parallel Comput, 1985. 2, 295–312.Google Scholar
12. Rizzi, A., Drougge, G. and Purcell, C. J. Euler Simulation of Shed Vortex Flows over the 65 Degree Delta Wings. In Ref. 4, 289–343.Google Scholar
13. Hirdes, R. H. C. US/European Vortex Flow Experiment Tests Report of Wind Tunnel Measurements on the 65° Wing in the NLR High Speed Wind Tunnel HST. NLR TR 85046 L. 1985.Google Scholar
14. Hartmann., K. US/European Transonic Vortex Flow Experiment — Data Lists of Pressure Measurements. DFVLR-IB 222-86 A 26, 1986.Google Scholar
15. Carcaillet., R., Manie, F., Pagan, D. and Solignac, J. L. Leading Edge Vortex Flow over a 75 Degree Swept Delta Wing: Experimental and Computational Results. 15th ICAS Congress. London. 7th-12th September 1986.Google Scholar
16. Tobak, M. and Peake, D. J. Topology of Three-Dimensional Separated Flows. Ann Rev Fluid Mech, 1982. 14, 61–85.Google Scholar