Document Type : Research Article

**Authors**

Malek Ashtar University of Technology, Tehran, Iran

**Abstract**

Unsteady compressible flows over a stationary 60-degree swept delta wing with a sharp

leading edge were computationally simulated at different Mach numbers and moderate angles of the

attack. An unstructured grid, Spalart-Allmaras Detached Eddy Simulation turbulence model, and a

dual-time implicit time integration were used. Vortical flow structures associated with various freestream

conditions are displayed and their variations versus time are studied. Variations of flow field

parameters, such as u velocity component and pressure coefficient with the flow time are demonstrated

at several point probes in the flow field. A Power Spectral Density frequency analysis is performed for

such unsteady behaviours to identify the dominant frequencies which exist in each flow condition. The

frequency analyses show that low frequencies associated with vortex breakdown oscillation are the most

dominant frequencies in all cases where vortex breakdown occurs. Dominant frequencies associated with

helical mode instability are also present at the probes downstream of breakdown. Dominant frequencies

related to the shear layer instabilities were observed for the low subsonic regime.

leading edge were computationally simulated at different Mach numbers and moderate angles of the

attack. An unstructured grid, Spalart-Allmaras Detached Eddy Simulation turbulence model, and a

dual-time implicit time integration were used. Vortical flow structures associated with various freestream

conditions are displayed and their variations versus time are studied. Variations of flow field

parameters, such as u velocity component and pressure coefficient with the flow time are demonstrated

at several point probes in the flow field. A Power Spectral Density frequency analysis is performed for

such unsteady behaviours to identify the dominant frequencies which exist in each flow condition. The

frequency analyses show that low frequencies associated with vortex breakdown oscillation are the most

dominant frequencies in all cases where vortex breakdown occurs. Dominant frequencies associated with

helical mode instability are also present at the probes downstream of breakdown. Dominant frequencies

related to the shear layer instabilities were observed for the low subsonic regime.

**Highlights**

[1] I. Gursul, Recent Developments in Delta Wing Aerodynamics, *Aeronautical Journal*, 108(1087) (2004) 437-452.

[2] I. Gursul, Reviews of Unsteady Vortex Flows over Slender Delta Wings, *Journal of Aircraft*, 42(2) (2005) 299-319.

[3] R.C. Nelson, A. Pelletier, The Unsteady Aerodynamics of Slender Wings and Aircraft Undergoing Large Amplitude Maneuvers, *Progress in Aerospace Sciences*, 39 (2003) 185-248.

[4] L.A. Schiavetta, K.J. Badcock, R.M. Cummings, Comparison of DES and URANS for Unsteady Vortical Flows over Delta wings, in: *45th AIAA aerospace science and meeting exhibit*, Reno, Nevada, USA, 2007.

[5] P.R. Spalart, W.H. Jou, M. Strelets, S.R. Allmaras, Comments on the Feasibility of LES for Wings and on a Hybrid RANS/LES Approach, in: Advances in DNS/ LES, *1st AFSOR international conference on DN/LES, AFSOR*, 1997.

[6] A.M. Mitchell, S.A. Morton, J.R. Forsythe, R.M. Cummings, Analysis of Delta Wing Vortical Substructures Using Detached Eddy Simulation, *AIAA Journal*, 44(5) (2006) 964-972.

[7] S.A. Morton, High Reynolds Number DES Simulations of Vortex Breakdown over a 70º Delta Wing, in: *21st applied aerodynamic conference*, 2003.

[8] D.S. Miller, R.M. Wood, Leeside Flows over Delta Wings at Supersonic Speeds, *Journal of Aircraft*, 21(9) (1984) 680-686.

[9] S.N. Seshadri, K.Y. Narayan, Possible Types of Flow on Lee-Surface of Delta Wings at Supersonic Speeds, *Aeronautical Journal*, 92(915) (1988) 185-199.

[10] M.D. Brodetsky, E. Krause, S.B. Nikiforov, A.A. Pavlov, A.M. Kharitonov, A.M. Shevchenko, Evolution of Vortex Structures on Leeward Side of a Delta Wing, *Journal of Applied Mechanics and Technical Physics*, 42(2) (2001) 243-254.

[11] M. Hadidoolabi, H. Ansarian, Computational Investigation of the Flow Structure over a Pitching Delta Wing at Supersonic Speeds, Proceedings of the Institution of Mechanical Engineers, Part G: *Journal of Aerospace Engineering*, 230(7) (2015) 1334-1347.

[12] M. Hadidoolabi, H. Ansarian, Computational Investigation of Vortex Breakdown over a Pitching Delta Wing at Supersonic Speeds, *Scientia Iranica *(B), In Press (2017).

[13] P.R. Spalart, S.R. Allmaras, A One Equation Turbulence Model for Aerodynamic Flows, in: *30th AIAA aerospace science and meeting exhibit*, USA, 1992.

[14] J.R. Forsythe, K.A. Hoffmann, F.F. Dieteker, Detached- Eddy Simulation of a Supersonic Axisymmetric Base Flow with an Unstructured Flow Solver, *AIAA Paper*, (2000).

**Keywords**

[1] I. Gursul, Recent Developments in Delta Wing Aerodynamics, *Aeronautical Journal*, 108(1087) (2004) 437-452.

[2] I. Gursul, Reviews of Unsteady Vortex Flows over Slender Delta Wings, *Journal of Aircraft*, 42(2) (2005) 299-319.

[3] R.C. Nelson, A. Pelletier, The Unsteady Aerodynamics of Slender Wings and Aircraft Undergoing Large Amplitude Maneuvers, *Progress in Aerospace Sciences*, 39 (2003) 185-248.

[4] L.A. Schiavetta, K.J. Badcock, R.M. Cummings, Comparison of DES and URANS for Unsteady Vortical Flows over Delta wings, in: *45th AIAA aerospace science and meeting exhibit*, Reno, Nevada, USA, 2007.

[5] P.R. Spalart, W.H. Jou, M. Strelets, S.R. Allmaras, Comments on the Feasibility of LES for Wings and on a Hybrid RANS/LES Approach, in: Advances in DNS/ LES, *1st AFSOR international conference on DN/LES, AFSOR*, 1997.

[6] A.M. Mitchell, S.A. Morton, J.R. Forsythe, R.M. Cummings, Analysis of Delta Wing Vortical Substructures Using Detached Eddy Simulation, *AIAA Journal*, 44(5) (2006) 964-972.

[7] S.A. Morton, High Reynolds Number DES Simulations of Vortex Breakdown over a 70º Delta Wing, in: *21st applied aerodynamic conference*, 2003.

[8] D.S. Miller, R.M. Wood, Leeside Flows over Delta Wings at Supersonic Speeds, *Journal of Aircraft*, 21(9) (1984) 680-686.

[9] S.N. Seshadri, K.Y. Narayan, Possible Types of Flow on Lee-Surface of Delta Wings at Supersonic Speeds, *Aeronautical Journal*, 92(915) (1988) 185-199.

[10] M.D. Brodetsky, E. Krause, S.B. Nikiforov, A.A. Pavlov, A.M. Kharitonov, A.M. Shevchenko, Evolution of Vortex Structures on Leeward Side of a Delta Wing, *Journal of Applied Mechanics and Technical Physics*, 42(2) (2001) 243-254.

[11] M. Hadidoolabi, H. Ansarian, Computational Investigation of the Flow Structure over a Pitching Delta Wing at Supersonic Speeds, Proceedings of the Institution of Mechanical Engineers, Part G: *Journal of Aerospace Engineering*, 230(7) (2015) 1334-1347.

[12] M. Hadidoolabi, H. Ansarian, Computational Investigation of Vortex Breakdown over a Pitching Delta Wing at Supersonic Speeds, *Scientia Iranica *(B), In Press (2017).

[13] P.R. Spalart, S.R. Allmaras, A One Equation Turbulence Model for Aerodynamic Flows, in: *30th AIAA aerospace science and meeting exhibit*, USA, 1992.

[14] J.R. Forsythe, K.A. Hoffmann, F.F. Dieteker, Detached- Eddy Simulation of a Supersonic Axisymmetric Base Flow with an Unstructured Flow Solver, *AIAA Paper*, (2000).

December 2017

Pages 219-232