Applications of AUSM+ Scheme on Subsonic, Supersonic and Hypersonic Flows Fields
The performance of Advection Upstream Splitting
Method AUSM schemes are evaluated against experimental flow
fields at different Mach numbers and results are compared with
experimental data of subsonic, supersonic and hypersonic flow fields.
The turbulent model used here is SST model by Menter. The
numerical predictions include lift coefficient, drag coefficient and
pitching moment coefficient at different mach numbers and angle of
attacks. This work describes a computational study undertaken to
compute the Aerodynamic characteristics of different air vehicles
configurations using a structured Navier-Stokes computational
technique. The CFD code bases on the idea of upwind scheme for the
convective (convective-moving) fluxes. CFD results for GLC305
airfoil and cone cylinder tail fined missile calculated on above
mentioned turbulence model are compared with the available data.
Wide ranges of Mach number from subsonic to hypersonic speeds are
simulated and results are compared. When the computation is done
by using viscous turbulence model the above mentioned coefficients
have a very good agreement with the experimental values. AUSM
scheme is very efficient in the regions of very high pressure gradients
like shock waves and discontinuities. The AUSM versions simulate
the all types of flows from lower subsonic to hypersonic flow without
oscillations.
[1] Liou, M.-S. and Steffen, C., "A New Flux Splitting Scheme," J. Comput.
Phys., Vol. 107, 23-39, 1993.
[2] Liou, M.-S., "A Sequel to AUSM: AUSM+" J. Comput. Phys., Vol. 129,
364-382, 1996.
[3] Wada, Y. and Liou, M.-S., "An Accurate and Robust Flux Splitting
Scheme for Shock and Contact Discontinuities," SIAM J. Scientific
Computing, Vol. 18, 633-657, 1997.
[4] Liou, M.-S., "A Sequel to AUSM, Part II: AUSM+-up" J. Comput.
Phys., Vol. 214, 137- 170, 2006.
[5] Edwards, J. R., Franklin, R., and Liou, M.-S., "Low-Diffusion Flux-
Splitting Methods for Real Fluid Flows with Phase Transitions," AIAA
J., Vol. 38, 1624-1633, 2000.
[6] Chang, C.-H. and Liou, M.-S., "A New Approach to the Simulation of
Compressible Multifluid Flows with AUSM+ Scheme," AIAA Paper
2003-4107, 16th AIAA CFD Conference, Orlando, FL, June 23-26,
2003.
[7] Edwards, J. R. and Liou, M.-S., "Low-Diffusion Flux-Splitting Methods
for Flows at All Speeds," AIAA J., Vol. 36, 1610-1617, 1998.
[8] Kim, K. H., Kim, C., and Rho, O., "Methods for the Accurate
Computations of Hypersonic Flows I. AUSMPW+ Scheme," J. Comput.
Phys., Vol. 174, 38-80, 2001.
[9] Mary, I. and Sagaut, P., "Large Eddy Simulation of Flow Around an
Airfoil Near Stall," AIAA J., Vol. 40, 1139-1145, 2002.
[10] Manoha, E., Redonnet, S., Terracol, M., and Guenanff, G., "Numerical
Simulation of Aerodynamics Noise," ECCOMAS 24-28 July 2004.
[11] Billet, G. and Louedin, O., "Adaptive Limiters for Improving the
Accuracy of the MUSCL Approach for Unsteady Flows," J. Comput.
Phys., Vol. 170, 161-183, 2001.
[12] Wada, K. and Koda, J., "Instabilities of Spiral Shock - I. Onset of
Wiggle Instability and its Mechanism," Monthly Notices of the Royal
Astronomical Society, Vol. 349, 270-280 (11), 2004.
[13] R. V. Chima and M. S. Liou.Comparison of the AUSM+ and H-CUSP
schemes for turbo machinery applications. NASA TM-2003-212457,
2003.
[14] M. S. Liou and C. J. Steffen, Jr. A new flux splitting scheme. Journal of
Computational Physics, 107(1):23-39, 1993.
[15] Herald E. Addy Jr. Glenn Research Center, Cleveland, Ohio" Ice
accretions and icing effect for modern airfoil" NASA/TP-2000-310021
[16] Bertrand Girard "wind tunnel test of DERV-ISL reference models at
supersonic speed(Series ISLFPWT-1) August 1997 DERV-TM-
9704.(Report)
[17] Jubaraj Sahu "Numerical computations of dynamic derivatives of finned
projectile using time accurate CFD method. AIAA 2007-6581(
Conference paper)
[18] Robert L. Calloway, Nancy H. White. Measured and Predicted Shock
Shapes and Aerodynamic Coefficients for Blunted Cones at Incidence in
Air at Mach 5.9. NASA Technical Paper 1652, 1980.
[19] Menter, F.R. "Zonal Two Equation k -w Turbulence Models for
Aerodynamic Flows". AIAA 24th Fluid Dynamics conference,6-9 July
1993: 93- 2906.
[20] Turbulence Modeling for CFD by David C. Wilcox ( book on
turbulence)
[21] A. Jameson, W. Schmidt, and E. Turkel. Numerical Solution of the Euler
Equations by Finite Volume Methods Using Runge-Kutta Time-
Stepping Schemes. Technical Report AIAA-81-1259, AIAA 14th Fluid
and Plasma Dynamics Conference, Palo Alto, California, June
1981.(conference paper).
[1] Liou, M.-S. and Steffen, C., "A New Flux Splitting Scheme," J. Comput.
Phys., Vol. 107, 23-39, 1993.
[2] Liou, M.-S., "A Sequel to AUSM: AUSM+" J. Comput. Phys., Vol. 129,
364-382, 1996.
[3] Wada, Y. and Liou, M.-S., "An Accurate and Robust Flux Splitting
Scheme for Shock and Contact Discontinuities," SIAM J. Scientific
Computing, Vol. 18, 633-657, 1997.
[4] Liou, M.-S., "A Sequel to AUSM, Part II: AUSM+-up" J. Comput.
Phys., Vol. 214, 137- 170, 2006.
[5] Edwards, J. R., Franklin, R., and Liou, M.-S., "Low-Diffusion Flux-
Splitting Methods for Real Fluid Flows with Phase Transitions," AIAA
J., Vol. 38, 1624-1633, 2000.
[6] Chang, C.-H. and Liou, M.-S., "A New Approach to the Simulation of
Compressible Multifluid Flows with AUSM+ Scheme," AIAA Paper
2003-4107, 16th AIAA CFD Conference, Orlando, FL, June 23-26,
2003.
[7] Edwards, J. R. and Liou, M.-S., "Low-Diffusion Flux-Splitting Methods
for Flows at All Speeds," AIAA J., Vol. 36, 1610-1617, 1998.
[8] Kim, K. H., Kim, C., and Rho, O., "Methods for the Accurate
Computations of Hypersonic Flows I. AUSMPW+ Scheme," J. Comput.
Phys., Vol. 174, 38-80, 2001.
[9] Mary, I. and Sagaut, P., "Large Eddy Simulation of Flow Around an
Airfoil Near Stall," AIAA J., Vol. 40, 1139-1145, 2002.
[10] Manoha, E., Redonnet, S., Terracol, M., and Guenanff, G., "Numerical
Simulation of Aerodynamics Noise," ECCOMAS 24-28 July 2004.
[11] Billet, G. and Louedin, O., "Adaptive Limiters for Improving the
Accuracy of the MUSCL Approach for Unsteady Flows," J. Comput.
Phys., Vol. 170, 161-183, 2001.
[12] Wada, K. and Koda, J., "Instabilities of Spiral Shock - I. Onset of
Wiggle Instability and its Mechanism," Monthly Notices of the Royal
Astronomical Society, Vol. 349, 270-280 (11), 2004.
[13] R. V. Chima and M. S. Liou.Comparison of the AUSM+ and H-CUSP
schemes for turbo machinery applications. NASA TM-2003-212457,
2003.
[14] M. S. Liou and C. J. Steffen, Jr. A new flux splitting scheme. Journal of
Computational Physics, 107(1):23-39, 1993.
[15] Herald E. Addy Jr. Glenn Research Center, Cleveland, Ohio" Ice
accretions and icing effect for modern airfoil" NASA/TP-2000-310021
[16] Bertrand Girard "wind tunnel test of DERV-ISL reference models at
supersonic speed(Series ISLFPWT-1) August 1997 DERV-TM-
9704.(Report)
[17] Jubaraj Sahu "Numerical computations of dynamic derivatives of finned
projectile using time accurate CFD method. AIAA 2007-6581(
Conference paper)
[18] Robert L. Calloway, Nancy H. White. Measured and Predicted Shock
Shapes and Aerodynamic Coefficients for Blunted Cones at Incidence in
Air at Mach 5.9. NASA Technical Paper 1652, 1980.
[19] Menter, F.R. "Zonal Two Equation k -w Turbulence Models for
Aerodynamic Flows". AIAA 24th Fluid Dynamics conference,6-9 July
1993: 93- 2906.
[20] Turbulence Modeling for CFD by David C. Wilcox ( book on
turbulence)
[21] A. Jameson, W. Schmidt, and E. Turkel. Numerical Solution of the Euler
Equations by Finite Volume Methods Using Runge-Kutta Time-
Stepping Schemes. Technical Report AIAA-81-1259, AIAA 14th Fluid
and Plasma Dynamics Conference, Palo Alto, California, June
1981.(conference paper).
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:62177", author = "Muhammad Yamin Younis and Muhammad Amjad Sohail and Tawfiqur Rahman and Zaka Muhammad and Saifur Rahman Bakaul", title = "Applications of AUSM+ Scheme on Subsonic, Supersonic and Hypersonic Flows Fields", abstract = "The performance of Advection Upstream Splitting
Method AUSM schemes are evaluated against experimental flow
fields at different Mach numbers and results are compared with
experimental data of subsonic, supersonic and hypersonic flow fields.
The turbulent model used here is SST model by Menter. The
numerical predictions include lift coefficient, drag coefficient and
pitching moment coefficient at different mach numbers and angle of
attacks. This work describes a computational study undertaken to
compute the Aerodynamic characteristics of different air vehicles
configurations using a structured Navier-Stokes computational
technique. The CFD code bases on the idea of upwind scheme for the
convective (convective-moving) fluxes. CFD results for GLC305
airfoil and cone cylinder tail fined missile calculated on above
mentioned turbulence model are compared with the available data.
Wide ranges of Mach number from subsonic to hypersonic speeds are
simulated and results are compared. When the computation is done
by using viscous turbulence model the above mentioned coefficients
have a very good agreement with the experimental values. AUSM
scheme is very efficient in the regions of very high pressure gradients
like shock waves and discontinuities. The AUSM versions simulate
the all types of flows from lower subsonic to hypersonic flow without
oscillations.", keywords = "Subsonic, supersonic, Hypersonic, AUSM+, Drag
Coefficient, lift Coefficient, Pitching moment coefficient, pressure
Coefficient, turbulent flow.", volume = "5", number = "1", pages = "231-7", }