Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations, the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At ARC a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft, and it solves the Euler/Navier-Stokes equations. The purpose of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric capabilities. During the last five years, the algorithms of the code have been enhanced extensively by using high-resolution upwind algorithms and efficient implicit solvers. The zonal capability of the code has been extended from a one-to-one grid interface to a mismatching unsteady zonal interface. The geometric capability of the code has been extended from a single oscillating wing case to a full-span wing-body configuration with oscillating control surfaces. Each time a new capability was added, a proper validation case was simulated, and the capability of the code was demonstrated

Obayashi, Shigeru

English

In the last two decades, there have been extensive developments in computational aerodynamics, which constitutes a major part of the general area of computational fluid dynamics. Such developments are essential to advance the understanding of the physics of complex flows, to complement expensive wind-tunnel tests, and to reduce the overall design cost of an aircraft, particularly in the area of aeroelasticity. Aeroelasticity plays an important role in the design and development of aircraft, particularly modern aircraft, which tend to be more flexible. Several phenomena that can be dangerous and limit the performance of an aircraft occur because of the interaction of the flow with flexible components. For example, an aircraft with highly swept wings may experience vortex-induced aeroelastic oscillations. Also, undesirable aeroelastic phenomena due to the presence and movement of shock waves occur in the transonic range. Aeroelastically critical phenomena, such as a low transonic flutter speed, have been known to occur through limited wind-tunnel tests and flight tests. Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is an order of magnitude more expensive than a parallel experiment involving only aerodynamics. By complementing the wind-tunnel experiments with numerical simulations the overall cost of the development of aircraft can be considerably reduced. In order to accurately compute aeroelastic phenomenon it is necessary to solve the unsteady Euler/Navier-Stokes equations simultaneously with the structural equations of motion. These equations accurately describe the flow phenomena for aeroelastic applications. At Ames a code, ENSAERO, is being developed for computing the unsteady aerodynamics and aeroelasticity of aircraft and it solves the Euler/Navier-Stokes equations. The purpose of this contract is to continue the algorithm enhancements of ENSAERO and to apply the code to complicated geometries. During the last year, the geometric capability of the code was extended to simulate transonic flows, a wing with oscillating control surface. Single-grid and zonal approaches were tested. For the zonal approach, a new interpolation technique was introduced. The key development of the algorithm was an interface treatment between moving zones for a control surface using the virtual-zone concept. The work performed during the period, 1 Apr. 1992 through 31 Mar. 1993 is summarized. Additional details on the various aspects of the study are given in the Appendices

NASA Technical Reports Server

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

MCAT Institute
Final Report
94-002
NASA-CR-195774
• /
/
ALGORITHM AND CODE
DEVELOPMENT FOR UNSTEADY
THREE-DIMENSIONAL
NAVIER-STOKES EQUATIONS
Shigeru Obayashi
(NASA-CR-195774) ALGCRITHM AND
CODE DEVELOPMENT FOR UNSTEADY
THREE-DIMENSIONAL NAVIER-STOKES
EQUATIONS (MCAT Inst.) & p
N94-29942
Unclas
G3/34 0003914
April 1994 NCC2-605
MCAT Institute
3933 Blue Gum Drive
San Jose, CA 95127
https://ntrs.nasa.gov/search.jsp?R=19940025437 2020-06-16T14:53:59+00:00Z
Algorithm and Code Development for Unsteady
Three-Dimensional Navier-Stokes Equations
Shigeru Obayashi
Introduction
In the last two decades, there have been extensive developments in computational
aerodynamics, which constitutes a major part of the general area of computational fluid
dynamics. 1 Such developments are essential to advance the understanding of the physics of
complex flows, to complement expensive wind-tunnel tests, and to reduce the overall
design cost of an aircraft, particularly in the area of aeroelasticity.
Aeroelasticity plays an important role in the design and development of aircraft, particularly
modem aircraft, which tend to be more flexible. Several phenomena that can be dangerous
and limit the performance of an aircraft occur because of the interaction of the flow with
flexible components. For example, an aircraft with highly swept wings may experience
vortex-induced aeroelastic oscillations. Also, undesirable aeroelastic phenomena due to the
presence and movement of shock waves occur in the transonic range. Aeroelastically
critical phenomena, such as a low transonic flutter speed, have been known to occur
through limited wind-tunnel tests and flight tests.
Aeroelastic tests require extensive cost and risk. An aeroelastic wind-tunnel experiment is
an order of magnitude more expensive than a parallel experiment involving only
aerodynamics. By complementing the wind-tunnel experiments with numerical simulations,
the overall cost of the development of aircraft can be considerably reduced. In order to
accurately compute aeroelastic phenomenon it is necessary to solve the unsteady
Euler/Navier-Stokes equations simultaneously with the structural equations of motion.
These equations accurately describe the flow phenomena for aeroelastic applications.
At Ames a code, ENSAERO, is being developed for computing the unsteady aerodynamics
and aeroelasticity of aircraft and it solves the Euler/Navier-Stokes equations. The purpose
of this cooperative agreement was to enhance ENSAERO in both algorithm and geometric
capabilities. During last five years, the algorithms of the code have been enhanced
extensively by using high-resolution upwind algorithms and efficient implicit solvers. The
zonal capability of the code has been extended from a one-to-one grid interface to a
mismatching unsteady zonal interface. The geometric capability of the code has been
extended from a single oscillating wing case to a full-span wing-body configuration with
oscillating control surfaces. Everytime when a new capability was added, a proper
validation case was simulated and the capability of the code was demonstrated.
Previous Results
Streamwise Upwind Algorithm and Its Higher-Order Extension
The initial cooperative agreement implemented an upwind algorithm into ENSAERO. The
existing ENSAERO code had the central-difference scheme with the second and fourth
order dissipation terms. It used the diagonal Beam-Warming approximate factorization
implicit solver. The new upwind algorithm implemented into the code was the streamwise
upwind algorithm that accounted for the multidimensionality to construct the numerical
flux. The computed results demonstrated the improved accuracy and robustness of the code
over the previous central-difference option3 -4
Freestream Capturing
When the governing equations are transformed to generalized coordinates, satisfaction of
the discretized conservation law is not trivial because of the numerical evaluation of the
metrics. It has more importance in moving grid cases. In this work, source of the error was
identified and a correct numerical procedure was presented:
Shock-Vortex Interaction on a Flexible Delta Wing
The upwind version of ENSAERO was applied to transonic flows over a clipped delta
wing at moderate angles of attack. Due to the wing planform with a highly swept leading
edge, a strong leading-edge vortex can form. This vortex can interact with a shock wave at
transonic Mach numbers. Simulations were performed for both rigid and flexible wings
successfully. It was found that the flexibility of the wing would delay occurrence of vortex
breakdown during the ramp motion of the wing:
Oscillating Control Surfaces
Geometric capability of the code was extended to simulate oscillating control surfaces.
Single-grid approach and zonal approach were proposed. In this study, the model geometry
was slightly modified to place a gap between the wing and the control surface. The gap
region was used to shear the grid as the control surface oscillated. The zonal approach
utilized a mismatching zonal interface. Test cases were chosen from the previous clipped
delta wing with a trailing-edge control surface. The result demonstrated the first successful
three-dimensional Navier-Stokes computation with a moving grid system. 7
Wing-Body Configuration with Oscillating Control Surfaces
In parallel to the control surface work, the code had been extended for unsteady Navier-
Stokes simulations of transonic flows over a wing-body configuration. The code inherited
the one-to-one matching zonal interface capability from the Transonic Navier-Stokes code,
TNS. After the control surface work was done, the geometric capability of the code was
extended to a full-span wing-body configuration, specifically an arrow-wing configuration
of supersonic transport-type aircraft with oscillating control surfaces. Four zones were
used and the total number of grid points were about one million. Comparison of computed
response characteristics between symmetric and antisymmetric control surface motions on
the right and left wings was studied. 8
Virtual Zones
To simulate the control surface oscillation without changing the model geometry, an idea of
virtual zones were implemented into the code. Virtual zones are zones of zero thickness (for
a finite volume formulation) which serve to transfer solid wall (or other) boundary
conditions to an interface condition. Thus multiple boundary conditions can be imposed on
a block face with the same flexibility as an interface condition. The orginal zoning
capability of the ENSAERO code was extended by including the above capability of
multiple interface conditions on a single block face. The virtual zone computation provided
a detailed flow field with fewer grid points than those necessary for the single grid. 9
Johnson-King Turbulence Model
To improve the accuracy of turbulent flow calculations, several turbulence models were
tested for transonic flows past the ONERA M6 wing. Our experience indicates that
correctly formulated models give poor prediction in general. However, the models that
include a coding error or wrong formulation sometimes predict the flow field perfectly. In
addition, the amount of artificial dissipation determines the performance of turbulence
models. It is very difficult to draw any concrete conclusion from those observations. The
computed results were submitted to CFD Validation Database.
Current Results
Under the extension period of this cooperative agreement since September 1993, new
capabilities have been added to ENSAERO to perforce static aeroelastic simulations
efficiently. Unsteady calculations are still too expensive for the current industrial needs. To
satisfy the near-term needs, the present research has been performed to improve the static
aeroelastic option of the code. The flow solver for solving the Navier-Stokes equations is
completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric
Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt)
upwind scheme. A pseudo-time marching method is used for the structural part of the code
to improve overall convergence rates for static analysis. Results are demonstrated for
transonic flows over rigid and flexible wings (see attachmen0.10
Concluding Remarks
The capabilities of the code, ENSAERO, have been greatly enhanced both in numerical
algorithm and in geometric flexibility. The code has been validated through a number of
numerical simulations and comparisons with experiment. The code can solve both static
and dynamic aeroelastic problems using the Navier-Stokes equations over wing, wing-
body, wing-control, and wing-body-control configurations.
The main future research will be to extend the code toward a complete aircraft. The next
mile stone in the geometric extension is Navier-Stokes computation with engine thrust. In
the algorithm development, second-order extension in time by using the Newton iteration
will be the next step. For the code validation, good experimental data will be required.
Research in turbulence modeling is still ongoing. Further improvements should be studied
for reliability.
References
1. Obayashi, S., "Progress in Unsteady Aerodynamics," Keynote Lecture, The 7th
Computational Fluid Dynamics Symposium, Tokyo, Japan, December 1993.
2. Obayashi, S. and Goorjian, P. M., "Improvements and Applications of a Streamwise
Upwind Algorithm," AIAA Paper 89-1957-CP, Proceedings of AIAA 9th
Computational Fluid Dynamics Conference, Buffalo, New York, June 1989.
3. Obayashi, S., Guruswamy, G. P., and Goorjian, P. M., "Streamwise Upwind
Algorithm for Computing Unsteady Transonic Flows Past Oscillating Wings," AIAA
Journal, Vol. 29, No. 10, pp. 1668-1677, October 1991.
4. Goorjian, P.M. and Obayashi, S., "Higher-Order Accuracy for Upwind Methods by
Using the Compatibility Equations," AIAA Journal, Vol. 31, No. 2, pp. 251-256,
February 1993.
5. Obayashi, S., "Freestream Capturing for Moving Coordinates in Three Dimensions,"
AIAA Journal, Vol. 30, No. 4, pp. 1125-1128, April 1992.
6. Obayashi, S and Guruswamy, G.P., "Unsteady Shock-Vortex Interaction on a Flexible
Delta Wing," Journal of Aircraft, Vol. 29, No. 5, pp. 790-798, September-October
1992.
7. Obayashi, S. and Guruswany, G. P., "Navier-Stokes Computations for Oscillating
Control Surface," to appear in Journal of Aircraft, May-June, 1994.
8. Klopfer, G.H. and Obayashi, S., "Virtual Zone Navier-Stokes Computations for
Oscillating Control Surfaces," AIAA Paper 93-3363-CP, Proceedings of AIAA 1 lth
Computational Fluid Dynamics Conference, Orlando, Florida, July 1993.
9. Obayashi, S., Chiu, I-T and Guruswamy, G.P., "Navier-Stokes Computations on Full-
Span Wing-Body Configuration with Oscillating Control Surfaces," AIAA Paper 93-
3687, August 1993.
10. Obayashi, S. and Guruswany, G. P., "Convergence Acceleration of an Aeroelastic
Navier-Stokes Solver," AIAA Paper 94-2268, June 1994.
Other Publications During the Cooperative Agreement
MCAT Reports
1. Obayashi, S., "Algorithm and Code Development for Unsteady Three-Dimensional
Navier-Stokes Equations," MCAT Institute Annual Report 91-005, June 1991.
2. Obayashi, S., "Algorithm and Code Development for Unsteady Three-Dimensional
Navier-Stokes Equations," MCAT Institute Annual Report 92-005, March 1992.
3. Obayashi, S., "Algorithm and Code Development for Unsteady Three-Dimensional
Navier-Stokes Equations," MCAT Institute Progress Report 93-08, March 1993.
Journal Publications
1. Chen, C. L., McCroskey, W. J. and Obayashi, S., "Numerical Solutions of Forward-
Flight rotor Flow Using an Upwind Method," Journal of Aircraft, Vol. 28, No. 6, pp.
374-380, June 1991.
2. Srinivasan, G.R., Baeder, J.D., Obayashi, S. and McCroskey, W.J., "Flowfield of a
Lifting Hovering Rotor- A Navier-Stokes Simulation," AIAA Journal, Vol. 30, No. 10,
pp. 2371-2378, October 1992.
3. Obayashi, S. and Wada, Y., "Practical Formulation of a Positively Conservative
Scheme," to appear in AIAA Journal, June 1994.
Published Proceedings
1. Goorjian, P.M. and Obayashi, S., "A Streamwise Upwind Algorithm Applied to
Vortical Flow Over a Delta Wing," Proceedings of the 8th GAMM Conference on
Numerical Methods in Fluid Dynamics, Notes on Numerical Fluid Mechanics, Vol. 29,
Springer-Verlag, 1990.
2. Goorjian, P. M., Obayashi, S. and Guruswamy, G. P.," Streamwise Upwind
Algorithm Development for the Navier-Stokes Equations," Proceedings of the 12th
International Conference on Numerical Methods in Fluid Dynamics, Lecture Notes in
Physics, Vol. 371, Springer-Verlag, 1991.
3. Goorjian, P.M. and Obayashi, S., "Higher Order Accuracy for Upwind Methods by
Using the Compatibility Equations," AIAA Paper 91-1543-CP, Proceedings of AIAA
10th Computational Fluid Dynamics Conference, Honolulu, Hawaii, June 1991.
4. Obayashi, S. and Guruswamy, G. P., "Unsteady Shock-Vortex Interaction on a
Flexible Delta Wing," Proceedings of the 4th International Symposium on computational
Fluid Dynamics, Davis, California, September 1991.
5. Guruswamy, G.P. and Obayashi, S., "Transonic Aeroelastic Computations in wings
Using Navier-Stokes Equations," Reference 22, AGARD Conference Proceedings 507,
Transonic Unsteady Aerodynamics and Aeroelasticity, March 1992.
6. Goorjian, P.M., Obayashi, S., Chaderjian, N.M. and Guruswamy, G.P., "Algorithm
Development with Applications to Aerodynamics and Aeroelasticity," VKILS 1992-04,
ComputationalFluidDynamics,von Karman Institute for Fluid Dynamics, Lecture Series
1991-1992, No. 6, March 1992.
Miscellaneous
1. Obayashi, S., "Progress in Unsteady Aerodynamics," NASA CR 177630, November
1993.
2. Goorjian, P.M. and Obayashi, S., "A Streamwise Upwind Algorithm Applied to
Vortical Flow Over a Delta Wing," NASA TM 102225, October 1989.
3. Obayashi, S., Goorjian, P. M., and Guruswamy, G. P., "Extension of a Streamwise
Upwind Algorithm to a Moving Grid System," NASA TM-102800, April 1990.
4. Obayashi, S., Guruswamy, G. P., and Goorjian, P. M., "Application of a Streamwise
Upwind Algorithm for Unsteady Transonic Computations over Oscillating Wings,"
AIAA Paper 90-3103, August 1990.
5. Srinivasan, G.R., Baeder, J.D., Obayashi, S. and McCroskey, W.J., "Flowfield of a
Lifting Hovering Rotor- A Navier-Stokes Simulation," NASA TM 102862, August
1990.
6. Obayashi, S., "Free-Stream Capturing in Fluid Conservation Law for Moving
Coordinates in Three Dimensions," NASA CR 177572, January 1991.
7. Obayashi, S. and Guruswamy, G. P., "Unsteady Shock-Vortex Interaction on a
Flexible Delta Wing," AIAA Paper 91-1109, April 1991.
8. Obayashi, S., Guruswamy, G. P. and Tu, E.L., "Unsteady Navier-Stokes
Computations on a Wing-Body Configuration in Ramp Motions," AIAA Paper 91-2865,
August 1991.
9. Obayashi, S. and Guruswamy, G. P., "Navier-Stokes Computations for Oscillating
Control Surface," AIAA Paper 92-4431, August 1992.
10. Tu, E.L., Obayashi, S. and Guruswamy, G.P., "Unsteady Navier-Stokes Simulation
of the Canard-Wing-Body Ramp Motion," AIAA Paper 93-3058, July 1993.



Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

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