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Algebraic Multigrid for Finite Element Method

The focus of this work is to speed-up a solver, applied to a system of equation A.x = b. The matrix A arises from finite element method applied to the Navier-Stokes equation with unstructured grid. Due to stress terms, A is not symmetric. Current approach is to treat the linear equation as a black-box and incoporate multigrid to equation itself, not the geometry of the mesh.

Wing Planform Optimization using an Adjoint Method
(Aug 2001 - March 2005)

Green: Baseline planform
Blue:  Modified planform
Simplified planform parameters; sweep, span, thickness, chords, and twist.

This research was the focus of my PhD dissertation. The description below is a summary from my dissertation. Reader who is interested in this work may find my dissertation interesting and is invited to download here.

"This research focuses on the problem of wing planform optimization for transonic aircraft based on the solution of Computational Fluid Dynamics (CFD) combined with an adjoint-gradient based numerical optimization procedure. It exploits the shock-free-wing technology, extensively developed during the past decade for wing section design, to ``cheat'' the conventional wisdom of the planform design. The integration of the shock-free concept and planform optimization enables a range of planform configurations previously prohibited by the strong compressibility  drag. This extended freedom can lead to a large reduction in both structural weight and the induced drag.

In order to incorporate this idea, we employ the wing planform as well as the wing sections as the design parameters. Because the two relevant disciplines are aerodynamics and weight, we focus on the aerodynamic optimization with a simplified structural weight model, treating a wing as fully-stressed  and rigid. This choice of cost function not only increases the reality of the design but also prevents unrealistic results by exposing the trade-off between the aerodynamics and structures.  To formulate our design tool, we extend the aerodynamic shape optimization tool that was initially developed for wing section design to include the planform optimization. The original tool was developed by combining CFD with gradient-based numerical optimization, and applied the adjoint formulation to calculate gradients of a large number of design parameters at very low computational cost, allowing the wing be treated as a ``free'' surface to achieve a shock-free shape. Then we extend the adjoint method to cover the planform variations and to compute the sensitivities of the structural weight of both the wing section and planform variations.

Results of a variety of long range transports at fixed-altitude cruise conditions indicate that significant improvement in both aerodynamics and
structures can be achieved simultaneously. They also reveal a similar trend from these improvements; by utilizing the shock-free concept, the
compressibility drag can be weakened and thus the wing does not require as large a sweep or as small a thickness-to-chord ratio as one that is
conventionally designed. The sweep reduction and thickness increment help reduce structural weight, which can be traded for a longer span. The increase of span reduces the induced drag, which is a large portion of drag at the cruise condition, and therefore results in large drag reduction without a penalty on the structural weight. Finally, inclusion of the structural weight and area-dependent viscosity prevents any unrealistic result.

Boeing 747 BAe Datum Wing Douglas MD-11

This figure shows a common pattern of planform changes on three long-range transport aircraft; Beoing 747, BAe datum wing, and Douglas MD-11. The baseline geometries are represented in green color and the modified geometries are in blue color. All modified wings have lower drag and wing weight. It has been found that by (1) stretching the span to reduce the induced drag, (2) de-sweeping the sweep and thickening the wing section to reduce the wing weight, and (3) using section modification to prevent shock formation, the drag and weight can be reduced simultaneously.

This wing planform optimization is the ``first step'' in the right direction beyond the pure aerodynamic shape optimization using the adjoint method for fixed planform. The  proof-of-concept optimal results indicate large improvements for both drag and structural weight.  The next step may require the incorporation of a higher-fidelity structural model, which can capture aero-elastic interaction and structure failure, and the implementations of constraints to satisfy performance, stability-and-control, and manufacturing requirements within the design envelope. It is important to note that additional constraints will certainly affect the results presented here. Yet, the design methodology presented in this work provides the basis for an extension to form a more complete wing design tool."

This figure shows Pareto front of the Boeing 747.

Quiet Supersonic Platform 
(Mar 2001- Jul 2001)

"The Quiet Supersonic Platform (QSP) program is directed towards development and validation of critical technology for long-range advanced supersonic aircraft with substantially reduced sonic boom, reduced takeoff and landing noise, and increased efficiency relative to current technology supersonic aircraft. Improved capabilities include supersonic flight over land without adverse sonic boom consequences with boom overpressure rise less than 0.3 pounds per square foot, increased unrefueled range approaching 6,000 nmi, gross take-off weight approaching 100,000 pounds, increased area coverage and lower overall operational cost. Highly integrated vehicle concepts will be explored to simultaneously meet the cruise range and noise level goals. Advanced airframe technologies will be explored to minimize sonic boom and vehicle drag including natural laminar flow, aircraft shaping, plasma, heat and particle injection, and low weight structures."#

During the time Kasidit joined this research, he focused on the so-called "Thomas Algorithm", which is employed to predict the strength of sonic boom at the ground level.

# http://www.darpa.mil/


Immersed Boundary
(July 2000 - Feb 2001)

It is clear that grid generation cost for a complex geometry is very high and it is very time consuming to get a good quality grid. The idea of the project is to create the fast and inexpensive Cartesian mesh throughout the domain, intersecting the body. The body is immersed in the mesh. The key idea is to apply a forcing term into Navier-Stokes equation as a source-sink in order for the velocity to satisfy applied boundary conditions. Kasidit has discovered that, with the extra forcing terms, he can force the flow to satisfy physics of the problem at some degree of accuracy.


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Last modified: August 03, 2005 05:09:55 PM