K. D. Lee

High-Lift Design Optimization Using Navier-Stokes Equations

This article presents a design optimization method for maximizing lift without increasing the drag of multielement airfoils at takeoff and landing configurations. It uses an incompressible Navier-Stokes flow solver (INS2D), a chimera overlaid grid system (PEGSUS), and a constrained numerical optimizer (DOT). Aerodynamic sensitivity derivatives are obtained using finite differencing. The method is first validated with single-element airfoil designs and then applied to three-element airfoil designs. Reliable design results are obtained at reasonable costs. Results demonstrate that numerical optimization can be an attractive design tool for the development of multielement high-lift systems.

Airfoil design optimization using the Navier-Stokes equations

A design optimization technique is presented which couples a computationally efficient Navier-Stokes code with a numerical optimization algorithm. The design method improves the aerodynamic performance of an airfoil subject to specified design objectives and constraints. Recent advances in computers and compputational fluid dynamics have permitted the use of the Navier-Stokes equations in the design procedure to include the nonlinear, rotational, viscous physics of transonic flows. Using numerical optimization guarantees that a better design will be produced even with strict design constraints. The method is demonstrated with several examples at transonic flow conditions.

Patched coordinate systems

Abstract : Numerical grid generation has been an excellent tool for producing curvilinear body-fitted coordinate systems. Curvilinear coordinate systems or grids are commonly used in the solution of partial differential equations in domains surrounding arbitrary geometrical boundary shapes. Body-fitted grids are particularly advantageous in the treatment of surface boundary conditions, and usually yield a degree of simplicity in the logic required to solve the hosted partial differential equations. In practice, numerical grid generation usually involves transformation of the physical domain of interest into a geometrically simple domain, such as a rectangular block or assembly of blocks. The solution of grid generation equations in the simple domain products the coordinates of a corresponding grid in the physical domain, subject to a variety of grid control procedures aimed at producing favorable grid characteristics. This process is usually straightforward when the topology of the physical domain is simple enough to allow transformation to a single rectangular domain. But when dealing with geometrically and topologically complex domains such as surround an aircraft configuration, the total issue of grid generation becomes more complex. The domain in general cannot be mapped into a single block. The configuration surface geometry itself may be nonanalytic, and these features will be manifest in any grid surrounding such complex boundary shapes.

Two-point transonic airfoil design using optimization for improved off-design performance

A two-point, aerodynamic design method is presented that improves the aerodynamic performance of transonic airfoils over a range of the flight envelope. It couples an Euler flow solver and a numerical optimization tool. The major limitation of single-point design is the poor off-design performance. Two-point design is used to extend the optimized performance range over more of the desired flight envelope. The method is applied to several transonic flow design points, and the results are compared to single-point design results. The secondary design points are chosen by varying the Mach number and the angle of attack. The two-point designs perform better than the single-point design over the design-point range.

Aerodynamic design via optimization

An aerodynamic design optimization method is presented that generates an airfoil, producing a specified surface pressure distribution at a transonic speed. The design procedure is based on the coupled Euler and boundary-layer technology to include the rotational viscous physics which characterizes transonic flows. A leastsquare optimization technique is used to minimize pressure discrepancies between the target and designed airfoils. The method is demonstrated with several examples at transonic speeds. The design optimization process converges quickly, that makes the method attractive for practical engineering applications. I. Introduction I N recent years, computational fluid dynamics (CFD) has become a valuable engineering tool in the aircraft industry. CFD plays a complementary role, not a replacement, to experiments in practical design communities. Rubbert1 showed some good examples of the use of CFD and experiment, in combination, for transonic design. A major strength of CFD is the ability to produce detailed insights into complex flow phenomena. The process of decomposition and parameterization can help identify the cause of weak aerodynamic performance, and the microscopic understanding of the flow can lead to improved design. Continuing advances in computer hardware and simulation techniques provide an unprecedented opportunity for CFD. Now simulations of more complete configurations with more complex physics can be performed at an affordable cost. Accuracy and reliability of the computation have been continuously improved. The use of high-level flow models and large-size refined grids enables one to analyze flows with complicated structures and various length scales. Compared to the remarkable advances in analysis capability, however, relatively few advances have been made in design technology. Conventional design practices, therefore, often depend on analysis methods through iterative cut-and-try approaches. A unique advantage of CFD is the capability of inverse design. Inverse design directly determines the airfoil geometry that produces the pressure distribution specified by a designer. Many existing inverse design methods are based on the potential flow assumption due to its simplicity. Volpe and Melnik2 employed an inverse design method using the nonlinear full potential formulation. Bauer and colleagues3 used the hodograph method that solves the full potential equation in the hodograph plane where the equations are linear. The potential flow model, however, cannot properly represent transonic features such as embedded shock waves and shock-boundarylayer interactions. An accurate analytic capability is a prerequisite for a successful design, because the quality of the design depends on the quality of the method used to predict the flowfield. Several inverse design methods were demonstrated using the Euler formulations by Giles and Drela,4 and Mani.5 Instead of achieving the prescribed pressure distribution, some design methods use a constrained optimization process

Transonic Airfoil Design by Constrained Optimization

A N aerodynamic design method is developed which cou- ples flow analysis and numerical optimization to find an airfoil shape with improved aerodynamic performance. The flow analysis code is based on the coupled Euler and bound- ary-layer equations in order to include the rotational, viscous physics of transonic flows. The numerical optimization pro- cess searches for the best feasible design for the specified design objective and design constraints. The method is dem- onstrated with several examples at transonic flow conditions. Contents The optimization process is performed with a commercially available constrained optimization tool.3 The sensitivity of the flow to the perturbation is calculated by finite differences. The effectiveness and efficiency of the design process are influenced by many factors: the number and the shape of the base functions, the number and the tolerance of the con- straints, the flow model and the grid used for flow analyses, and the flight condition at the design point. Design Demonstration The objective of the present design is to produce minimum drag at a specified transonic flight condition. Inequality con- straints are imposed on lift, pitching moment, and cross-sec- tional area of the optimized airfoil. The lift and the area of the optimized airfoil should not be smaller than those of the original airfoil, and the pitching moment should not increase in absolute value. Also imposed are side constraints which limit the magnitude of the design variables. Side constraints are important because a large geometry change can cause boundary-layer separation leading to a termination of the flow solver.

THE BEHAVIOR OF SOME SOLUTION ACCELERATION TECHNIQUES IN CFD

SUMMARY Several solution acceleration techniques, used to obtain steady-state CFD solutions as quickly as possible, are applied to an upwind Euler scheme to evaluate their effectiveness. Generalized minimal residual (GMRES), multigrid (MG), and ADI are compared to a four-stage Runge-Kutta scheme using several grids. The use of different acceleration schemes combinations of produces a complementary effect: the convergence becomes relatively independent of both size and quality of the grid.

Effects of gas models on hypersonic base flow calculations

Numerical solutions for the Navier-Stokes equations are obtained for laminar, hypersonic flows around a flatbased projectile using perfect gas, equilibrium air, and nonequilibrium air models. The effects of different gas models are investigated for a freestream condition of Mach 20 at an altitude of 73 km. The species compositions for the equilibrium and nonequilibrium gases are obtained by minimizing the Helmholtz free energy and by solving species continuity equations, respectively. The chemical equations are combined with the gasdynamics equations using a loosely coupled technique. A finite volume method is implemented with the flux vector splitting of Steger and Warming for convective terms and centered differencing for viscous terms. Both explicit and implicit time integration schemes are used.

A Flight Mechanics-Centric Review of Bird-Scale Flapping Flight

This paper reviews the flight mechanics and control of birds and bird-size aircraft. It is intended to fill a niche in the current survey literature which focuses primarily on the aerodynamics, flight dynamics and control of insect scale flight. We review the flight mechanics from first principles and summarize some recent results on the stability and control of birds and bird-scale aircraft. Birds spend a considerable portion of their flight in the gliding (i.e., non-flapping) phase. Therefore, we also review the stability and control of gliding flight, and particularly those aspects which are derived from the unique control features of birds.

Numerical Simulation of the Wind Tunnel Environment by a Panel Method

A simulation technique has been developed to analyze the testing environment of practical three-dimensional subsonic wind tunnels. By using a higher-order panel method, the present technology can simulate interference effects due to various geometrical features that are ignored in most previously published approaches. Among them are the effects of the three-dimensional test sections, the finite test section length, the corner fillet, the model size and location, the model mounting system, and instrumentation. Results for different wind tunnel environments are presented to demonstrate their significance on the wind tunnel interference. The present technique provides a diagnostic tool for the interpretation of experimental data and an effective means for designing a test environment with minimum interference.