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All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation

A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finite-difference gradients and several design examples are presented.

Anderson, W. Kyle↗
NASA NTRS1992

Aerodynamic design and optimization in one shot

This paper describes an efficient numerical approach for the design and optimization of aerodynamic bodies. As in classical optimal control methods, the present approach introduces a cost function and a costate variable (Lagrange multiplier) in order to achieve a minimum. High efficiency is achieved by using a multigrid technique to solve for all the unknowns simultaneously, but restricting work on a design variable only to grids on which their changes produce nonsmooth perturbations. Thus, the effort required to evaluate design variables that have nonlocal effects on the solution is confined to the coarse grids. However, if a variable has a nonsmooth local effect on the solution in some neighborhood, it is relaxed in that neighborhood on finer grids. The cost of solving the optimal control problem is shown to be approximately two to three times the cost of the equivalent analysis problem. Examples are presented to illustrate the application of the method to aerodynamic design and constraint optimization.

Ta'asan, Shlomo↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine and compared to earlier methods. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS2002

Turbomachinery Airfoil Design Optimization Using Differential Evolution

An aerodynamic design optimization procedure that is based on a evolutionary algorithm known at Differential Evolution is described. Differential Evolution is a simple, fast, and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems, including highly nonlinear systems with discontinuities and multiple local optima. The method is combined with a Navier-Stokes solver that evaluates the various intermediate designs and provides inputs to the optimization procedure. An efficient constraint handling mechanism is also incorporated. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated. Substantial reductions in the overall computing time requirements are achieved by using the algorithm in conjunction with neural networks.

Madavan, Nateri K.↗
NASA NTRS1972

Turbomachinery design for Space Shuttle auxiliary power systems.

Review of the major factors affecting Space Shuttle auxiliary power system design decisions, and discussion of turbine aerodynamic design optimization techniques. The working fluid to be used and the vehicle mission requirements are shown to be the two major factors that affect auxiliary power system design decisions. Analytical techniques developed for optimization of turbine aerodynamic design parameters are shown to be applicable to transient-state simulation and design optimization of other components, including the turbine controller.

Burriss, W. L.↗
NASA NTRS1993

Formulation for Simultaneous Aerodynamic Analysis and Design Optimization

An efficient approach for simultaneous aerodynamic analysis and design optimization is presented. This approach does not require the performance of many flow analyses at each design optimization step, which can be an expensive procedure. Thus, this approach brings us one step closer to meeting the challenge of incorporating computational fluid dynamic codes into gradient-based optimization techniques for aerodynamic design. An adjoint-variable method is introduced to nullify the effect of the increased number of design variables in the problem formulation. The method has been successfully tested on one-dimensional nozzle flow problems, including a sample problem with a normal shock. Implementations of the above algorithm are also presented that incorporate Newton iterations to secure a high-quality flow solution at the end of the design process. Implementations with iterative flow solvers are possible and will be required for large, multidimensional flow problems.

Hou, G. W.↗
NASA NTRS1992

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest.

Taylor, Arthur C., III↗
NASA NTRS2000

Global Design Optimization for Aerodynamics and Rocket Propulsion Components

Modern computational and experimental tools for aerodynamics and propulsion applications have matured to a stage where they can provide substantial insight into engineering processes involving fluid flows, and can be fruitfully utilized to help improve the design of practical devices. In particular, rapid and continuous development in aerospace engineering demands that new design concepts be regularly proposed to meet goals for increased performance, robustness and safety while concurrently decreasing cost. To date, the majority of the effort in design optimization of fluid dynamics has relied on gradient-based search algorithms. Global optimization methods can utilize the information collected from various sources and by different tools. These methods offer multi-criterion optimization, handle the existence of multiple design points and trade-offs via insight into the entire design space, can easily perform tasks in parallel, and are often effective in filtering the noise intrinsic to numerical and experimental data. However, a successful application of the global optimization method needs to address issues related to data requirements with an increase in the number of design variables, and methods for predicting the model performance. In this article, we review recent progress made in establishing suitable global optimization techniques employing neural network and polynomial-based response surface methodologies. Issues addressed include techniques for construction of the response surface, design of experiment techniques for supplying information in an economical manner, optimization procedures and multi-level techniques, and assessment of relative performance between polynomials and neural networks. Examples drawn from wing aerodynamics, turbulent diffuser flows, gas-gas injectors, and supersonic turbines are employed to help demonstrate the issues involved in an engineering design context. Both the usefulness of the existing knowledge to aid current design practices and the need for future research are identified.

Shyy, Wei↗
NASA NTRS2001

Simultaneous Aerodynamic and Structural Design Optimization (SASDO) for a 3-D Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic and Structural Design Optimization (SASDO) is shown as an extension of the Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) method. It is extended by the inclusion of structure element sizing parameters as design variables and Finite Element Method (FEM) analysis responses as constraints. The method aims to reduce the computational expense. incurred in performing shape and sizing optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, FEM structural analysis and sensitivity analysis tools. SASDO is applied to a simple. isolated, 3-D wing in inviscid flow. Results show that the method finds the saine local optimum as a conventional optimization method with some reduction in the computational cost and without significant modifications; to the analysis tools.

Gumbert, Clyde R.↗
NASA NTRS2001

Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) for a 3-D Flexible Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) are extended from single discipline analysis (aerodynamics only) to multidisciplinary analysis - in this case, static aero-structural analysis - and applied to a simple 3-D wing problem. The method aims to reduce the computational expense incurred in performing shape optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, Finite Element Method (FEM) structural analysis and sensitivity analysis tools. Results for this small problem show that the method reaches the same local optimum as conventional optimization. However, unlike its application to the win,, (single discipline analysis), the method. as I implemented here, may not show significant reduction in the computational cost. Similar reductions were seen in the two-design-variable (DV) problem results but not in the 8-DV results given here.

Gumbert, Clyde R.↗
NASA NTRS2001

Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) for a 3-D Flexible Wing

The formulation and implementation of an optimization method called Simultaneous Aerodynamic Analysis and Design Optimization (SAADO) are extended from single discipline analysis (aerodynamics only) to multidisciplinary analysis - in this case, static aero-structural analysis and applied to a simple 3-D wing problem. The method aims to reduce the computational expense incurred in performing shape optimization using state-of-the-art Computational Fluid Dynamics (CFD) flow analysis, Finite Element Method (FEM) structural analysis and sensitivity analysis tools. Results for this small problem show that the method reaches the same local optimum as conventional optimization. However, unlike its application to the rigid wing (single discipline analysis), the method, as implemented here, may not show significant reduction in the computational cost. Similar reductions were seen in the two-design-variable (DV) problem results but not in the 8-DV results given here.

Gumbert, Clyde R.↗
NASA NTRS1997

An Efficient Multiblock Method for Aerodynamic Analysis and Design on Distributed Memory Systems

The work presented in this paper describes the application of a multiblock gridding strategy to the solution of aerodynamic design optimization problems involving complex configurations. The design process is parallelized using the MPI (Message Passing Interface) Standard such that it can be efficiently run on a variety of distributed memory systems ranging from traditional parallel computers to networks of workstations. Substantial improvements to the parallel performance of the baseline method are presented, with particular attention to their impact on the scalability of the program as a function of the mesh size. Drag minimization calculations at a fixed coefficient of lift are presented for a business jet configuration that includes the wing, body, pylon, aft-mounted nacelle, and vertical and horizontal tails. An aerodynamic design optimization is performed with both the Euler and Reynolds Averaged Navier-Stokes (RANS) equations governing the flow solution and the results are compared. These sample calculations establish the feasibility of efficient aerodynamic optimization of complete aircraft configurations using the RANS equations as the flow model. There still exists, however, the need for detailed studies of the importance of a true viscous adjoint method which holds the promise of tackling the minimization of not only the wave and induced components of drag, but also the viscous drag.

Reuther, James↗
NASA NTRS1983

Iterative optimal subcritical aerodynamic design code including profile drag

A subcritical aerodynamic design computer code has been developed, which uses linearized aerodynamics along with sweep theory and airfoil data to obtain minimum total drag preliminary designs for multiple planform configurations. These optimum designs consist of incidence distributions yielding minimum total drag at design values of Mach number and lift and pitching moment coefficients. Linear lofting is used between airfoil stations. Solutions for isolated transport wings have shown that the solution is unique, and that including profile drag effects decreases tip loading and incidence relative to values obtained for minimum induced drag solutions. Further, including effects of variation of profile drag with Reynolds number can cause appreciable changes in the optimal design for tapered wings. Example solutions are also discussed for multiple planform configurations.

Kuhlman, J. M.↗
NASA NTRS2018

Aerodynamic Design and Optimization of Fan Stage for Boundary Layer Ingestion Propulsion System

The present paper addresses the process of preliminary design of a low-pressure fan and outlet guide vane (OGV) of a boundary layer ingestion (BLI) propulsion system. The tail-cone thruster systems of NASA's STARC_ABL (Single-aisle Turboelectric Aircraft with an Aft Boundary-Layer propulsor) adopts an axi-symmetric BLI type inlet as opposed to other embedded engine systems. Thus, the focus of the present work is placed on maximizing the efficiency of the fan and OGV stages under a significant radial distortion. A parameterization with B-spline function for camber line angles, metal chord, thickness distribution and stacking axis of blades is presented. The flowpath lines are also parameterized by B-spline function and aggregated in the design system of blades. The design optimization with evolutionary algorithm is performed with constraints of fan pressure ratio, OGV exit swirl angle and nozzle exit properties. The inlet conditions for the turbo-machinery CFD (Computational Fluid Dynamics) domain and the design goal of the fan stage are driven by a propulsion airframe integration (PAI) model that uses a 3-D unstructured RANS (Reynolds Average Navier Stokes) solver and actuator disk model. The expected power saving of the BLI propulsor is quantified via PAI analysis and the resulting preliminary design of the fan stages is compared with a clean-inlet flow propulsor.

Turbo-machinery↗
NASA NTRS1995

Aerodynamic shape optimization directed toward a supersonic transport using sensitivity analysis

This investigation was conducted from March 1994 to August 1995, primarily, to extend and implement the previously developed aerodynamic design optimization methodologies for the problems related to a supersonic transport design. These methods had demonstrated promise to improve the designs (more specifically, the shape) of aerodynamic surfaces, by coupling optimization algorithms (OA) with Computational Fluid Dynamics (CFD) algorithms via sensitivity analyses (SA) with surface definition methods from Computer Aided Design (CAD). The present extensions of this method and their supersonic implementations have produced wing section designs, delta wing designs, cranked-delta wing designs, and nacelle designs, all of which have been reported in the open literature. Despite the fact that these configurations were highly simplified to be of any practical or commercial use, they served the algorithmic and proof-of-concept objectives of the study very well. The primary cause for the configurational simplifications, other than the usual simplify-to-study the fundamentals reason, were the premature closing of the project. Only after the first of the originally intended three-year term, both the funds and the computer resources supporting the project were abruptly cut due to their severe shortages at the funding agency. Nonetheless, it was shown that the extended methodologies could be viable options in optimizing the design of not only an isolated single-component configuration, but also a multiple-component configuration in supersonic and viscous flow. This allowed designing with the mutual interference of the components being one of the constraints all along the evolution of the shapes.

Baysal, Oktay↗
NASA NTRS1983

Computational methods for aerodynamic design using numerical optimization

Five methods to increase the computational efficiency of aerodynamic design using numerical optimization, by reducing the computer time required to perform gradient calculations, are examined. The most promising method consists of drastically reducing the size of the computational domain on which aerodynamic calculations are made during gradient calculations. Since a gradient calculation requires the solution of the flow about an airfoil whose geometry was slightly perturbed from a base airfoil, the flow about the base airfoil is used to determine boundary conditions on the reduced computational domain. This method worked well in subcritical flow.

Peeters, M. F.↗
NASA NTRS2015

Aerodynamic Shape Optimization Benchmarks with Error Control and Automatic Parameterization

Results are presented for four optimization benchmark problems posed by the AIAA Aerodynamic Design Optimization Discussion Group. The benchmarks are intended to exercise optimization frameworks on representative airfoil and wing design problems. All problems involve drag minimization subject to geometric and aerodynamic constraints. Our design approach involves two forms of adaptation. First, the shape parameterization is gradually and automatically enriched from an initially coarse search space. Second, adjoint solutions are used to drive adaptive mesh refinement to control discretization error. The error threshold is tailored so that the nest meshes, with the greatest accuracy, are used only when nearing the optimum. On the inviscid airfoil design problem, while reducing the drag by a factor of 10, we show how the combination of progressive parameterization and tiered discretization error control can dramatically accelerate the optimization. On the viscous airfoil design problem, we use inviscid analysis-driven optimization to reduce the total drag by a factor of two. Next, we improve the span efficiency factor of a wing by performing twist optimization. Finally, we optimize the Common Research Model wing, managing to hold drag roughly fixed, while targeting an initially-violated pitching moment constraint. Our approach aims to introduce greater complexity and accuracy only when necessary to improve the design, and also support a greater degree of automation.

Anderson, George R.↗
NASA NTRS1996

Observations Regarding Use of Advanced CFD Analysis, Sensitivity Analysis, and Design Codes in MDO

Observations regarding the use of advanced computational fluid dynamics (CFD) analysis, sensitivity analysis (SA), and design codes in gradient-based multidisciplinary design optimization (MDO) reflect our perception of the interactions required of CFD and our experience in recent aerodynamic design optimization studies using CFD. Sample results from these latter studies are summarized for conventional optimization (analysis - SA codes) and simultaneous analysis and design optimization (design code) using both Euler and Navier-Stokes flow approximations. The amount of computational resources required for aerodynamic design using CFD via analysis - SA codes is greater than that required for design codes. Thus, an MDO formulation that utilizes the more efficient design codes where possible is desired. However, in the aerovehicle MDO problem, the various disciplines that are involved have different design points in the flight envelope; therefore, CFD analysis - SA codes are required at the aerodynamic 'off design' points. The suggested MDO formulation is a hybrid multilevel optimization procedure that consists of both multipoint CFD analysis - SA codes and multipoint CFD design codes that perform suboptimizations.

Newman, Perry A.↗