Engineering topics

Pulliam, Thomas H.

Publications and source records attributed to Pulliam, Thomas H..

At least 37 records · Page 2

NASA NTRS2011

Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation

An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.

Buning, Pieter G.↗

NASA NTRS2010

Drag Prediction for the NASA CRM Wing-Body-Tail Using CFL3D and OVERFLOW on an Overset Mesh

In response to the fourth AIAA CFD Drag Prediction Workshop (DPW-IV), the NASA Common Research Model (CRM) wing-body and wing-body-tail configurations are analyzed using the Reynolds-averaged Navier-Stokes (RANS) flow solvers CFL3D and OVERFLOW. Two families of structured, overset grids are built for DPW-IV. Grid Family 1 (GF1) consists of a coarse (7.2 million), medium (16.9 million), fine (56.5 million), and extra-fine (189.4 million) mesh. Grid Family 2 (GF2) is an extension of the first and includes a superfine (714.2 million) and an ultra-fine (2.4 billion) mesh. The medium grid anchors both families with an established build process for accurate cruise drag prediction studies. This base mesh is coarsened and enhanced to form a set of parametrically equivalent grids that increase in size by a factor of roughly 3.4 from one level to the next denser level. Both CFL3D and OVERFLOW are run on GF1 using a consistent numerical approach. Additional OVERFLOW runs are made to study effects of differencing scheme and turbulence model on GF1 and to obtain results for GF2. All CFD results are post-processed using Richardson extrapolation, and approximate grid-converged values of drag are compared. The medium grid is also used to compute a trimmed drag polar for both codes.

Sclafani, Anthony J.↗

NASA NTRS2010

Development of Implicit Methods in CFD NASA Ames Research Center 1970's - 1980's

The focus here is on the early development (mid 1970's-1980's) at NASA Ames Research Center of implicit methods in Computational Fluid Dynamics (CFD). A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The emphasis will be on the Euler equations. A review of material pertinent to the solution of the Euler equations within the framework of implicit methods will be presented. The eigensystem of the equations will be used extensively in developing a framework for various methods applied to the Euler equations. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented.

Pulliam, Thomas H.↗

NASA NTRS2004

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Nelson, Andrea↗

NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗

NASA NTRS2004

On the Use of Parmetric-CAD Systems and Cartesian Methods for Aerodynamic Design

Automated, high-fidelity tools for aerodynamic design face critical issues in attempting to optimize real-life geometry arid in permitting radical design changes. Success in these areas promises not only significantly shorter design- cycle times, but also superior and unconventional designs. To address these issues, we investigate the use of a parmetric-CAD system in conjunction with an embedded-boundary Cartesian method. Our goal is to combine the modeling capabilities of feature-based CAD with the robustness and flexibility of component-based Cartesian volume-mesh generation for complex geometry problems. We present the development of an automated optimization frame-work with a focus on the deployment of such a CAD-based design approach in a heterogeneous parallel computing environment.

Nemec, Marian↗

NASA NTRS2003

CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method

A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.

Nemec, Marian↗

NASA NTRS2003

Evaluation of Genetic Algorithm Concepts Using Model Problems: Multi-Objective Optimization - Part 2

A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

Holst, Terry L.↗

NASA NTRS2003

Evaluation of Genetic Algorithm Concepts using Model Problems: Single-Objective Optimization - Part 1

A genetic-algorithm-based optimization approach is described and evaluated using a simple hill-climbing model problem. The model problem utilized herein allows for the broad specification of a large number of search spaces including spaces with an arbitrary number of genes or decision variables and an arbitrary number hills or modes. In the present study, only single objective problems are considered. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all problems attempted. The most difficult problems - those with large hyper-volumes and multi-mode search spaces containing a large number of genes - require a large number of function evaluations for GA convergence, but they always converge.

Holst, Terry L.↗

NASA NTRS2003

Implementation of Preconditioned Dual-Time Procedures in OVERFLOW

Preconditioning methods have become the method of choice for the solution of flowfields involving the simultaneous presence of low Mach and transonic regions. It is well known that these methods are important for insuring accurate numerical discretization as well as convergence efficiency over various operating conditions such as low Mach number, low Reynolds number and high Strouhal numbers. For unsteady problems, the preconditioning is introduced within a dual-time framework wherein the physical time-derivatives are used to march the unsteady equations and the preconditioned time-derivatives are used for purposes of numerical discretization and iterative solution. In this paper, we describe the implementation of the preconditioned dual-time methodology in the OVERFLOW code. To demonstrate the performance of the method, we employ both simple and practical unsteady flowfields, including vortex propagation in a low Mach number flow, flowfield of an impulsively started plate (Stokes' first problem) arid a cylindrical jet in a low Mach number crossflow with ground effect. All the results demonstrate that the preconditioning algorithm is responsible for improvements to both numerical accuracy and convergence efficiency and, thereby, enables low Mach number unsteady computations to be performed at a fraction of the cost of traditional time-marching methods.

Pandya, Shishir A.↗

NASA NTRS2003

Aerodynamic Shape Optimization using an Evolutionary Algorithm

A method for aerodynamic shape optimization based on an evolutionary algorithm approach is presented and demonstrated. Results are presented for a number of model problems to access the effect of algorithm parameters on convergence efficiency and reliability. A transonic viscous airfoil optimization problem-both single and two-objective variations is used as the basis for a preliminary comparison with an adjoint-gradient optimizer. The evolutionary algorithm is coupled with a transonic full potential flow solver and is used to optimize the inviscid flow about transonic wings including multi-objective and multi-discipline solutions that lead to the generation of pareto fronts. The results indicate that the evolutionary algorithm approach is easy to implement, flexible in application and extremely reliable.

Hoist, Terry L.↗

NASA NTRS2003

Aerodynamic Design of Complex Configurations Using Cartesian Methods and CAD Geometry

The objective for this paper is to present the development of an optimization capability for the Cartesian inviscid-flow analysis package of Aftosmis et al. We evaluate and characterize the following modules within the new optimization framework: (1) A component-based geometry parameterization approach using a CAD solid representation and the CAPRI interface. (2) The use of Cartesian methods in the development Optimization techniques using a genetic algorithm. The discussion and investigations focus on several real world problems of the optimization process. We examine the architectural issues associated with the deployment of a CAD-based design approach in a heterogeneous parallel computing environment that contains both CAD workstations and dedicated compute nodes. In addition, we study the influence of noise on the performance of optimization techniques, and the overall efficiency of the optimization process for aerodynamic design of complex three-dimensional configurations. of automated optimization tools. rithm and a gradient-based algorithm.

Nemec, Marian↗

NASA NTRS2002

Transonic Wing Shape Optimization Using a Genetic Algorithm

A method for aerodynamic shape optimization based on a genetic algorithm approach is demonstrated. The algorithm is coupled with a transonic full potential flow solver and is used to optimize the flow about transonic wings including multi-objective solutions that lead to the generation of pareto fronts. The results indicate that the genetic algorithm is easy to implement, flexible in application and extremely reliable.

Holst, Terry L.↗

NASA NTRS2001

Aerodynamic Shape Optimization Using A Real-Number-Encoded Genetic Algorithm

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

Holst, Terry L.↗

NASA NTRS1996

Practical Aspects of Krylov Subspace Iterative Methods in CFD

Implementation issues associated with the application of Krylov subspace iterative methods, such as Newton-GMRES, are presented within the framework of practical computational fluid dynamic (CFD) applications. This paper categorizes, evaluates, and contrasts the major ingredients (function evaluations, matrix-vector products, and preconditioners) of Newton-GMRES Krylov subspace methods in terms of their effect on the local linear and global nonlinear convergence, memory requirements, and accuracy. The discussion focuses on Newton-GMRES in both a structured multi-zone incompressible Navier-Stokes solver and an unstructured mesh finite-volume Navier-Stokes solver. Approximate versus exact matrix-vector products, effective preconditioners, and other pertinent issues are addressed.

Pulliam, Thomas H.↗

NASA NTRS1995

Aerodynamic design optimization via reduced Hessian SQP with solution refining

An all-at-once reduced Hessian Successive Quadratic Programming (SQP) scheme has been shown to be efficient for solving aerodynamic design optimization problems with a moderate number of design variables. This paper extends this scheme to allow solution refining. In particular, we introduce a reduced Hessian refining technique that is critical for making a smooth transition of the Hessian information from coarse grids to fine grids. Test results on a nozzle design using quasi-one-dimensional Euler equations show that through solution refining the efficiency and the robustness of the all-at-once reduced Hessian SQP scheme are significantly improved.

Feng, Dan↗

NASA NTRS1995

Aerodynamic design optimization via reduced Hessian SQP with solution refining

Feng, Dan↗

NASA NTRS1995

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Feng, Dan↗