Practical aerodynamic shape design problems must balance performance optimization over a range of on-design operating conditions with constraint satisfaction at off-design operating conditions. A multipoint optimization formulation can be used to represent on-design and off-design conditions with corresponding objective or constraint functions. Two methods are presented for obtaining optimal airfoil designs that satisfy all design objectives and constraints. The first method uses an unconstrained optimization algorithm where optimal design is achieved by minimizing a weighted sum of objective functions at each of the conditions. To address competing design objectives between on-design and off-design conditions, an automated procedure is used to weight off-design objective functions to limit their influence on the overall optimization. The second method uses the constrained optimization algorithm SNOPT, allowing aerodynamic constraints imposed at off-design conditions to be treated explicitly. Both methods are applied to the design of an airfoil for a hypothetical aircraft, which is formulated as an 18-point multipoint optimization.

Practical aerodynamic shape design problems must balance performance optimization over a range of on-design operating conditions with constraint satisfaction at off-design operating conditions. A multipoint optimization formulation can be used to represent on-design and off-design conditions with corresponding objective or constraint functions. Two methods are presented for obtaining optimal airfoil designs that satisfy all design objectives and constraints. The first method uses an unconstrained optimization algorithm where optimal design is achieved by minimizing a weighted sum of objective functions at each of the conditions. To address competing design objectives between on-design and off-design conditions, an automated procedure is used to weight off-design objective functions to limit their influence on the overall optimization. The second method uses the constrained optimization algorithm SNOPT, allowing aerodynamic constraints imposed at off-design conditions to be treated explicitly. Both methods are applied to the design of an airfoil for a hypothetical aircraft, which is formulated as an 18-point multipoint optimization.

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The increase in the availability and power of computational resources over the last fifteen years has contributed to the development of many different types of numerical optimization methods and created a large area of research focussed on numerical aerodynamic shape optimization and, more recently, high-fidelity multidisciplinary optimization. Numerical optimization provides dramatic savings when designing new aerodynamic configurations, as it allows the designer to focus more on the development of a well-posed design problem rather than on performing an exhaustive search of the design space via the traditional cut-and-try approach, which is expensive and time-consuming. It also reduces the dependence on the designer’s experience and intuition, which can potentially lead to more optimal designs. Numerical optimization methods are particularly attractive when designing novel, unconventional aircraft for which the designer has no pre-existing studies or experiences from which to draw; these methods have the potential to discover new designs that might never have been arrived at without optimization. This work presents an extension of an efficient gradient-based numerical aerodynamic shape optimization algorithm to enable optimization in turbulent flow. The algorithm includes an integrated geometry parameterization and mesh movement scheme, an efficient parallel Newton-Krylov-Schur algorithm for solving the Reynolds-Averaged Navier-Stokes (RANS) equations, which are fully coupled with the one-equation Spalart-Allmaras turbulence model, and a discrete-adjoint gradient evaluation. In order to develop an efficient methodology for optimization in turbulent flows, the viscous and turbulent terms in the ii governing equations were linearized by hand. Additionally, a set of mesh refinement tools was introduced in order to obtain both an acceptable control volume mesh and a sufficiently refined computational mesh from an initial coarse mesh. A series of drag minimization studies was carried out which show that the algorithm is able to maintain robustness in the mesh movement and flow analysis in the presence of large shape changes, an important requirement for performing exploratory optimizations aiming to discover novel configurations and for multidisciplinary optimization. Additionally, the algorithm is able to find incremental improvements when given well-designed initial planar and nonplanar geometries. A comparison of Euler-based and RANS-based optimizations highlights the importance of considering viscous and turbulent effects. A multi-point optimization demonstrates that the algorithm is able to address practical aerodynamic design problems.

The increase in the availability and power of computational resources over the last fifteen years has contributed to the development of many different types of numerical optimization methods and created a large area of research focussed on numerical aerodynamic shape optimization and, more recently, high-fidelity multidisciplinary optimization. Numerical optimization provides dramatic savings when designing new aerodynamic configurations, as it allows the designer to focus more on the development of a well-posed design problem rather than on performing an exhaustive search of the design space via the traditional cut-and-try approach, which is expensive and time-consuming. It also reduces the dependence on the designer’s experience and intuition, which can potentially lead to more optimal designs. Numerical optimization methods are particularly attractive when designing novel, unconventional aircraft for which the designer has no pre-existing studies or experiences from which to draw; these methods have the potential to discover new designs that might never have been arrived at without optimization. This work presents an extension of an efficient gradient-based numerical aerodynamic shape optimization algorithm to enable optimization in turbulent flow. The algorithm includes an integrated geometry parameterization and mesh movement scheme, an efficient parallel Newton-Krylov-Schur algorithm for solving the Reynolds-Averaged Navier-Stokes (RANS) equations, which are fully coupled with the one-equation Spalart-Allmaras turbulence model, and a discrete-adjoint gradient evaluation. In order to develop an efficient methodology for optimization in turbulent flows, the viscous and turbulent terms in the ii governing equations were linearized by hand. Additionally, a set of mesh refinement tools was introduced in order to obtain both an acceptable control volume mesh and a sufficiently refined computational mesh from an initial coarse mesh. A series of drag minimization studies was carried out which show that the algorithm is able to maintain robustness in the mesh movement and flow analysis in the presence of large shape changes, an important requirement for performing exploratory optimizations aiming to discover novel configurations and for multidisciplinary optimization. Additionally, the algorithm is able to find incremental improvements when given well-designed initial planar and nonplanar geometries. A comparison of Euler-based and RANS-based optimizations highlights the importance of considering viscous and turbulent effects. A multi-point optimization demonstrates that the algorithm is able to address practical aerodynamic design problems.

Increasing environmental concerns and fuel prices motivate the study of alternative, unconventional aircraft configurations. One such example is the blended-wing-body configuration, which has been shown to have several advantages over the conventional tube-and-wing aircraft configuration. In this thesis, a blended-wing-body aircraft is studied and optimized aerodynamically using a high-fidelity Euler-based flow solver, integrated geometry parameterization and mesh movement, adjoint-based gradient evaluation, and a sequential quadratic programming algorithm. Specifically, the aircraft is optimized at transonic conditions to minimize the sum of induced and wave drag. These optimizations are carried out with both fixed and varying airfoil sections. With varying airfoil sections and increased freedom, up to 52% drag reduction relative to the baseline geometry was achieved: at the target lift coefficient of 0.357, a drag coefficient of 0.01313 and an inviscid lift-to-drag ratio of 27.2 were obtained.

Increasing environmental concerns and fuel prices motivate the study of alternative, unconventional aircraft configurations. One such example is the blended-wing-body configuration, which has been shown to have several advantages over the conventional tube-and-wing aircraft configuration. In this thesis, a blended-wing-body aircraft is studied and optimized aerodynamically using a high-fidelity Euler-based flow solver, integrated geometry parameterization and mesh movement, adjoint-based gradient evaluation, and a sequential quadratic programming algorithm. Specifically, the aircraft is optimized at transonic conditions to minimize the sum of induced and wave drag. These optimizations are carried out with both fixed and varying airfoil sections. With varying airfoil sections and increased freedom, up to 52% drag reduction relative to the baseline geometry was achieved: at the target lift coefficient of 0.357, a drag coefficient of 0.01313 and an inviscid lift-to-drag ratio of 27.2 were obtained.

This dissertation describes detailed performance engineering and optimization of an unstructured computational aerodynamics software system with irregular memory accesses on various multi- and many-core emerging high performance computing scalable architectures, which are expected to be the building blocks of energy-austere exascale systems, and on which algorithmic- and architecture-oriented optimizations are essential for achieving worthy performance. We investigate several state-of-the-practice shared-memory optimization techniques applied to key kernels for the important problem class of unstructured meshes. We illustrate for a broad spectrum of emerging microprocessor architectures as representatives of the compute units in contemporary leading supercomputers, identifying and addressing performance challenges without compromising the floating-point numerics of the original code. While the linear algebraic kernels are bottlenecked by memory bandwidth for even modest numbers of hardware cores sharing a common address space, the edge-based loop kernels, which arise in the control volume discretization of the conservation law residuals and in the formation of the preconditioner for the Jacobian by finite-differencing the conservation law residuals, are compute-intensive and effectively exploit contemporary multi- and many-core processing hardware. We therefore employ low- and high-level algorithmic- and architecture-specific code optimizations and tuning in light of thread- and data-level parallelism, with a focus on strong thread scaling at the node-level. Our approaches are based upon novel multi-level hierarchical workload distribution mechanisms of data across different compute units (from the address space down to the registers) within every hardware core. We analyze the demonstrated aerodynamics application on specific computing architectures to develop certain performance metrics and models to bespeak the upper and lower bounds of the performance. We present significant full application speedup relative to the baseline code, on a succession of many-core processor architectures, i.e., Intel Xeon Phi Knights Corner (5.0x) and Knights Landing (2.9x). In addition, the performance of Knights Landing outperforms, at significantly lower power consumption, Intel Xeon Skylake with nearly twofold speedup. These optimizations are expected to be of value for many other unstructured mesh partial differential equation-based scientific applications as multi- and many- core architecture evolves.

O estudo de métodos de modelagem de escoamentos aerodinâmicos em regime transônico é de grande importância para a engenharia aeronáutica. O maior desafio no tratamento desses escoamentos está na sua característica não linear devido aos efeitos de compressibilidade e formação de ondas de choque. Tais efeitos não lineares influenciam no desempenho de superfícies aerodinâmicas em geral, bem como são responsáveis pelo aparecimento de fenômenos danosos para a resposta aeroelástica de aeronaves. O equacionamento para esses tipos de escoamentos pode ser obtido via as equações básicas da mecânica dos fluidos. No entanto, apenas soluções numéricas de tais equações são possíveis de ser obtidas de forma prática no presente momento. Para o caso específico do tratamento de problemas transônicos, as equações de Euler formam um conjunto de equações diferenciais a derivadas parciais capazes de capturar os efeitos não lineares de escoamentos compressíveis, porém os efeitos da viscosidade não são levados em consideração. O objetivo desse trabalho é implementar uma rotina computacional capaz de resolver numericamente escoamentos em regime transônico em torno de aerofólios. Para isso as equações de Euler não lineares são utilizadas e o campo de fluido ao redor de um perfil aerodinâmico é discretizado pelo método das diferenças finitas. Uma malha estruturada do tipo C discretizando o fluido ao redor de um aerofólio NACA0012 é considerada. A metodologia para solução numérica é baseada no método explícito de MacCormack de segunda ordem de precisão no tempo e espaço. Baseados na aproximação upwind, termos de dissipação artificial com coeficientes não lineares também são adicionados ao método. A solução do escoamento transônico estacionário ao redor do aerofólio NACA0012 é obtida e as principais propriedades do escoamento são apresentadas. Observa-se a formação de ondas de choque através de contornos de número de Mach ao redor do aerofólio. Gráficos das distribuições de pressão no intra e extradorso do aerofólio são mostrados, onde se identificam aos efeitos da brusca variação de pressão devido as ondas de choque. Os resultados são validados com valores de distribuição de pressão para o mesmo aerofólio encontradas na literatura técnica. Os resultados obtidos combinam bem com os fornecidos em códigos computacionais para solução do mesmo problema aerodinâmico / The study of aerodynamic modeling methods for the transonic flow regime is of great importance in aeronautical engineering. Major challenge on the treatment of those flows is on their nonlinear features due to compressibility effects and shock waves (appearance). Such nonlinear effects present a strong influence on aerodynamic performance, as well as they are responsible for harmful aeroelastic response phenomena in aircraft. Equations for transonic flows can be obtained from the basic fluid mechanic equations. However, only numerical methods are able to attain practical solutions for those set of differential equations at the present moment. For the specific case of treating transonic flow problems, the nonlinear Euler equations provide a set of partial differential equations with features to capture nonlinear effects of typical compressible flows, despite of not accounting for viscous flows effects. The aim of this work is to implement a computational routine for the numerical solution of transonic flows around airfoils. The Euler equations are used and the flow field around a aerodynamic profile is discretized by finite difference method. A C-type structured mesh is used to discretize the flow around a NACA0012 airfoil. The methodology for numerical solution is based on the explicit MacCormack method which has second order accuracy in time and space. Based on the upwind approximation, artificial dissipation with nonlinear coefficients is incorporated to the method. The steady transonic flow around the NACA0012 airfoil numerical solution is assessed and the main flow properties are presented. Shock wave structure can also be observed by means of the Mach number contours around the airfoil. Pressure distributions on upper and lower surfaces for different flow conditions are also shown, thereby allowing the observation of the effects of the abrupt pressure change due to shock waves. The results are validated using data presented in the technical literature. The present code solutions agree well with the solution obtained in other computational codes used for the same problem

O estudo de métodos de modelagem de escoamentos aerodinâmicos em regime transônico é de grande importância para a engenharia aeronáutica. O maior desafio no tratamento desses escoamentos está na sua característica não linear devido aos efeitos de compressibilidade e formação de ondas de choque. Tais efeitos não lineares influenciam no desempenho de superfícies aerodinâmicas em geral, bem como são responsáveis pelo aparecimento de fenômenos danosos para a resposta aeroelástica de aeronaves. O equacionamento para esses tipos de escoamentos pode ser obtido via as equações básicas da mecânica dos fluidos. No entanto, apenas soluções numéricas de tais equações são possíveis de ser obtidas de forma prática no presente momento. Para o caso específico do tratamento de problemas transônicos, as equações de Euler formam um conjunto de equações diferenciais a derivadas parciais capazes de capturar os efeitos não lineares de escoamentos compressíveis, porém os efeitos da viscosidade não são levados em consideração. O objetivo desse trabalho é implementar uma rotina computacional capaz de resolver numericamente escoamentos em regime transônico em torno de aerofólios. Para isso as equações de Euler não lineares são utilizadas e o campo de fluido ao redor de um perfil aerodinâmico é discretizado pelo método das diferenças finitas. Uma malha estruturada do tipo C discretizando o fluido ao redor de um aerofólio NACA0012 é considerada. A metodologia para solução numérica é baseada no método explícito de MacCormack de segunda ordem de precisão no tempo e espaço. Baseados na aproximação upwind, termos de dissipação artificial com coeficientes não lineares também são adicionados ao método. A solução do escoamento transônico estacionário ao redor do aerofólio NACA0012 é obtida e as principais propriedades do escoamento são apresentadas. Observa-se a formação de ondas de choque através de contornos de número de Mach ao redor do aerofólio. Gráficos das distribuições de pressão no intra e extradorso do aerofólio são mostrados, onde se identificam aos efeitos da brusca variação de pressão devido as ondas de choque. Os resultados são validados com valores de distribuição de pressão para o mesmo aerofólio encontradas na literatura técnica. Os resultados obtidos combinam bem com os fornecidos em códigos computacionais para solução do mesmo problema aerodinâmico / The study of aerodynamic modeling methods for the transonic flow regime is of great importance in aeronautical engineering. Major challenge on the treatment of those flows is on their nonlinear features due to compressibility effects and shock waves (appearance). Such nonlinear effects present a strong influence on aerodynamic performance, as well as they are responsible for harmful aeroelastic response phenomena in aircraft. Equations for transonic flows can be obtained from the basic fluid mechanic equations. However, only numerical methods are able to attain practical solutions for those set of differential equations at the present moment. For the specific case of treating transonic flow problems, the nonlinear Euler equations provide a set of partial differential equations with features to capture nonlinear effects of typical compressible flows, despite of not accounting for viscous flows effects. The aim of this work is to implement a computational routine for the numerical solution of transonic flows around airfoils. The Euler equations are used and the flow field around a aerodynamic profile is discretized by finite difference method. A C-type structured mesh is used to discretize the flow around a NACA0012 airfoil. The methodology for numerical solution is based on the explicit MacCormack method which has second order accuracy in time and space. Based on the upwind approximation, artificial dissipation with nonlinear coefficients is incorporated to the method. The steady transonic flow around the NACA0012 airfoil numerical solution is assessed and the main flow properties are presented. Shock wave structure can also be observed by means of the Mach number contours around the airfoil. Pressure distributions on upper and lower surfaces for different flow conditions are also shown, thereby allowing the observation of the effects of the abrupt pressure change due to shock waves. The results are validated using data presented in the technical literature. The present code solutions agree well with the solution obtained in other computational codes used for the same problem