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Algorithm Developments for Discrete Adjoint Methods
, 2001
"... This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed ..."
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This paper presents a number of algorithm developments for adjoint methods using the `discrete' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed
Adjoint code developments using the exact discrete approach. AIAA Paper
, 2001
"... This paper presents a number of algorithm developments for adjoint methods using the `discrete ' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equaitons, exact nu ..."
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Cited by 12 (5 self)
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This paper presents a number of algorithm developments for adjoint methods using the `discrete ' approach in which the discretisation of the nonlinear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equaitons, exact numerical equivalence is maintained between the linear and adjoint discretisations. The incorporation of strong boundary conditions within the discrete approach is discussed, as well as a new application of adjoint methods to linear unsteady
ow in turbomachinery.
Stabilization of Linear Flow Solver for Turbomachinery Aeroelasticity Using Recursive Projection Method
"... The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitud ..."
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Cited by 7 (1 self)
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The linear analysis of turbomachinery aeroelasticity relies on the assumption of small level of unsteadiness and requires the solution of both the nonlinear steady and the linear unsteady flow equations. The objective of the analysis is to compute a complex flow solution that represents the amplitude and phase of the unsteady flow perturbation for the frequency of unsteadiness of interest. The solution procedure of the linear harmonic Euler/Navier–Stokes solver of the HYDRA suite of codes consists of a preconditioned fixedpoint iteration, which in some circumstances becomes numerically unstable. Previous work had already highlighted the physical origin of these numerical instabilities and demonstrated the code stabilization achieved by wrapping the core part of the linear code with a Generalized Minimal Residual (GMRES) solver. The implementation and the use of an alternative algorithm, namely, the Recursive Projection Method, is summarized. This solver is shown to be well suited for both stabilizing the fixedpoint iteration and improving its convergence rate in the absence of numerical instabilities. In the framework of the linear analysis of turbomachinery aeroelasticity, this method can be computationally competitive with the GMRES approach. I.
Adjoint calculation of sensitivities of turbomachinery objective functions
 AIAA Journal of Propulsion and Power
"... This paper presents an overview of the steady and harmonic adjoint methods for turbomachinery design using the `discrete ' approach in which the discretized nonlinear Euler/NavierStokes equations are linearized and the resulting matrix is then transposed. Steady adjoint solvers give the linear ..."
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This paper presents an overview of the steady and harmonic adjoint methods for turbomachinery design using the `discrete ' approach in which the discretized nonlinear Euler/NavierStokes equations are linearized and the resulting matrix is then transposed. Steady adjoint solvers give the linear sensitivity of steadystate functionals such as mass
ow and average exit
ow angle to arbitrary changes in the geometry of the blades and this linear sensitivity information can then be used as part of a nonlinear optimization procedure. The harmonic adjoint method is based on a single frequency of unsteadiness and allows one to determine the generalized force acting on the blades due to arbitrary incoming timeperiodic gusts. When the forcing is due to the wakes of the upstream blades the adjoint approach can be used to tailor the shape of the incoming wakes to greatly reduce the level of forced vibration they induce. The presented suite of testcases includes the Inlet Guide Vane and the rotor of a High Pressure Turbine. 1
Language and Content
 Implicit Policy, Invisible, Language: Policies and Practices of International Degree Programmes in Finnish Higher Education’. in EnglishMedium Instruction at Universities. Global Challenges
, 1984
"... A challenge for 21st century molecular biology and biochemistry: what are the causes of obligate autotrophy and methanotrophy? for at least one of the three components of the aketoglutarate dehydrogenase complex in these obligate organisms. It is recognized that absence of a single functional enzym ..."
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A challenge for 21st century molecular biology and biochemistry: what are the causes of obligate autotrophy and methanotrophy? for at least one of the three components of the aketoglutarate dehydrogenase complex in these obligate organisms. It is recognized that absence of a single functional enzyme may not explain obligate autotrophy in all cases and may indeed be only be one of a 2. Genome sequences and bioinformatic databases as untapped resources................ 337 3. Background to obligate metabolic modes of life................................ 337 3.1. Bacterial obligate autotrophy and methanotrophy and their relationship to autotrophy in Archaea............................................ 337 obiology.org by guest on Septem ber 16, 2016
Total Pressure Losses Minimization in Turbomachinery Cascades, using a New Continuous Adjoint Formulation
"... A new continuous adjoint formulation for the optimization of cascade airfoils with minimum total pressure losses, i.e. an objective function which has never been used before along with the continuous adjoint, is presented. To support a steepest descent algorithm, the adjoint method computes the grad ..."
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A new continuous adjoint formulation for the optimization of cascade airfoils with minimum total pressure losses, i.e. an objective function which has never been used before along with the continuous adjoint, is presented. To support a steepest descent algorithm, the adjoint method computes the gradient of the objective function with respect to the design variables. The function is defined as the difference in total pressure between the inlet to and the outlet from the cascade. In contrast to other known continuous adjoint approaches in aerodynamics (such as inverse designs based on target pressure distributions or drag–lift optimization for isolated airfoils), where the functional is defined over the parameterized solid walls, the present functional consists of integrals over the inlet/outlet boundaries only. To cope with this particular situation, the method of characteristics is used to impose inlet/outlet adjoint boundary conditions. It is worth noting that the objective function gradient is expressed as an integral over the solid walls. The minimization of losses in linear and peripheral compressor cascades, constrained by the desirable flow turning and minimum allowed blade thickness, are demonstrated.
Sensitivity analysis of limit cycle oscillations
"... Many unsteady problems equilibrate to periodic behavior. For these problems the sensitivity of periodic outputs to system parameters are often desired, and must be estimated from a finite time or frequency domain calculation. Sensitivities computed in the time domain over a finite time span can take ..."
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Many unsteady problems equilibrate to periodic behavior. For these problems the sensitivity of periodic outputs to system parameters are often desired, and must be estimated from a finite time or frequency domain calculation. Sensitivities computed in the time domain over a finite time span can take excessive time to converge, or fail altogether to converge to the periodic value. We derive a theoretical basis for this error and demonstrate it using two examples: a van der Pol oscillator and vortex shedding from a low Reynolds number airfoil. We show that output windowing enables the accurate computation of periodic output sensitivities, and may allow for decreased simulation time to compute both timeaveraged outputs and sensitivities. We classify two distinct window types: longtime, over a large, not necessarily integer number of periods; and shorttime, over a small, integer number of periods. Finally, from these two classes we investigate several examples of window shape and demonstrate their convergence with window size and error in the period approximation, respectively. Keywords: sensitivity analysis, unsteady, limit cycles, periodic
Fifty Years of Aerodynamics: Successes, Challenges, and Opportunities
"... This paper presents a review of developments in aerodynamics during the last 50 years. Progress in aerodynamic design, theoretical aerodynamics, wind tunnel testing, and especially computational fluid dynamics (CFD) is discussed. Where appropriate, applications to aircraft design are presented, as a ..."
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This paper presents a review of developments in aerodynamics during the last 50 years. Progress in aerodynamic design, theoretical aerodynamics, wind tunnel testing, and especially computational fluid dynamics (CFD) is discussed. Where appropriate, applications to aircraft design are presented, as are new aircraft concepts. Topics of Canadian interest are presented and the paper includes several examples of research and development in aerodynamics at de Havilland. RÉSUMÉ Le document présente une revue du secteur de l’aérodynamique depuis les 50 dernières années. On y traite des progrès réalisés en conception aérodynamique, en aérodynamique théorique, dans les essais en soufflerie et, surtout, en simulation numérique en mécanique des fluides (CFD). Le cas échéant, des applications dans la conception des aéronefs sont présentées, comme de nouveaux aéronefs concepts. Des sujets d’intérêt pour le Canada sont présentés, et le document renferme plusieurs exemples de recherche et de développement en aérodynamique chez de Havilland.
and
"... This paper presents an adjoint method for the optimum shape design of unsteady threedimensional viscous flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the nonlinear frequencydomain method. First, this paper presents the compl ..."
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This paper presents an adjoint method for the optimum shape design of unsteady threedimensional viscous flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the nonlinear frequencydomain method. First, this paper presents the complete formulation of the timedependent optimal design problem. Second, we present the nonlinear frequencydomain adjoint equations for threedimensional viscous transonic flows. Third, we present results that demonstrate the application of the theory to a threedimensional wing. Nomenclature b = boundary velocity component d = artificial dissipation flux E = internal energy F = numerical flux vector f = flux vector G = gradient I = cost function i, j = cell indices
DESIGN OF GAS TURBINE ENGINES USING CFD
, 2004
"... Abstract. This paper describes a general purpose design system being developed at RollsRoyce plc. The key elements of the system are a parametric design and rapid meshing capability; a stateoftheart CFD solver with an adjoint capability; and, an advanced optimisation system consisting of a libr ..."
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Abstract. This paper describes a general purpose design system being developed at RollsRoyce plc. The key elements of the system are a parametric design and rapid meshing capability; a stateoftheart CFD solver with an adjoint capability; and, an advanced optimisation system consisting of a library of optimisers. A description is given of each element in the design system. To illustrate its use and flexibility, five different applications of the system to a gas turbine are described. These are: optimisation of the guide vanes in the bypass duct to minimise excitation of the fan rotor; the same bypass guide vane optimisation using sensitivity gradients from the adjoint solver; optimisation of a compressor stage to improve efficiency whilst constraining flow rate, pressure ratio and outlet flow angle; minimisation of the forced excitation of a turbine rotor by modifying the wake of the upstream nozzle guide vane; and, optimisation of a fan rotor to reduce tone noise. 1 Leigh Lapworth and Shahrokh Shahpar