Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

Lyu, Zhoujie; Kenway, Gaetan K.; Paige, Cody; Martins, Joaquim R. R. A.

doi:10.2514/6.2013-2581

Cited by 97 publications

(90 citation statements)

References 37 publications

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“…The 1-equation Spalart-Allmaras turbulence model is loosely coupled to the mean flow equations and is iterated using a diagonally dominant alternating direction implicit (DDADI) method. A discrete adjoint method for the Euler and RANS equations is implemented within SUmb [18,19], enabling the efficient computation of gradients of functions of interest with respect to any number of design variables. More information of the RANS adjoint implementation is given Lyu [18].…”

Section: Cfd Solver and Mesh Deformationmentioning

confidence: 99%

Aerostructural optimization of the Common Research Model configuration

Kenway

Kennedy

Martins

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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The NASA Common Research Model (CRM) has become a standard test case for verification and validation of Reynolds averaged Navier-Stokes computational fluid dynamics codes. In this paper we evaluate the suitability of the CRM for aerostructural and aeroelastic optimization studies. Since the CRM was originally intended for aerodynamic studies only, the undeformed geometry is not available. To address this issue, we designed a jig shape and the corresponding wingbox structure for the CRM using an inverse design procedure. The results are verified by computing the drag coefficient of the aerostructural solution with the jig shape at the nominal CRM operating conditions. The drag differs by less than one drag count relative to the CRM original shape. Using the CRM jig geometry, a sample high-fidelity aerostructural optimization is performed to determine the potential decrease in fuel burn for a long-range design mission when varying wing planform and airfoil shapes. The optimization increases the aspect ratio of the wing from 9.0 to 12.6 and reduces the fuel burn by 8.8%. We also perform a series of gust load analysis on both the initial and optimized designs and determine that the optimized structure is critical under gust loads. The aerostructural optimization produces a high aspect ratio wing with effective passive aeroelastic tailoring, but additional load cases with cruise-like lift distributions are required to produce a more realistic wing design.

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Section: Cfd Solver and Mesh Deformationmentioning

confidence: 99%

Aerostructural optimization of the Common Research Model configuration

Kenway

Kennedy

Martins

2014

15th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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“…In the context of the discrete adjoint, full account of the viscous effects and linearization of the RANS equations coupled with a turbulence model has been attempted by several authors [36,37,38,39,40]. Applications to realistic aerodynamic optimization problems can also be found in [41] for fixed wing aircraft, and in Mani and Mavriplis [42] for rotorcraft.…”

Section: Past Work On Adjoint For Aircraft and Rotorcraft Applicationsmentioning

confidence: 99%

“…It is interesting to quantify the inaccuracies introduced into the gradients by such approximation, as in Dwight and Brezillon [36] and in Lyu et al [37] for the Spalart-Allmaras one-equation turbulence model, and in Marta et al [38] for the k-ω two-equation model. In a discrete adjoint solver, the frozen turbulence can be simulated by simply disabling the differentiated code computing the turbulence model derivatives.…”

Section: Naca0012 Aerofoil In Turbulent Flowmentioning

confidence: 99%

Fully Implicit Discrete-Adjoint Methods for Rotorcraft Applications

2016

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This paper presents the development of a fully implicit, low-memory, discrete adjoint method by means of automatic source-code differentiation applied to the Helicopter Multi-Block computational fluid dynamics solver. The method is suitable for applications in flight mechanics as well as shape optimization, and is demonstrated in this paper for popular flow cases reported in the literature. In particular, adjoint CFD computations were undertaken for airfoils, wings and rotor blade cases, and the obtained results were found to agree well with published solutions and with finite differences of flow derivatives. The method has been demonstrated for inviscid and viscous cases and results suggest that the current implementation is robust and efficient. The cost of the adjoint computations is relatively low due to the employed source-code differentiation and most of the times it is no more than the cost of a steady-state flow solution.

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“…The aim of the present optimization is therefore to reduce the drag. The drag minimization of a swept wing with the ONERA M6 wing as initial geometry is widely used for testing aerodynamic optimization methods [31,112,179]. Although the transonic flow regime encountered in this situation is not representative for the flow around a wind turbine rotor, it perfectly serves the purpose of demonstrating the capabilities of the present method for solving aerodynamic shape optimization problems.…”

Section: Drag Minimization In Transonic Flowmentioning

confidence: 99%

“…Moreover, this graph colouring also depends on which approach is taken for computing the convective flux. For Roe's scheme with linear reconstruction about the centre of mass of the control volume, the following function for computing the colour number is used [112] c = (i + 7j + 27k) mod 38.…”

Section: ∂R ∂Xmentioning

confidence: 99%

O a method for simulation-based wind turbine blade design

Jongsma¹

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SummaryW ind turbines are an important means for the production of renewable energy. This energy, commonly referred to as wind energy, is produced by extracting the kinetic energy from the wind and to subsequently convert it, usually via a rotational motion, to electrical energy. Wind conditions vary from one site to another and the design of a horizontal axis wind turbine depends on these local wind conditions. One of the important aspects of the design of a wind turbine concerns the aerodynamic shape of the rotor blades. The research presented in this thesis focusses on the development of a computational method that can be used for aerodynamic shape optimization.Other aspects -apart from the aerodynamic shape of a wind turbine rotor bladeare also important in the design of a wind turbine, for instance the structural design of the blade. To take this multidisciplinary character of wind turbine design into account, one of the aims of the research presented in this thesis has been that the aerodynamic shape optimization method seamlessly fits into the design process. Moreover, the optimization method is required to be efficient and fully automatic.A suitable method for the parametrization of the wind turbine blade geometry has been investigated. This investigation lead to the choice to use a non-uniform rational basis spline (NURBS) surface for representing the aerodynamic shape of the wind turbine blade. Such a description of the parametrization of the geometry is compatible with computer aided design methods, which eases the incorporation of the aerodynamic shape optimization method in the multidisciplinary design process. A model optimization problem has been considered to determine the relation between the number of design variables that is required to sufficiently accurately represent the design space for solving an aerodynamic shape optimization problem to the number of design variables that is required to realize an accurate NURBS representation of an aerodynamic shape. For the purpose of obtaining a NURBS surface representation of a wind turbine rotor blade, a fitting procedure has been developed. The accuracy of the resulting fit for two representative wind turbine blades is presented. It has been found that sufficient accuracy can be achieved with a NURBS surface described by 13 chordwise sections with 13 control points each.In the present research, objective functions are considered for which the evaluation requires the solution of partial differential equations that govern flow: the Euler equations. Since only for very particular flow configurations an analytical solution of these equations can be found, an approximate solution is computed by solving the discretized equations. Solving the discretized Euler equations requires the discretization of the whole flow domain. During the optimization procedure, the geometry of the rotor blade adapts, i Summary requiring a discrete representation of the new flow domain. To accommodate the change in shape during the optimization, a hyperbolic grid generation me...

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Automatic Differentiation Adjoint of the Reynolds-Averaged Navier-Stokes Equations with a Turbulence Model

Cited by 97 publications

References 37 publications

Aerostructural optimization of the Common Research Model configuration

Aerostructural optimization of the Common Research Model configuration

Fully Implicit Discrete-Adjoint Methods for Rotorcraft Applications

O a method for simulation-based wind turbine blade design

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