Am Morris

Domain-element method for aerodynamic shape optimization applied to a modern transport wing

Generic wraparound aerodynamic shape optimization technology is presented and applied to a modern commercial aircraft wing in transonic cruise. The wing geometry is parameterized by a novel domain-element method, which uses efficient global interpolation functions to deform both the surface geometry and corresponding computational fluid dynamics volume mesh. The technique also provides a method that allows geometries to be parameterized at various levels, ranging from global three-dimensional planform alterations to detailed local surface changes. Combining all levels of parameterization allows for free-form design control with very few design variables. The method provides an efficient combined shape parameterization and high-quality mesh deformation technique that is totally independent of mesh type (structured or unstructured). Optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient-based optimizer by finite differences. The entire optimization suite has also been parallelized to allow optimization with highly flexible parameterization in practical times. Results are presented for highly constrained optimizations of the modern aircraft wing in transonic cruise, using three levels of parameterization (number of design variables) to assess the effect of parameterization level on the optimization. The highest-level optimization results in a totally-shock-free geometry with an associated substantial reduction in drag.

Computational-Fluid-Dynamics-Based Twist Optimization of Hovering Rotors

Twist optimization of a helicopter rotor in hover is presented using compressible computational fluid dynamics as the aerodynamic model. A domain-element shape parameterization method has been developed, which solves both the geometry control and the volumemesh deformation problems simultaneously, using radial basis function global interpolation. This provides direct transfer of domain-element movements into deformations of the design surface and the computational fluid dynamics volume mesh, which is deformed in a high-quality fashion. The method is independent ofmesh type (structured or unstructured), and it has been linked to an advancedparallel gradient-based algorithm, for which independence from the flow solver is achieved by obtaining sensitivity information by finite differences. This has resulted in aflexible andversatilemodularmethod ofwraparound optimization. Previousfixedwing results have shown that a large proportion of the design space is accessible with the parameterization method, and heavily constrained drag optimization demonstrated significant performance improvements. In the present work, themethod is extended to a rotor blade, and this is optimized forminimum torque in hovering flight with strict constraints. Twist optimization results are presented for three tip Mach numbers, and the effects of different parameterization levels are analyzedusing various combinations of two levels: global and local. Torque reductions of over 12% are shown for a fully subsonic case, and for over 24% for a transonic case, using only three global and 15 local twist parameters.

Aerodynamic shape optimization of a modern transport wing using only planform variations

Abstract Generic aerodynamic shape optimization technology is presented, based on a domain element approach linked with global interpolation functions. This allows an efficient shape parameterization from which both the design surface geometry and corresponding computational fluid dynamics volume mesh can be deformed directly, in a high quality and robust fashion. The technique also provides a method that allows geometries to be parameterized at various levels, ranging from general planform alterations to detailed local surface changes. The global interpolation developed is totally independent of mesh type (structured or unstructured), and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient-based optimizer (feasible sequential quadratic programming) by finite differences. Results have been presented recently for two-dimensional aerofoil cases, and drag reductions of up to 45 per cent were demonstrated. Hence, this article presents initial extension of the method to three dimensions. Results are presented for highly constrained optimization of a modern aircraft wing in transonic cruise, using only planform parameters (design variables), i.e. wing sections can move but may not deform locally. This is done to test and validate the method before moving on to higher fidelity optimizations, and more computationally expensive applications. Even with this fidelity of parameterization, only 30 parameters are used, optimization produces an 8 per cent reduction in drag.

Wing Design by Aerodynamic and Aeroelastic Shape Optimisation

Aerodynamic shape optimisation technology is presented, comprising an efficient variable fidelity shape parameterisation method, an efficient andhigh quality mesh deformation scheme, and a parallel optimisation algorithm. The objective of the research presented here is the comparison of truly three-dimensional optimisations of aircraft wings in both aerodynamic and aeroelastic environments. The novel shape parameterisation technique allows various fidelities of design parameters, ranging from detailed surface changes to novel truly three-dimensional planform adjustments. An efficient interpolation scheme, using radial basis functions, transfers domain element movements into direct deformations of the design surface and corresponding CFD mesh, thus allowing total independence from the grid generation package and type (structured or unstructured). Optimisation is independent from the CFD flow solver by obtaining sensitivity information for an advanced parallel gradient-based optimiser by finite-differences. This ‘wrap-around’ optimisation technique is applied to a modern large transport aircraft wing in the cruise flight condition for minimum drag with stringent constraints in lift, volume, and two root moments. The objective of all optimisations is aerodynamic, however the static aeroelastic deflection provided by an aeroelastic solver will give that particular optimisation increased accuracy and real world relevance. The result of a constrained inviscid aerodynamic optimisation is presented and has a significant reduction in drag when compared to the initial wing with no violation of any constraints. The shape parameterisation method demonstrates that only a low number of design variables are necessary to achieve innovative planform and surface geometries with dramatically improved performance. Computational fluid dynamics (CFD) methods are now commonplace in aerospace industries, and at the forefront of analysis capabilities, providing a fast and effective method of predicting a design’s aerodynamic performance. However, with ever increasing complexity of designs, engineers can often struggle to interpret the intricacies of the CFD results sufficiently to be able to manually alter the geometry to improve performance. Hence, there has been an increase in demand for intelligent and automatic shape optimisation schemes. This requires combining geometry control methods with numerical optimisation algorithms, to provide a mechanism to mathematically seek improved and optimum designs, using CFD as the analysis tool. Optimisation requires consideration of three issues, each of which have numerous solutions: shape parameterisation including CFD surface and volume mesh deformation, computation of design variable derivatives, and effective use of these derivatives to improve design. Geometry parameterisation is critical for effective shape optimisation. This is the method of representing the design surface, and defines the degrees of freedom in which the geometry can be altered and, ideally, this should be linked with an effective method of deforming the CFD surface and volume mesh in a corresponding fashion. Parameterising complex shapes is a problem that remains a serious obstacle to both manual and automatic CFD-based optimisation. A wide variety of shape control and morphing methods have been developed, but many do not allow sufficiently

CFD-Based Aerodynamic Shape Optimization of Hovering Rotors

A modular, generic optimization scheme is applied to CFD-based shape optimization of helicopter rotors in hovering flight. An efficient domain element shape parameterization method is linked to a radial basis function global interpolation to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh, which is deformed in a high-quality fashion, and the parameterization method requires very few design variables to allow free-form design. The method of shape and CFD mesh parameterization is independent of mesh type (structured or unstructured), and optimization independence from the flow solver (inviscid, viscous, aeroelastic) is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference. This has resulted in a flexible and versatile method of ’wrap-around’ optimization. Previous fixed-wing results have shown that a large proportion of the design space is accessible with the parameterization method and heavily constrained drag optimization has shown that significant improvements over existing designs can be achieved. In the present work, the method is extended to a rotor blade, and this is optimized for minimum torque in hovering flight with rigid constraints in thrust, internal volume and pitching moments. Initial results presented here use only twist parameters, at two levels, global and local, as a method of both validating the approach and investigating the effects of different parameterization levels. Torque reductions of 9% are shown for a fully subsonic case, and 15% for a transonic case, using only three and 15 twist parameters.

CFD-Based Twist Optimization of Hovering Rotors

Aerodynamic shape optimization of a helicopter rotor in hover is presented, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterization method is presented which overcomes both the geometry control and volume mesh deformation problems simultaneously. Radial basis function global interpolation is used to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh, which is deformed in a high-quality fashion, and the parameterization method requires very few design variables to allow free-form design. This method is independent of mesh type (structured or unstructured) or size, and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference. This has resulted in a flexible and versatile modular method of ’wrap-around’ optimization. Previous fixed-wing results have shown that a large proportion of the design space is accessible with the parameterization method and heavily constrained drag optimization has shown that significant improvements over existing designs can be achieved. In the present work, the method is extended to a rotor blade, and this is optimized for minimum torque in hovering flight with rigid constraints on thrust, internal volume and pitching moments. Twist optimization results are presented for three tip Mach numbers, and the effects of different parameterization levels analysed, using various combinations of two levels; global and local. Torque reductions of over 12% are shown for a fully subsonic case, and over 24% for a transonic case, using only three global and 15 local twist parameters.

Aerodynamic Optimisation of Modern Transport Wing using Efficient Variable Fidelity Shape Parameterisation

Generic wrap-around aerodynamic shape optimisation technology is presented, and applied to a modern commercial aircraft wing in transonic cruise. The wing geometry is parameterised by a novel domain element method, which uses efficient global interpolation functions to deform both the surface geometry and corresponding CFD volume mesh. The technique also provides a method that allows geometries to be parameterised at various levels, ranging from global three-dimensional planform alterations to detailed local surface changes. Combining all levels of parameterisation allows for free-form design control with very few design variables. The method provides an efficient combined shape parameterisation and high quality mesh deformation technique that is totally independent of mesh type (structured or unstructured). Optimisation independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient-based optimiser (FSQP) by finite-differences. Results are presented for highly constrained optimisations of the modern aircraft wing in transonic cruise, using three levels of parameterisation (number of design variables), to assess the effect of parameterisation fidelity on the optimisation. The highest fidelity optimisation results in a totally shock-free geometry with an associated substantial reduction in drag.

A Framework for Parallel High-Fidelity Aerodynamic and Aeroelastic Optimisation

A novel, generic, and efficient domain element shape parameterisation method is presented. The parameterisation technique uses radial basis functions (RBFs) to provide an interpolation between a domain element and the surface geometry. Complex, multi-element, two- and three-dimensional geometries can be easily parameterised in a hierarchical manner, i.e. the geometry can deform at multiple scales, enabling free-form design of a two or three-dimensional geometry requiring only a few intuitive design variables. The interpolation is also extended to the aerodynamic CFD mesh; there is no requirement for connectivity information and as such any mesh topology, structured or unstructured can be parameterised. As both surface geometry and its associated CFD mesh can be parameterised and deformed using the same high quality geometry control interpolation, this provides a fast an efficient method that can be combined with automatic optimisation procedures. The optimisation framework developed can be ’wrapped-around’ any existing CFD codes, and independence from the flow solver (either inviscid, viscous, aeroelastic) by obtaining sensitivity information by finite-differences. An advanced sequential quadratic programming optimisation method has been integrated into the technology, and the entire framework has also been parallelised. The flexibility and versatility of the parameterisation method developed have enabled the application to many varying aerodynamic shape optimisation problems, and applications include; two-dimensional inverse design problems, highly constrained aerofoil, threedimensional wing and rotor optimisations, and most notably wing aeroelastic optimisation. Two-dimensional inverse design problems have demonstrated that a large proportion of the design space is feasible with a relatively low number of design variables. Heavily constrained two-dimensional aerofoil and three-dimensional wing and rotor optimisations have also shown that innovative designs can be found using very few design variables, providing substantial performance improvements over existing designs.