scholarly journals Tiltrotor CFD Part II - aerodynamic optimisation of tiltrotor blades

2017 ◽  
Vol 121 (1239) ◽  
pp. 611-636
Author(s):  
A. Jimenez-Garcia ◽  
M. Biava ◽  
G.N. Barakos ◽  
K.D. Baverstock ◽  
S. Gates ◽  
...  
Keyword(s):  
Single Point ◽  
Optimal Solution ◽  
High Fidelity ◽  
Blade Design ◽  
Discrete Adjoint ◽  
Blade Shape ◽  
Gradient Based ◽  
Flow Gradients ◽  
Flight Regimes ◽  
Quasi Newton

ABSTRACTThis paper presents aerodynamic optimisation of tiltrotor blades with high-fidelity computational fluid dynamics. The employed optimisation framework is based on a quasi-Newton method, and the required high-fidelity flow gradients were computed using a discrete adjoint solver. Single-point optimisations were first performed to highlight the contrasting requirements of the helicopter and aeroplane flight regimes. It is then shown how a trade-off blade design can be obtained using a multi-point optimisation strategy. The parametrisation of the blade shape allowed the twist and chord distributions to be modified and a swept tip to be introduced. The work shows how these main blade shape parameters influence the optimal performance of the tiltrotor in helicopter and aeroplane modes, and how an optimised blade shape can increase the overall tiltrotor performance. Moreover, in all the presented cases, the accuracy of the adjoint gradients resulted in a small number of flow evaluations for finding the optimal solution, thus indicating gradient-based optimisation as a viable tool for modern tiltrotor design.

Development of Adjoint Solvers for Engineering Gradient-Based Turbomachinery Design Applications

2009 ◽  
Author(s):  
Andre C. Marta ◽  
Sriram Shankaran ◽  
D. Graham Holmes ◽  
Alexander Stein
Keyword(s):  
Adjoint Method ◽  
Automatic Differentiation ◽  
High Fidelity ◽  
Optimization Approach ◽  
Discrete Adjoint ◽  
Gradient Based ◽  
Computational Fluid Dynamics Cfd ◽  
And Function ◽  
Turbomachinery Design ◽  
Fine Tune

High-fidelity computational fluid dynamics (CFD) are common practice in turbomachinery design. Typically, several cases are run with manually modified parameters based on designer expertise to fine-tune a machine. Although successful, a more efficient process is desired. Choosing a gradient-based optimization approach, the gradients of the functions of interest need to be estimated. When the number of variables greatly exceeds the number of functions, the adjoint method is the best-suited approach to efficiently estimate gradients. Until recently, the development of CFD adjoint solvers was regarded as complex and difficult, which limited their use mostly to academia. This paper focuses on the problem of developing adjoint solvers for legacy industrial CFD solvers. A discrete adjoint solver is derived with the aid of an automatic differentiation tool that is selectively applied to the CFD code that handles the residual and function evaluations. The adjoint-based gradients are validated against finite-difference and complex-step derivative approximations.

Fully Parametric High-Fidelity CFD Model for the Design Optimisation of the Cyclic Stagger Pattern of a Set of Fan Outlet Guide Vanes

2009 ◽  
Author(s):  
Andrea Milli ◽  
Olivier Bron
Keyword(s):  
Complex Geometry ◽  
Single Point ◽  
Sensitivity Study ◽  
Operating Conditions ◽  
High Fidelity ◽  
Cfd Model ◽  
Design Optimisation ◽  
Guide Vanes ◽  
High Loss ◽  
Design Variables

The present paper deals with the redesign of cyclic variation of a set of fan outlet guide vanes by means of high-fidelity full-annulus CFD. The necessity for the aerodynamic redesign originated from a change to the original project requirement, when the customer requested an increase in specific thrust above the original engine specification. The main objectives of this paper are: 1) make use of 3D CFD simulations to accurately model the flow field and identify high-loss regions; 2) elaborate an effective optimisation strategy using engineering judgement in order to define realistic objectives, constraints and design variables; 3) emphasise the importance of parametric geometry modelling and meshing for automatic design optimisation of complex turbomachinery configurations; 4) illustrate that the combination of advanced optimisation algorithms and aerodynamic expertise can lead to successful optimisations of complex turbomachinery components within practical time and costs constrains. The current design optimisation exercise was carried out using an in-house set of software tools to mesh, resolve, analyse and optimise turbomachinery components by means of Reynolds-averaged Navier-Stokes simulations. The original configuration was analysed using the 3D CFD model and thereafter assessed against experimental data and flow visualisations. The main objective of this phase was to acquire a deep insight of the aerodynamics and the loss mechanisms. This was important to appropriately limit the design scope and to drive the optimisation in the desirable direction with a limited number of design variables. A mesh sensitivity study was performed in order to minimise computational costs. Partially converged CFD solutions with restart and response surface models were used to speed up the optimisation loop. Finally, the single-point optimised circumferential stagger pattern was manually adjusted to increase the robustness of the design at other flight operating conditions. Overall, the optimisation resulted in a major loss reduction and increased operating range. Most important, it provided the project with an alternative and improved design within the time schedule requested and demonstrated that CFD tools can be used effectively not only for the analysis but also to provide new design solutions as a matter of routine even for very complex geometry configurations.

Determining Human Control Intent Using Inverse LQR Solutions

2013 ◽  
Author(s):  
M. Cody Priess ◽  
Jongeun Choi ◽  
Clark Radcliffe
Keyword(s):  
Human Subjects ◽  
Optimal Solution ◽  
Linear Matrix ◽  
Minimization Method ◽  
Human Control ◽  
Balance Task ◽  
Lqr Problem ◽  
Seated Balance ◽  
Gradient Based ◽  
Time Invariant

In this paper, we have developed a method for determining the control intention in human subjects during a prescribed motion task. Our method is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? We describe an efficient Linear Matrix Inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Additionally, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. We develop a model for an upright seated-balance task which will be suitable for identification of human control intent once experimental data is available.

Pure Design Method for Aerofoils in Cascade

1969 ◽  
Vol 11 (5) ◽  
pp. 454-467 ◽  
Author(s):  
K. Murugesan ◽  
J. W. Railly
Keyword(s):  
Exact Solution ◽  
Velocity Distribution ◽  
Design Problem ◽  
Design Method ◽  
Tangential Velocity ◽  
Surface Velocity ◽  
Normal Velocity ◽  
Blade Design ◽  
Blade Shape

An extension of Martensen's method is described which permits an exact solution of the inverse or blade design problem. An equation is derived for the normal velocity distributed about a given contour when a given tangential velocity is imposed about the contour and from this normal velocity an initial arbitrarily chosen blade shape may be successively modified until a blade is found having a desired surface velocity distribution. Five examples of the method are given.

scholarly journals Assessing the Sensitivity of Stall-Regulated Wind Turbine Power to Blade Design Using High-Fidelity Computational Fluid Dynamics

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Andrea G. Sanvito ◽  
Giacomo Persico ◽  
M. Sergio Campobasso
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Field Testing ◽  
Turbine Rotor ◽  
Operating Conditions ◽  
High Fidelity ◽  
Blade Design ◽  
Computationally Efficient ◽  
Wind Speeds ◽  
Wide Range

Abstract This study provides a novel contribution toward the establishment of a new high-fidelity simulation-based design methodology for stall-regulated horizontal axis wind turbines. The aerodynamic design of these machines is complex, due to the difficulty of reliably predicting stall onset and poststall characteristics. Low-fidelity design methods, widely used in industry, are computationally efficient, but are often affected by significant uncertainty. Conversely, Navier–Stokes computational fluid dynamics (CFD) can reduce such uncertainty, resulting in lower development costs by reducing the need of field testing of designs not fit for purpose. Here, the compressible CFD research code COSA is used to assess the performance of two alternative designs of a 13-m stall-regulated rotor over a wide range of operating conditions. Validation of the numerical methodology is based on thorough comparisons of novel simulations and measured data of the National Renewable Energy Laboratory (NREL) phase VI turbine rotor, and one of the two industrial rotor designs. An excellent agreement is found in all cases. All simulations of the two industrial rotors are time-dependent, to capture the unsteadiness associated with stall which occurs at most wind speeds. The two designs are cross-compared, with emphasis on the different stall patterns resulting from particular design choices. The key novelty of this work is the CFD-based assessment of the correlation among turbine power, blade aerodynamics, and blade design variables (airfoil geometry, blade planform, and twist) over most operational wind speeds.

Efficient Gradient-Based Algorithms for the Construction of Pareto Fronts

2011 ◽  
Author(s):  
Sriram Shankaran ◽  
Brian Barr
Keyword(s):  
Pareto Front ◽  
Computational Cost ◽  
High Fidelity ◽  
Simulation Tools ◽  
Pareto Points ◽  
Uniform Spacing ◽  
Design Variables ◽  
Gradient Based ◽  
Pareto Fronts ◽  
Sampling Approach

The objective of this study is to develop and assess a gradient-based algorithm that efficiently traverses the Pareto front for multi-objective problems. We use high-fidelity, computationally intensive simulation tools (for eg: Computational Fluid Dynamics (CFD) and Finite Element (FE) structural analysis) for function and gradient evaluations. The use of evolutionary algorithms with these high-fidelity simulation tools results in prohibitive computational costs. Hence, in this study we use an alternate gradient-based approach. We first outline an algorithm that can be proven to recover Pareto fronts. The performance of this algorithm is then tested on three academic problems: a convex front with uniform spacing of Pareto points, a convex front with non-uniform spacing and a concave front. The algorithm is shown to be able to retrieve the Pareto front in all three cases hence overcoming a common deficiency in gradient-based methods that use the idea of scalarization. Then the algorithm is applied to a practical problem in concurrent design for aerodynamic and structural performance of an axial turbine blade. For this problem, with 5 design variables, and for 10 points to approximate the front, the computational cost of the gradient-based method was roughly the same as that of a method that builds the front from a sampling approach. However, as the sampling approach involves building a surrogate model to identify the Pareto front, there is the possibility that validation of this predicted front with CFD and FE analysis results in a different location of the “Pareto” points. This can be avoided with the gradient-based method. Additionally, as the number of design variables increases and/or the number of required points on the Pareto front is reduced, the computational cost favors the gradient-based approach.

Design Optimization by Integration of Evolutionary Search and Cumulative Approximation

2005 ◽  
Author(s):  
Kikuo Fujita ◽  
Tomoki Ushiro ◽  
Noriyasu Hirokawa
Keyword(s):  
Design Optimization ◽  
Computational Cost ◽  
Optimal Solution ◽  
Response Surfaces ◽  
Evolutionary Search ◽  
Design Problems ◽  
Real Coded Genetic Algorithm ◽  
Cumulative Function ◽  
Gradient Based ◽  
New Framework

This paper proposes a new design optimization framework by integrating evolutionary search and cumulative function approximation. While evolutionary algorithms are robust even under multi-peaks, rugged natures, etc., their computational cost is inferior to ordinary schemes such as gradient-based methods. While response surface techniques such as quadratic approximation can save computational cost for complicated design problems, the fidelity of solution is affected by density of samples. The new framework simultaneously performs evolutionary search and constructs response surfaces. That is, in its early phase the search is performed over roughly but globally approximated surfaces with the relatively small number of samples, and in its later phase the search is performed intensively around promising regions, which are revealed in the preceded phases, over response surfaces enhanced with additional samples. This framework is expected to be able to robustly find the optimal solution with less sampling. An optimization algorithm is implemented by combining a real-coded genetic algorithm and a Voronoi diagram based cumulative approximation, and it is applied to some numerical examples for discussing its potential and promises.

Aerofoil profile and sweep optimisation for a blended wing-body aircraft using a discrete adjoint method

2006 ◽  
Vol 110 (1111) ◽  
pp. 589-604 ◽  
Author(s):  
A. Le Moigne ◽  
N. Qin
Keyword(s):  
Sequential Quadratic Programming ◽  
Adjoint Method ◽  
Navier Stokes ◽  
High Fidelity ◽  
Sweep Angle ◽  
Sqp Method ◽  
Discrete Adjoint ◽  
Design Variables ◽  
Variable Fidelity ◽  
Blended Wing Body

Abstract Aerodynamic optimisations of a blended wing-body (BWB) aircraft are presented. A discrete adjoint solver is used to calculate efficiently the gradients, which makes it possible to optimise for a large number of design variables. The optimisations employ either a variable-fidelity method that combines low- and high-fidelity models or a direct sequential quadratic programming (SQP) method. Four Euler optimisations of a BWB aircraft are then presented. The optimisation is allowed to change a series of master sections defining the aircraft geometry as well as the sweep angle on the outer wing for two of the optimisations. Substantial improvements are obtained, not only in the Euler mode but also when the optimised geometries are evaluated using Reynolds-averaged Navier-Stokes solutions. Some interesting features of the optimised wing profiles are discussed.

scholarly journals Accelerating Symmetric Rank-1 Quasi-Newton Method with Nesterov’s Gradient for Training Neural Networks

2021 ◽  
Author(s):  
S. Indrapriyadarsini ◽  
Shahrzad Mahboubi ◽  
Hiroshi Ninomiya ◽  
Takeshi Kamio ◽  
Hideki Asai
Keyword(s):  
Neural Networks ◽  
Newton Method ◽  
Trust Region ◽  
Nonlinear Problems ◽  
Classification Problem ◽  
Second Order ◽  
Highly Nonlinear ◽  
Gradient Based ◽  
Quasi Newton ◽  
Second Order Methods

Gradient based methods are popularly used in training neural networks and can be broadly categorized into first and second order methods. Second order methods have shown to have better convergence compared to first order methods, especially in solving highly nonlinear problems. The BFGS quasi-Newton method is the most commonly studied second order method for neural network training. Recent methods have shown to speed up the convergence of the BFGS method using the Nesterov’s acclerated gradient and momentum terms. The SR1 quasi-Newton method though less commonly used in training neural networks, are known to have interesting properties and provide good Hessian approximations when used with a trust-region approach. Thus, this paper aims to investigate accelerating the Symmetric Rank-1 (SR1) quasi-Newton method with the Nesterov’s gradient for training neural networks and briefly discuss its convergence. The performance of the proposed method is evaluated on a function approximation and image classification problem.

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