multi point optimization Research Articles (Page 1)

In actual flight, aircraft rarely operate under a single design condition; multiple flight states must be considered to meet performance requirements. With the push for green and low-carbon aviation, there is growing demand for high-performance, fuel-efficient aircraft. This study focuses on the Blended Wing Body (BWB) configuration. To address large-scale design variables and multiple constraints, a discrete adjoint-based aerodynamic optimization method is developed, improving computational efficiency and reducing cost.The optimization results show reduced drag coefficients across various flight conditions and enhanced drag divergence performance. The robustness of the multi-point optimization approach is validated, confirming its ability to improve aircraft performance across different states. The proposed method is practical and provides an effective reference for aerodynamic design of BWB aircraft.

The ability to morph the shape of an aircraft wing to optimize performance is widely accepted as a path to improved aircraft efficiency. A simpler approach is to change the wing camber using existing control surfaces. In this work, a Reynolds-averaged Navier–Stokes-based aerodynamic shape optimization methodology is applied to the design of a business jet with variable camber. Variable camber is achieved using the three existing control surfaces on each wing. Multipoint optimization is performed over a range of cruise operating conditions with and without variable camber. Variable camber is found to yield a reduction in drag of approximately 3–11 counts, or 1–5%, over a range of cruise conditions, with the largest reductions seen at lower lift coefficients. The control surface deflections are used to reduce the wing camber at lower lift cruise conditions, leading to an increase in the aircraft angle of attack across most operating points. The increased angles of attack transfer lift to the fuselage, which enables reductions in induced, wave, and trim drag. This additional drag reduction mechanism has not been identified in previous studies and cannot be seen in optimizations that do not include the fuselage and a trim constraint.

Natural laminar-flow wings are one of the most promising technologies for reducing fuel burn and emissions for commercial aviation. However, there is a lack of tools for performing shape optimization of wings based on computational fluid dynamics considering laminar-to-turbulent transition. To address this need, we develop a discrete adjoint-based optimization framework where transition is modeled. The core of this framework is a Reynolds-averaged Navier–Stokes solver that is coupled with a simplified method to predict Tollmien–Schlichting and laminar separation-induced transition that consists of a laminar boundary-layer code and a database method for flow stability analysis. The transition prediction is integrated with a Spalart–Allmaras turbulence model through a smoothed intermittency function, which makes it suitable for gradient-based optimization. A coupled-adjoint approach that uses transpose Jacobian-vector products derived via automatic differentiation computes the transition prediction derivatives. Lift-constrained drag minimizations of airfoils for a single-point design and a multipoint design problem are performed. The results show that the optimizer successfully reduces the drag coefficient by increasing the extent of laminar flow. The multipoint optimization formulation produces an airfoil with a significant amount of laminar flow that is maintained at several flight conditions. The proposed methods make it possible to perform aerodynamic shape optimization considering laminar-to-turbulent transition in airfoil optimization.

In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new sweep algorithm which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimization problems encounters serious difficulties in passing through nodal points. The results are illustrated with a specific numerical example.

PurposeTo develop a postprocessing algorithm for multiecho chemical‐shift encoded water–fat separation that estimates proton density fat fraction (PDFF) maps over the full dynamic range (0‐100%) using multipeak fat modeling and multipoint search optimization. To assess its accuracy, reproducibility, and agreement with state‐of‐the‐art complex‐based methods, and to evaluate its robustness to artefacts in abdominal PDFF maps.MethodsWe introduce MAGO (MAGnitude‐Only), a magnitude‐based reconstruction that embodies multipeak liver fat spectral modeling and multipoint optimization, and which is compatible with asymmetric echo acquisitions. MAGO is assessed first for accuracy and reproducibility on publicly available phantom data. Then, MAGO is applied to N = 178 UK Biobank cases, in which its liver PDFF measures are compared using Bland‐Altman analysis with those from a version of the hybrid iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL) algorithm, LiverMultiScan IDEAL (LMS IDEAL, Perspectum Diagnostics Ltd, Oxford, UK). Finally, MAGO is tested on a succession of high field challenging cases for which LMS IDEAL generated artefacts in the PDFF maps.ResultsPhantom data showed accurate, reproducible MAGO PDFF values across manufacturers, field strengths, and acquisition protocols. Moreover, we report excellent agreement between MAGO and LMS IDEAL for 6‐echo, 1.5 tesla human acquisitions (bias = −0.02% PDFF, 95% confidence interval = ±0.13% PDFF). When tested on 12‐echo, 3 tesla cases from different manufacturers, MAGO was shown to be more robust to artefacts compared to LMS IDEAL.ConclusionMAGO resolves the water–fat ambiguity over the entire fat fraction dynamic range without compromising accuracy, therefore enabling robust PDFF estimation where phase data is inaccessible or unreliable and complex‐based and hybrid methods fail.

Traditionally, computational design optimization of commercial aircraft is performed by considering a small number of representative operating conditions. These conditions are based on the design Mach number, altitude, payload, and range for which the aircraft will be flown. However, the design also influences which routes and mission parameters are optimal, and so there is coupling that is ignored when using the traditional approach. Here, the aircraft design, mission profiles, and the allocation of aircraft to routes in an airline network are simultaneously optimized. This is a mixed-integer nonlinear programming problem that is reformulated as a nonlinear programming problem because of the large number of design variables. The reformulated problem is solved using a gradient-based optimization approach with a parallel computational framework that facilitates the multidisciplinary analysis and the derivative computation. A surrogate model is used for the computational fluid dynamics analysis that is retrained in each optimization iteration given the new set of shape design variables. The resulting optimization problem contains over 4,000 design variables and close to 14,000 constraints. The optimization results show a 2% increase in airline profit compared with the traditional multipoint optimization approach. The wing area increases to the upper bound, enabling a higher cruise altitude that improves propulsive efficiency. This study finds that simultaneously optimizing the allocation, mission, and design to maximize airline profit results in a different optimized wing design from that resulting from the multipoint optimization approach.

A three-dimensional blade of a low solidity circular cascade diffuser in centrifugal blowers is designed by means of a multi-point optimization technique. The optimization aims at improving static pressure coefficient at a design point and at a small flow rate condition. Moreover, a clear definition of secondary flow expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three-dimensional blade reaches to 10 in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design freedom. Optimization results show clear Pareto front and selected optimum design shows good improvement of pressure rise in diffuser at small flow rate conditions. It is found that three-dimensional blade has advantage to stabilize the secondary flow effect with improving pressure recovery of the low solidity circular cascade diffuser.

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.

Erratum to: The application of the gradient-based adjoint multi-point optimization of single and double shock control bumps for transonic airfoils

Optimization of aerodynamic shapes using numerical methods has always been of engineering interest. This paper presents a highly efficient aerodynamic optimization method for hypersonic wings based on local piston theory. The objective of the optimization is to improve the aerodynamic characteristics of original airfoils or wings generated from NACA0012 while satisfying constraints on structure requirements. In the optimization procedure, a genetic algorithm is employed for optimum search, the Hicks–Henne bump function is used for airfoil geometrical modification, and local piston theory is used for unsteady pressure perturbations caused by geometrical modification from the baseline. Because unsteady pressure perturbations at supersonic or hypersonic conditions could be calculated by local piston theory based on initial flowfield results in the optimum searching process, only one steady-state solution without any use of moving or deforming grids is required. Therefore, the optimization method described in this paper is an extremely efficient technique that combines the advantages of steady computational fluid dynamics and the local piston theory and thus has very low computational cost in an optimum search process. Optimization results of airfoils and wings, including single and multipoint optimization for a flat wing without any sweep, and backswept wing, demonstrate the effectiveness and efficiency of the aerodynamic optimization method for hypersonic wings.

Three dimensional blade of a low solidity circular cascade diffuser in a centrifugal blower is successfully designed by means of multi-point optimization technique. The optimization is aiming at improving the static pressure coefficient at design point and at small flow rate condition while constraining the slope of the lift coefficient curve. Moreover, a clear definition of secondary flow which expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three dimensional blade reaches to ten in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design of freedom. Optimization results show a clear pareto front and selected optimum design shows good improvement of diffuser pressure rise at small flow rate conditions. It is found that three dimensional blade has advantage for stabilize the secondary flow effect with improving pressure recovery in the low solidity circular cascade diffuser.

Design of adaptive transonic laminar airfoils using the [formula omitted] transition model

A multipoint optimization approach is used to solve aerodynamic design problems encompassing a broad range of operating conditions in the objective function and constraints. The designer must specify the range of on-design operating conditions, the objective function to be minimized, a weighting function based on the mission or fleet requirements, and a set of performance and geometric constraints. Based on this designer input, a weighted-integral objective function is developed. The numerical optimization problem is then formulated as a constrained multipoint problem with the weight assigned to each operating condition determined by a quadrature rule. The approach is illustrated with several design problems for transonic civil transport aircraft and is extended to the formulation of aircraft range and endurance objective functions for use in the design of an unmanned aerial vehicle. The results demonstrate that the approach enables the designer to design an airfoil that is precisely tailored to the problem specification. Pareto fronts are presented as a means of providing the designer with information on tradeoffs that can be used to guide the problem specification.

This paper proposes a multi-point combinatorial optimization method based on Proximate Optimality Principle (POP), which method has several advantages for solving large-scale combinatorial optimization problems. The proposed algorithm uses not only the distance between search points but also the interaction among search points in order to utilize POP in several types of combinatorial optimization problems. The proposed algorithm is applied to several typical combinatorial optimization problems, a knapsack problem, a traveling salesman problem, and a flow shop scheduling problem, in order to verify the performance of the proposed algorithm. The simulation results indicate that the proposed method has higher optimality than the conventional combinatorial optimization methods.

Multi-Point Shape Optimization of Airfoils at Low Reynolds Numbers

Results for 2-D airfoil shape optimization in transonic regime are presented. Airfoil shapes are represented by nonuniform rational B-splines with appropriate regularity properties. A Navier-Stokes flow solver is used to compute the flow field and to obtain aerodynamic coefficients. A design of experiment is conducted to select the most sensitive design variables among the nonuniform rational B-splines parameters to reduce their number in the final optimization process. Single-point and multipoint formulations of the optimization problem are proposed and compared. The nonuniform rational B-splines parameterization guarantees smooth optimized airfoils. The multipoint optimization formulation combined with the nonuniform rational B-splines parameterization leads to airfoils with good performance over a specified Mach range.

Coach rollover is a less frequent accident characterized by a high risk of injuries for the passengers. The vehicle should absorb the impact energy by plastic deformation of the structural components it is made of. At the same time the survival space for passengers has to be preserved by avoiding the intrusion of structural components as prescribed in ECE 66 regulation. The purpose of the present study is to improve the coach design in order to guarantee the safety of belted passengers while fulfilling the requirements of the regulation. With this aim a multi-point optimization methodology has been applied on a mixed multibody and FEM model that simulates a coach module during a rollover accident. EuroSID-1 dummies have been introduced in the module for the evaluation of the passenger injury risk.

We present a new Lagrangian-based shock-e tting technique for inversely designing transonic turbomachinery cascade geometries. Thismethod, which consistsofa two-dimensional e owe eld integrator, a camberline generator, and a passage-averaged momentum/pressure boundary condition, generates a cascade geometry to match a prescribed e ow turning distribution. A complex-lamellar e ow decomposition is used, e rst to show how discontinuous geometries are created when one’ s total turning distribution is specie ed to be continuous and shock-generated entropy gradients are present and then to construct a shock-e tting treatment that actively modie es the specie ed turning distribution to counter this effect. Finally, numerical results are presented to illustrate that, with this new shock-e tting approach, our transonic cascades are both geometrically continuous and faithful to the prescribed e ow turning distribution. I. Introduction W ITH the increase in their accuracy and efe ciency, numerical simulations are now being implemented into every aspect of the aerodynamic design process. In fact, whereas they were once used mainly for generating postmortem analyses of intermediate designs, numerical methods are now being used for both design optimization 1i3 and inverse design. 4i6 Although inverse methods are often most efe cient, they require one to specify loading or pressure distributions, which, without proper judgement, can lead to poorly performing designs. Target distributions are often specie ed without any prior knowledge of their appropriateness or ability to be actively modie ed throughout the inverse design procedure. Thus, design-optimization schemes have begun to attract a tremendous amount of attention. In these schemes, one examines a large design space in hopes of identifying the optimal solution to a given number of constraints and objective functions. Unfortunately, global optimums are not easily obtained without careful construction of the appropriate geometric constraints, adjoint equations, and objective functions. 7;8 In fact, Drela 9 has shown that, whereas a multipoint optimization is needed to control both design andoff-design performances,geometries that havebeenoptimized overmultiple objectivefunctions areoftensusceptible to small-scale irregularities of signie cant consequence in viscous and transonic e ows. Thus, mixed inverse design/design optimization scheme are being developed to exploit the strengths of each of these approaches. 1;10;11 With this work we present a new Lagrangian-based shock-e tting techniqueforinverselydesigningtransonicturbomachinerycascade geometries. This technique, which is based on the inverse-design theoriesofHawthorneetal. 4 andTanetal. 12 ingeneral,andDang 5 in