Christophe Tribes

Airfoil Shape Optimization Using a Nonuniform Rational B-Splines Parametrization Under Thickness Constraint

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.

Decomposition of multidisciplinary optimization problems: formulations and application to a simplified wing design

Several formulations for solving multidisciplinary design optimization (MDO) problems are presented and applied to a test case. Two bi-level hierarchical decomposition approaches are compared with two classical single-level approaches without decomposition of the optimization problem. A methodology to decompose MDO problems and a new formulation based on this decomposition are proposed. The problem considered here for validation of the different formulations involves the shape and structural optimization of a conceptual wing model. The efficiency of the design strategies are compared on the basis of optimization results.

Airfoil Shape Optimization Using NURBS Representation Under Thickness Constraint

Results for 2D airfoil shape optimization in transonic regime are presented. A Navier-Stokes flow solver is used to compute the flow-field. Single-point and multipoint formulations of the optimization problem are proposed and compared. A NURBS representation of the airfoils allows smooth optimized airfoils to be obtained which do not experience severe performances losses in off-design condition. The multipoint formulation, combined with the NURBS representation, allows to obtain airfoils with good performance over a specific Mach range. A design of experiment is conducted to determine the most sensitive design variables in order to reduce their number in the optimization process.

Direct Search Airfoil Optimization Using Far-Field Drag Decomposition Results

For this research project, two airfoils have been optimized using a Direct Search optimization algorithm and a cost function determined from the results of a fareld drag decomposition method. The latter is a powerful tool allowing to breakdown the drag into wave, viscous, induced and spurious drags. The latter type of drag is caused by numerical and truncation errors, as well as by the addition of arti cial viscosity by most solvers to smooth strong gradients. Furthermore, the spurious drag is dependent on the con guration: a blunt body will produce more spurious drag than a slender body. Thus, if an optimization process is based on the total drag it will tend to nd a con guration that reduces among others, the spurious drag which can limit its e ciency. The optimization process in this research used the net drag only, excluding the spurious drag. First, the NACA0012 airfoil in an Euler ow at Ma = 0.85 was optimized. The nal conguration had a at nose shape and an almost constant thickness along the chord. The computed net drag was 74 d.c., an improvement of 393 d.c. An additional control optimization was done, but on the total drag. The optimized con guration was more rounded, which is a direct consequence of including the spurious drag in the objective function. This shows that the spurious drag has a large in uence on the optimum airfoil. Second, the RAE2822 airfoil in viscous ow with a constant lift coe cient of 0.824 and a Mach number of 0.734 was optimized. The nal con guration was thinner than the original airfoil on the rst 50% of the chord length, then got thicker for the rest of the chord length. The con guration also showed a cambered trailing edge typical of supercritical airfoils. The computed net drag value was 104.3 d.c., an improvement of 83 d.c. Most of the improvement had been achieved by the wave drag reduction.

Airfoil Generation and Optimization using Multiresolution B-Spline Control with Geometrical Constraints

This paper presents a scheme that combines multiresolution curve editing with linear constraints: thickness and camber. This framework allows to perform multiresolution manipulation of piecewise polynomial B-spline curves, while specifying and satisfying various constraints on the curves. An easy computable multiresolution curve editing technique is investigated for the purpose of airfoil design as a novel tool for the generation and optimization of 2D wing profile. Thickness and camber constraints imposed at several sections of the profile are incorporated into this freeform curve generating environment, as it will be shown. The aimed objective was the improvement of an aerodynamic module included into a complete wing generator designed for multidisciplinary design optimization (MDO) purposes. The behavior of the profile generator under multiresolution decomposition while applying thickness and camber constraints will be presented, as well as some geometric and aerodynamic optimization test cases involving large changes in shape. A noteworthy aspect of this technique is the possibility of using a variable number of parameters in the optimization process from low to high, and the smoothness of the profile shape obtained.

Preliminary Multidisciplinary Design Optimization System: A Software Solution for Early Gas Turbine Conception

Preliminary Multidisciplinary Design Optimization (PMDO) project addresses the development and implementation of the Multidisciplinary Design Optimization (MDO) methodology in the Concept/Preliminary stages of the gas turbine design process. These initial phases encompass a wide range of coupled engineering disciplines. The PMDO System is a software tool intended to integrate existing design and analysis tools, decompose coupled multidisciplinary problems and, therefore, allow optimizers to speed-up preliminary engine design process. The current paper is a brief presentation of the specifications for the PMDO System as well as a description of the prototype being developed and evaluated. The current assumed e xible architecture is based on three software components that can be installed on different computers: a Java/XML MultiServer, a Java Graphical User Interface and a commercial optimization software.Copyright

Framework for the Robust Design Optimization of an Airframe and its Engines

The optimization studies for the next generation of aircraft and engine families are typically associated with the insertion of technological advances to improve fuel efficiency, noise levels, and overall aircraft economics. In the conceptual study phase, the optimization process needs to address the uncertainties related to the anticipation of market requirements and potential technological advances at the time of entry into service, along with the fidelity of the modeling applied in the analysis. The current paper presents a framework using a robust design optimization methodology to mitigate these uncertainties when an airframe and its engines are designed jointly. The optimization of a seventy passenger aircraft illustrates the approach with a formulation seeking to optimize the design, while attenuating its sensitivity to the potentially adverse effects of uncertainties.

Multi-Objective Optimization of Runner Blades Using a Multi-Fidelity Algorithm

A robust multi-fidelity design optimization methodology has been developed to integrate advantages of high- and low-fidelity analyses and alleviate their weaknesses. The aim of this methodology is to reach more efficient turbine runners with respect to different constraints, in reasonable computational time and cost. In such a framework, an inexpensive low-fidelity (inviscid) solver handles most of the computational burden by providing data for the optimizer to evaluate objective functions and constraint values in the low-fidelity phase. An open-source derivative-free optimizer, NOMAD, explores the search space. Promising candidates are selected among all feasible solutions using a filtering process. The proposed filtering process accounts for Pareto optimal solutions and considers solutions which are different in the design variable space and are dominant in their local territories. A high-fidelity (viscous) solver is used outside the optimization loop to accurately evaluate filtered solutions. Accurate information achieved by high-fidelity analyses is also employed to recalibrate the low-fidelity optimization.The developed methodology demonstrated its ability to redesign a Francis turbine blade for a given best efficiency operating condition. The original and optimized cases were evaluated and compared for a complete range of operating conditions by calculating the efficiency curves and losses of different components. The optimal blade has provided an efficient runner for the given operating conditions considering the design constraints.Copyright

Multi-fidelity design optimization of Francis turbine runner blades

A robust multi-fidelity design algorithm has been developed, focusing to efficiently handle industrial hydraulic runner design considerations. The computational task is split between low- and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a derivative-free optimization method employs an inviscid flow solver to obtain the major desired characteristics of a good design in a relatively fast iterative process. A limited number of candidates are selected among feasible optimization solutions by a newly developed filtering process. The main function of the filtering process is to select some promising candidates to be sent into the high-fidelity phase, which have significantly different geometries, and also are dominant in their own territories. The high-fidelity phase aims to accurately evaluate those promising candidates in order to select the one which is closest to design targets. A low-head runner case study has shown the ability of this methodology to identify an optimized blade through a relatively low computational effort, which is significantly different from the base geometry.

GATE: a genetic algorithm designed for expensive cost functions

The present paper introduces the GATE algorithm, which was specifically designed to lessen the cost of GAs for engineering design problems. The main strength of the algorithm is to find a good design using a relatively low number of function evaluations. The heart of the algorithm is a new heuristic called territorial core evolution (TE). TE regulates the mean step and the permitted search area of the GAs’ random search operators, depending on the state of convergence of the algorithm. As a result, more global or more local searches are made when necessary to better fit the specificities of each problem. GATE, which was initially calibrated using a Gaussian landscape generator as test case, is shown to be very efficient to solve that kind of topology, especially for large scale problems. Application of the GATE algorithm to various classical test cases allows a better understanding of the strengths and limitations of this algorithm.