Robust design in aerodynamics using third‐order sensitivity analysis based on discrete adjoint. Application to quasi‐1D flows

Papoutsis‐Kiachagias, Evangelos M.; Papadimitriou, Dimitrios; Giannakoglou, Kyriakos C.

doi:10.1002/fld.2604

Cited by 19 publications

(18 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. The computation of the second and third-order sensitivity derivatives is presented in detail in [24][25][26]. For instance, in the discrete sense, the highest-order derivative…”

Section: Robust Shape Optimization Using Third-order Sensitivitiesmentioning

confidence: 99%

Aerodynamic Shape Optimization Using “Turbulent” Adjoint And Robust Design in Fluid Mechanics

Giannakoglou

Papadimitriou

Papoutsis‐Kiachagias

et al. 2015

Computational Methods in Applied Sciences

View full text Add to dashboard Cite

This article presents adjoint methods for the computation of the firstand higher-order derivatives of objective functions F used in optimization problems governed by the Navier-Stokes equations in aero/hydrodynamics. The first part of the chapter summarizes developments and findings related to the application of the continuous adjoint method to turbulence models, such as the Spalart-Allmaras and k-ε ones, in either their low-or high-Reynolds number (with wall functions) variants. Differentiating the turbulence model, over and above to the differentiation of the mean-flow equations, leads to the computation of the exact gradient of F, by overcoming the frequently made assumption of neglecting turbulence variations. The second part deals with higher-order sensitivity analysis based on the combined use of the adjoint approach and the direct differentiation of the governing PDEs. In robust design problems, the so-called second-moment approach requires the computation of second-order derivatives of F with respect to (w.r.t.) the environmental or uncertain variables; in addition, any gradient-based optimization algorithm requires third-order mixed derivatives w.r.t. both the environmental and design variables; various ways to compute them are discussed and the most efficient is adopted. The equivalence of the continuous and discrete adjoint for this type of computations is demonstrated. In the last part, some other relevant recent achievements regarding the adjoint approach are discussed. Finally, using the aforementioned adjoint methods, industrial geometries are optimized. The application domain includes both incompressible or compressible fluid flow applications.

show abstract

“…. The computation of the second and third-order sensitivity derivatives is presented in detail in [24][25][26]. For instance, in the discrete sense, the highest-order derivative…”

Section: Robust Shape Optimization Using Third-order Sensitivitiesmentioning

confidence: 99%

Aerodynamic Shape Optimization Using “Turbulent” Adjoint And Robust Design in Fluid Mechanics

Giannakoglou

Papadimitriou

Papoutsis‐Kiachagias

et al. 2015

Computational Methods in Applied Sciences

View full text Add to dashboard Cite

show abstract

“…the design variablesb, which means that third-order mixed derivatives of F w.r.t the environmental (twice) and the design variables (once) are required. This has been presented, for the first time in the literature, by the NTUA group in [9,11]. In this work, the computation of theμ F andˆ F relies on the PCE technique [1,12].…”

Section: Introductionmentioning

confidence: 99%

“…To decrease the cost of MC, techniques such as Quasi-MC [7] and Latin-Hypercube Sampling [8] have been developed. On the other hand, a rival method to cope with the same problem is the Method of Moments [9], in which the adjoint method [10] and direct differentiation are used to compute up to second-order derivatives of F with respect to (w.r.t.) the environmental variablesc in order to get the first two statistical moments of F with second-order accuracy.…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic Shape Optimization Under Flow Uncertainties Using Non-Intrusive Polynomial Chaos and Evolutionary Algorithms

Liatsikouras¹,

Asouti²,

Giannakoglou³

et al. 2017

Proceedings of the 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

View full text Add to dashboard Cite

Abstract. The existence of uncertainties, associated with the operating conditions or manufacturing imperfections, occur quite often in aerodynamic optimization problems. In this paper, a workflow for shape optimization in the presence of environmental uncertain flow conditions, varying stochastically around an average value with an a-priori known standard deviation, is presented. To do so, the Uncertainty Quantification (UQ) for the objective function needs to be carried out. This is based on the non-intrusive Polynomial Chaos Expansion (niPCE) method [1], which allows for a controllable number of calls to the CFD tool used to evaluate each candidate solution, compared to other sampling methods such as Monte-Carlo. Within the proposed workflow, PCE is combined with the optimization platform EASY (Evolutionary Algorithms SYstem) [2], which undertakes the optimization task. The overall process is fully automated. The shape under consideration is parameterized using CAD-free approaches, such as Radial Basis Function techniques or the combined use of two cages and the corresponding Harmonic Coordinates, which are responsible only for surface deformations whereas, as it will be explained below, other morphing/smoothing [3] tool undertakes the adaptation of the CFD mesh to the updated boundaries at each optimization cycle. The PCE method selects the points (Gaussian nodes) in the design space to be evaluated and the computed performance metrics are integrated with weights indicated by the Gauss integration rules, in order to compute the mean value and standard deviation of the objective function of the flow problem under uncertainties. The aforementioned tools are applied in two problems, in which OpenFOAM is the CFD evaluation software.

show abstract

“…These are based on the minimization of the mean value and standard deviation of F computed using surrogate models [7,8], the method of moments [9][10][11], or the numerical integration of a limited number of evaluated points [12][13][14]. The results of several runs of the gradient-based optimization algorithm are put together in a single plot to form the optimal Pareto front of non-dominated solutions on the plane of mean value and standard deviation of F. This paper is an extension of a recent publication by the same authors [42]. Robust design methods for multi-objective six sigma design using evolutionary algorithms can also be found [18,19].…”

mentioning

confidence: 99%

“…Methods including Taguchi or Monte Carlo techniques have also been proposed [15][16][17]. In [42], the computation of up-to third-order sensitivities was presented only for one-dimensional problems (here, this is extended to 2D problems). A multi-objective robust design algorithm, based on the Kriging model, for minimum mean value and standard deviation of the drag coefficient of an airfoil is presented in [20].…”

mentioning

confidence: 99%

Third‐order sensitivity analysis for robust aerodynamic design using continuous adjoint

Papadimitriou

Giannakoglou

2012

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

SUMMARY Robust design problems in aerodynamics are associated with the design variables, which control the shape of an aerodynamic body, and also with the so‐called environmental variables, which account for uncertainties. In this kind of problems, the set of design variables, which leads to optimal performance, taking into account possible variations in the environmental variables, is sought. One of the possible ways to solve this problem is by means of the second‐order second‐moment approach, which requires first‐order and second‐order derivatives of the objective function with respect to the environmental variables. Should the minimization problem be solved using a gradient‐based method, algorithms for the computation of up to third‐order sensitivity derivatives (twice with respect to the environmental variables and once with respect to the shape controlling design variables) must be devised. In this paper, a combination of the continuous adjoint variable method and direct differentiation to compute the third‐order sensitivities is proposed. This is shown to be the most efficient among all alternative methods provided that the environmental variables are much less than the design ones. Apart from presenting the method formulation, this paper focuses on the assessment of the so‐computed up‐to third‐order mixed derivatives through comparison with costly finite‐difference schemes. To this end, the robust design of a two‐dimensional duct is performed. Then, using the validated method, the robust design of a two‐dimensional cascade airfoil is demonstrated. Although both cases are handled as inverse design problems, the method can be extended to other objective functions or three‐dimensional problems in a straightforward manner. Copyright © 2012 John Wiley & Sons, Ltd.

show abstract

Robust design in aerodynamics using third‐order sensitivity analysis based on discrete adjoint. Application to quasi‐1D flows

Cited by 19 publications

References 37 publications

Aerodynamic Shape Optimization Using “Turbulent” Adjoint And Robust Design in Fluid Mechanics

Aerodynamic Shape Optimization Using “Turbulent” Adjoint And Robust Design in Fluid Mechanics

Aerodynamic Shape Optimization Under Flow Uncertainties Using Non-Intrusive Polynomial Chaos and Evolutionary Algorithms

Third‐order sensitivity analysis for robust aerodynamic design using continuous adjoint

Contact Info

Product

Resources

About