Aerodynamic Optimization of Car Shapes Using the Continuous Adjoint Method and an RBF Morpher

Papoutsis‐Kiachagias, Evangelos M.; Porziani, Stefano; Groth, Corrado; Biancolini, Marco Evangelos; Costa, Emiliano; Giannakoglou, Kyriakos C.

doi:10.1007/978-3-319-89988-6_11

Cited by 13 publications

(11 citation statements)

References 17 publications

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“…By determining € x 1 from equation (1) and substituting it in equation (2), the error dynamics can be written as…”

Section: Sliding Mode Controller Designmentioning

confidence: 99%

“…In recent decades, the automotive industry has witnessed rapid progress, and several studies in the cases of design of car shape based on aerodynamic optimization [1], [2], optimization of the air intake system of the engine [3], investigation of sound quality for passenger car [4], stress analysis and design improvement of door hinge for compact cars [5], study of fuel consumption for various driving styles in conventional and hybrid electric vehicles [6,7], design optimization of the cowl cross bar-light [8], investigation of a rear independent suspension for light vehicle [9], and study of nonlinear control of suspension system [10][11][12] have been conducted to develop and optimize different aspects of vehicle performance. e suspension system is one of the main components of a car which plays an important role in providing passenger comfort.…”

Section: Introductionmentioning

confidence: 99%

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Applied Mechatronics: Designing a Sliding Mode Controller for Active Suspension System

Azizi

Mobki

2021

Complexity

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The suspension system is referred to as the set of springs, shock absorbers, and linkages that connect the car to the wheel system. The main purpose of the suspension system is to provide comfort for the passengers, which is created by reducing the effects of road bumpiness. It is worth noting that reducing the effects of such vibrations also diminishes the noise and undesirable sound as well as the effects of fatigue on mechanical parts of the vehicle. Due to the importance of the abovementioned issues, the objective of this article is to reduce such vibrations on the car by implementing an active control method on the suspension system. For this purpose, a conventional first-order sliding mode controller has been designed for stochastic control of the quarter-car model. It is noteworthy that this controller has a significant ability to overcome the stochastic effects, uncertainty, and deal with nonlinear factors. To design a controller, the governing dynamical equation of the quarter-car system has been presented by considering the nonlinear terms in the springs and shock absorber, as well as taking into account the uncertainty factors in the system and the actuator. The design process of the sliding mode controller has been presented and its stability has been investigated in terms of the Lyapunov stability. In the current research, road surface variations are considered as Gaussian white noise. The dynamical system behavior for controlled and uncontrolled situations has been simulated and the extracted results have been presented. Besides, the effects of existing uncertainty in the suspension system and actuator have been evaluated and controller robustness has been checked. Also, the obtained quantitative and qualitative compressions have been presented. Moreover, the effect of controller parameters on the basin of attraction set and its extensiveness has been assessed. The achieved results have indicated the good performance and significant robustness of the designed controller to stabilize the suspension system and mitigate the effects of road bumpiness in the presence of uncertainty and noise factors.

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“…By determining € x 1 from equation (1) and substituting it in equation (2), the error dynamics can be written as…”

Section: Sliding Mode Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Applied Mechatronics: Designing a Sliding Mode Controller for Active Suspension System

Azizi

Mobki

2021

Complexity

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“…The mesh with ∼4.2 × 10 6 nodes, ∼3.58 × 10 5 of which are surface mesh nodes, consists of various types of elements, with up to 22-face polyhedra. The reference mesh is displaced to the deformed one, as a result of a shape optimization for minimizing drag [52] (not included in the paper). Mesh quality metrics are listed in Table 4.…”

Section: Parametric Study On the Predictor Matrix Sizementioning

confidence: 99%

A two–step radial basis function-based CFD mesh displacement tool

Gagliardi

Giannakoglou

2019

Advances in Engineering Software

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Mesh displacement based on Radial Basis Functions (RBF) interpolation is known for its ability to preserve the validity and quality of the mesh, even for large displacements, without being affected by mesh connectivity. However, in the case of large meshes, such as those used in real-world Computational Fluid Dynamics (CFD) applications, RBF interpolation, in its standard formulation, becomes excessively expensive. This paper proposes a cost reduction technique for mesh displacement based on RBF, by splitting the process into two steps. In the first step, named predictor, a data reduction algorithm that adaptively agglomerates mesh boundary nodes by reducing the RBF interpolation problem size is used. Upon completion of the first step, due to the agglomeration and the fact that the RBF interpolation is applied to the boundary nodes too, the so-displaced boundaries do not match the given displacements; thus, the position of the boundary nodes must be corrected during the second step, named corrector. The latter performs a local deformation based on RBF kernels with local support, to make the boundary conform to the known displacements of its nodes. The proposed method is accelerated by employing the Sparse Approximate Inverse preconditioner based on geometrical considerations and the Fast Multipole Method. The method and the programmed software are validated on three test cases related to the deformation of CFD meshes inside a duct and a turbine stator row as well as around a car model.

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“…A variety of stochastic and gradient‐based methods have been devised to solve aerodynamic shape optimization problems such as the design of ducts or manifolds for minimum power losses, cars with optimal combination of drag and lift, 1 aircraft/wings for maximum lift 2,3 or minimum drag, 4 and so forth. During the optimization, a technique to deal with the necessary changes of the boundaries (surface mesh), namely, to adapt the computational mesh (volume mesh) to the updated geometry, is required.…”

Section: Introductionmentioning

confidence: 99%

Finite transformation rigid motion mesh morpher; A grid deformation approach

Liatsikouras

Fougeron

Eleftheriou

et al. 2020

Numerical Methods in Fluids

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Summary In any shape optimization framework and specifically in the context of computational fluid dynamics, a robust and reliable grid deformation tool is necessary to undertake the adaptation of the computational mesh to the updated boundaries at each optimization cycle. Grid deformation has its share of challenges, namely, to maintain high mesh quality (avoid distorted elements and tangles) even when dealing with extreme deformations. In this work a novel grid deformation algorithm, the finite transformation rigid motion mesh morpher (FT‐R3M) is proposed. FT‐R3M is essentially a mesh‐free grid deformation approach, since it does not require any inertial quantities and it gracefully propagates the movement of the boundaries (surface mesh) to the internal nodes of the mesh (volume mesh), by keeping the motion of its parts (referred to as stencils) as‐rigid‐as‐possible. It is an optimization‐based method, which means that the interior nodes of the computational mesh are displaced to minimize a distortion metric related to the elastic deformation energy, by favoring rigidity in critical directions, thus being able to handle mesh anisotropies very efficiently. Results are presented for three test cases; a rotated airfoil with a mesh appropriate for viscous flow; a simulation of a low Reynolds duct case; a beam.

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Aerodynamic Optimization of Car Shapes Using the Continuous Adjoint Method and an RBF Morpher

Cited by 13 publications

References 17 publications

Applied Mechatronics: Designing a Sliding Mode Controller for Active Suspension System

Applied Mechatronics: Designing a Sliding Mode Controller for Active Suspension System

A two–step radial basis function-based CFD mesh displacement tool

Finite transformation rigid motion mesh morpher; A grid deformation approach

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