### Grant Program

Faculty Development Competitive Research Grant Program 2018-2020

### Project Description

The present research proposal focuses on the development of computational tools for optimizing the design of aeronautical and marine/maritime functional free-form surfaces, such as airfoils/hydrofoils, wings, blades, and propellers. As a common feature, the functionality of these products depends on their shape and even small variations of it may have significant impact on their performance. The goal of this proposal is to develop seamlessly integrated advanced tools for modeling and simulation, targeting the materialization of the design-through-analysis concept, which nowadays constitutes a prerequisite for efficient PLM (Product Lifecycle Management) in all industrial sectors producing highly-complex products.

Traditional analysis, via standard computational meshes, e.g., finite elements or boundary elements, approximates the body/surface geometry and consequently introduces errors in simulation results, especially in challenging, shape-sensitive applications. Hence, an approach that secures an exact representation of the employed surface/body geometry during the numerical simulation phase is crucial for the achievement of adequate accuracy and precision. This becomes even more important if – and this is likely to be the case in contemporary industrial practice - the simulation is to be subsequently used in an optimization loop, where it is essential to have an automated, direct, and accurate link between design parameters of the exact geometry and simulation results. Unfortunately, analysis-suitable models are not automatically created or readily meshed from CAD (Computer Aided Design) geometry. As Ted Blacker, Manager of Simulation Sciences at Sandia National Laboratories US, reports, the mesh-generation accounts for about 20% of overall analysis time, whereas creation of the analysis-suitable geometry requires about 60%, and only 20% of overall time is devoted to analysis per se. Although the report corresponds to Sandia Laboratories, this 80/20 modeling/analysis ratio seems to be a very common industrial experience, and there is a strong desire to reverse it; see also [Cottrel et. al., 2009]

Computational tools that represent body shapes exactly, securing in this way that mesh generation is an error-free process from the geometric point of view, provide users with great promise and researchers with an analogously great challenge. The idea of bridging the gap between CAD and Analysis (simulation tools) has recently gained a significant momentum, which was initiated by the introduction of the IsoGeometric Analysis (IGA) approach, suggested by [Hughes et. al., 2005]. With this proposal, we want to take up this idea and demonstrate its efficiency in aeronautical, shipbuilding and power generation technologies and especially in the problems of shape optimization, starting from 2D airfoils/hydrofoils and extending our framework to 3D applications involving wind/tidal turbine blades, marine propellers and lifting appendages near the water free surface.

IGA method can be accomplished by extending the isoparametric concept in Finite-Element and Boundary-Element Methods (FEM, BEM) via adopting bases, such as Bézier, B-splines and NURBS (Non-Uniform Rational B-Splines). NURBS representation constitutes the de-facto industrial standard and thus, IGA-based computational tools can guarantee exact geometric representation of all products generated by contemporary CAD systems. Furthermore, more general basis functions have been recently introduced, advancing the coverage and efficiency of IGA. These bases include the so-called T-splines [Sederberg et. al., 2003, Bazilevs et. al., 2010] and PHT-splines (Polynomial splines over Hierarchical T-meshes) [Deng et. al., 2008] among others, which, in contrast with the global nature of tensor-product single or multi-patch NURBS, allow for local refinement. This in turn leads to significantly lower numbers of Degrees–of–Freedom (DoF) for modeling the same geometry and guarantees improved smoothness since T-splines can represent highly complex geometries as a single surface patch. In summary, the combination of IGA method with NURBS secures the exact representation of model geometry at the coarsest level of discretization, thus eliminating geometry approximation errors from the very beginning of the numerical scheme. At the same time, using the very same NURBS basis for approximating the physical quantities of interest, we expect good convergence rates and smoothness in the representation of the numerical solution; see e.g., [Politis et. al., 2009]. Furthermore, employing more modern geometry representations, such as T-splines, allows the achievement of improved convergence rates and higher smoothness level of the numerical solution with a lower number of DoF, which is very advantageous for the performance and computational cost of the process; see e.g., [Ginnis et. al., 2014]. IGA method has been so far mainly applied in FEM context, which requires exact representation of the corresponding volumetric domain (for 3D problems), although CAD systems usually adopt the B-rep (Boundary-representation) approach for representing solids. Different methods for volumetric parameterization have been proposed, e.g., lofting, swept-volume parameterization, Coons patches, etc. Nevertheless, there is a lack of mature (robust and efficient) techniques for representing volumetrically complex domains. To bypass the need for domain parameterization, a rather new approach to isogeometric analysis, based on a Boundary Integral Equation (BIE) formulation of the considered problem, can be used. In the context of this formulation, the governing equations and the boundary conditions of the problem are transformed, using a fundamental solution of it, into an integral equation on the body boundary and, possibly, on other boundaries of the domain. This approach is widely used in free-surface hydrodynamics, and especially in potential-flow problems, due to the infinite extent of the fluid domain. Adopting this approach, namely developing a NURBS/T-spline based Isogeometric Boundary Element Method for potential-flow problems, is the key scope of this proposal that can be itemized in the following objectives:

1.To establish new BEM tools for assessing the design of aeronautical and marine/maritime functional free-form surfaces (airfoils/hydrofoils, wind/tidal turbine blades and marine propellers) based on IsoGeometric Analysis (IGA).

2.To achieve a seamless integration of Computer-Aided-Design (CAD) and numerical-simulation tools by exploiting NURBS and T-splines technology for the exact and low-cost representation of complex geometries.

3.To establish an optimization framework that allows the automatic shape optimization of the geometric entities under investigation.

4.To apply these tools in design, simulation, and optimization of functional free-form surfaces, which are of significance in aeronautical, shipbuilding and green energy technologies.

5.To demonstrate the enhanced properties of the adopted approach through software prototypes for optimizing the performance of airfoils/hydrofoils, wind/tidal turbine blades and marine propellers.

Traditional analysis, via standard computational meshes, e.g., finite elements or boundary elements, approximates the body/surface geometry and consequently introduces errors in simulation results, especially in challenging, shape-sensitive applications. Hence, an approach that secures an exact representation of the employed surface/body geometry during the numerical simulation phase is crucial for the achievement of adequate accuracy and precision. This becomes even more important if – and this is likely to be the case in contemporary industrial practice - the simulation is to be subsequently used in an optimization loop, where it is essential to have an automated, direct, and accurate link between design parameters of the exact geometry and simulation results. Unfortunately, analysis-suitable models are not automatically created or readily meshed from CAD (Computer Aided Design) geometry. As Ted Blacker, Manager of Simulation Sciences at Sandia National Laboratories US, reports, the mesh-generation accounts for about 20% of overall analysis time, whereas creation of the analysis-suitable geometry requires about 60%, and only 20% of overall time is devoted to analysis per se. Although the report corresponds to Sandia Laboratories, this 80/20 modeling/analysis ratio seems to be a very common industrial experience, and there is a strong desire to reverse it; see also [Cottrel et. al., 2009]

Computational tools that represent body shapes exactly, securing in this way that mesh generation is an error-free process from the geometric point of view, provide users with great promise and researchers with an analogously great challenge. The idea of bridging the gap between CAD and Analysis (simulation tools) has recently gained a significant momentum, which was initiated by the introduction of the IsoGeometric Analysis (IGA) approach, suggested by [Hughes et. al., 2005]. With this proposal, we want to take up this idea and demonstrate its efficiency in aeronautical, shipbuilding and power generation technologies and especially in the problems of shape optimization, starting from 2D airfoils/hydrofoils and extending our framework to 3D applications involving wind/tidal turbine blades, marine propellers and lifting appendages near the water free surface.

IGA method can be accomplished by extending the isoparametric concept in Finite-Element and Boundary-Element Methods (FEM, BEM) via adopting bases, such as Bézier, B-splines and NURBS (Non-Uniform Rational B-Splines). NURBS representation constitutes the de-facto industrial standard and thus, IGA-based computational tools can guarantee exact geometric representation of all products generated by contemporary CAD systems. Furthermore, more general basis functions have been recently introduced, advancing the coverage and efficiency of IGA. These bases include the so-called T-splines [Sederberg et. al., 2003, Bazilevs et. al., 2010] and PHT-splines (Polynomial splines over Hierarchical T-meshes) [Deng et. al., 2008] among others, which, in contrast with the global nature of tensor-product single or multi-patch NURBS, allow for local refinement. This in turn leads to significantly lower numbers of Degrees–of–Freedom (DoF) for modeling the same geometry and guarantees improved smoothness since T-splines can represent highly complex geometries as a single surface patch. In summary, the combination of IGA method with NURBS secures the exact representation of model geometry at the coarsest level of discretization, thus eliminating geometry approximation errors from the very beginning of the numerical scheme. At the same time, using the very same NURBS basis for approximating the physical quantities of interest, we expect good convergence rates and smoothness in the representation of the numerical solution; see e.g., [Politis et. al., 2009]. Furthermore, employing more modern geometry representations, such as T-splines, allows the achievement of improved convergence rates and higher smoothness level of the numerical solution with a lower number of DoF, which is very advantageous for the performance and computational cost of the process; see e.g., [Ginnis et. al., 2014]. IGA method has been so far mainly applied in FEM context, which requires exact representation of the corresponding volumetric domain (for 3D problems), although CAD systems usually adopt the B-rep (Boundary-representation) approach for representing solids. Different methods for volumetric parameterization have been proposed, e.g., lofting, swept-volume parameterization, Coons patches, etc. Nevertheless, there is a lack of mature (robust and efficient) techniques for representing volumetrically complex domains. To bypass the need for domain parameterization, a rather new approach to isogeometric analysis, based on a Boundary Integral Equation (BIE) formulation of the considered problem, can be used. In the context of this formulation, the governing equations and the boundary conditions of the problem are transformed, using a fundamental solution of it, into an integral equation on the body boundary and, possibly, on other boundaries of the domain. This approach is widely used in free-surface hydrodynamics, and especially in potential-flow problems, due to the infinite extent of the fluid domain. Adopting this approach, namely developing a NURBS/T-spline based Isogeometric Boundary Element Method for potential-flow problems, is the key scope of this proposal that can be itemized in the following objectives:

1.To establish new BEM tools for assessing the design of aeronautical and marine/maritime functional free-form surfaces (airfoils/hydrofoils, wind/tidal turbine blades and marine propellers) based on IsoGeometric Analysis (IGA).

2.To achieve a seamless integration of Computer-Aided-Design (CAD) and numerical-simulation tools by exploiting NURBS and T-splines technology for the exact and low-cost representation of complex geometries.

3.To establish an optimization framework that allows the automatic shape optimization of the geometric entities under investigation.

4.To apply these tools in design, simulation, and optimization of functional free-form surfaces, which are of significance in aeronautical, shipbuilding and green energy technologies.

5.To demonstrate the enhanced properties of the adopted approach through software prototypes for optimizing the performance of airfoils/hydrofoils, wind/tidal turbine blades and marine propellers.

Status | Active |
---|---|

Effective start/end date | 3/20/18 → 12/31/20 |

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Shape optimization

Splines

Geometry

Hydrofoils

Propellers

Computer aided design

Airfoils

Parameterization

Turbomachine blades

Mesh generation

Turbines

Shipbuilding

Potential flow

Boundary element method

Computer aided analysis

Boundary integral equations

Computer simulation

Integral equations

Power generation

Tensors