Free-form Deformation Technique Research Articles

Automated shape and thickness optimization for non-matching isogeometric shells using free-form deformation

AbstractIsogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analysis model by employing non-uniform rational B-splines (NURBS) as basis functions. However, structural optimization for real-world CAD geometries consisting of multiple non-matching NURBS patches remains a challenging task. In this work, we propose a unified formulation for shape and thickness optimization of separately parametrized shell structures by adopting the free-form deformation (FFD) technique, so that continuity with respect to design variables is preserved at patch intersections during optimization. Shell patches are modeled with isogeometric Kirchhoff–Love theory and coupled using a penalty-based method in the analysis. We use Lagrange extraction to link the control points associated with the B-spline FFD block and shell patches, and we perform IGA using the same extraction matrices by taking advantage of existing finite element assembly procedures in the FEniCS partial differential equation (PDE) solution library. Moreover, we enable automated analytical derivative computation by leveraging advanced code generation in FEniCS, thereby facilitating efficient gradient-based optimization algorithms. The framework is validated using a collection of benchmark problems, demonstrating its applications to shape and thickness optimization of aircraft wings with complex shell layouts.

Optimization and numerical investigation of combined design of blade and endwall on rotor 67

Abstract In this work, a combined design of blade and endwall using the Extended Free Form Deformation technique is proposed and implemented on a transonic compressor rotor (the NASA Rotor 67). The best combined design is explored by numerical investigations and optimization via Kriging surrogate model method. As a result, by only modifying the hub and blade under 15 % span, the peak adiabatic efficiency is increased by 0.4 % and the overall aerodynamic performance for all operating conditions is also improved. An analysis shows that the enlarged dihedral angle between the hub and blade restrains boundary layer intersection and development. Meanwhile, the optimized hub changes the pressure distribution and prevents migration of cross-flow. As a result, the low-energy flow in the corner is accelerated downstream and the separation is limited, leading to an effective improvement in throughflow capability and aerodynamic performance in the corner region.

Multi-objective shape optimization of doubly offset serpentine diffuser using Adjoint method

Doubly offset serpentine diffusers are needed in the compact designs of modern stealth fighters with highly integrated propulsion systems. In addition, these doubly offset serpentine diffusers are also essential to provide reduced radar cross-section (RCS) due to the blockage of a complete line of sight. In this research, shape optimization of the doubly offset serpentine diffuser is achieved using a multi-objective approach to maximize the pressure recovery (PR) and minimize the flow swirl angle (α) and distortion coefficient (DC) at the aerodynamic interface plane (AIP). A computationally efficient Adjoint-based method was implemented for the optimization. For baseline geometry, an additional offset is added to NASA’s M2129 single serpentine duct to make it doubly offset serpentine diffusers. The freeform deformation technique was used to parametrize the baseline shape using 180 control points. A steady-state flow solution through the diffuser was achieved by solving Reynolds-Averaged Navier-Stokes (RANS) equations using a general-purpose computational analysis tool, i.e., ANSYS Fluent. The sensitivity of objective functions from the Adjoint solver was used to compute the required design change in the direction of minima or maxima of the objective functions using the steepest descent optimization technique. Subsequently, the calculated design changes were implemented through mesh Morpher. The Adjoint-based approach and freeform deformation resulted in a powerful and efficient optimization framework. The optimized shape showed a significant reduction in distortion coefficient and flow swirl angle, along with a slight increase in pressure recovery.

Data-Driven Reduced Order Modelling for Patient-Specific Hemodynamics of Coronary Artery Bypass Grafts with Physical and Geometrical Parameters

In this work the development of a machine learning-based Reduced Order Model (ROM) for the investigation of hemodynamics in a patient-specific configuration of Coronary Artery Bypass Graft (CABG) is proposed. The computational domain is referred to left branches of coronary arteries when a stenosis of the Left Main Coronary Artery (LMCA) occurs. The method extracts a reduced basis space from a collection of high-fidelity solutions via a Proper Orthogonal Decomposition (POD) algorithm and employs Artificial Neural Networks (ANNs) for the computation of the modal coefficients. The Full Order Model (FOM) is represented by the incompressible Navier-Stokes equations discretized using a Finite Volume (FV) technique. Both physical and geometrical parametrization are taken into account, the former one related to the inlet flow rate and the latter one related to the stenosis severity. With respect to the previous works focused on the development of a ROM framework for the evaluation of coronary artery disease, the novelties of our study include the use of the FV method in a patient-specific configuration, the use of a data-driven ROM technique and the mesh deformation strategy based on a Free Form Deformation (FFD) technique. The performance of our ROM approach is analyzed in terms of the error between full order and reduced order solutions as well as the speed-up achieved at the online stage.

Aerodynamic Shape Optimization of an Aircraft Propulsor Air Intake with Boundary Layer Ingestion

The growth of the airline industry has highlighted the need for more environmentally conscious aviation, leading to the conceptualization of more fuel-efficient aircraft. One concept that has received significant attention and has been associated with improved fuel efficiency is the boundary layer ingesting (BLI) propulsion system, which refers to the ingesting of the aircraft wake by the propulsors. Although BLI has theoretically been proven to reduce fuel burn, this can potentially be offset by the reduced efficiency and stability experienced by the propulsor in the presence of distorted inflow. Therefore, engine intakes must be optimized in order to mitigate the effects of BLI on the propulsion system. In this work, the shape optimization of a BLI intake is investigated using a free-form deformation technique in combination with a multi-objective genetic algorithm, in order to minimize pressure losses and distortion at the engine inlet. The optimization is performed on an S-duct intake at a cruise altitude of approximately 37,000 feet and a free stream Mach number of 0.7. An optimization strategy was developed for the task which was able to produce a Pareto optimal set of designs with improved pressure recovery and distortion. The general trend of the optimal designs shows that to reduce distortion the optimizer accelerates the flow to reduce the size of the low total pressure region and increase the dynamic pressure at the engine inlet. In contrast, the pressure recovery was increased by reducing velocity as well as shifting the maximum velocity region to the outlet, which reduces the viscous dissipation losses within the intake. The final result is a fully autonomous optimization strategy resulting in reduced pressure losses and reduced distortion leading to higher efficiency BLI S-duct intake designs.

Large eddy simulation and combined control of corner separation in a compressor cascade

Due to the demand for higher aerodynamic performance of compressors, thoroughly investigating the high-loss flow in the corner region and effectively controlling it are important. In this paper, a novel parameterization method based on the extended free form deformation (EFFD) technique and the constraints for EFFD's control points is proposed. Then, considering the features of typical control techniques and the degrees of freedom of both the blade and hub geometries, the combined control approach is implemented in the corner region of a linear cascade. Furthermore, large eddy simulation is used to simulate the flow, verify the effects of the combined control approach, and explore the underlying physical mechanisms of corner separation. The numerical results show that the combined control can significantly decrease the mean total pressure loss. The loss reduction at the design point reaches 6.05%, while it decreases by almost 2.5% near the stall/blockage operating conditions. The combined control increases the radial pressure gradient at the rear of the blade by depressing the hub and stretching the suction surface. Consequently, although the radial flow slightly increases the mixing loss in the mainstream at large incidences, the accumulation of low-energy flow in the boundary layer and the corresponding development of the corner vortex are significantly restrained. Moreover, by redistributing the static pressure on the hub, the combined control weakens the migration of crossing flow and obstructs the low-velocity flow from the pressure side involved in the separation. Overall, the combined control contributes to reducing the corner separation and improving the aerodynamic performance.

Shape optimization of airfoil in ground effect based on free-form deformation utilizing sensitivity analysis and surrogate model of artificial neural network

Wings operate in proximity to surfaces for using ground effect to enhance lift-to-drag ratio, but the stability meets challenges. Changing airfoil shape could satisfy the requirement of stability and maximize lift-to-drag ratio, like performing single-objective optimization under a constraint. This research uses free-form deformation technique to adjust the airfoil curve by control points, and reduces the dimension of control variables by sensitivity analysis. Sampling airfoils and corresponding aerodynamics feeds an artificial neural network. Then, the neural network plays as a surrogate to predict fitness value for genetic algorithm execution. It is found that lift-to-drag ratio and static stability height are sensitive to vertical adjustments near the leading edge, one quarter chord point and trailing edge. The trained two-hidden-layer MLP generalizes well. The deformed optimum airfoil with S-shape camber line reduces lift-to-drag ratio to gain adequate static stability. The cause is that the aerodynamic center of pitch and that of altitude are moved upstream together, while the former’s interval is longer than the latter’s. The procedure provides reference for the optimization of airfoil under more states in ground effect zone, and the S-type deformation offers guidance for refinement on wing-in-ground stability.

A Sequential Approach for Aerodynamic Shape Optimization with Topology Optimization of Airfoils

The objective of this work is to study the coupling of two efficient optimization techniques, Aerodynamic Shape Optimization (ASO) and Topology Optimization (TO), in 2D airfoils. To achieve such goal two open-source codes, SU2 and Calculix, are employed for ASO and TO, respectively, using the Sequential Least SQuares Programming (SLSQP) and the Bi-directional Evolutionary Structural Optimization (BESO) algorithms; the latter is well-known for allowing the addition of material in the TO which constitutes, as far as our knowledge, a novelty for this kind of application. These codes are linked by means of a script capable of reading the geometry and pressure distribution obtained from the ASO and defining the boundary conditions to be applied in the TO. The Free-Form Deformation technique is chosen for the definition of the design variables to be used in the ASO, while the densities of the inner elements are defined as design variables of the TO. As a test case, a widely used benchmark transonic airfoil, the RAE2822, is chosen here with an internal geometric constraint to simulate the wing-box of a transonic wing. First, the two optimization procedures are tested separately to gain insight and then are run in a sequential way for two test cases with available experimental data: (i) Mach 0.729 at α=2.31°; and (ii) Mach 0.730 at α=2.79°. In the ASO problem, the lift is fixed and the drag is minimized; while in the TO problem, compliance minimization is set as the objective for a prescribed volume fraction. Improvements in both aerodynamic and structural performance are found, as expected: the ASO reduced the total pressure on the airfoil surface in order to minimize drag, which resulted in lower stress values experienced by the structure.

Aerodynamic design optimization of a hypersonic rocket sled deflector using the free-form deformation technique

An aerodynamic design optimization of a hypersonic rocket sled deflector is presented using the free-form deformation (FFD) technique. The objective is to optimize the aerodynamic shape of the hypersonic rocket sled deflector to increase its negative lift and enhance the motion stability of the rocket sled. The FFD technique is selected as the aerodynamic shape parameterization method, and the continuous adjoint method based on the gradient method is used to search the optimization in the geometric shape parameter space; the computational fluid dynamics method for a hypersonic rocket sled is employed. An automatic design optimization method for the deflector is carried out based on the aerodynamic requirements of the rocket sled. The optimization results show that the optimized deflector meets the design requirement of increasing the negative lift under the constraint of drag. By improving the pressure distribution on the surface of the deflector, the negative lift is increased by 7.39%, which confirms the effectiveness of the proposed method.

The application of support vector regression and mesh deformation technique in the optimization of transonic compressor design

With the development of modern aero-engine, the compressor is required to achieve higher performance such as transonic operation, high stage pressure ratio and efficiency. At present, the traditional blade design methods have the disadvantage of highly relying on designer's experience and heavy computational burden. In order to reduce design variables used to define blade geometry, the present work introduces the Free-Form Deformation technique. It can achieve high degree-of-freedom deformation and update mesh and geometry simultaneously. To further alleviate computational cost, the Support Vector Regression surrogate model is adopted to replace the time-consuming numerical simulation. It performs well in small sample learning problems. On this basis, a surrogate-based optimization design framework is established by combining the Advanced Latin hypercube sample and NSGA-II multi-objective genetic algorithm. Then an aerodynamic optimization of the transonic NASA Rotor 37 is conducted as a validation. The results show that the pressure ratio and isentropic efficiency are increased by 4.2% and 2.5%, respectively. The optimized shape sweeps forward with a slight increase in twist angle, and shock loss is reduced effectively. Compared with traditional optimization method, the proposed framework can improve the optimization efficiency by decreasing design variables and training samples.

Multidisciplinary Design Optimization for Performance Improvement of an Axial Flow Fan Using Free-Form Deformation

Abstract This paper describes a multidisciplinary design optimization for performance improvement of an electric-ducted fan rotor using free-form deformation (FFD) and data mining techniques. A practical partitioning approach for FFD parameterization was applied in combination with engineering design parameters to optimize the fan rotor. Regression analysis was used to initially determine an approximation function for the blade static stress and subsequently integrated into a fully coupled iterative loop to optimize the blade considering two operating points. Two optimization solutions for 10 and 12 blades were performed. Percentage improvements in the efficiency of 1.05% and 1.32% were realized for 10 and 12 blades, respectively, at near peak efficiency flowrate. Also, blade static stress was reduced by percentages of 5.49% and 12.37% for 10 and 12 blades compared with the baseline. Data mining results revealed key design variable sensitivities where blade twist, sweep, chord, and hub thickness distribution were found to be the most influential for 12 blades while for 10 blades, blade lean, sweep and chord at the midspan and tip. The optimized blades were found to have a significant increase in chord from midspan to tip mimicking a wide chord fan blade particularly for 10 blades. Analysis of the flow field revealed that the axial velocity from 0.4 to 0.8 spanwise length increased significantly for the optimum blades due to the increase in blade twist and chord length at all stable operating points. However, the leakage trajectory relative to the blade chord was observed to be larger and interacted with the trailing edge wake flow downstream for the optimum blades at near-stall conditions. Furthermore, the increase in chord length and the thinning of the blade close to the trailing edge from 0.4 to 0.8 span reduced the suction-side blade loading and static stress.

3D facial attractiveness enhancement using free form deformation

Physical attractiveness has an important and great influence in human social life as it was widely linked to the possession of a variety of positive qualities that makes an individual better than the others, as well as offering many advantages to the individual’s life especially in a society obsessed with beauty and attractiveness. As consequences to the attractiveness influence, people tend to look more and more attractive using makeup or in most of the time plastic surgeries. In parallel to the increased need to plastic surgeries, the need to simplify and show how the face will look like after the surgery is recommended, to plan the procedures, verify the satisfaction of the patient, and reduce the risks during the surgery as well. In this paper, we introduce a novel system to analyze and enhance the attractiveness of 3D faces using a Free Form Deformation technique based on the Bézier function. This system was tested on two 3D face datasets and the experimental results show that the edited 3D faces are more attractive compared to the original faces in terms of respecting the beauty canons which are: facial symmetry, golden ration, neoclassical proportions, and the angular profile.

Rotation and torsion of the left ventricle with cardiovascular magnetic resonance tagging: comparison of two analysis methods

BackgroundLeft ventricle rotation and torsion are fundamental components of myocardial function, and several software packages have been developed for analysis of these components. The purpose of this study was to compare the suitability of two software packages with different technical principles for analysis of rotation and torsion of the left ventricle during systole.MethodsA group of hypertrophic cardiomyopathy (HCM) patients (N = 14, age 43 ± 11 years), mutation carriers without hypertrophy (N = 10, age 34 ± 13 years), and healthy relatives (N = 12, age 43 ± 17 years) underwent a cardiovascular magnetic resonance examination, including spatial modulation of magnetization tagging sequences in basal and apical planes of the left ventricle. The tagging images were analyzed offline using a harmonic phase image analysis method with Gabor filtering and a non-rigid registration-based free-form deformation technique. Left-ventricle rotation and torsion scores were obtained from end-diastole to end-systole with both software.ResultsAnalysis was successful in all cases with both software applications. End-systolic torsion values between the study groups were not statistically different with either software. End-systolic apical rotation, end-systolic basal rotation, and end-systolic torsion were consistently higher when analyzed with non-rigid registration than with harmonic phase-based analysis (p < 0.0001). End-systolic rotation and torsion values had significant correlations between the two software (p < 0.0001), most significant in the apical plane.ConclusionsWhen comparing absolute values of rotation and torsion between different individuals, software-specific reference values are required. Harmonic phase flow with Gabor filtering and non-rigid registration-based methods can both be used reliably in the analysis of systolic rotation and torsion patterns of the left ventricle.

Automatic Shape Optimization of Patient-Specific Tissue Engineered Vascular Grafts for Aortic Coarctation.

This paper proposes a computational framework for automatically optimizing the shapes of patient-specific tissue engineered vascular grafts. We demonstrate a proof-of-concept design optimization for aortic coarctation repair. The computational framework consists of three main components including 1) a free-form deformation technique exploring graft geometries, 2) high-fidelity computational fluid dynamics simulations for collecting data on the effects of design parameters on objective function values like energy loss, and 3) employing machine learning methods (Gaussian Processes) to develop a surrogate model for predicting results of high-fidelity simulations. The globally optimal design parameters are then computed by multistart conjugate gradient optimization on the surrogate model. In the experiment, we investigate the correlation among the design parameters and the objective function values. Our results achieve a 30% reduction in blood flow energy loss compared to the original coarctation by optimizing the aortic geometry.

A robust methodology for the design optimization of diffuser augmented wind turbine shrouds

Shrouded wind turbines represent an attractive solution of high potential that could improve significantly the feasibility of renewable energy production at sites characterized by poor wind resources. This work presents the development of a modular optimization scheme for the aerodynamic shape optimization of diffuser-augmented wind turbine (DAWT) shrouds. For the numerical simulation of the incompressible flow field, an axisymmetric RANS solver has been implemented, based on the artificial compressibility method and SST turbulence model. The major features of the RANS solver are demonstrated, while its validity is assessed against both numerical and experimental data. Mesh and geometry parameterization are simultaneously succeeded by employing an in-house developed computational tool, based on the well-known Free-Form Deformation (FFD) technique. The backbone of the optimization framework is formed by a parallel and asynchronous Differential Evolution (DE) algorithm, which is assisted by Artificial Neural Network (ANN) meta-models. The proposed methodology is applied to the design optimization of an axisymmetric shroud (diffuser) for a 15 kW wind turbine, aiming to maximize the mean velocity speed-up ratio and minimize drag, under geometrical constrains. The resulting designs are capable of providing high velocity accelerations, accompanied by considerable reduction in drag and volume.

Innovative method for rapid development of shoes and footwear

In the present work, a novel set of software tools for the rapid development of shoes and footwear is presented aimed at strongly reducing the design time and then the time-to-market of the products. These tools are mainly based on an implementation of Constrained Free Form Deformation techniques and on the use of modern surface scanning methods. The proposed approach allows, in many cases, to avoid the mathematical surface reconstruction and to quickly generate the complex geometries that CAM systems will process in order to generate the tool paths for mold manufacturing.

Interactive design and variation of hull shapes: pros and cons of different CAD approaches

Modern paradigms to design complex engineering systems focus on interactive approaches able to simultaneously handle results from multidisciplinary applications. Keeping this in mind and considering that from a ship design perspective the definition of a hull shape is the first step of the whole design process, a reliable computer aided design model for shape representation and morphing becomes a key feature to navigate trough the design spiral. The proposed research focuses on the comparison of two different approaches to handle hull shape variations, namely the fully parametric model and a non-parametric method relying on the free form deformation technique. The comparison is developed considering both the easiness of building the shape of the reference model with its transformations laws and the resulting number of free design variables. The two methods are analyzed in the light of attainable hull shape variation in two design and modification test cases. The first is limited to the bulbous bow of a conventional hull while the second focuses on the whole surface of a fast, displacement, round-bilge hull.

Statistical shape modelling versus linear scaling: Effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis

Marker-based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models, although large errors have been reported using these methods. This study aimed to investigate if statistical shape models could improve prediction of the hip joint centre (HJC) location. The inclusion of complete pelvis imaging data from computed tomography (CT) was also explored to determine if free-form deformation techniques could further improve HJC estimates. Mean Euclidean distance errors were calculated between HJC from CT and estimates from shape modelling methods, and functional- and regression-based linear scaling approaches. The HJC of a generic musculoskeletal model was also perturbed to compute the root-mean squared error (RMSE) of the hip muscle moment arms between the reference HJC obtained from CT and the different scaling methods. Shape modelling without medical imaging data significantly reduced HJC location error estimates (11.4 ± 3.3 mm) compared to functional (36.9 ± 17.5 mm, p = <0.001) and regression (31.2 ± 15 mm, p = <0.001) methods. The addition of complete pelvis imaging data to the shape modelling workflow further reduced HJC error estimates compared to no imaging (6.6 ± 3.1 mm, p = 0.002). Average RMSE were greatest for the hip flexor and extensor muscle groups using the functional (16.71 mm and 8.87 mm respectively) and regression methods (16.15 mm and 9.97 mm respectively). The effects on moment-arms were less substantial for the shape modelling methods, ranging from 0.05 to 3.2 mm. Shape modelling methods improved HJC location and muscle moment-arm estimates compared to linear scaling of musculoskeletal models in patients with hip osteoarthritis.

Efficient Aerodynamic Shape Optimization of the Hypersonic Lifting Body Based on Free Form Deformation Technique

Aerodynamic shape optimization (ASO) of hypersonic lifting body has become a significant research topic due to its significant performance advantages. As a universal parameterization, the free form deformation (FFD) technique has benefits including geometric independence, random deformation, and mesh synchronization. In this paper, an effective design method to apply the FFD technique in the ASO of a hypersonic lifting body is presented. Some commonly used basis functions are researched in FFD modeling of the windward side of a typical lifting body, including the Bernstein polynomial, the B-spline function, and the non-uniform rational B-spline (NURBS) function. An efficient aerodynamic simulation method combining Euler equations (non-viscous component) and skin friction drag (viscous component based on the compressible turbulence model) is then developed to minimize computational requirements. The accuracy of the proposed method is validated, and a significant decrease in processing time is observed. In addition, a kriging surrogate model combined with infilling sampling expected improvement (EI) criterion is developed to improve optimization efficiency. To obtain a lifting body with high lift-to-drag ratio that satisfies inner loading constraint, a baseline is optimized by manipulating its shape using the NURBS-based FFD technique. The results show that the optimal shape displays outstanding aerodynamic performance, and the effective design method can provide practical support for ASO of the hypersonic lifting body.

CYFFD Parameterization Method for Cylindrical Components of Aircrafts

This paper proposes a parameterization method using cylindrical coordinates based free-form deformation(CYFFD) technique by introducing a coordinate transformation method and a virtual lattice method. The method is suitable for axisymmetric and non-axisymmetric cylindrical applications. CYFFD is able to deform radially and circumferentially and to maintain first order and curvature continuity across frame border. First, the coordinate transformation step helps capture geometrical characteristics of cylindrical objects to conduct radial and circumferential deformation. Due to the need of delicate shape design, FFD lattice need be set up closely around cylinder-like objects and this will cause the boundary of FFD frame to intersect with the objects, which lead to derivative discontinuity at the intersection. The virtual lattice method is introduced to reuse some control points as virtual ones so that first order and curvature continuity can be preserved. A cylinder deformation example compares the capability of CYFFD with that of conventional FFD for radial and circumferential deformation and keeping derivative continuity. An airplane nose example shows the possibility to use CYFFD and NFFD together for complex shape. A nacelle deformation example and fitting example show that CYFFD is valuable for non-axisymmetric cylindrical objects with complex shapes. The optimization example on cylinder nose shape indicates that CYFFD can give good optimization results and it is valuable for parameterizing cylinder-like objects.