Twist Distribution Research Articles

A Reformulated-Vortex-Particle-Method-Based Aerodynamic Multi-Objective Design Optimization Strategy for Proprotor in Hover and High-Altitude Cruise

An improved multi-objective design optimization framework is proposed for the efficient design of proprotor blades tailored to specific high-altitude mission requirements. This framework builds upon existing methods by leveraging a reformulated Vortex Particle Method (rVPM) and incorporates three key stages: (1) rapid determination of overall proprotor parameters using a semi-empirical model, (2) optimized blade chord and twist distribution bounds based on minimum energy loss theory, and (3) global optimization with a high-fidelity rVPM-based aerodynamic solver coupled with a multi-objective hybrid optimization algorithm. Applied to a small high-altitude tiltrotor, the framework produced Pareto-optimal proprotor designs with a figure of merit of 0.814 and cruise efficiency of 0.896, exceeding mission targets by over 15%. Key findings indicate that large taper ratios and low twist improve hover performance, while elliptical blade planforms with high twist enhance cruise efficiency, and a tip anhedral further boosts overall performance. This framework streamlines the industrial customization of proprotor blades, significantly reducing the design space for advanced optimization while improving performance in demanding high-altitude environments.

A novel multi-fidelity optimization framework for high-altitude propellers

A novel optimization methodology is presented for optimizing high-altitude propellers operating in the lower stratosphere. The proposed methodology combines a Bayesian optimization approach for most design variables and Vortex Theory for the optimization of twist distribution and rotational velocity. For the Bayesian optimization part of the problem, a multi-fidelity approach is employed with three levels of modeling fidelity. The considered fidelity levels, from lower to higher, are: Vortex Theory, and 3D Reynolds-Averaged Navier-Stokes (RANS) with the use of γ−Reθ transition model, converged with first-order upwind, and second-order upwind for the momentum equations. Additionally, the optimization problem involves two objectives: maximizing the cruise efficiency and minimizing the total volume of the propeller. To enhance the performance of multi-fidelity, multi-objective (MFMO) acquisition functions, a novel algorithm is proposed. The proposed optimization methodology demonstrates its effectiveness in generating several high-performing propeller designs and proves to be more efficient than an equivalent problem formulation relying solely on Bayesian optimization. Post-processing of optimization data reveals new design variable bounds that correspond to more efficient blade shapes. These findings provide insights into some important geometric features of high-altitude propellers and establish guidelines for future optimization efforts within the specified thrust and power consumption ranges. Finally, simulations of the best-performing designs across a range of advance ratios and altitudes confirm their high performance in various operating conditions.

Influence of Laminate Twist and Clamping Pressure on Bonding Performance of Low-Grade Lumber in Cross-Laminated Timber

Abstract The geometric variations of low-grade lumber raise concerns about bond strength of cross-laminated timber (CLT) produced from such lumber. This study seeks to investigate the effect of low clamping pressure and geometric variations of laminates on the bond strength of CLT. CLT panels were manufactured from low-grade grand fir (Abies grandis). Block shear tests and cyclic delamination tests were conducted on specimens randomly taken at specific points that correspond to a wide range of twist magnitude. Twist distribution in the lumber used as laminates in the CLT ranges from 0 to 160 mm. Results showed that twist magnitude and clamping pressure have significant effect on bond performance, with twist magnitude having an overriding effect on pressure.

Transferable machine learning model for the aerodynamic prediction of swept wings

With their development, machine learning models can be used instead of computational fluid dynamics simulations to predict flow fields in aerodynamic optimization. However, it is difficult to construct a prediction model for swept wings with various planform geometries because too many samples are required to cover the parameter space. In the present paper, a new model framework is proposed to predict wing surface pressure and friction distributions with fewer samples. The distributed geometry parameters along spanwise are used as model inputs instead of the global planform parameters, and processors are designed to help the model better learn the local effect of geometric variation. The model is trained and tested on simple swept wings with single segment and linear twist distribution, where it outperforms the global input model by 57.6% in terms of lift coefficient prediction errors on small dataset sizes. The distributed input also enables the model to be transferred from single wings to more engineering-practical yet complex kink wings. After fine-tuning with a few samples, model accuracy for kink wings can be similar to that of simple wings, which proves the model for wings with complex planform geometries can be efficiently built with the proposed method.

Development of a control co-design optimization framework with aeroelastic-control coupling for floating offshore wind turbines

Sequential design optimization is frequently used to design floating offshore wind turbines. This method simplifies the design problem by implementing each of the disciplines successively and independently with the direct/dynamic coupling between them neglected. However, if the coupling between disciplines is strong, the global optimum may not be found by sequential design. Control co-design optimization is an approach that integrates all physics in a single optimization formulation to achieve the global optimum. However, it is challenging to achieve due to the highly complex system-control coupling in floating offshore wind turbines. This paper describes a control co-design optimization framework developed for floating offshore wind turbines. In particular, the blade airfoil chord and twist distributions are parameterized to change aerodynamics while the blade structural characteristics can be updated. The rotor speed and blade pitch controllers are tuned automatically based on the properties of the new plant model. For demonstration, a 10 MW reference wind turbine is used in the case study. The annual energy production is maximized, and the blade mass is minimized. The blade shape and control parameters are optimized simultaneously, subject to constraints on geometric design variables, fatigue loads, ultimate loads, and blade deflection. To solve this high-dimensional, nonlinear, and constrained problem, a genetic algorithm is used, and the Pareto front of the design space is found. The design solutions on the Pareto front showed an improvement in the blade mass and annual energy production. These design alternatives also showed reduced structural ultimate and fatigue loads, and generator torque. This revealed the potential of control co-design to reach a better performance than the sequential method.

Genetic algorithm for the response of arbitrarily twisted nematic liquid crystals to an applied field.

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equationsare derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The full range of twist angles from -90^{∘} to 90^{∘} is considered. In this way, the predictions of our routine strongly support the experimentally observed polarization transformations of light incident on different spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.

<i>In Situ</i> Measurement of Twist Propagation and Yarn Tension with Superconducting Magnetic Bearing Twisting Element for Ring Spinning Process

The twisting of yarn in one of the most widely used conventional ring spinning processes is based on the ring/traveler system. The existing limitation of productivity in the ring spinning process lies on the prevailing force relation between ring, traveler and yarn as well as the frictional heat between traveler and ring, principally in the ring traveler system. Recently, a frictional free twisting element based on a superconducting magnetic bearing (SMB) was developed to increase the productivity of ring spinning drastically, which was patented by ITM and Leibniz IFW Dresden. This SMB consists of a circular superconductor and a permanent magnet (PM) ring. In the superconducting state, the PM ring levitates and can freely rotate even up to an angular speed of 50.000 rpm. It is connected with the spindle via the yarn through a guide attached to the PM ring to impart yarn twist. Through the rotation of the PM ring, the twist propagates to the nip point of the delivery rollers. The twist propagation rate depends on different parameters, e.g., spindle speed, balloon geometry, and friction between yarn and yarn guides. A change in the level of twist affects the process, yarn tension, yarn breakage rate, and yarn properties. Hence, it is important to investigate the twist distribution to derive effective measures for improving the twist propagation especially at higher angular spindle speeds and thus eliminate weak points to increase process stability and yarn quality. The aim of these measurements is to analyze the twist distribution along the yarn path to understand the causes of yarn breakages. In this study, the yarn path was traced at different regions by in-situ measuring the helix angle of twisted yarn using a high-speed camera. From the recorded images, the number of twists per unit length was determined using the image processing software ‘Image J’. Thus, the measurement method allows a new insight into the problem of yarn breakages originating from twist propagation in order to take optimized measures at higher angular spindle speeds.

Effect of Subsonic Compressibility and Constraints on Generation of 3-D Optimal Camber Shapes

A flat surface wing is optimized for minimum induced drag for low and high subsonic Mach numbers. Wing for transport airplane role is considered. Optimal warp is separated into twist and camber. Effect of compressibility is analysed on the camber shape generated for two different Mach numbers. Constraint of lift is firstly used for developing an objective function for drag minimization. Next the lift and wing root bending moment constraints are considered to form objective function. Analysis is made on the resulting camber and twist distributions.

Aerodynamic Modeling of a Flying Wing Featuring Ludwig Prandtl’s Bell Spanload

This paper presents the aerodynamic modeling of a flying wing featuring Ludwig Prandtl’s bell spanload. The aerodynamic models are developed using a medium fidelity vortex-lattice method and using a Reynolds-Averaged Navier–Stokes computational fluid dynamics solution across a wide range of in-flow angle conditions. A methodology is developed to directly compare the spanwise force distributions from each method. Excellent agreement is seen in the prediction of spanwise inertial aerodynamic forces from each method, as well as in stability and control derivatives dominated by lift and moment contributions. The phenomenon of proverse yaw, caused by the twist distribution necessary to produce the bell spanload, is seen in the high and low-order analysis, with similar off-axis control power predicted.

Study pion distribution amplitudes from the electromagnetic form factor by data-driven dispersion relation

We study the pion electromagnetic form factor in the modulus squared dispersion relation, and do the model independent extraction of the chiral mass embedded in the sub-leading twist light-cone distribution amplitude. The motivation of this work is the recent measurement of timelike form factor in the resonant regions, which makes up the piece lacking solid QCD-based calculation. With the perturbative QCD calculation up to next-to-leading-order of strong coupling and twist four level of meson distribution amplitudes, we obtain the chiral mass of pion meson as m_0^pi (1 , textrm{GeV}) = 1.31^{+0.27}_{-0.30} , textrm{GeV}. Due to the chiral enhancement contribution from the sub-leading twist distribution amplitudes in the perturbative QCD calculation, we can not extract the lowest Gegenbauer moments of pion from the study of electromagnetic form factor. This problem could be settled down with the foresee Belle-II and BESIII measurement of the transition form factor especially in the large momentum transfers regions.

Effect of rubbing symmetry on polarization distribution in ferroelectric nematic liquid crystal cells

It is a significant issue in controlling the polarization distribution in ferroelectric nematic liquid crystal cells. We investigated the polarization configuration of ferroelectric nematic liquid crystals on the surface and in the bulk of parallel/anti-parallel cells with rubbed substrates and proposed the polarization models in each cell. It is found that on the surface of rubbed polyimide films, the polarization direction is fixed and opposite to the rubbing direction. Splay and twist distribution of the polarization are formed in parallel and anti-parallel cells, respectively.

Conceptual Design and Optimization of Distributed Electric Propulsion General Aviation Aircraft

The interaction between the slipstream of the propellers and the wing of an aircraft with distributed electric propulsion (DEP) could benefit aerodynamics. A conceptual design and optimization are carried out in order to increase the range of an electric general aviation aircraft without affecting its takeoff and landing velocity in the same fuselage condition. Propellers are modelled using the actuator disk (AD) theory, and the aircraft is modelled using the vortex lattice method (VLM) to obtain DEP aircraft’s aerodynamics in conceptual design. The DIRECT method is used for global optimization. To concentrate on the layout of the propellers and wing, a propeller with the same chord distribution, twist distribution, and number of blades is selected. The design and optimization of DEP aircraft’s range is carried out with the objective of achieving the maximum product of the lift–drag ratio with propeller efficiency under force balance constrains. Additionally, to decrease the takeoff and landing distance, the DEP aircraft’s takeoff and landing performance are optimized with the objective of the smallest velocity at an angle near the tail down angle under the constrains of acceleration bigger than 0 and a Mach number at the tip of blades smaller than 0.7. The CFD simulation was used to confirm the DEP aircraft’s pretty accurate aerodynamics. Compared to the reference aircraft, the improved DEP aircraft with 10 high-lift propellers on the leading edge of the wing and 2 wing-tip propellers may boost cruise performance by 6% while maintaining takeoff and landing velocity. Furthermore, it has been shown that the stall speed of DEP aircraft with smaller wings would rise proportionally when compared to conventional design aircraft, and the power need of DEP aircraft will be increased as a result of the operation of high-lift propellers. The conceptual design and optimal approach suggested in this work has some reference value for the design and research of the fixed-wing DEP general aviation aircraft.

A discrete adjoint full potential formulation for fast aerostructural optimization in preliminary aircraft design

Preliminary aircraft design is often carried out with the help of multidisciplinary optimization processes. Because there is a strong coupling between the flow and the structure of the aircraft, and because new composite materials have a unique capability of being designed for anisotropic directional stiffness and strength, these processes must model the aeroelastic behavior of the aircraft in order to be effective. Since many design variables are involved during the preliminary design stage, the optimization problems, formulated using high or medium fidelity models, can be solved using the adjoint method. Moreover, the level of fidelity of the fluid model and the associated simulation technique must also be selected with care, as they tend to be the main contributors to the computational cost. The novel contribution of the present work is twofold. Firstly, the discretized gradients of the full potential flow equation, which is a medium-fidelity model, are derived analytically so that they can be used in adjoint optimization problems. Moreover, the full potential flow solution and the computation of the gradients are implemented in an open-source and readily available finite element code. Secondly, aerodynamic shape and aerostructural optimization calculations are carried out on example wings to demonstrate the effectiveness and the computational efficiency of the proposed method. Overall, the results show that the newly implemented discrete adjoint nonlinear potential flow formulation is able to quickly optimize both the shape and the structural parameters of a typical wing. More specifically, the twist distribution along the wingspan is adapted to reduce the induced drag, the airfoils become more supercritical so that the shock strength and the associated wave drag are reduced, and the thickness of the structural elements is tailored to the loads to reduce the internal stresses. The present methodology is therefore able to deliver results at a low computational cost which are sufficiently accurate for the early design stages. Furthermore, the results obtained using the proposed methodology could be used as a starting point for the optimization calculations performed in later design stages.

High-Fidelity Modeling and Investigation on Blade Shape and Twist Angle Effects on the Efficiency of Small-Scale Wind Turbines

A high-fidelity analysis is carried out in order to evaluate the effects of blade shape, airfoil cross-section. as well as twist angle distribution on the yielded torque and generated power of a horizontal axis Small-Scale Wind Turbine (SSWT). A computational modeling and an effective design for a small turbine with a blade length of 25 cm subject to a 4 m/s freestream velocity are presented, in which a segregated RANS solver is utilized. Four airfoil profiles are assessed, namely NACA0012, NACA0015, NACA4412, and NACA4415, and two blade shape configurations, rectangular and tapered, are evaluated. The flow around the rotating turbines is investigated along with blade stresses and performance output for each configuration. Subsequently, the impact of various linear and nonlinear twist distributions on SSWT efficiency is also examined. Results show that for the studied operating conditions corresponding to low-speed flows, the rectangular blade configuration outperforms the tapered blade shape from the generated torque and power perspectives, while the tapered shape configuration represents an attractive design choice from the yielded stresses point of view. Additionally, while the nonlinear twist configuration results in the best performance among the configurations studied, an SSWT blade design implementing a linear twist distribution can be highly competitive provided that a good slope is carefully selected.

RANS-Based Aeroacoustic Global Sensitivity Study and Optimization of UAV Propellers

Modeling of Unmanned Aerial Vehicles (UAV) propellers in a global, multidisciplinary aeroacoustic optimization was investigated. The modeling consists of three aspects: geometry, aerodynamics, and aeroacoustics. Firstly, a parametric geometry model was established using chord, twist, and sweep distributions along the radius, defined by splines to ensure smoothness. Additionally, airfoil parameters including maximum camber and its position, as well as the position of maximum thickness, were added. Secondly, a blade geometry-resolved aerodynamic model based on steady RANS was established. A two-equation SST turbulence model was used for compressible flow with periodic boundary conditions. Thirdly, an aeroacoustic model for far-field tonal noise calculation was defined, based on the Ffowcs Williams and Hawkings analogy and a RANS solution. A global sensitivity analysis was performed to establish the importance of individual design variables. Consequently, surrogate modeling-based optimization strategy was devised to efficiently establish Pareto front of propeller geometries in multi-objective aeroacoustic optimization.

Investigating Pre-eruptive Magnetic Properties at the Footprints of Erupting Magnetic Flux Ropes

It is well established that solar eruptions are powered by free magnetic energy stored in the current-carrying magnetic field in the corona. It has also been generally accepted that magnetic flux ropes (MFRs) are a critical component of many coronal mass ejections. What remains controversial is whether MFRs are present well before the eruption. Our aim is to identify progenitors of MFRs, and investigate pre-eruptive magnetic properties associated with these progenitors. Here we analyze 28 MFRs erupting within 45° from the disk center from 2010 to 2015. All MFRs’ feet are well identified by conjugate coronal dimmings. We then calculate the magnetic properties at the feet of the MFRs, prior to their eruptions, using Helioseismic and Magnetic Imager vector magnetograms. Our results show that only 8 erupting MFRs are associated with significant nonneutralized electric currents, 4 of which also exhibit pre-eruptive dimmings at the footprints. Twist and current distributions are asymmetric at the two feet of these MFRs. The presence of pre-eruption dimmings associated with nonneutralized currents suggests the preexisting MFRs. Furthermore, the evolution of conjugate dimmings and electric currents within the footprints can provide clues about the internal structure of MFRs and their formation mechanism.

MAFIAT: Magnetic field analysis tools

The magnetic twist is one of the key defining parameters of solar flux ropes (FRs). The routine computation of the winding of magnetic field lines, referred to as the twist, has the potential to lead to significant advancement in the field of solar physics and solar—terrestrial research, e.g., by enabling more accurate investigations of FR morphology, stability, and temporal evolution. However, this has been hampered by the axial-dependence of the solution and the availability of simpler, albeit approximate, methods. Here we introduce the Magnetic Field Analysis Tools (MAFIAT) python library and Jupyter notebooks for the computation and exploitation of this quantity. The required axis location is specified manually by the user, either with their own preferred method, or using the twist number calculated from the parallel current by Magnetic Field Analysis Tools. The notebooks allow users to create a variety of novel visualisations of FRs and their twist distributions for scientific study. Magnetic Field Analysis Tools is written in Python and is released under the BSD 3-Clause Licence. Code available at: https://github.com/pricedj/mafiat.

An automatic parallel scheme to design an augmented hydrokinetic river turbine using a simulation-based optimization approach

The effect of diffuser-enhanced flow on the energy extraction performance of hydrokinetic turbines is widely reported in the literature. In this context, this work combines automatic scripting for geometry construction and meshing, together with a simulation-based approach using particle-swarm optimization with Computational Fluid Dynamics (CFD) to design an augmented hydrokinetic river turbine (HKRT). The goal is to achieve an increase in mass flow in the throat of the diffuser and then to design an ad-hoc set of rotor blades. The optimization is performed in two separate stages: Continuous optimization for the diffuser and discrete optimization for the rotor blades. The complex shape of the rotor blades in terms of the chord, twist, and thickness distribution was parametrized with second-order Bezier curves, which facilitates the correlation between the blade’s shape and its performance, proving to be more intuitive to the experienced designer. Furthermore, a novel search and discrete arrangement of feasible design variables are proposed, which allows for reducing the computational costs of this large optimization problem. Results show that the optimized diffuser achieved a flow rate increase of 279%, and the ad-hoc 1.5 [m] in diameter rotor delivers a power of 11.98 [kW] with an efficiency of 0.3385%.

A robust estimation of the twist distribution in magnetic clouds

Context. Magnetic clouds (MCs) are observed in situ by spacecraft. The rotation of their magnetic field is typically interpreted as the crossing of a twisted magnetic flux tube, or flux rope, which was launched from the solar corona. Aims. The detailed magnetic measurements across MCs permit us to infer the flux rope characteristics. Still, the precise spatial distribution of the magnetic twist is challenging, and thus is debated. Methods. In order to improve the robustness of the results, we performed a superposed epoch analysis (SEA) of a set of well observed MCs at 1 au. While previous work was done using the MC central time, we here used the result of a fitted flux rope model to select the time of the closest approach to the flux rope axis. This implies a precise separation of the in- and outbound regions to coherently phase the observed signals. We also searched for and minimised the possible biases such as magnetic asymmetry and a finite impact parameter. Results. We applied the SEA to derive the median profiles both for the flux rope remaining when crossed by the spacecraft and to recover the one present before erosion. In particular, the median azimuthal B component is nearly a linear function of the radius. More generally, the results confirm our previous results realised without such a deep analysis. The twist profile is nearly uniform in the flux rope core, with a steep increase at the border of the flux rope and with similar profiles in the in- and outbound regions. The main difference with our previous study is a larger twist by ∼20%.

Aerodynamic Shape Optimisation Using Parametric CAD and Discrete Adjoint

This paper presents an optimisation framework based on an open-source CAD system and CFD solver. In this work, the high-fidelity flow solutions and surface sensitivities are obtained using the primal and discrete adjoint formulations of SU2. This paper shows the direct use of CAD models for optimisation by developing a CAD system application programming interface and creating a link between the CAD-MESH-CFD analysis. A methodology to obtain geometric sensitivities is introduced, enabling the calculation of accurate gradients with respect to CAD variables and the deformation of the analysis mesh during the optimisation process. This methodology guarantees that the new surface mesh lies exactly on the CAD geometry. The optimisation framework is applied to a rectangular wing and a three section high-lift aerofoil configuration derived from the NASA CRM-HL configuration. Both geometries are created using FreeCAD. The performance objectives are to decrease the drag while constraining the lift to be above a desired value. The twist distribution of the wing was parameterised within the CAD system, allowing the minimisation of the induced drag by obtaining a nearly elliptical lift distribution. For the high-lift configuration, the position and rotation of the flap and slat were parameterised with respect to the original section; the final optimised positions yield a drag reduction of approximately 16.5%. These results show that the CAD parameterisation can be reliably used to obtain efficient optimums while operating directly on the CAD geometries.