Blade Shape Optimization Research Articles

Blade shape optimization in hover and forward flight

Blade shape optimization in hover and forward flight

A ML strategy for the identification of optimal LPT design region and related blade shape

This work presents a machine-learning (ML) strategy for the identification of the design region that guarantees minimum losses for Low Pressure Turbine (LPT) blades, allowing the definition of the optimal blade shape. The data-driven procedure is twofold. Firstly, an advanced loss-correlation model (M1) that describes the LPT efficiency as a function of the main flow and geometrical parameters, also accounting for unsteady effects, has been trained from a numerical database. Then, a second model (M2) has been tuned to interpret the corresponding blade geometries. Proper Orthogonal Decomposition (POD) has been applied to formally decompose the blade shape into modes and coefficients. The modes provide basis functions, while the coefficients give the weights that, depending on the combination of the design parameters, define the blade shape. Gaussian Process (GP) and Cross-Validation techniques have been used for tuning both M1 and M2. Once properly tuned, the overall procedure provides the loss-correlation model (M1) for the identification of the design region that is expected to minimize losses, and the geometrical model (M2) for a quick definition of the corresponding optimal blade shape. The procedure can be extended to other engineering applications where own efficiency and geometrical data are available.

Knowledge transfer accelerated turbine blade optimization via an sample-weighted variational autoencoder

The aerodynamic shape optimization (ASO) of turbine blades is a typical expensive black-box problem. With the ever increasingly strict design requirements, high-fidelity simulations are demanded, and the related simulation cost increases sharply, which means fewer simulation calls are allowed within a design optimization cycle. Then, the problem as “how to achieve better solution with fewer simulations” becomes rather crucial. Inspired by the concept of transfer learning, we propose to leverage the samples of related completed tasks (also known as source samples) to address the above problem. Specifically, an sample-weighted variational autoencoder (VAE) is proposed, which includes the source samples as part of the training dataset to boost the proportion of high-scoring solution candidates in the learnt design space of target problem, and thus increasing the probability of attaining substantially better solutions. The including of source samples in VAE training also helps to increase the accuracy of reparameterizing the source samples in target design space. Furthermore, a multi-fidelity surrogate is used to guide the optimization search, which extracts information from the source samples to help the algorithm to more quickly arrive at the small neighborhood of the true optimal of the target problem. With the above, a knowledge transfer accelerated aerodynamic shape optimization procedure is proposed for the turbine blade design, labeled as KT-ASO. Through test on a highly-loaded low-pressure turbine blade and compared against the ASO procedures without knowledge transfer, the proposed KT-ASO is shown to reduce at least 50% function calls when achieving similar optimal solutions. In the meantime, under the same sample budget, our proposed KT-ASO is shown to attain much better solutions than the compared ASO procedures.

Performance estimation of small‐scale horizontal axis wind turbine blade

AbstractThe extracted energy from the wind is mainly influenced by the geometry of the rotor blades. Determining the aerodynamic optimum blade shape is one of the main tasks of the wind turbine designer. In the current study, the mixed airfoil technique was employed by using “Blade‐Element‐Momentum” (BEM) and “Computational‐Fluid‐Dynamics” (CFD) analysis to predict the aerodynamic performance of a small‐scale horizontal axis wind turbine blade. The BEM was then run using the open‐source wind turbine design and performance computation program Q‐Blade. The numerical simulation is carried out by Ansys Fluent. Here, the k‐ω Shear Stress Transport (SST) model was used. The results were compared with existing experimental data on lift and drag coefficients at the optimal angle of attack. The results of the two approaches were compared for different tip speed ratio values and a good agreement between CFD and BEM results was found.

Aerodynamic shape optimization of wind turbine rotor blades using the continuous adjoint method

Aerodynamic shape optimization of wind turbine rotor blades using the continuous adjoint method

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

Objective Functions for the Blade Shape Optimisation of a Cross-Flow Tidal Turbine under Constraints

Hydro-kinetic cross-flow tidal turbines (CFTT) are omni-directional and offer higher area-based power density compared to horizontal-axis tidal turbines, making them very attractive for tidal energy exploitation. However, the rotating motion around the vertical axis results in continuously varying angles of attack, causing alternating loads, which may lead to fatigue failure and structural damage. The OPTIDE Project addresses these challenges by implementing intracycle blade pitching to individually control the angle of attack, increasing the power coefficient CP and reducing structural loads. For this purpose a Darrieus turbine is designed with embedded actuators in each blade. Firstly a blade shape optimization will be conducted to fit the actuator at the quarter-chord position while ensuring sufficient thickness. The optimization procedure couples Computational Fluid Dynamics (CFD) with a Genetic Algorithm. The employed optimizer OPAL++ sets ten variables for each individual, which describe the hydrofoil shape, length and tip speed ratio (TSR). A smooth hydrofoil shape is generated from the variables, followed by an automatic mesh generation. Subsequently, numerical simulations of each individual at the desired TSR are conducted, while keeping the blade pitch angle constant. Simulation results provide the CP and stress acting on the turbine blades, which are the two optimization objectives (maximize CP while minimizing stress). This process is repeated during the optimization, aiming to determine the most suitable blade shape, that fits the actuator, and operating point (TSR) in a trade-off between CP and structural loads. This will lead to the increase of efficiency and a longer turbine lifetime.

A novel method of optimizing the Savonius hydrokinetic turbine blades using Bezier curve

Renewable electricity is increasingly gaining importance due to the quest for energy security and the harmful effects of fuel-based energy sources. Savonius hydrokinetic turbine (SHKT) can be a suitable means to provide electricity using rivers, canals, etc. Optimization of blade shape can play a vital role in enhancing the efficiency of SHKTs. A novel method to generate blade shapes has been proposed in this work using a Bezier curve with six control points. The method involves splitting a blade into two halves and optimizing those separately to simultaneously increase the pressure difference and the normal incoming velocity. The generated blade shapes were studied using a 3D transient computational model, which was validated with the obtained experimental results. Results showed that the blades generated using the proposed model show superior performance compared to conventional semicircular blades as well as the blades generated using four points Taguchi method. The most optimum blade profile achieved a maximum power coefficient of 0.21 at a tip speed ratio of 0.8. The efficiency of this new blade profile was found to be 16.7% higher compared to the semicircular blade, while the best blade using four points method was merely 2.1% more efficient than the semicircular blade.

Wind turbine optimization through optimal blade shape design for low wind speeds

Current electricity needs continue to rely on depleting fossil fuels such as fossil fuel and coal. The current government effort is to find non-fossil fuel alternative energy sources. Wind energy is one of the efforts to use ecologically friendly renewable alternative energy. Studies on the development and use of new and renewable energy are now undertaken. One of them is a series of research on the utilization of wind in numerous places of Indonesia through the construction of wind turbines. The blade that explicitly makes contact with the wind is one of the most critical sections of a wind turbine. The shape of the airfoil determines whether or not the blade is used. The focus of this research was to determine the optimal type of airfoil by comparing the coefficient of power (Cp), maximum power, and lowest power produced by various NACA (National Advisory Committee for Aeronautics) airfoils. NACA 4410, 4412, and 4415 airfoils were employed in this study.

Continuous adjoint‐based shape optimization of a turbomachinery stage using a 3D volumetric parameterization

AbstractThis work presents a novel volumetric parameterization technique along with the continuous adjoint method to support gradient‐based CFD shape optimization of turbomachinery stages. The proposed parameterization retains axisymmetry and periodicity by acting on a transformed coordinate system. The same volumetric model controls the shape and the computational volume mesh in a seamless manner, avoiding the additional use of a mesh deformation tool. Moreover, it is differentiated to compute mesh sensitivities (i.e., derivatives of nodal coordinates with respect to the design variables) and is combined with the flow and continuous adjoint, multi‐row solvers of the in‐house PUMA software. Flow field solutions in successive rows communicate based on the mixing plane approach; the development of continuous adjoint to the latter is also presented in this article. The adjoint to the turbulence model and distance‐from‐the‐wall (Hamilton–Jacobi) equations are solved, increasing the accuracy of the computed sensitivity derivatives. All these tools run on modern GPUs, accelerating both flow/adjoint solutions and shape/mesh manipulations. The capabilities of these tools are demonstrated in the shape optimization of the rotor blades of the MT1 high‐pressure, transonic, turbine stage, aiming at maximum stage isentropic efficiency with constraints on stage reaction and inlet capacity.

Rapid Blade Shape Optimization for Contra-Rotating Propellers for eVTOL Aircraft Considering the Aerodynamic Interference

The rising interest in the evolvability of electric vertical takeoff and landing (eVTOL) promises substantial potential in the field of urban air mobility (UAM). Challenges in energy storage density and geometry restriction both emphasize the propeller efficiency for endurance and takeoff weight, whereas the contra-rotating propellers (CRP) advantage is balancing high thrust and efficiency over a single propeller. The aim of this paper is twofold: (i) to present a novel rapid CRP blade shape optimization framework and (ii) to study the impact of the dual propellers revolution speed allocations on the overall CRP power efficiency. The core of the framework is the blade element momentum theory (BEMT)-based blade shape optimization considering the wake effect of the upper propeller by the rotational CFD (computational fluid dynamics) actuator-disc simulation method. The results show that for the same thrust, the optimized CRP at the equal revolution speed is superior to the original (upper-lower-identical) one by 5.9% in thrust-to-power ratio. The overall efficiency can be additionally lifted by 5.3% when the dual propellers share similar torques. By excluding the integral propeller CFD simulation and empirical parameters estimation, the framework enables the swift obtaining of an optimized CRP scheme while maintaining robustness as well.

Метод оценки теоретических характеристик малых осевых гидротурбин

Energy supply to remote areas remains a technical and social challenge. Construction of transmission lines to provide electricity to such areas is expensive and not always possible. One of the promising areas in this area is local energy generation based on local resources, in particular small watercourses, using small hydroelectric power plants. Small hydroelectric power plants are small hydropower facilities that use the energy of small watercourses to generate electricity. They have a number of advantages over traditional energy sources, such as environmental friendliness, low operating costs and high efficiency. However, the widespread introduction of small hydroelectric power plants is hampered by the lack of mass production of small hydraulic turbines and difficulties in designing low-power plants. Designing hydraulic turbines is a complex task that requires solving the inverse problem of hydrodynamics and finding the optimal shape of the flow path. To simplify the design of hydraulic turbines in the modern world, specialized software is used using various methods, including flow analysis, energy loss and blade shape optimization. This article based on an analysis of existing methods for designing and using a mathematical model of a hydraulic turbine with simplified blades, proposes a method for designing and analyzing the theoretical characteristics of the resulting hydraulic turbine. In conclusion, taking into account the use of the methodology for designing a hydraulic turbine for given parameters, its assessment is given, as well as ways to possibly improve the accuracy of the results obtained. Possible areas of application of the outlined design methodology are indicated.

The blade shape optimization of a low-pressure axial fan using the surrogate-based multi-objective optimization method

The blade shape optimization of a low-pressure axial fan using the surrogate-based multi-objective optimization method

Attributes of Bi-Directional Turbomachinery for Pumped Thermal Energy Storage

Abstract In this paper, we (i) present a methodology for determining the aerodynamic performance of bi-directional turbomachines for pumped thermal energy storage, i.e., turbomachines designed to operate as a compressor in one direction, and then as a turbine in the opposite direction, (ii) carry out performance computations for such turbomachines, and (iii) propose principles for conceptual design of these devices. Focus is placed on using the energy storage cycle not only to identify the novel requirements placed on bi-directional turbomachines but also to estimate the effect of these requirements on the efficiency of the energy storage process. In particular, the difference between aerodynamic loading in forward and in backward operation causes the blading to work at incidences leading to the performance below maximum efficiency, resulting in a lower round-trip efficiency. The description of the design principles includes determination of the number of stages, definition of nondimensional parameters for blading selection, and optimization of two-dimensional blading for bi-directional operation. The assessment of stage count shows the relationship between relative Mach number, pressure ratio, and round-trip efficiency. The nondimensional parameters are assessed through a bi-directional analogue to existing “Smith charts,” for the efficiency of single-direction turbomachines, as a function of camber and stagger. The blade shape evaluation and optimization show how the blade profile can be modified to address the requirements of a bi-directional turbomachine, enabling an increase in round-trip efficiency of two percentage points compared to a baseline double circular arc configuration.

Blade shape optimization of Savonius wind turbine using radial based function model and marine predator algorithm

In order to overcome the problems of low efficiency and poor results of classical optimization methods, an efficient, intelligent, and reliable method for optimizing the shape of the blades of the Savonius wind turbine is proposed in this paper. Firstly, the shape of the blade is parameterized by the third-order Bezier curve, and then a certain number of design schemes in the design space are obtained by the Latin hypercube sampling method and the torque coefficient of each design scheme is evaluated based on CFD simulation, and next a radial basis function surrogate model is constructed based on these design schemes and their torque coefficients, and finally the optimal design scheme is obtained by solving the surrogate model using the marine predator algorithm, and is verified using the CFD simulation. The results show that when the tip speed ratio is 1, the average torque coefficient of the optimized blade obtained by the above method is about 7% higher than that of the classical semicircular blade, and under other tip speed ratios, the average torque coefficients of the optimized blade is also significantly higher than that of the classical blade. Furthermore, compared with the classical semicircular blade, about 11% materials can be saved in the manufacturing of the optimized blade.

Optimal design of Savonius wind turbine blade based on support vector regression surrogate model and modified flower pollination algorithm

Blade shape has a significant effect on the wind-capturing ability of the Savonius wind turbine. This paper proposes an intelligent optimization method for optimizing the shape of the blade of the Savonius wind turbine. This method firstly uses the cubic Bezier curve with four design parameters (x1, y1, x2, y2) to characterize the complex blade shape, and then uses the Latin hypercube sampling method to sample some design schemes throughout the design space, and uses computational fluid dynamics simulation to evaluate the response value, i.e. the moment coefficient, of each scheme, and then uses the support vector regression surrogate model to describe the relationship between the design parameters and their response values, finally uses modified flower pollination algorithm to solve the surrogate model to obtain the optimal blade shape. After comparing and analyzing the optimized blade and the classical semicircular blade, it is found that compared with the classical semicircular blade, the optimized blade has a better wind-capturing ability. When the wind speed is 7 m/s and the tip speed ratio is 1, its average power coefficient Cp is significantly increased from 0.260027 to 0.277902 (about 6.87% higher). In addition, the aerodynamic performance of the optimized blade is also better than the classical semicircular blade at other tip speed ratios (TSRs = 0.6–1.2). It is shown that the wind turbine with the optimized blade has great potential in a practical application environment.

Integrated Aerodynamic and Structural Blade Shape Optimization of Axial Turbines Operating With Supercritical Carbon Dioxide Blended With Dopants

Abstract Within this study, the blade shape of a large-scale axial turbine operating with sCO2 blended with dopants is optimized using an integrated aerodynamic-structural three-dimensional (3D) numerical model, whereby the optimization aims at maximizing the aerodynamic efficiency whilst meeting a set of stress constraints to ensure safe operation. Specifically, three candidate mixtures are considered, namely, CO2 blended with titanium tetrachloride (TiCl4), hexafluorobenzene (C6F6), or sulfur dioxide (SO2), where the selected blends and boundary conditions are defined by the EU project, SCARABEUS. A single passage axial turbine numerical model is setup and applied to the first stage of a large-scale multistage axial turbine design. The aerodynamic performance is simulated using a 3D steady-state viscous computational fluid dynamic (CFD) model while the blade stress distribution is obtained from a static structural finite element analysis simulation (FEA). A genetic algorithm is used to optimize parameters defining the blade angle and thickness distributions along the chord line while a surrogate model is used to provide fast and reliable model predictions during optimization using a genetic aggregation response surface. The uncertainty of the surrogate model, represented by the difference between the surrogate model results and the CFD/FEA model results, is evaluated using a set of verification points and is found to be less than 0.3% for aerodynamic efficiency and 1% for both the mass-flow rate and the maximum equivalent stresses. The comparison between the final optimized blade cross section has shown some common trends in optimizing the blade design by decreasing the stator and rotor trailing edge thickness, increasing the stator thickness near the trailing edge, and decreasing the rotor thickness near the trailing edge and decreasing the rotor outlet angle. Further investigations of the loss breakdown of the optimized and reference blade designs are presented to highlight the role of the optimization process in reducing aerodynamic losses. It has been noted that the performance improvement achieved through shape optimization is mainly due to decreasing the endwall losses with both the stator and rotor passages.

Study on the effects of runner geometric parameters on the performance of micro Francis turbines used in water supply system of high-rise buildings

With the increasing emphasis on clean energy, there is growing attention to the use of microturbines or pumps as turbines (PATs) to recover excess hydraulic energy in the water supply system (WSS) of high-rise buildings. In this paper, a micro Francis turbine for WSS in high-rise buildings was presented, and the effects of runner geometric parameters on turbine performance were investigated through computational fluid dynamics (CFD) and lab tests. In the research process, based on the theoretical design results and the numerical optimization of blade exit angle and blade shape, a turbine model was obtained for laboratory testing. The test results show that the Francis turbine has a relatively good performance in both energy generation and water head reduction. In addition, the feasibility of the used runner design method was verified in this special working condition by comparing the experimental performance of turbines with different runner inlet widths. Based on a numerical model that has been validated by experimental results, further optimization for blade thickness and blade number was carried out through CFD simulations. The simulation results show that blade thickness and blade number can affect energy consumption and pressure distribution in the runner and thus affect turbine performance, and there are optimal values to achieve optimal turbine performance. And the optimized model had an output power of 148 W and an efficiency of 21.23% at the design condition.

Efficient aerostructural optimization of helicopter rotors toward aeroacoustic noise reduction using multilevel hierarchical kriging model

Aerostructural design optimizations of helicopter rotors based-on high-fidelity numerical simulations present a great challenge due to extremely large computational costs. In order to improve optimization efficiency by introducing assistance from cheap low-fidelity simulations, this article proposes to use a multilevel hierarchical kriging (MHK) model, which can incorporate three or more levels of fidelity to accelerate the convergence of a high-fidelity aerostructural optimization of helicopter rotors towards the global optimum. The optimization strategy is implemented by three steps. Firstly, a single-fidelity optimization is conducted based on kriging models and low-fidelity simulations. Secondly, a bi-fidelity optimization is performed based on hierarchical kriging (HK) models with pre-calculated low-fidelity samples and additional medium-fidelity samples. Finally, a multi-fidelity optimization is conducted towards the high-fidelity optimum based on MHK models with pre-generated low- and medium-fidelity samples and additional high-fidelity samples. The high-fidelity analysis is defined as coupled computational structural dynamics (CSD) and computational fluid dynamics (CFD) simulations, and the medium- and low-fidelity analyses are defined as merely CFD simulations on fine and coarse computational grids, respectively. To verify the effectiveness of MHK models in rotor optimizations, a blade shape optimization for aeroacoustic noise reduction is carried out by using the proposed optimization strategy. Results show that the total cost of an MHK-based optimization is around 49% less than that of a kriging-based optimization. Besides, by using kriging- and HK-based optimizations the aeroacoustic noises are reduced by 6.84 dB after 175 evaluations and 102 evaluations, respectively, while an MHK-based optimization could achieve the same noise reduction with only 54 evaluations. This example demonstrates that an MHK-based multi-fidelity optimization method can significantly improve the efficiency of aerostructural optimizations for helicopter rotors.

PEDS18: Automated CFD Shape Optimization of Stator Blades for the PediaFlow Pediatric VAD

PEDS18: Automated CFD Shape Optimization of Stator Blades for the PediaFlow Pediatric VAD