Static and dynamic calculation of a Francis turbine runner with some remarks on accuracy

The work presented in this paper describes both the static deformation under centrifugal forces and water pressure, and the natural vibrations of a hydraulic runner of the Francis type. First, the method of calculation is described; it uses finite elements and considers only one sector of the structure with appropriate boundary conditions. Second, preliminary test calculations with two simple bodies are shown; these tests were performed in order that we might familiarise ourselves with the method, in particular with the plane and curved shell elements used, and they had to provide information about the accuracy that could be expected from the results. Finally, several calculations of the Francis runner are presented and their main features are discussed.     

Toward design optimization of a Pelton turbine runner

The objective of the present paper is to propose a strategy to optimize the performance of a Pelton runner based on a parametric model of the bucket geometry, massive particle based numerical simulations and advanced optimization strategies to reduce the dimension of the design problem. The parametric model of the Pelton bucket is based on four bicubic Bézier patches and the number of free parameters is reduced to 21. The numerical simulations are performed using the finite volume particle method, which benefits from a conservative, consistent, arbitrary Lagrangian Eulerian formulation. The resulting design problem is of High-dimension with Expensive Black-box (HEB) performance function. In order to tackle the HEB problem, a preliminary exploration is performed using 2’000 sampled runners geometry provided by a Halton sequence. A cubic multivariate adaptive regression spline surrogate model is built according to the simulated performance of these runners. Moreover, an original clustering approach is proposed to decompose the design problem into four sub-problems of smaller dimensions that can be addressed with more conventional optimization techniques.     

Numerical simulation of fluid added mass effect on a francis turbine runner

In this paper, a numerical simulation to analyze the influence of the surrounding water in a turbine runner has been carried out using finite element method (FEM). First, the sensitivity of the FEM model on the element shape and mesh density has been analysed. Secondly, with the optimized FEM model, the modal behaviour with the runner vibrating in air and in water has been calculated. The added mass effect by comparing the natural frequencies and mode shapes in both cases has been determined.The numerical results obtained have been compared with experimental results available. The comparison shows a good agreement in the natural frequency values and in the mode shapes. The added mass effect due to the fluid structure interaction has been discussed in detail.Finally, the added mass effect on the submerged runner is quantified using a non-dimensional parameter so that the results can be extrapolated to runners with geometrical similarity.     

Computation of stresses in a steam turbine casing during lifting

The finite element method, using flat shell elements, is applied for determining the stress levels induced in a typical steam turbine casing due to its self weight. Computer programs have been developed for the analysis and frontal solution technique with diagonal pivoting has been used for the solution of the finite element equations. Various loading histories corresponding to different orientations of the casing during mechanical handling were considered in the analysis. The results of the analysis were compared with limited amount of experimental data and were found to be in good agreement.     

Thermal stresses of a wind turbine blade made of orthotropic material

This study is to investigate the thermal stress of a wind turbine blade made of wood composite material. First, the governing partial differential equation on heat conduction is stated, then, a finite element procedure using a variational approach is employed for the solution of the governing equation. Thus, the temperature field throughout the blade is determined. Next, based on the temperature field, a finite element procedure using potential energy approach is applied to determine the thermal stress field. A set of results is obtained through the use of a computer, which is considered to be satisfactory.     

Multi-objective shape optimization of a hydraulic turbine runner using efficiency,strength and weight criteria

An approach for multi-discipline automatic optimization of the hydraulic turbine runner shape is presented. The approach accounts hydraulic efficiency, mechanical strength and the weight of the runner. In order to effectively control the strength and weight of the runner, a new parameterization of the blade thickness function is suggested. Turbine efficiency is evaluated through numerical solution of Reynolds-averaged Navier-Stokes equations, while the finite element method is used to evaluate the von Mises stress in the runner. An objective function, being the weighted sum of maximal stress and the blade volume, is suggested to account for both the strength and weight of the runner. Multi-objective genetic algorithm is used to solve the optimization problem. The suggested approach has been applied to automatic design of a Francis turbine runner. Series of three-objective optimization runs have been carried out. The obtained results clearly indicate that simultaneous account of stress and weight objectives accompanied by thickness variation allows obtaining high efficiency, light and durable turbine runners.     

Modelling the vibration response of a gas turbine using machine learning

This work deals with modelling the vibration response of a gas turbine obtained during the start-up process until reaching the nominal speed for power generation. Analysing the vibrations of a complex systems like a gas turbine is useful for the diagnostic of faults or damages in the internal mechanical components of the different stages that integrate a turbine. This work focuses on the study of the shaft vibrations of the bearing radial type mounted between the shaft and the bearing compressor associated with the speed of the turbine. This relationship is studied using experimental data collected from a particular gas turbine model. In particular, we propose a methodology to synthesize a computational model following a supervised learning approach implemented through different machine learning techniques, including a multi-layers perceptron network, support vector machine (SVM), random forest (RF) and genetic programming (GP) with local search. Results show that SVM, RF and GP perform very well in this task, producing accurate predictive models. Moreover, there are some interesting trade-offs between the methods, regarding generalization error, overfitting and model interpretability that are relevant for future applications and research.     

Wind turbine mechanical stresses reduction and contribution to frequency regulation

The aim of the present research work has been to design an optimal MIMO LQG controller to reduce the drive-train, blades and tower mechanical stresses of a wind turbine (WT), and at the same time, to involve the WT in the grid primary frequency regulation when it is operating in full load (FL) zone. To verify the effectiveness of the proposed controller, the achieved results are compared to those obtained by a base-line controller based on a PI regulator.Simulation results show that thanks to these controllers, WT can effectively contribute to the grid frequency regulation, tracking tightly the generator power reference which depends on that frequency. Compared with the base-line controller, the LQG controller significantly reduces the mechanical stresses of the WT׳s most costly components.     

Side-wall effect of runner casing on performance of Darrieus-type hydro turbine with inlet nozzle for extra-low head utilization

A ducted Darrieus-type turbine has been proposed for hydropower utilization of extra-low head less than 2 m.Though the hydro turbine system,in general,might consist of an intake,runner casing section and a draft tube for higher efficiency operation,it was clarified in previous experiment that there was no need of the side-walls of runner casing section and a draft-tube for keeping the efficiency high in the case of duct with an inlet nozzle.This would yield a simplification of the structure of the turbine s...     

Simulations of unsteady cavitating turbulent flow in a Francis turbine using the RANS method and the improved mixture model of two-phase flows

This paper reports the simulation results for the unsteady cavitating turbulent flow in a Francis turbine using the mixture model for cavity–liquid two-phase flows. The RNG k–ε turbulence model is employed in the Reynolds averaged Navier–Stokes equations in this study. In the mixture model, an improved expression for the mass transfer is employed which is based on evaporation and condensation mechanisms with considering the effects of the non-dissolved gas, the turbulence, the tension of interface at cavity and the effect of phase change rate and so on. The computing domain includes the guide vanes, the runner, and the draft tube, which is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations of the mixture model and a full coupled method is combined into the algorithm to accelerate the solution. The computing results with the mixture model have been compared with those by the single-phase flow model as well as the experimental data. The simulation results show that the cavitating flow computation based on the improved mixture model agrees much better with experimental data than that by the single-phase flow calculation, in terms of the amplitude and dominated frequency of the pressure fluctuation. It is also observed from the present simulations that the amplitude of the pressure fluctuation at small flow rate is larger than that at large flow rate, which accords with the experimental data.     

Modelling of the cutting tool stresses in machining of Inconel 718 using artificial neural networks

This study covers two main subjects: (i) The experimental and theoretical analysis: the cutting forces and indirectly cutting tool stresses, affecting the cutting tool life during machining in metal cutting, are one of very important parameters to be necessarily known to select the economical cutting conditions and to mount the workpiece on machine tools securely. In this paper, the cutting tool stresses (normal, shear and von Mises) in machining of nickel-based super alloy Inconel 718 have been investigated in respect of the variations in the cutting parameters (cutting speed, feed rate and depth of cut). The cutting forces were measured by a series of experimental measurements and the stress distributions on the cutting tool were analysed by means of the finite element method (FEM) using ANSYS software. ANSYS stress results showed that in point of the cutting tool wear, especially from von Mises stress distributions, the ceramic cutting insert may be possible worn at the distance equal to the depth of cut on the base cutting edge of the cutting tool. Thence, this wear mode will be almost such as the notch wear, and the flank wear on the base cutting edge and grooves in relief face. In terms of the cost of the process of machining, the cutting speed and the feed rate values must be chosen between 225 and 400 m/min, and 0.1 and 0.125 mm/rev, respectively. (ii) The mathematical modelling analysis: the use of artificial neural network (ANN) has been proposed to determine the cutting tool stresses in machining of Inconel 718 as analytic formulas based on working parameters. The best fitting set was obtained with ten neurons in the hidden-layer using back propagation algorithm. After training, it was found the R² values are closely 1.     

Modelling the nonlinear dynamic behaviour of a boiler‐turbine system using a radial basis function neural network

Building an appropriate mathematical model that describes the system behaviour with a certain degree of satisfaction is quite challenging owing to the uncertain and volatile nature of thermodynamic constants and geometric parameters. In this paper, we present a technique to approximate and validate the dynamic behaviour of the Aström–Bell boiler‐turbine power plant based on an RBFNN over a large operating range. The proposed RBFNN is applied to solve the parametric identification problem for nonlinear and complex systems using an optimiser based on a hybrid genetic algorithm. This optimiser is composed of the gradient descent optimiser and a genetic algorithm for fast convergence. Two simulations were performed to show the effectiveness of the proposed technique under different situations with several boiler‐turbine input variables. The optimal structure and parameters of the obtained RBFNN‐based model emulates well the dynamic behaviour of the Aström–Bell boiler‐turbine system. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling of residual stresses in the shot peened material C-1020 by artificial neural network

This study consists of two cases: (i) The experimental analysis: Shot peening is a method to improve the resistance of metal pieces to fatigue by creating regions of residual stress. In this study, the residual stresses induced in steel specimen type C-1020 by applying various strengths of shot peening, are investigated using the electrochemical layer removal method. The best result is obtained using 0.26 mm A peening strength and the stress encountered in the shot peened material is ?276 MPa, while the maximum residual stress obtained is ?363 MPa at a peening strength of 0.43 mm A. (ii) The mathematical modelling analysis: The use of ANN has been proposed to determine the residual stresses based on various strengths of shot peening using results of experimental analysis. The back-propagation learning algorithm with two different variants and logistic sigmoid transfer function were used in the network. In order to train the neural network, limited experimental measurements were used as training and test data. The best fitting training data set was obtained with four neurons in the hidden layer, which made it possible to predict residual stress with accuracy at least as good as that of the experimental error, over the whole experimental range. After training, it was found the R² values are 0.996112 and 0.99896 for annealed before peening and shot peened only, respectively. Similarly, these values for testing data are 0.995858 and 0.999143, respectively. As seen from the results of mathematical modelling, the calculated residual stresses are obviously within acceptable uncertainties.     

Heat transfer enhancement using flow-induced vibration of a microfin array

Advanced computers are facing thermal engineering challenges from both high heat generation due to rapid performance improvement and the reduction of an available heat removal surface due to large packaging density. Efficient cooling technology is desired to provide reliable operation of microelectronic devices. This paper investigates the feasibility of heat transfer enhancement in laminar flow using the flow-induced vibration of a microfin array. The microfins are initially bent due to the residual stress difference. In order to characterize the dynamics of the microfin flow-induced vibration, a microfin sensor is fabricated. Increase in air velocity provides larger vibrating deflection, while the vibrating frequency of the microfin is independent of the air velocity. The thermal resistances are measured to evaluate the thermal performance of the microfin heat sink and compared with those of a plain-wall heat sink. For a fluid velocity of 4.4 m/s, the thermal resistance of the microfin array heat sink is measured to be 4.45°C/W and that of the plain-wall heat sink to be 4.69°C/W, which indicates a 5.5% cooling enhancement. At a flow velocity of 5.5 m/s, the thermal resistance of the microfin array heat sink is decreased by 11.5%. From the experimental investigations, it is concluded that the vibrating deflection plays a key role in enhancing the heat transfer rate.     

Strong stabilisation of a wind turbine tower model in the plane of the turbine blades

We investigate the strong stabilisation of a wind turbine tower model in the plane of the turbine blades, which comprises a nonuniform NASA Spacecraft Control Laboratory Experiment (SCOLE) system and a two-mass drive-train model (with gearbox). The control input is the torque created by the electrical generator. Using a strong stabilisation theorem for a class of impedance passive linear systems with bounded control and observation operators, we show that the wind turbine tower model can be strongly stabilised. The control is by static output feedback from the angular velocities of the nacelle and the generator rotor.     

Numerical simulation of flow-induced cavity noise in self-sustained oscillations

The generation and near-field radiation of aerodynamic sound from a low-speed unsteady flow over a two-dimensional automobile door cavity is simulated by using a source-extraction-based coupling method. In the coupling procedure, the unsteady cavity flow field is first computed solving the Reynolds- averaged Navier–Stokes (RANS) equations. The radiated sound is then calculated by using a set of acoustic perturbation equations with acoustic source terms which are extracted from the time-dependent solutions of the unsteady flow. The aerodynamic and its resulting acoustic field are computed for the Reynolds number of 53,266 based on the base length of the cavity. The free stream flow velocity is taken to be 50.9 m/s. As first stage of the numerical investigation of flow-induced cavity noise, laminar flow is assumed. The CFD solver is based on a cell-centered finite volume method. A dispersion-relation-preserving (DRP), optimized, fourth-order finite difference scheme with fully staggered-grid implementation is used in the acoustic solver.     

Dynamic optimization of a turbine foundation

In this paper, the dynamic optimization problem for the frame foundation of a turbine is formulated and solved by sequential linear programming. A new scheme is presented to evaluate the response sensitivity when Solokin's damping is considered. This scheme is applied in the multiple-objective optimization of the turbine foundation, where the structural weight and the forced vibration amplitude are to be minimized. Numerical results show that more satisfactory designs can be obtained by this approach.     

Investigation on design flow of a millimeter-scale radial turbine for micro gas turbine

Microsystem Technologies - As compared to the conventional large scale gas turbines, the aerothermodynamics design of a micro gas turbine will be quite different not only due to the small scale...     

Fluid-structure modeling of flow-induced alveolar epithelial cell deformation

Fluid buildup in the small pulmonary airways can exert injurious stresses on the epithelial cells which line airway walls. Under these conditions, the amount of deformation-induced cell injury may depend on the magnitude of the hydrodynamic stresses and the cells’ mechanical properties. In this study, we present 2D and 3D fluid-structure interaction models of flow-induced cell deformation. We report wall shear stress on the cells and cell membrane strain for a range of cell and membrane stiffness values. Results indicate that more compliant cells experience lower wall shear stresses but higher membrane strains. We correlate our results to experimental studies of cellular injury under airway reopening conditions and validate our computational method by comparison to an analytical solution of flow over a rigid protrusion in a channel.     

Modelling a packet-switching network

The basic traffic parameters involved in the analysis of a packet-switching network and its nodes are identified. The paper considers a virtual call of the CCITT X.25 protocol to derive the basic flow in a network. Traffic offered to the various hierarchical levels of the network depends on the information increase imposed by the protocol. Several efficiency levels are derived at different time levels, and are used to relate network traffic to user traffic. The sensitivities of these packet levels to packet size, packet delay and window size are evaluated for both interactive and batch traffic.