3D Euler flow simulation in hydro turbines: unsteady analysis and automatic design

Parametric automatic optimal design of USV hull form with respect to wave resistance and seakeeping

The use of lower order approximations in the neighborhood of boundaries coupled with higher order interior approximations is examined for the mixed initial boundary-value problem for hyperbolic partial differential equations.Uniform error can be maintained using smaller grid intervals with the lower order approximations near the boundaries.Stability results are presented for approximations to the initial boundary-value problem for the model equation uf + cux = 0 which are fourth order in space and second order in time in the interior and second order in both space and time near the boundaries.These results are generalized to a class of methods of this type for hyperbolic systems.Computational results are presented and comparisons are made with other methods.

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.

An optimal shape of two-dimensional asymmetric diffuser with maximum pressure recovery at the exit is numerically obtained using a mathematical theory based on the variational calculus and gradient algorithm. The initial diffuser is taken to be a two-dimensional asymmetric diffuser for which much experimental and numerical data are available. The Reynolds number based on the bulk mean velocity and the channel height at the diffuser entrance is 1.8 × × 10 4 .F rom this initial shape, optimal diffuser shapes are designed for six different geometric constraints, such as the streamwise length and height of the diffuser. The optimality condition for maximum pressure recovery is obtained to be zero skin friction along the diffuser wall. The turbulent flow inside the diffuser is predicted using the k‐� ‐v2‐f model, and optimal shapes are obtained through iterative procedures to satisfy the optimality condition. With the shape design, flow separation that appeared in the initial diffuser is completely removed or significantly reduced. For one of the optimal diffuser shapes obtained, large-eddy simulation is carried out to validate the result of the shape design. The wall shear stress, wall pressure, mean velocity, and turbulence quantities obtained from large-eddy simulation are in good agreement with those from the simulation using the turbulence model.

An introductory study of helicopter main rotor blade aerodynamic shape optimization problem is presented. Optimization process is carried out in compressible, viscous, quasi‐steady fluid flow field of hovering rotor described by thin layer Navier‐Stokes equations. Since the gradient‐based optimization technique is chosen the discrete adjoint equation method is used for gradient calculations. The airfoils in the blade cross‐sections are parameterized with Non‐Uniform Rational B‐Splines (NURBS). Inverse three dimensional blade shape optimization example is given to demonstrate the efficiency of the numerical procedure.

Aiming at the problems such as low efficiency of initial structure optimization design of traditional refractive optical system and overreliance on experience in structure selection. In this paper, an initial structure automatic optimization design method of refractive optical system based on deep learning is proposed. The structural characteristic data of the reference lens in the optical lens library are learned through supervised training. Unsupervised training model based on ray tracing is constructed to improve the generalization ability of deep neural network model. Through the network model generated by training, the optical system structure parameters including real glass are output, and the automatic optimal design of the initial structure of the refractive optical system is realized. The design results show that the initial structure spot radius of optical system in full field and full spectrum optimized by network model are close to the reference lens. The initial structure of the optical system can be designed according to different focal length requirements. The success rate of one million initial structures designed in this paper is greater than 96.403%, which indicates that the network model has good generalization ability. The method proposed in this paper contributes to automatically generate the initial structure of the refractive optical system rapidly and provides a new solution for the optimization of complex optical system.

This thesis describes a novel approach for designing 7-segment and 5-angle pocket and collar planar antennas (for operation at 900 MHz). The motivation for this work originates from the problem of security of children in rural Nigeria where there is risk of abduction. There is a strong potential benefit to be gained from hidden wireless tracking devices (and hence antennas) that can protect their security. An evolutionary method based on a genetic algorithm was used in conjunction with electromagnetic simulation. This method determines the segment length and angle between segments through several generations. The simulation of the antenna was implemented using heuristic crossover with non-uniform mutation. Antennas obtained from the algorithm were fabricated and measured to validate the proposed method.This first part of this research has been limited to linear wire antennas because of the wide range and flexibility of this class of antennas. Linear wire antennas are used for the design of high or low gain, broad or narrow band antennas. Wire antennas are easy and inexpensive to build. All the optimised linear wire antenna samples exhibit similar performances, most of the power is radiated within the GSM900 frequency band. The reflection coefficient (S11) is generally better than -10dB. The method of moment (MoM-NEC2) and FIT (CST Studio Suite 2015) solvers were used for this design. MATLAB is used to as an interface to control computational electromagnetic solvers for antenna designs and analysis. The genetic algorithm procedures were written in MATLAB. The second part of the work focuses on meshed ground planes for applications at 900 MHz global system for mobile communications (GSM), 2.45 GHz industrial, scientific, and medical (ISM) band and 5 GHz wearable wireless local area networks (WLAN) frequencies. Square ground planes were developed and designed using linear equations in MATLAB. The ground plane was stitched using embroidery machines. To examine the effect of meshing on the antenna performance and to normalise the meshed antenna to a reference, solid patch antenna was designed, fabricated on an FR4 substrate. A finite grid of resistors was created for numerical simulation in MATLAB. The resistance from the centre to any node of a finite grid of resistors are evaluated using nodal analysis. The probability that a node connects to each node in the grid was computed. The circuit model has been validated against the experimental model by measurement of the meshed ground plane. A set of measurement were collected from a meshed and compared with the numerical values, they show good agreement.

Design optimization of the wind turbine of a NREL 1.5-MW HAWT blade was studied to minimize the fluctuation of the bending moment of the blade in turbulent wind. In order to analyze the unsteady aerodynamic load of a wind turbine, FAST code was used as the analysis code. To consider turbulent wind as the wind input model in FAST, TurbSim was used as a turbulent wind simulator. For effective geometrical representation of the aerodynamic shape of a wind turbine blade, the shape modeling function was used to represent the chord length and twist angle. The fluctuation of the out-of-plane bending moment at the blade root was minimized by maintaining the required power of the wind turbine. Through the redistribution of the section force in the radial direction between both the primary and tip regions, the magnitude of the fluctuation of the out-of-plane bending moment was reduced by about 20%, and the rated power of 1.5-MW was maintained. The local angles of attack for the optimized blade were near the point of the maximum lift-to-drag ratio in the primary and tip regions compared to the baseline blade. The fluctuating unsteady aerodynamic load in the optimized blade was reduced within the operating range of the wind speed. With the optimized blade shape, the wind turbine can be operated with decreased fluctuating aerodynamic loads and have a longer life in turbulent wind.

We construct a posteriori error estimators for approximate solutions of linear parabolic equations. We consider discretizations of the problem by modified discontinuous Galerkin schemes in time and continuous Galerkin methods in space. Especially, finite element spaces are permitted to change at different time levels. Exploiting Crank-Nicolson reconstruction idea introduced by Akrivis, Makridakis & Nochetto [2], we derive space-time a posteriori error estimators of second order in time for the Crank-Nicolson-Galerkin finite element method.

Computation of steady and oscillatory convection in saturated porous media

We investigate the three-dimensional mathematical model of crystal growth called PFC (Phase Field Crystal) in a hyperbolic modification. This model is also called the modified model PFC (originally PFC model is formulated in parabolic form) and allows to describe both slow and rapid crystallization processes on atomic length scales and on diffusive time scales. Modified PFC model is described by the differential equation in partial derivatives of the sixth order in space and second order in time. The solution of this equation is possible only by numerical methods. Previously, authors created the software package for the solution of the Phase Field Crystal problem, based on the method of isogeometric analysis (IGA) and PetIGA program library. During further investigation it was found that the quality of the solution can strongly depends on the discretization parameters of a numerical method. In this report, we show the features that should be taken into account during constructing the computational grid for the numerical simulation.

In this article, a uniformly convergent numerical scheme is developed to solve a singularly perturbed convection‐diffusion equation with a small delay having a boundary layer along the left side. A priori bounds of continuous solution and its derivatives are discussed. To solve the problem, the Crank–Nicolson scheme in the time direction and the exponentially fitted finite difference scheme in the space direction are used. The stability of the method is analyzed. It is proved that the developed scheme converges uniformly with first order in space and second order in time. To validate the applicability of the theoretical finding of the developed scheme, numerical experiments are carried out by considering two test examples.

A fourth-order compact finite difference scheme for the quantum Zakharov system that perfectly inherits both mass and energy conservation

This paper introduces a novel algorithm for solving time-dependent two-parameter singularly perturbed parabolic convection–diffusion-reaction equations with Dirichlet boundary conditions. The algorithm is formulated using the Crank-Nicolson (CN) scheme for the temporal derivative discretization. Then, the Trigonometric Quintic B-spline (TQBS) is applied to approximate the state variable and its spatial derivatives on nonuniform collocation points. We conducted a comprehensive convergence analysis and stability of the proposed method and proved that the scheme achieved a parameter-uniform convergence of approximately fourth order in space and second order in time. To make additional evidence to support the theoretical findings and further assess the proposed method, we implemented the numerical algorithm to solve three test examples. Furthermore, using these test examples, we demonstrated the parameter-uniform convergence of the proposed numerical scheme.

ABSTRACTA new and efficient numerical scheme for approximating one-dimensional nonlinear modified Burgers equation has been illustrated in this study. The method makes use of collocation of quintic splines and Crank Nicolson scheme for spatial and temporal discretization, respectively. Linearization involves a quasilinearization process. Since splines are smooth functions which do not exhibit oscillations associated with polynomials and possess easily computable derivatives, working with splines has a computational edge over other existing methods. The method is unconditionally stable, which is justified by von Neumann stability analysis. Convergence analysis of the method is performed and it is proved that the method has fourth-order convergence in space and second order in time. Performance of the method is assessed by computing the CPU time, and small values of CPU time ascertains that the method is highly time efficient. Proposed method yields good numerical results for moderate values of viscosity. Efficiency of the scheme is established from the fact that the and error norms are minute. Results achieved using the proposed numerical scheme are more precise and reliable as compared to many existing works on modified Burgers equation. This method is robust, fast, flexible and easy to implement.