Dissertation•
Numerical Simulation of the Lux Vertical Axis Wind Turbine
01 Mar 2019-
TL;DR: In this paper, the authors developed a simulation model in an open-source software package called OpenFOAM to investigate the performance characteristics of the Lux Vertical Axis Wind Turbine (VAWT).
Abstract: Wind energy can be characterized as a cheap, clean, and renewable energy source that is absolutely sustainable. With increasing demand for wind energy, it is productive to investigate the structural and operational factors that undermine the proficiency and the characteristic performance of the wind turbine. Of paramount importance to efficient wind energy generation is the aerodynamics of the wind turbine blades. The aerodynamic factors, such as drag, airfoil profiles, and wake interactions that often reduce the performance of the wind turbines, can be investigated through computational mathematics using computational fluid dynamics (CFD). CFD offers basic techniques and tools for simulating physical processes and proffers important insights into the flow data, which are demanding and costly to measure experimentally. In this thesis, we develop a simulation model in an open-source software package called OpenFOAM to investigate the performance characteristics of the Lux Vertical Axis Wind Turbine (VAWT). The Lux VAWT has a simpler design than its horizontal counterparts; however, its performance is affected by the unsteady aerodynamic due to a complex flow field. The turbulent flow field is governed by the incompressible Navier– Stokes equations. Simulations are carried out with an unsteady incompressible and dynamic flow solver, PimpleDyMFoam, on an unstructured mesh surface of the Lux VAWT geometry. The computational domain includes both the stationary and rotating mesh domains to accommodate the rotating motion of the turbine blades and the free-stream zone. The arbitrary mesh interface is applied as a boundary condition for the patches between the two domains to enable computation across disconnected but adjacent mesh domains. Meshing was done using two separate meshing tools, snappyHexMesh and ANSYS Mesher. The snappyHexMesh tool offered the most flexible and effective control over the mesh generation and quality. In order to derive the maximal power output from the Lux VAWT simulations, the Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations are solved with different time-stepping methods; the objective is to reduce the computational costs. While attempting to reduce the numerical diffusion from the non-transient terms of URANS, a stabilized trapezoidal rule with a second-order backward differentiation formula (TR–BDF2) time-stepping method was implemented in OpenFOAM. As a result, the transient aerodynamic forces of the blades, the torque, and power output are evaluated. The findings demonstrate that most of the transient aerodynamic force is generated along the axis of rotation of the rotor during one complete revolution. Similarly, the computations indicate that the BDF2 method results in the least computational cost and predicts a turbine power that is somewhat comparable to the experimental results. The difference between the simulation results and the experimental data is attributed partly to the pressure fluctuations on the turbine blades due to the mesh topology.
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01 Jan 1997
TL;DR: The boundary layer equations for plane, incompressible, and steady flow are described in this paper, where the boundary layer equation for plane incompressibility is defined in terms of boundary layers.
Abstract: The boundary layer equations for plane, incompressible, and steady flow are
$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$
2,598 citations
01 Jan 2016
TL;DR: The numerical heat transfer and fluid flow is universally compatible with any devices to read and is available in the authors' digital library an online access to it is set as public so you can get it instantly.
Abstract: Thank you for reading numerical heat transfer and fluid flow. Maybe you have knowledge that, people have search numerous times for their favorite books like this numerical heat transfer and fluid flow, but end up in infectious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they cope with some malicious virus inside their computer. numerical heat transfer and fluid flow is available in our digital library an online access to it is set as public so you can get it instantly. Our books collection spans in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the numerical heat transfer and fluid flow is universally compatible with any devices to read.
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22 Oct 2007
TL;DR: The fifth edition of "Numerical Methods for Engineers" continues its tradition of excellence and expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical engineering.
Abstract: The fifth edition of "Numerical Methods for Engineers" continues its tradition of excellence. Instructors love this text because it is a comprehensive text that is easy to teach from. Students love it because it is written for them--with great pedagogy and clear explanations and examples throughout. The text features a broad array of applications, including all engineering disciplines. The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. Approximately 80% of the end-of-chapter problems are revised or new to this edition. The expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical engineering. Users will find use of software packages, specifically MATLAB and Excel with VBA. This includes material on developing MATLAB m-files and VBA macros.
578 citations
TL;DR: This new edition has been extensively updated, and includes new chapters on developing subject areas: geometric numerical integration, an emerging paradigm for numerical computation that exhibits exact conservation of important geometric and structural features of the underlying differential equation.
Abstract: Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for realnumber calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis both of ordinary and partial differential equations. The point of departure is mathematical, but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. This new edition has been extensively updated, and includes new chapters on developing subject areas: geometric numerical integration, an emerging paradigm for numerical computation that exhibits exact conservation of important geometric and structural features of the underlying differential equation; spectral methods, which have come to be seen in the last two decades as a serious competitor to finite differences and finite elements; and conjugate gradients, one of the most powerful contemporary tools in the solution of sparse linear algebraic systems. Other topics covered include numerical solution of ordinary differential equations by multistep and Runge–Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques for their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics.
166 citations
References
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TL;DR: In this paper, two new two-equation eddy-viscosity turbulence models are presented, which combine different elements of existing models that are considered superior to their alternatives.
Abstract: Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity
15,459 citations
TL;DR: In this paper, the authors present a review of the applicability and applicability of numerical predictions of turbulent flow, and advocate that computational economy, range of applicability, and physical realism are best served by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour.
11,866 citations
TL;DR: In this paper, the Navier-Stokes equation is derived for an inviscid fluid, and a finite difference method is proposed to solve the Euler's equations for a fluid flow in 3D space.
Abstract: This brief paper derives Euler’s equations for an inviscid fluid, summarizes the Cauchy momentum equation, derives the Navier-Stokes equation from that, and then talks about finite difference method approaches to solutions. Typical texts for this material are apparently Acheson, Elementary Fluid Dynamics and Landau and Lifschitz, Fluid Mechanics. 1. Basic Definitions We describe a fluid flow in three-dimensional space R as a vector field representing the velocity at all locations in the fluid. Concretely, then, a fluid flow is a function ~v : R× R → R that assigns to each point (t, ~x) in spacetime a velocity ~v(t, ~x) in space. In the special situation where ~v does not depend on t we say that the flow is steady. A trajectory or particle path is a curve ~x : R→ R such that for all t ∈ R, d dt ~x(t) = ~v(t, ~x(t)). Fix a t0 ∈ R; a streamline at time t0 is a curve ~x : R→ R such that for all t ∈ R, d dt ~x(t) = ~v(t0, ~x(t)). In the special case of steady flow the streamlines are constant across times t0 and any trajectory is a streamline. In non-steady flows, particle paths need not be streamlines. Consider the 2-dimensional example ~v = [− sin t cos t]>. At t0 = 0 the velocities all point up and the streamlines are vertical straight lines. At t0 = π/2 the velocities all point left and the streamlines are horizontal straight lines. Any trajectory is of the form ~x = [cos t + C1 sin t + C2] >; this traces out a radius-1 circle centered at [C1 C2] >. Indeed, all radius-1 circles in the plane arise as trajectories. These circles cross each other at many (in fact, all) points. If you find it counterintuitive that distinct trajectories can pass through a single point, remember that they do so at different times. 2. Acceleration Let f : R × R → R be some scalar field (such as temperature). Then ∂f/∂t is the rate of change of f at some fixed point in space. If we precompose f with a 1 Fluid Dynamics Math 211, Fall 2014, Carleton College trajectory ~x, then the chain rule gives us the rate of change of f with respect to time along that curve: D Dt f := d dt f(t, x(t), y(t), z(t)) = ∂f ∂t + ∂f ∂x dx dt + ∂f ∂y dy dt + ∂f ∂z dz dt = ( ∂ ∂t + dx dt ∂ ∂x + dy dt ∂ ∂y + dz dt ∂ ∂z ) f = ( ∂ ∂t + ~v · ∇ ) f. Intuitively, if ~x describes the trajectory of a small sensor for the quantity f (such as a thermometer), then Df/Dt gives the rate of change of the output of the sensor with respect to time. The ∂f/∂t term arises because f varies with time. The ~v ·∇f term arises because f is being measured at varying points in space. If we apply this idea to each component function of ~v, then we obtain an acceleration (or force per unit mass) vector field ~a(t, x) := D~v Dt = ∂~v ∂t + (~v · ∇)~v. That is, for any spacetime point (t, ~x), the vector ~a(t, ~x) is the acceleration of the particle whose trajectory happens to pass through ~x at time t. Let’s check that it agrees with our usual notion of acceleration. Suppose that a curve ~x describes the trajectory of a particle. The acceleration should be d dt d dt~x. By the definition of trajectory, d dt d dt ~x = d dt ~v(t, ~x(t)). The right-hand side is precisely D~v/Dt. Returning to our 2-dimensional example ~v = [− sin t cos t]>, we have ~a = [− cos t − sin t]>. Notice that ~v · ~a = 0. This is the well-known fact that in constant-speed circular motion the centripetal acceleration is perpendicular to the velocity. (In fact, the acceleration of any constant-speed trajectory is perpendicular to its velocity.) 3. Ideal Fluids An ideal fluid is one of constant density ρ, such that for any surface within the fluid the only stresses on the surface are normal. That is, there exists a scalar field p : R × R → R, called the pressure, such that for any surface element ∆S with outward-pointing unit normal vector ~n, the force exerted by the fluid inside ∆S on the fluid outside ∆S is p~n ∆S. The constant density condition implies that the fluid is incompressible, meaning ∇ · ~v = 0, as follows. For any region of space R, the rate of flow of mass out of the region is ∫∫ ∂R ρ~v · ~n dS = ∫∫∫
9,804 citations
Book•
01 Jan 1972
TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.
Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08
8,276 citations