Power Generation Using Kites in a GroundGen Airborne Wind Energy System: A Numerical Study

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Alireza Mahdavi Nejad ◽  
Gretar Tryggvason
Keyword(s):  
Wind Energy ◽  
High Speed ◽  
Stokes Equations ◽  
Numerical Study ◽  
Energy System ◽  
Staggered Grid ◽  
Immersed Boundary ◽  
Uniform Mesh ◽  
Two Dimensional ◽  
Time Step

Abstract A computational model of a massless kite that produces power in an airborne wind energy (AWE) system is presented. AWE systems use tethered kites at high altitudes to extract energy from the wind and are being considered as an alternative to wind turbines since the kites can move in high-speed cross-wind motions over large swept areas to increase power production. In our model, the kite completes successive power-retraction cycles where the kite angle of attack is altered as required to vary the resultant aerodynamic forces on the kite. The flow field is found in a two-dimensional domain near the flexible kite by solving the full Navier–Stokes equations using an Eulerian grid together with a Lagrangian representation of the kite. The flow solver is a finite volume projection method using a non-uniform mesh on a staggered grid and corrector–predictor technique to ensure a second-order accuracy in time. The two-dimensional kite shape is modeled as a slightly cambered immersed boundary that moves with the flow. The flexible kite is modeled with a set of linear springs following Hooke’s law. The unstretched length of each elastic tether at a given time step is controlled using periodic triangular wave shapes to achieve the required power-retraction phases. A study was conducted in which the wave shape amplitude, frequency, and phase (between two tethers) were adjusted to achieve a suitably high net power output. The results are in good agreement with predictions for Loyd’s simple kite in two-dimensional motion. Aerodynamic coefficients for the kite, tether tensions, tether reel-out and reel-in speeds, and the vorticity fields in the kite wake are also determined.

Numerical Modeling of Kites for Power Generation

2014 ◽  
Author(s):  
Alireza Mahdavi Nejad ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
High Speed ◽  
Stokes Equations ◽  
Second Order ◽  
Staggered Grid ◽  
Immersed Boundary ◽  
Uniform Mesh ◽  
Two Dimensional ◽  
Time Step

A computational model of a massless kite that produces power in an airborne wind energy system (AWE) is presented. AWE systems use tethered kites at high altitudes to extract energy from the wind, and are being considered as an alternative to wind turbines since the kites can move in high-speed cross-wind motions over large swept areas to increase power production. In our model the kite completes successive power-retraction cycles where the kite angle of attack is altered as required to vary the resultant aerodynamic forces on the kite. The numerical simulation models the flow field in a two-dimensional domain near the flexible kite by solving the full Navier-Stokes equations. Eulerian grid points for the flow domain together with a Lagrangian representation of the kite are employed. The flow field is determined through a second-order finite difference projection method using a non-uniform mesh on a staggered grid. A corrector-predictor technique is employed to ensure the second-order accuracy in time of the numerical simulation. The two-dimensional kite shape is modeled as a slightly cambered immersed boundary that evolves with the flow. The flexible kite surface is modeled with a set of linear springs following Hooke’s law. The unstretched length of each elastic tether at a given time step is controlled using periodic triangular wave shapes to achieve the required power-retraction phases. A study was conducted in which the wave shape amplitude, frequency, and phase (between two tethers) was adjusted to achieve a suitably high net power output with very good agreement to predictions for Loyd’s simple kite in two-dimensional motion. Aerodynamic coefficients for the kite, tether tensions, tether reel-out and reel-in speeds, and vorticity flowfields in the kite wake are also determined.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Wave Loads on Floaters of Aquaculture Plants

2008 ◽  
Author(s):  
David Kristiansen ◽  
Odd M. Faltinsen
Keyword(s):  
Stokes Equations ◽  
Model Tests ◽  
Staggered Grid ◽  
Physical Parameters ◽  
Surface Zone ◽  
Two Dimensional ◽  
Wave Loads ◽  
Wave Load ◽  
Constrained Interpolation ◽  
Advection Term

This paper addresses wave loads on horizontal cylinders in the free surface zone by means of model tests and numerical simulations. This has relevance for the design of floating fish farms at exposed locations. Two model geometries were tested, where two-dimensional flow conditions were sought. The cylinders were fixed and exposed to regular wave trains. Wave overtopping the models were observed. A two-dimensional Numerical Wave Tank (NWT) for wave load computations is described. The NWT is based on the finite difference method and solves the incompressible Navier-Stokes equations on a non-uniform Cartesian staggered grid. The advection term is treated separately by the CIP (Constrained Interpolation Profile) method. A fractional and validation of the NWT is emphasized. Numerical results from simulations with the same physical parameters as in the model tests are performed for comparison. Deviations are discussed.

Numerical simulation of the Late Jurassic closure of the Vardar Tethys

2021 ◽  
Author(s):  
Nikola Stanković ◽  
Vesna Cvetkov ◽  
Vladica Cvetković
Keyword(s):  
Boundary Conditions ◽  
Numerical Simulations ◽  
Stokes Equations ◽  
Numerical Study ◽  
Phase Evolution ◽  
Staggered Grid ◽  
Second Phase ◽  
Weak Zone ◽  
Ongoing Research ◽  
Magmatic Complex

<p>We report updated results of our ongoing research on constraining geodynamic conditions associated with the final closure of the Vardar branch of the Tethys Ocean by means of application of numerical simulations (previous interim results reported in EGU2020-5919).</p><p>The aim of our numerical study is to test the hypothesis that a single eastward subduction in the Jurassic is a valid explanation for the occurrence of three major, presently observed geological entities that are left behind after the closure of the Vardar Tethys. These include: ophiolite-like igneous rocks of the Sava-Vardar zone and presumably subduction related Timok Magmatic Complex, both Late Cretaceous in age as well as Jurassic ophiolites obducted onto the Adriatic margin. In our simulations we initiate an intraoceanic subduction in the Early/Middle Jurassic, which eventually transitions into an oceanic closure and subsequent continental collision processes.</p><p>In the scope of our study numerical simulations are performed by solving a set of partial differential equations: the continuity equation, the Navier-Stokes equations and the temperature equation. To this end we used I2VIS thermo-mechanical code which utilizes marker in cell approach with finite difference discretization of equations on a staggered grid [Gerya et al., 2000; Gerya&Yuen, 2003].</p><p>The 2D model consists of two continental plates separated by two oceanic slabs connected at a mid-oceanic ridge. Intraoceanic subduction is initiated along the ridge by assigning a weak zone beneath the ridge. Time-dependent boundary conditions for velocity are imposed on the simulation in order to model a transient spreading period. The change of sign in plate velocities is found to be useful for both obtaining obduction / ophiolite emplacement [Duretz et al., 2016] and causing back-arc extension. Changes in velocities are linear in time. Simulations follow a three-phase evolution of velocity boundary conditions consisting of two convergent phases separated by a single divergent phase where spreading regime is dominant. Effect of duration and magnitude of the second phase on model evolution is also explored.</p><p>Our so far obtained simulations were able to reproduce the westward obduction and certain extension processes along the active (European) margin, which match the existing geological relationships. However, the simulations involve an unreasonably short geodynamic event (cca 15-20 My) and we are working on solving this problem with new simulations. </p>

Vortex dynamics and new lift enhancement mechanism of wing–body interaction in insect forward flight

2016 ◽  
Vol 795 ◽  
pp. 634-651 ◽  
Author(s):  
Geng Liu ◽  
Haibo Dong ◽  
Chengyu Li
Keyword(s):  
Vortex Dynamics ◽  
High Speed ◽  
Stokes Equations ◽  
The Body ◽  
Immersed Boundary ◽  
Dramatic Improvement ◽  
Forward Flight ◽  
Body Interaction ◽  
Enhancement Mechanism ◽  
Lift Enhancement

The effects of wing–body interaction (WBI) on aerodynamic performance and vortex dynamics have been numerically investigated in the forward flight of cicadas. Flapping wing kinematics was reconstructed based on the output of a high-speed camera system. Following the reconstruction of cicada flight, three models, wing–body (WB), body-only (BD) and wings-only (WN), were then developed and evaluated using an immersed-boundary-method-based incompressible Navier–Stokes equations solver. Results have shown that due to WBIs, the WB model had a 18.7 % increase in total lift production compared with the lift generated in both the BD and WN models, and about 65 % of this enhancement was attributed to the body. This resulted from a dramatic improvement of body lift production from 2 % to 11.6 % of the total lift produced by the wing–body system. Further analysis of the associated near-field and far-field vortex structures has shown that this lift enhancement was attributed to the formation of two distinct vortices shed from the thorax and the posterior of the insect, respectively, and their interactions with the flapping wings. Simulations are also used to examine the new lift enhancement mechanism over a range of minimum wing–body distances, reduced frequencies and body inclination angles. This work provides a new physical insight into the understanding of the body-involved lift-enhancement mechanism in insect forward flight.

scholarly journals Numerical Study of the Internal Flow Field of a Centrifugal Impeller

1994 ◽  
Author(s):  
Mou-jin Zhang ◽  
Chuan-gang Gu ◽  
Yong-miao Miao
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Internal Flow ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
High Reynolds

The complex three-dimensional flow field in a centrifugal impeller with low speed is studied in this paper. Coupled with high–Reynolds–number k–ε turbulence model, the fully three–dimensional Reynolds averaged Navier–Stokes equations are solved. The Semi–Implicit Method for Pressure–Linked Equations (SIMPLE) algorithm is used. And the non–staggered grid arrangement is also used. The computed results are compared with the available experimental data. The comparison shows good agreement.

Numerical Study on Electrokinetic Interaction Between a Pair of Cylindrical Colloidal Particles

2009 ◽  
Author(s):  
Dolfred Vijay Fernandes ◽  
Sangmo Kang ◽  
Yong Kweon Suh
Keyword(s):  
Flow Field ◽  
Electric Field ◽  
Colloidal Particles ◽  
Stokes Equations ◽  
Separation Efficiency ◽  
Numerical Study ◽  
Interaction Force ◽  
Surface Element ◽  
Immersed Boundary ◽  
Interaction Forces

Electrophoresis is the motion of dispersed particles relative to a fluid under the influence of an electric field. Presently this phenomenon of electrokinetics is widely used in biotechnology for the separation of proteins, sequencing of polypeptide chains etc. The separation efficiency of these biomolecules is affected by their aggregation. Thus it is important to study the interaction forces between the molecules. In this study we calculate the electrophoretic motion of a pair of colloidal particles under axial electric field. The hydrodynamic and electric double layer (EDL) interaction forces are calculated numerically. The EDL interaction force is calculated from electric field distribution around the particle using Maxwell stress tensor and the hydrodynamic force is calculated from the flow field obtained from the solution of Stokes equations. The continuous forcing approach of immersed boundary method is used to obtain flow field around the moving particles. The EDL distribution around the particles is obtained by solving Poisson-Nernst-Planck (PNP) equations on a hybrid grid system. The EDL interaction force calculated from numerical solution is compared with the one obtained from surface element integration (SEI) method.

Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates

2019 ◽  
Vol 40 (4) ◽  
pp. 2584-2625 ◽  
Author(s):  
Hussain A Ibdah ◽  
Cecilia F Mondaini ◽  
Edriss S Titi
Keyword(s):  
Data Assimilation ◽  
Error Estimates ◽  
Stokes Equations ◽  
Time Discretization ◽  
Dissipative Systems ◽  
Complete Analysis ◽  
Two Dimensional ◽  
Time Error ◽  
Time Step ◽  
Fully Discrete

Abstract Our aim is to approximate a reference velocity field solving the two-dimensional Navier–Stokes equations (NSE) in the absence of its initial condition by utilizing spatially discrete measurements of that field, available at a coarse scale, and continuous in time. The approximation is obtained via numerically discretizing a downscaling data assimilation algorithm. Time discretization is based on semiimplicit and fully implicit Euler schemes, while spatial discretization (which can be done at an arbitrary scale regardless of the spatial resolution of the measurements) is based on a spectral Galerkin method. The two fully discrete algorithms are shown to be unconditionally stable, with respect to the size of the time step, the number of time steps and the number of Galerkin modes. Moreover, explicit, uniform-in-time error estimates between the approximation and the reference solution are obtained, in both the $L^2$ and $H^1$ norms. Notably, the two-dimensional NSE, subject to the no-slip Dirichlet or periodic boundary conditions, are used in this work as a paradigm. The complete analysis that is presented here can be extended to other two- and three-dimensional dissipative systems under the assumption of global existence and uniqueness.

Numerical Study of Wave Slamming on an Oscillating Flap

2014 ◽  
Author(s):  
Yanji Wei ◽  
Alan Henry ◽  
Olivier Kimmoun ◽  
Frederic Dias
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Ocean Waves ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Numerical Studies ◽  
Wave Slamming ◽  
Volume Method

Bottom hinged Oscillating Wave Surge Converters (OWSCs) are efficient devices for extracting power from ocean waves. There is limited knowledge about wave slamming on such devices. This paper deals with numerical studies of wave slamming on an oscillating flap to investigate the mechanism of slamming events. In our model, the Navier–Stokes equations are discretized using the Finite Volume method with the Volume of Fluid (VOF) approach for interface capturing. Waves are generated by a flap-type wave maker in the numerical wave tank, and the dynamic mesh method is applied to model the motion of the oscillating flap. Basic mesh and time step refinement studies are performed. The flow characteristics in a slamming event are analysed based on numerical results. Various simulations with different flap densities, water depths and wave amplitudes are performed for a better understanding of the slamming.

A Discrete-Forcing Immersed Boundary Method for the Fluid-Structure Interaction of an Elastic Slender Body

2011 ◽  
Author(s):  
Injae Lee ◽  
Haecheon Choi
Keyword(s):  
Immersed Boundary Method ◽  
Present Method ◽  
Stokes Equations ◽  
Slender Body ◽  
Body Motion ◽  
Computational Time ◽  
Immersed Boundary ◽  
Flexible Beam ◽  
Time Step ◽  
Boundary Method

In the present study, a new immersed boundary method for the simulation of flow around an elastic slender body is suggested. The present method is based on the discrete-forcing immersed boundary method by Kim et al. (J. Comput. Phys., 2001) and is fully coupled with the elastic slender body motion. The incompressible Navier-Stokes equations are solved in an Eulerian coordinate and the elastic slender body motion is described in a Lagrangian coordinate, respectively. The elastic slender body is modeled as a thin flexible beam and is segmented by finite number of blocks. Each block is then moved by the external and internal forces such as the hydrodynamic, tension, bending, and buoyancy forces. With the proposed method, we simulate several flow problems including flows over a flexible filament, an oscillating insect wing, and a flapping flag. We show that the present method does not impose any severe limitation on the size of computational time step. The results obtained agree very well with those from previous studies.

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