scholarly journals A Nonlinear Computational Model of Tethered Underwater Kites for Power Generation

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Power Output ◽  
Current Velocity ◽  
High Speed ◽  
Stokes Equations ◽  
Hydrodynamic Forces ◽  
Two Dimensions ◽  
Ocean Current ◽  
Design Parameters ◽  
Immersed Boundary ◽  
Flow Equations

The dynamic motion of tethered undersea kites (TUSK) is studied using numerical simulations. TUSK systems consist of a rigid winged-shaped kite moving in an ocean current. The kite is connected by tethers to a platform on the ocean surface or anchored to the seabed. Hydrodynamic forces generated by the kite are transmitted through the tethers to a generator on the platform to produce electricity. TUSK systems are being considered as an alternative to marine turbines since the kite can move at a high-speed, thereby increasing power production compared to conventional marine turbines. The two-dimensional Navier–Stokes equations are solved on a regular structured grid to resolve the ocean current flow, and a fictitious domain-immersed boundary method is used for the rigid kite. A projection method along with open multiprocessing (OpenMP) is employed to solve the flow equations. The reel-out and reel-in velocities of the two tethers are adjusted to control the kite angle of attack and the resultant hydrodynamic forces. A baseline simulation, where a high net power output was achieved during successive kite power and retraction phases, is examined in detail. The effects of different key design parameters in TUSK systems, such as the ratio of tether to current velocity, kite weight, current velocity, and the tether to kite chord length ratio, are then further studied. System power output, vorticity flow fields, tether tensions, and hydrodynamic coefficients for the kite are determined. The power output results are shown to be in good agreement with the established theoretical results for a kite moving in two dimensions.

Computational Simulation of the Tethered Undersea Kites for Power Generation

2015 ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Power Output ◽  
High Speed ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Hydrodynamic Forces ◽  
Two Dimensions ◽  
Ocean Current ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Flow Equations

The dynamic motion of tethered undersea kites (TUSK) is studied using numerical simulations. TUSK systems consist of a rigid-winged kite moving in an ocean current. The kite is connected by tethers to a platform on the ocean surface or anchored to the seabed. Hydrodynamic forces generated by the kite are transmitted through the tethers to a generator on the platform to produce electricity. TUSK systems are being considered as an alternative to marine turbines since the kite can move in high speed motions to increase power production compared to conventional marine turbines. The two-dimensional Navier-Stokes equations are solved on a regular structured grid that comprises the ocean current flow, and an immersed boundary method is used for the rigid kite. A two-step projection method along with Open Multi-Processing (OpenMP) is employed to solve the flow equations. The reel-out and reel-in velocities of the two tethers are adjusted to control the kite angle of attack and the resultant hydrodynamic forces. A baseline simulation was studied where a high net power output was achieved during successive kite power and retraction phases. System power output, vorticity flow fields, tether tensions, and hydrodynamic coefficients for the kite are determined. The power output results are in good agreement with established theoretical results for a kite moving in two dimensions.

Simulation of Tethered Underwater Kites Moving in Three Dimensions for Power Generation

2017 ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Numerical Simulation ◽  
Power Generation ◽  
Stokes Equations ◽  
Simulation Models ◽  
Three Dimensions ◽  
Ocean Current ◽  
Design Parameters ◽  
Immersed Boundary ◽  
Computational Domain ◽  
Flow Equations

In this paper, a numerical simulation of tether undersea kites (TUSK) used for power generation is undertaken. The effect of varying key design parameters in these systems is studied. TUSK systems consist of a rigid-winged kite, or glider, moving in an ocean current. One proposed TUSK concept uses a tethered kite which is connected by a flexible tether to a support structure with a generator on a surface buoy. The numerical simulation models the flow field in a three-dimensional domain near the rigid undersea kite wing by solving the full Navier-Stokes equations. A moving computational domain method is used to reduce the computational run times. A second-order corrector-predictor method, along with Open Multi-Processing (OpenMP), is employed to solve the flow equations. In order to track the rigid kite, which is a rectangular planform wing with a NACA 0021 airfoil, an immersed boundary method is used. The tension force in the elastic tether is modeled by a simple Hooke’s law, and the effect of tether damping is added. PID control methods are used to adjust the kite pitch, roll and yaw angles during power (tether reel-out) and retraction (reel-in) phases to obtain the desired kite trajectories. During the reel-out phase the kite moves in successive cross-current motions in a figure-8 pattern, the tether length increases and power is generated. During reel-in the kite motion is along the tether, and kite hydrodynamic forces are reduced so that net positive power is produced. The effects of different key design parameters in TUSK systems, such as the ratio of tether to current velocity, and tether retraction velocity, are then further studied. System power output, kite trajectories, and vorticity flow fields for the kite are also determined.

Simulation of Tethered Underwater Kites: Three Dimensional Trajectories for Power Generation

2016 ◽  
Author(s):  
Amirmahdi Ghasemi ◽  
David J. Olinger ◽  
Gretar Tryggvason
Keyword(s):  
Numerical Simulation ◽  
Power Generation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Simulation Models ◽  
Hydrodynamic Forces ◽  
Ocean Current ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Flow Equations

In this paper, a numerical simulation of three dimensional motion of tether undersea kites (TUSK) for power generation is studied. TUSK systems consist of a rigid-winged kite, or glider, moving in an ocean current. One proposed concept uses a tethered kite which is connected by a flexible tether to a support structure with a generator on the ocean surface. The numerical simulation models the flow field in a three-dimensional domain near the rigid undersea kite wing by solving the full Navier-Stokes equations. A two-step projection method along with Open Multi-Processing (OpenMP) is employed to solve the flow equations. In order to track the rigid kite, an immersed boundary method is used. A NACA 0021 airfoil is used for the cross section shape of the kite, and the tension forces in the elastic tethers are modeled by a simple Hooke’s law. A grid refinement study has been carried out to ensure the independence of the numerical results on the grid mesh resolution. Also, the Reynolds number independency has been studied. PID control methods are used to adjust the kite pitch, roll and yaw angles during power (tether reel-out) and retraction (reel-in) phases to obtain desired kite trajectories. During the reel-out phase the kite moves in successive cross-current motions in a figure-8 pattern, the tether length increases and power is generated. During reel-in the kite motion is along the tether, and kite hydrodynamic forces are reduced so that net positive power is produced. Kite trajectories, hydrodynamic forces on the kite, kite tether tension and output power are determined and analyzed for a baseline TUSK simulation.

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.

Flows produced by the combined oscillatory rotation and translation of a circular cylinder in a quiescent fluid

2014 ◽  
Vol 764 ◽  
pp. 148-170 ◽  
Author(s):  
Christopher Koehler ◽  
Philip Beran ◽  
Marcos Vanella ◽  
Elias Balaras
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Bluff Body ◽  
Stokes Equations ◽  
Time Windows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Immersed Boundary ◽  
Dimensionless Time ◽  
Quiescent Fluid

AbstractFlows produced by a circular cylinder undergoing oscillatory rotation and translation in a quiescent fluid have been studied via direct numerical simulations. The incompressible Navier–Stokes equations were solved for large dimensionless time windows using an immersed boundary method with adaptive Cartesian grid refinement. Parametric studies were conducted in two dimensions on the Reynolds number, Keulegan–Carpenter number and phase shift. In addition to the previously reported net thrust case (Blackburn et al., Phys. Fluids, vol. 11, 1999, pp. 4–6), the study catalogued the appearance of several streaming jet regimes with varying deflection angles, deflected and horizontal vortex shedding regimes, and a double mirrored jet regime with varying inter-jet angles, as well as several chaotic cases. Visualizations are presented to clarify each observed flow regime and to illustrate the parameter space. Connections are drawn between these canonical bluff-body deflected wakes and a similar phenomenon observed in aerofoils oscillating at high reduced frequencies in a cross-flow. Also, the discovery of the streaming jet regimes with varying deflection angles opens the door for using these flows as a low-Reynolds-number propulsive mechanism requiring only a two-degree-of-freedom actuator. Simulation results suggest that the flow phenomena observed in two dimensions persist in three dimensions, despite spanwise fluctuations.

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.

Modeling and Simulation of Tethered Undersea Kites

2016 ◽  
Author(s):  
Yao Wang ◽  
David J. Olinger
Keyword(s):  
Modeling And Simulation ◽  
Power Output ◽  
Equations Of Motion ◽  
Axial Flow ◽  
Turbine Rotor ◽  
Hydrodynamic Forces ◽  
Ocean Current ◽  
Lagrange Equations ◽  
Blade Tip ◽  
Cross Current

In this work an emerging hydrokinetic energy technology, Tethered UnderSea Kites (TUSK), is studied. TUSK systems use an axial-flow turbine and generator mounted on a rigid, underwater winged kite that is tethered to a floating surface buoy to extract power from an ocean current. The tethered underwater kite is controlled to travel in cross-current motions at a high velocity which is at least four to five times larger than the ocean current velocity. This higher velocity significantly increases the potential power output compared to conventional fixed marine turbines. Modeling and simulation of the kite-tether dynamics in a TUSK system is studied by developing and solving governing equations of motion derived from Euler-Lagrange equations. Models for physical effects appropriate to TUSK systems are developed, including for turbine power and turbine drag, kite wing hydrodynamic forces, and the effect of turbine blade tip cavitation on turbine power output. A baseline simulation that includes these modeled effects and a simple kite control scheme is studied to estimate cross-current kite trajectories, turbine power output, kite hydrodynamic forces, kite pitch, roll and yaw dynamics, and tether tensions. Once the baseline simulation case has been fully explored, a parametric study is conducted that varies key design and flow parameters including ocean current speed, kite weight and wing area, turbine rotor area, tether length, and kite control system parameters.

scholarly journals Partial regularisation of the incompressible 𝜇(I)-rheology for granular flow

2017 ◽  
Vol 828 ◽  
pp. 5-32 ◽  
Author(s):  
T. Barker ◽  
J. M. N. T. Gray
Keyword(s):  
High Speed ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Functional Dependence ◽  
Granular Flows ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Major Step ◽  
Ill Posed ◽  
Well Posed

In recent years considerable progress has been made in the continuum modelling of granular flows, in particular the $\unicode[STIX]{x1D707}(I)$-rheology, which links the local viscosity in a flow to the strain rate and pressure through the non-dimensional inertial number $I$. This formulation greatly benefits from its similarity to the incompressible Navier–Stokes equations as it allows many existing numerical methods to be used. Unfortunately, this system of equations is ill posed when the inertial number is too high or too low. The consequence of ill posedness is that the growth rate of small perturbations tends to infinity in the high wavenumber limit. Due to this, numerical solutions are grid dependent and cannot be taken as being physically realistic. In this paper changes to the functional form of the $\unicode[STIX]{x1D707}(I)$ curve are considered, in order to maximise the range of well-posed inertial numbers, while preserving the overall structure of the equations. It is found that when the inertial number is low there exist curves for which the equations are guaranteed to be well posed. However when the inertial number is very large the equations are found to be ill posed regardless of the functional dependence of $\unicode[STIX]{x1D707}$ on $I$. A new $\unicode[STIX]{x1D707}(I)$ curve, which is inspired by the analysis of the governing equations and by experimental data, is proposed here. In order to test this regularised rheology, transient granular flows on inclined planes are studied. It is found that simulations of flows, which show signs of ill posedness with unregularised models, are numerically stable and match key experimental observations when the regularised model is used. This paper details two-dimensional transient computations of decelerating flows where the inertial number tends to zero, high-speed flows that have large inertial numbers, and flows which develop into granular rollwaves. This is the first time that granular rollwaves have been simulated in two dimensions, which represents a major step towards the simulation of other complex granular flows.

scholarly journals An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 164 ◽  
Author(s):  
Bourantas ◽  
Zwick ◽  
Joldes ◽  
Loukopoulos ◽  
Tavner ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Implicit Methods ◽  
Time Step ◽  
Flow Equations ◽  
Point Collocation ◽  
Flow Past ◽  
Flow Past A Cylinder

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.

Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids

2001 ◽  
Vol 123 (3) ◽  
pp. 568-582 ◽  
Author(s):  
L. Sbardella ◽  
M. Imregun
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Laplacian Operator ◽  
Finite Volume Scheme ◽  
Test Case ◽  
Flow Equations ◽  
Mixed Element

The paper describes the theory and the numerical implementation of a three-dimensional finite volume scheme for the solution of the linearized, unsteady Favre-averaged Navier–Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangles and quadrilaterals in two dimensions, and of tetrahedra, triangular prisms, and hexahedra in three dimensions. The linearized unsteady viscous flow equations are derived by assuming small harmonic perturbations from a steady-state flow and the resulting equations are solved using a pseudo-time marching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow computations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element meshes, the use of a Laplacian operator, which results in a nearest neighbor stencil, and the full linearization of the Spalart–Allmaras turbulence model. Four different test cases are presented for the validation of the proposed method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the second test case is to check the computational results against the asymptotic analytical solution derived by Lighthill for an unsteady laminar flow. The third test case examines the implications of using inviscid, frozen-turbulence, and fully turbulent models when linearizing the unsteady flow over a transonic turbine blade, the so-called 11th International Standard Configuration. The final test case is a rotor/stator interaction, which not only checks the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady flow data for the last two cases and good overall agreement was obtained.

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