Local Blockage Effects for Idealised Turbines in Tidal Channels

2019 ◽  
Author(s):  
Lei Chen ◽  
Paul A. J. Bonar ◽  
Christopher R. Vogel ◽  
Thomas A. A. Adcock
Keyword(s):  
Oscillatory Flow ◽  
Numerical Models ◽  
Numerical Results ◽  
Tidal Channels ◽  
One Dimensional ◽  
Scale Theory ◽  
Actuator Disc ◽  
Tidal Turbine ◽  
The One ◽  
Turbine Arrays

Abstract In this paper, idealised analytical and numerical models are used to explore the potential for local blockage effects to enhance the performance of turbines in tidal channels. Arrays of turbines modelled using the volume-flux-constrained actuator disc and blade element momentum theories are embedded within one-dimensional analytical and two-dimensional numerical channel domains. The effects of local blockage on the performance of arrays comprising one and five rows of actuator discs and tidal rotors operating in steady and oscillatory channel flow are then examined. In the case of steady flow, numerical results are found to agree very well with the two-scale actuator disc theory of Nishino & Willden [1]. In the case of oscillatory flow, however, numerical results show that the shorter and more highly blocked arrays produce considerably more power than predicted by the one-dimensional two-scale theory. These results support the findings of Bonar et al. [2], who showed that under certain oscillatory flow conditions, the power produced by a partial-width tidal turbine array can be much greater than predicted by two-scale theory. The departure from theory is most noticeable in the case of five turbine rows, where the two-scale theory predicts that the maximum available power should decrease with increasing local blockage but the numerical model shows the maximum available power to increase. The effects of local blockage are found to be less pronounced for the more realistic tidal rotor than for the highly idealised actuator disc but for both models, the results show that in oscillatory flow, considerably more power is available to the shorter and more highly blocked turbine arrays.

scholarly journals A Note on the Effects of Local Blockage and Dynamic Tuning on Tidal Turbine Performance

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Lei Chen ◽  
Paul A.J. Bonar ◽  
Christopher R. Vogel ◽  
Thomas A.A. Adcock
Keyword(s):  
Oscillatory Flow ◽  
Tidal Channels ◽  
Scale Theory ◽  
Dynamic Tuning ◽  
Tidal Turbines ◽  
Turbine Performance ◽  
Actuator Disc ◽  
Tidal Turbine ◽  
Tuning Strategy ◽  
Blade Element

Abstract Numerical simulations are used to explore the potential for local blockage effects and dynamic tuning strategies to enhance the performance of turbines in tidal channels. Full- and partial-width arrays of turbines, modeled using the volume-flux-constrained actuator disc and blade element momentum theories, are embedded within a two-dimensional channel with a naturally low ratio of drag to inertial forces. For steady flow, the local blockage effect observed by varying the cross-stream spacing between the turbines is found to agree very well with the predictions of the two-scale actuator disc theory of Nishino and Willden (2012, “The Efficiency of an Array of Tidal Turbines Partially Blocking a Wide Channel,” J. Fluid Mech., 708, pp. 596–606). For oscillatory flow, however, results show that, consistent with the findings of Bonar et al. (2019, “On the Arrangement of Tidal Turbines in Rough and Oscillatory Channel Flow,” J. Fluid Mech., 865, pp. 790–810), the shorter and more highly blocked arrays produce considerably more power than predicted by two-scale theory. Results also show that, consistent with the findings of Vennell (2016, “An Optimal Tuning Strategy for Tidal Turbines,” Proc. R. Soc. A, 472(2195), p. 20160047), the “dynamic” tuning strategy, in which the tuning of the turbines is varied over the tidal cycle, can only produce significantly more power than a temporally fixed turbine tuning if the array has a large number of turbine rows or a large local blockage ratio. For all cases considered, trends are consistent between the two turbine representations but the effects of local blockage and dynamic tuning are found to be much less significant for the more realistic tidal rotor than for the idealized actuator disc.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

scholarly journals Mechanics and thermodynamics of a new minimal model of the atmosphere

2020 ◽  
Vol 135 (10) ◽  
Author(s):  
Gabriele Vissio ◽  
Valerio Lucarini
Keyword(s):  
Numerical Models ◽  
Preliminary Evidence ◽  
Chaotic Motions ◽  
One Dimensional ◽  
Fundamental Properties ◽  
Multiscale Dynamics ◽  
Energy Cycle ◽  
The One ◽  
Lorenz 96 ◽  
Model Features

AbstractThe understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz ’96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The model’s evolution is controlled by two contributions—a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth’s atmosphere.

scholarly journals Turbulence and Wake Effects in Tidal Stream Turbine Arrays

2018 ◽  
Author(s):  
Martin Nuernberg ◽  
Longbin Tao
Keyword(s):  
Flow Field ◽  
Electricity Generation ◽  
Large Scale ◽  
Numerical Models ◽  
Turbulence Models ◽  
Ambient Flow ◽  
Wake Effects ◽  
Tidal Turbine ◽  
Turbine Arrays ◽  
Good Agreement

Electricity generation from tidal current can provide a reliable and predictable addition to a reduced carbon energy sector in the future. Following the deployment of the first multi-turbine array, significant cost reduction can be achieved by moving beyond demonstrator projects to large scale tidal turbine arrays. The interactions between multiple turbines installed in close proximity can affect the total electricity generation and thus require knowledge of the resulting flow field within and downstream of the array. Results are presented for experimental and numerical studies investigating the flow field characteristics in terms of velocity deficit and turbulence intensity in a staggered tidal turbine array section. Multiple configuration with varying longitudinal and transverse spacing between devices in a three-turbine array are tested. Comparison between numerical and experimental flow characteristics shows that open source numerical models with dynamic mesh features achieve good agreement and can be used for the investigation of array wake effects. The standard k–ω SST shows good agreement with experiments at reduced computational efficiency compared to higher order turbulence models (RSM). The importance of mixing with ambient flow is highlighted by identifying areas of significantly reduced velocity recovery within closely spaced arrays where ambient flow does not penetrate between adjacent wakes.

Space-Time Chebyshev Pseudospectral Method for Burgers Equation

2013 ◽  
Vol 475-476 ◽  
pp. 1075-1078
Author(s):  
Jia Chun Liu ◽  
Xiao Hui Qian
Keyword(s):  
Burgers Equation ◽  
Dimensional Space ◽  
Pseudospectral Method ◽  
High Accuracy ◽  
Space Time ◽  
Numerical Results ◽  
One Dimensional ◽  
Chebyshev Pseudospectral Method ◽  
The One ◽  
Chebyshev Pseudospectral

In this paper, we present a new method for solving of the one dimensional Burgers equation, that is the space-time Chebyshev pseudospectral method. Firstly, we discretize the Burgers equation in one dimensional space with Chebyshev pseudospectral method. Finally, numerical results obtained by this way are compared with the exact solution to show the efficiency of the method. The numerical results demonstrate high accuracy and stability of this method.

The Effects of Recombination in Expanding Gas Flows

1969 ◽  
Vol 22 (6) ◽  
pp. 739
Author(s):  
RL Pope
Keyword(s):  
Numerical Solutions ◽  
Numerical Results ◽  
Gas Flows ◽  
Approximate Analysis ◽  
One Dimensional ◽  
Different Types ◽  
Frozen State ◽  
The One

An approximate analysis of the one� dimensional expanding flow of an ideal dissociating gas, which is initially in a frozen state, is presented. The different types of solutions of the equations of the flow, for variations in the rates of expansion and recombination, are discussed. Some numerical results indicating the distances and other dimensions involved are included. The results of the approximate analysis are compared with some numerical solutions and are found to be valid for all cases in which the analysis can be expected to apply.

SPLINE TECHNIQUES FOR SOLVING RELATIVISTIC CONSERVATION EQUATIONS

1993 ◽  
Vol 04 (04) ◽  
pp. 723-747 ◽  
Author(s):  
D. J. DEAN ◽  
C. BOTTCHER ◽  
M. R. STRAYER
Keyword(s):  
Three Dimensional ◽  
Heavy Ion ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Relativistic Heavy Ion Collisions ◽  
Spline Collocation ◽  
One Dimensional ◽  
Ion Collisions ◽  
Collocation Approach ◽  
The One

We discuss a new numerical method for solving the relativistic hydrodynamic equations based upon the basis-spline collocation approach. Analytical and numerical results are compared for several problems, including one-dimensional expansions and collisions for which analytical solutions exist. Our methods, which may be easily and massively parallelized, are shown to give numerical results which agree to within a few percent of the analytic solutions. We discuss the relevance of the υ = z/t scaling solutions for the one-dimensional problem when applied to relativistic heavy-ion collisions. Finally, we discuss applications to three-dimensional problems, and present results for a typical three-dimensional expansion.

Drying Rate of Wood Particles With Longitudinal Mass Transfer

1985 ◽  
Vol 107 (1) ◽  
pp. 12-18 ◽  
Author(s):  
B. Dorri ◽  
A. F. Emery ◽  
P. C. Malte
Keyword(s):  
Numerical Models ◽  
Spherical Particles ◽  
Drying Rate ◽  
Evaporation Front ◽  
Dimensional Model ◽  
One Dimensional ◽  
Wood Particles ◽  
Small Wood ◽  
The One ◽  
Rectangular Model

The drying of small wood particles of shape L:W:t = 3 to 5:2:1 is examined by three numerical models, and results are compared to measurements. (i) A one-dimensional rectangular model has liquid water concentrated in the center of a particle, and this is removed as an evaporation front propagates into the liquid. (ii) The one-dimensional model is also treated by the volume-averaged, or “smeared” approach, for which the moisture at any point is a distribution of liquid and vapor. For the simple rectangular geometry, the frontal and smeared models give similar results. (iii) Equivalent spherical particles are analyzed by a smeared model which includes capillarity. Reasonable agreement is obtained between the spherical results and the measurements, though an overprediction in drying rate occurs for slender particles.

scholarly journals A New Diffusion Scheme for Numerical Models Based on Full Irreversibility

2009 ◽  
Vol 24 (2) ◽  
pp. 595-600 ◽  
Author(s):  
C. Liu ◽  
Y. Liu ◽  
H. Xu
Keyword(s):  
Numerical Models ◽  
Weather Prediction ◽  
Forecast Accuracy ◽  
Second Law Of Thermodynamics ◽  
New Physics ◽  
Numerical Weather Prediction Model ◽  
One Dimensional ◽  
Diffusion Scheme ◽  
The One ◽  
Mean Square Errors

Abstract In this work, the forecast accuracy of a numerical weather prediction model is improved by emulating physical dissipation as suggested by the second law of thermodynamics, which controls the irreversible evolutionary direction of a many-body system like the atmosphere. The ability of the new physics-based scheme to improve model accuracy is demonstrated via the case of the one-dimensional viscous Burgers equation and the one-dimensional diffusion equation, as well as a series of numerical simulations of the well-known 1998 successive torrential rains along the Yangtze River valley and 365 continuous 24-h simulations during 2005–06 with decreased root-mean-square errors and improved forecasts in all of the simulations.

Design of a Tidal Turbine Array for the Bohai Strait, China

2018 ◽  
Author(s):  
Lei Chen ◽  
Paul A. J. Bonar ◽  
Thomas A. A. Adcock
Keyword(s):  
Design Strategies ◽  
Stream Power ◽  
Tidal Turbines ◽  
Actuator Disc ◽  
Tidal Turbine ◽  
Tidal Stream ◽  
Flow Through ◽  
Turbine Arrays ◽  
Theoretical Results ◽  
Bohai Strait

In this paper, we consider array design strategies to maximise the power available to turbines placed in the Bohai Strait, which is considered to be one of China’s most promising candidate sites for tidal stream power. The discontinuous Galerkin version of the open-source hydrodynamic model ADCIRC is used to simulate flow through the strait and tidal turbines are introduced using a sub-grid scale actuator disc model. New design algorithms based on key theoretical results are used to build large arrays, which are then compared in terms of both the collective power output and the power produced per turbine. The results of the analysis are used to draw general conclusions about the optimal design of tidal turbine arrays.

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