scholarly journals The curled wake model: a three-dimensional and extremely fast steady-state wake solver for wind plant flows

2021 ◽  
Vol 6 (2) ◽  
pp. 555-570
Author(s):  
Luis A. Martínez-Tossas ◽  
Jennifer King ◽  
Eliot Quon ◽  
Christopher J. Bay ◽  
Rafael Mudafort ◽  
...  
Keyword(s):  
Steady State ◽  
Wind Power ◽  
Power Plants ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Mean Power ◽  
Wake Model

Abstract. Wind turbine wake models typically require approximations, such as wake superposition and deflection models, to accurately describe wake physics. However, capturing the phenomena of interest, such as the curled wake and interaction of multiple wakes, in wind power plant flows comes with an increased computational cost. To address this, we propose a new hybrid method that uses analytical solutions with an approximate form of the Reynolds-averaged Navier–Stokes equations to solve the time-averaged flow over a wind plant. We compare results from the solver to supervisory control and data acquisition data from the Lillgrund wind plant obtaining wake model predictions which are generally within 1 standard deviation of the mean power data. We perform simulations of flow over the Columbia River Gorge to demonstrate the capabilities of the model in complex terrain. We also apply the solver to a case with wake steering, which agreed well with large-eddy simulations. This new solver reduces the time – and therefore the related cost – it takes to simulate a steady-state wind plant flow (on the order of seconds using one core). Because the model is computationally efficient, it can also be used for different applications including wake steering for wind power plants and layout optimization.

scholarly journals The curled wake model: A three-dimensional and extremely fast steady-state wake solver for wind plant flows

2020 ◽  
Author(s):  
Luis A. Martínez-Tossas ◽  
Jennifer King ◽  
Eliot Quon ◽  
Christopher J. Bay ◽  
Rafael Mudafort ◽  
...  
Keyword(s):  
Steady State ◽  
Wind Power ◽  
Power Plants ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Good Agreement

Abstract. This work focuses on minimizing the computational cost of steady-state wind power plant flow simulations that take into account wake steering physics. We present a simple wake solver with a computational cost on the order of seconds for large wind plants. The solver uses a simplified form of the Reynolds-averaged Navier-Stokes equations to obtain a parabolic equation for the wake deficit of a wind plant. We compare results from the model to supervisory control and data acquisition (SCADA) from the Lillgrund wind plant; good agreement is obtained. Results for the solver in complex terrain are also shown. Finally, the solver is demonstrated for a case with wake steering showing good agreement with power reported by large-eddy simulations. This new solver minimizes the time – and therefore the related cost – it takes to conduct a steady-state wind plant flow simulation to about a second on a personal laptop. This solver can be used for different applications including wake steering for wind power plants and layout optimization, and it will soon be available within the FLOw Redirection and Induction in Steady State (FLORIS) framework.

Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers

1995 ◽  
Vol 291 ◽  
pp. 369-392 ◽  
Author(s):  
Ronald D. Joslin
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simulation Results ◽  
Dimensional Simulation ◽  
Attachment Line

The spatial evolution of three-dimensional disturbances in an attachment-line boundary layer is computed by direct numerical simulation of the unsteady, incompressible Navier–Stokes equations. Disturbances are introduced into the boundary layer by harmonic sources that involve unsteady suction and blowing through the wall. Various harmonic-source generators are implemented on or near the attachment line, and the disturbance evolutions are compared. Previous two-dimensional simulation results and nonparallel theory are compared with the present results. The three-dimensional simulation results for disturbances with quasi-two-dimensional features indicate growth rates of only a few percent larger than pure two-dimensional results; however, the results are close enough to enable the use of the more computationally efficient, two-dimensional approach. However, true three-dimensional disturbances are more likely in practice and are more stable than two-dimensional disturbances. Disturbances generated off (but near) the attachment line spread both away from and toward the attachment line as they evolve. The evolution pattern is comparable to wave packets in flat-plate boundary-layer flows. Suction stabilizes the quasi-two-dimensional attachment-line instabilities, and blowing destabilizes these instabilities; these results qualitatively agree with the theory. Furthermore, suction stabilizes the disturbances that develop off the attachment line. Clearly, disturbances that are generated near the attachment line can supply energy to attachment-line instabilities, but suction can be used to stabilize these instabilities.

High Level Languages Implementation and Analysis of 3D Navier-Stokes Solvers

2011 ◽  
Vol 3 (3) ◽  
pp. 370-388
Author(s):  
Valerio Grazioso ◽  
Carlo Scalo ◽  
Giuseppe de Felice ◽  
Carlo Meola
Keyword(s):  
Stokes Equations ◽  
Complex Geometry ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Computationally Efficient ◽  
Flamelet Model ◽  
Advection Scheme ◽  
Variable Ordering ◽  
Pressure Variable ◽  
High Level

AbstractIn this work we introduce PRIN-3D (PRoto-code for Internal flows modeled by Navier-Stokes equations in 3-Dimensions), a new high level algebraic language (Matlab®) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on designing a memory and computationally efficient code that, due to the typical conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special pressure variable ordering patterns that lead to a block-structured Poisson-like matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model.

A Quasi-Generalized-Coordinate Approach for Numerical Simulation of Complex Flows

2006 ◽  
Vol 128 (6) ◽  
pp. 1394-1399 ◽  
Author(s):  
Donghyun You ◽  
Meng Wang ◽  
Rajat Mittal ◽  
Parviz Moin
Keyword(s):  
Coordinate System ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Effective ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Curvilinear Coordinate ◽  
Generalized Coordinate

A novel structured grid approach which provides an efficient way of treating a class of complex geometries is proposed. The incompressible Navier-Stokes equations are formulated in a two-dimensional, generalized curvilinear coordinate system complemented by a third quasi-curvilinear coordinate. By keeping all two-dimensional planes defined by constant third coordinate values parallel to one another, the proposed approach significantly reduces the memory requirement in fully three-dimensional geometries, and makes the computation more cost effective. The formulation can be easily adapted to an existing flow solver based on a two-dimensional generalized coordinate system coupled with a Cartesian third direction, with only a small increase in computational cost. The feasibility and efficiency of the present method have been assessed in a simulation of flow over a tapered cylinder.

Strongly Coupled Fluid-Structure Interactions via a New Navier-Stokes Method for Prediction of Vortex-Induced Vibrations

2005 ◽  
Author(s):  
Yannis Kallinderis ◽  
Hyung Taek Ahn
Keyword(s):  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Design Tool ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibrations ◽  
Offshore Industry

Numerical prediction of vortex-induced vibrations requires employment of the unsteady Navier-Stokes equations. Current Navier-Stokes solvers are quite expensive for three-dimensional flow-structure applications. Acceptance of Computational Fluid Dynamics as a design tool for the offshore industry requires improvements to current CFD methods in order to address the following important issues: (i) stability and computation cost of the numerical simulation process, (ii) restriction on the size of the allowable time-step due to the coupling of the flow and structure solution processes, (iii) excessive number of computational elements for 3-D applications, and (iv) accuracy and computational cost of turbulence models used for high Reynolds number flow. The above four problems are addressed via a new numerical method which employs strong coupling between the flow and the structure solutions. Special coupling is also employed between the Reynolds-averaged Navier-Stokes equations and the Spalart-Allmaras turbulence model. An element-type independent spatial discretization scheme is also presented which can handle general hybrid meshes consisting of hexahedra, prisms, pyramids, and tetrahedral.

scholarly journals THREE-DIMENSIONAL INSTANTANEOUS STREAMLINESOF GAS FLOWS FOR SIMULATION THE STEADY-STATE OUTPUT OF AN ARTIFICIAL TORNADO

2018 ◽  
pp. 71-76
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Complete System ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Gas Flows ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Coriolis Forces

The method of parallelizing a numerical solution of the complete system of Navier - Stokes equations is used to describe three-dimensional unsteady flows of a viscous compressible heat-conducting gas in ascending swirling flows. In this case the action of gravity and Coriolis forces is taken into account, and the coefficients of viscosity and thermal conductivity are assumed to be constant. The results of the numerical construction of instantaneous streamlines characterizing complex three-dimensional flows are presented for simulation the steady-state output of an ascend-ing swirling air flow in an artificial tornado.

A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids

2017 ◽  
Vol 21 (5) ◽  
pp. 1231-1257 ◽  
Author(s):  
Jian Cheng ◽  
Xiaodong Liu ◽  
Tiegang Liu ◽  
Hong Luo
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Computational Cost ◽  
Three Dimensional ◽  
High Order ◽  
Navier Stokes ◽  
Attractive Alternative ◽  
Order Of Accuracy ◽  
Navier Stokes Equations ◽  
Hybrid Grids

AbstractA parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.

Validation of a CFD Code for the Analysis of Hydrogen Behaviors and Thermal Hydraulics in Containments

2018 ◽  
Author(s):  
Meilan Chen ◽  
Zeming Zheng
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Convection Heat Transfer ◽  
Navier Stokes ◽  
Thermal Hydraulics ◽  
Navier Stokes Equations ◽  
Water Metal ◽  
Water Reactors

During the process of core melt-down accident in light water reactors, large quantities of hydrogen generated by drastic water-metal reaction are released to the containment. Subsequently, hydrogen-rich layer may be formed under the dome of the containment, threatening the integrity of nuclear Power Plants (NPPs). In the framework of a China national R&D project, China Nuclear Power Research Institute (CNPRI) has developed a three dimensional CFD Code for the assessment of hydrogen behaviors and relative thermal hydraulics in containment. The code solves the time-dependent Navier-Stokes Equations with multi-gas species. Validation with International Standard Problems (ISP) and other test data based on a Phenomena Identification and Ranking Table (PIRT) has been undergoing together with the development of this code. In this paper, the test cases of HYJET, COPAIN and TOSQAN 101 Test are validated. Stratification, buoyancy induced mixing in gases, convection heat transfer and condensation on surface are evaluated in the former two cases, while gas entrainment and mixing by spray droplets in the later one. Excellent agreements between experimental data and model predictions are obtained. In order to meet the requirements for application of the code in practical NPP design and safety analysis, further validations of other phenomena in PIRT should be performed in the near future.

CFD Studies on Burner Secondary Air Flow

2004 ◽  
Author(s):  
Anil K. Purimetla ◽  
Jie Cui ◽  
Stephen Idem ◽  
Sastry Munukutla
Keyword(s):  
Power Plants ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Scale Model ◽  
Cfd Modeling ◽  
Navier Stokes ◽  
Dust Deposition ◽  
Navier Stokes Equations ◽  
Secondary Air ◽  
The Individual

In many fossil power plants operating today, there is insufficient means to assure the proper balancing of the secondary airflows between the individual burners of wall-fired units in addition there is a problem of dust deposition on the floor. This mismatch leads to decreased boiler efficiency and increased emissions. In this study, a Computational Fluid Dynamics (CFD) modeling of a fossil power plant wind box scale model is performed using the commercial software CFX5.6. The model solves the three dimensional Reynolds averaged Navier-Stokes equations with the K-epsilon turbulence model. The CFD results are validated by the experimental data taken from a 1/8th scale model of a wall fired fossil unit. Simulations under various flow conditions are obtained to identify the optimum design in terms of the equalization of the secondary airflow through the burners.

Fluid motion inside a spinning nutating cylinder

1985 ◽  
Vol 150 ◽  
pp. 121-138 ◽  
Author(s):  
Harold R. Vaughn ◽  
William L. Oberkampf ◽  
Walter P. Wolfe
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Internal Fluid

The incompressible three-dimensional Navier–Stokes equations are solved numerically for a fluid-filled cylindrical cannister that is spinning and nutating. The motion of the cannister is characteristic of that experienced by spin-stabilized artillery projectiles. Equations for the internal fluid motion are derived in a non-inertial aeroballistic coordinate system. Steady-state numerical solutions are obtained by an iterative finite-difference procedure. Flow fields and liquid induced moments have been calculated for viscosities in the range of 0.9 × 104−1 × 109 cSt. The nature of the three-dimensional fluid motion inside the cylinder is discussed, and the moments generated by the fluid are explained. The calculated moments generally agree with experimental measurements.

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