scholarly journals A pressure-driven atmospheric boundary layer model satisfying Rossby- and Reynolds number similarity

2021 ◽  
Author(s):  
Maarten Paul van der Laan ◽  
Mark Kelly ◽  
Mads Baungaard
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Atmospheric Boundary Layer ◽  
Wind Farm ◽  
Three Dimensional ◽  
Computation Time ◽  
Wind Farms ◽  
The Mean ◽  
Horizontal Momentum ◽  
Pressure Driven

Abstract. Idealized models of the atmospheric boundary layer (ABL) can be used to leverage understanding of the interaction between the ABL and wind farms, towards improvement of wind farm flow modelling. We propose a pressure-driven one-dimensional ABL model without wind veer, which can be used as an inflow model for three-dimensional wind farm simulations for isolating the effects of wind veer and ABL depth. The model is derived from the horizontal momentum equations, and follows both Rossby- and Reynolds number similarity; use of such similarity reduces computation time and allows rational comparison between different conditions. The proposed ABL model compares well with solutions of the mean momentum equations that include wind veer, if the forcing variable is employed as a free parameter.

scholarly journals A pressure-driven atmospheric boundary layer model satisfying Rossby and Reynolds number similarity

2021 ◽  
Vol 6 (3) ◽  
pp. 777-790
Author(s):  
Maarten Paul van der Laan ◽  
Mark Kelly ◽  
Mads Baungaard
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Atmospheric Boundary Layer ◽  
Wind Farm ◽  
Three Dimensional ◽  
Computation Time ◽  
Wind Farms ◽  
The Mean ◽  
The Impact ◽  
Pressure Driven

Abstract. Idealized models of the atmospheric boundary layer (ABL) can be used to leverage understanding of the interaction between the ABL and wind farms towards the improvement of wind farm flow modeling. We propose a pressure-driven one-dimensional ABL model without wind veer, which can be used as an inflow model for three-dimensional wind farm simulations to separately demonstrate the impact of wind veer and ABL depth. The model is derived from the horizontal momentum equations and follows both Rossby and Reynolds number similarity; use of such similarity reduces computation time and allows rational comparison between different conditions. The proposed ABL model compares well with solutions of the mean momentum equations that include wind veer if the forcing variable is employed as a free parameter.

scholarly journals An experimental study of a three-dimensional pressure-driven turbulent boundary layer

1995 ◽  
Vol 290 ◽  
pp. 225-262 ◽  
Author(s):  
Semİh M. Ölçmen ◽  
Roger L. Simpson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Coordinate System ◽  
Normal Stress ◽  
Three Dimensional ◽  
Mean Velocity ◽  
Vector Direction ◽  
The Mean ◽  
Pressure Driven

A three-dimensional, pressure-driven turbulent boundary layer created by an idealized wing–body junction flow was studied experimentally. The data presented include time-mean static pressure and directly measured skin-friction magnitude on the wall. The mean velocity and all Reynolds stresses from a three-velocity-component fibre-optic laser-Doppler anemometer are presented at several stations along a line determined by the mean velocity vector component parallel to the wall in the layer where the $\overline{u^2}$ kinematic normal stress is maximum (normal-stress coordinate system). This line was selected by intuitively reasoning that overlap of the near-wall flow and outer-region flow occurs at the location where $\overline{u^2}$ is maximum. Along this line the flow is subjected to a strong crossflow pressure gradient, which changes sign for the downstream stations. The shear-stress vector direction in the flow lags behind the flow gradient vector direction. The flow studied here differs from many other experimentally examined three-dimensional flows in that the mean flow variables depend on three spatial axes rather than two axes, such as flows in which the three-dimensionality of the flow has been generated either by a rotating cylinder or by a pressure gradient in one direction only throughout the flow.The data show that the eddy viscosity of the flow is not isotropic. These and other selected data sets show that the ratio of spanwise to streamwise eddy viscosities in the wall-shear-stress coordinate system is less scattered and more constant (about 0.6) than in the local free-stream coordinate system or the normal stress coordinate system. For y+ > 50 and y/δ < 0.8, the ratio of the magnitude of the kinematic shear stress |τ/ρ| to the kinematic normal stress $\overline{v^2}$ is approximately a constant for three-dimensional flow stations of both shear-driven and pressure-driven three-dimensional flows. In the same region, the ratio of the kinematic shear stresses $-\overline{vw}/-\overline{uw}$ appears to be a function of y+ in wall-stress coordinates for three-dimensional pressure-driven flows.

scholarly journals Dynamics of Large Scale Turbulence in Finite-sized Wind Farm Canopy using Proper Orthogonal Decomposition and a Novel Fourier-POD Framework

2020 ◽  
Author(s):  
Tanmoy Chatterjee ◽  
Yulia T. Peet
Keyword(s):  
Boundary Layer ◽  
Power Generation ◽  
Atmospheric Boundary Layer ◽  
Large Scale ◽  
Wind Farm ◽  
Scaling Laws ◽  
Wind Farms ◽  
Orthogonal Decomposition ◽  
Pod Analysis ◽  
Proper Orthogonal

Large scale coherent structures in atmospheric boundary layer (ABL) are known to contribute to the power generation in wind farms. In the current paper, we perform a detailed analysis of the large scale structures in a finite sized wind turbine canopy using modal analysis from three dimensional proper orthogonal decomposition (POD). While POD analysis sheds light on the large scale coherent modes and scaling laws of the eigenspectra, we also observe a slow convergence of the spectral trends with the available number of snapshots. Since the finite sized array is periodic in the spanwise direction, we propose to adapt a novel approach of performing POD analysis of the spanwise/lateral Fourier transformed velocity snapshots instead of the snapshots themselves. This methodology not only helps in decoupling the length scales in the spanwise and the streamwise direction when studying the energetic coherent modes, but also provides a detailed guidance towards understanding the convergence of the eigenspectra. In particular, the Fourier-POD eigenspectra helps us illustrate if the dominant scaling laws observed in 3D POD are actually contributed by the laterally wider or thinner structures and provide more detailed insight on the structures themselves. We use the database from our previous large eddy simulation (LES) studies on finite-sized wind farms which uses wall-modeled LES for modeling the Atmospheric boundary layer laws, and actuator lines for the turbine blades. Understanding the behaviour of such structures would not only help better assess reduced order models (ROM) for forecasting the flow and power generation but would also play a vital role in improving the decision making abilities in wind farm optimization algorithms in future. Additionally, this study also provides guidance for better understanding the POD analysis in the turbulence and wind farm community.

scholarly journals MATHEMATICAL MODELING AND NUMERICAL STUDY OF ATMOSPHERIC BOUNDARY LAYER NEAR WINDFARMS

2021 ◽  
Vol 3 (65) ◽  
pp. 33-40
Author(s):  
Vladislav N. Kovalnogov ◽  
◽  
Yuriy A. Khakhalev ◽  
Ekaterina V. Tsvetova ◽  
Larisa V. Khakhaleva ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Wind Turbines ◽  
High Performance ◽  
Wind Farm ◽  
Numerical Study ◽  
Wind Farms ◽  
Time Range ◽  
Winter Period

The article analyzes Russian and foreign sources relating to the interaction of wind turbines with the surface layers of the atmosphere. It specifies the main problems of mathematical modeling of the atmospheric boundary layer near the wind farms due to adverse meteorological conditions, in particular, constant zero crossings in the autumn-winter period, various precipitation, a wide time range, air parameters, terrain and other features. The authors analyze the evolution of mathematical models of turbulence to describe the boundary layer near wind turbines from earlier to rapidly developing and currently used. To achieve greater accuracy and naturalism, it is proposed to use high-performance efficient algorithms based on combining scales and physics of phenomena. The authors propose a mathematical model for studying the state of the atmospheric polydisperse boundary layer under conditions of the Ulyanovsk wind farm, taking into account the dispersed particles in the flow, surface curvature, pressure gradient and other influences.

Turbulence and Control of Wind Farms

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Carl R. Shapiro ◽  
Genevieve M. Starke ◽  
Dennice F. Gayme
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Atmospheric Boundary Layer ◽  
Wind Farm ◽  
Autonomous Systems ◽  
Wind Farms ◽  
Annual Review ◽  
Publication Date ◽  
Dynamic Interactions ◽  
Loop Control

The dynamics of the turbulent atmospheric boundary layer play a fundamental role in wind farm energy production, governing the velocity field that enters the farm as well as the turbulent mixing that regenerates energy for extraction at downstream rows. Understanding the dynamic interactions among turbines, wind farms, and the atmospheric boundary layer can therefore be beneficial in improving the efficiency of wind farm control approaches. Anticipated increases in the sizes of new wind farms to meet renewable energy targets will increase the importance of exploiting this understanding to advance wind farm control capabilities. This review discusses approaches for modeling and estimation of the wind farm flow field that have exploited such knowledge in closed-loop control, to varying degrees. We focus on power tracking as an example application that will be of critical importance as wind farms transition into their anticipated role as major suppliers of electricity. The discussion highlights the benefits of including the dynamics of the flow field in control and points to critical shortcomings of the current approaches. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

scholarly journals Diurnal variability of the atmospheric boundary layer height over a tropical station in the Indian monsoon region

2017 ◽  
Vol 17 (1) ◽  
pp. 531-549 ◽  
Author(s):  
Sanjay Kumar Mehta ◽  
Madineni Venkat Ratnam ◽  
Sukumarapillai V. Sunilkumar ◽  
Daggumati Narayana Rao ◽  
Boddapaty V. Krishna Murthy
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Diurnal Variation ◽  
Indian Monsoon ◽  
Winter Season ◽  
Monsoon Region ◽  
Diurnal Variability ◽  
The Mean ◽  
Indian Monsoon Region ◽  
Tropical Station

Abstract. The diurnal variation of atmospheric boundary layer (ABL) height is studied using high-resolution radiosonde observations available at 3 h intervals for 3 days continuously from 34 intensive campaigns conducted during the period December 2010–March 2014 over a tropical station Gadanki (13.5° N, 79.2° E; 375 m), in the Indian monsoon region. The heights of the ABL during the different stages of its diurnal evolution, namely, the convective boundary layer (CBL), the stable boundary layer (SBL), and the residual layer (RL) are obtained to study the diurnal variabilities. A clear diurnal variation is observed in 9 campaigns out of the 34 campaigns. In 7 campaigns the SBL did not form in the entire day and in the remaining 18 campaigns the SBL formed intermittently. The SBL forms for 33–55 % of the time during nighttime and 9 and 25 % during the evening and morning hours, respectively. The mean SBL height is within 0.3 km above the surface which increases slightly just after midnight (02:00 IST) and remains almost constant until the morning. The mean CBL height is within 3.0 km above the surface, which generally increases from morning to evening. The mean RL height is within 2 km above the surface which generally decreases slowly as the night progresses. The diurnal variation of the ABL height over the Indian region is stronger during the pre-monsoon and weaker during winter season. The CBL is higher during the summer monsoon and lower during the winter season while the RL is higher during the winter season and lower during the summer season. During all the seasons, the ABL height peaks during the afternoon (∼ 14:00 IST) and remains elevated until evening (∼ 17:00 IST). The ABL suddenly collapses at 20:00 IST and increases slightly in the night. Interestingly, it is found that the low level clouds have an effect on the ABL height variability, but the deep convective clouds do not. The lifting condensation level (LCL) is generally found to occur below the ABL for the majority of the database and they are randomly related.

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