Computing turbulent far-wake development behind a wind turbine with and without swirl

During recent years, wind energy has moved from an emerging technology to a nearly competitive technology. This fact, coupled with an increasing global focus on environmental concern and a political desire of a certain level of diversification in the energy supply, ensures wind energy an important role in the future electricity market. For this challenge to be met in a cost-efficient way, a substantial part of new wind turbine installations is foreseen to be erected in big onshore or offshore wind farms. This fact makes the production, loading and reliability of turbines operating under such conditions of particular interest.

As wind turbines operate within the atmospheric boundary layer (ABL), the study of their interaction with the ABL flow can help us better understand and predict their performance. In addition to the performance of wind turbines, this interaction has an effect on the flow both upwind and downwind (i.e., wake region) of the turbines. In particular, the study of turbine wakes is of great importance because they are the main cause of power losses and fatigue loads in wind farms. In the current thesis, four studies are conducted to fully examine the turbine interaction with the ABL flow, with an emphasis on turbine wakes. In the first study, a new analytical wake model is proposed and validated to predict the wind velocity distribution in the far-wake region, where downwind turbines usually operate. The proposed model is derived by applying the conservation of mass and momentum and assuming a Gaussian distribution for the velocity deficit in the wake. This simple model only requires one parameter to predict the velocity distribution in the far wake of a wind turbine. In general, it is found that the velocity deficit in the wake predicted by the proposed analytical model is in good agreement with the experimental and numerical data. Furthermore, the results show that the new model predicts the power extracted by downwind wind turbines more accurately than other common analytical models, some of which are based on less accurate assumptions like considering a top-hat shape for the velocity deficit. In the second study, wind tunnel measurements are carried out to systematically investigate turbine wakes under yawed conditions. The detailed experimental data are used to perform a budget study of the continuity and Reynolds-averaged Navier-Stokes equations. This theoretical analysis reveals some notable features of the wakes of yawed turbines, such as the asymmetric distribution of the wake skew angle with respect to the wake center. Under highly yawed conditions, the formation of a counter-rotating vortex pair in the wake cross-section as well as the vertical displacement of the wake center are also shown and analyzed. Finally, this study enables us to develop general governing equations upon which a simple and computationally inexpensive analytical model is built. The proposed model aims at predicting the wake deflection and the far-wake velocity distribution for yawed turbines. The findings of this study can be especially useful to assess the possibility of optimizing wind-farm power production by controlling the yaw angle of the turbines. In the third study, comprehensive wind tunnel experiments are performed to study the interaction of a turbulent boundary layer with a wind turbine operating under different tip-speed ratios and yaw angles. Force and power measurements are performed to characterize the wind turbine performance. Moreover, a high-resolution stereoscopic particle-image velocimetry (S-PIV) system and hot-wire anemometry are used to study the flow in the upwind, near-wake and far-wake regions. This study provides new insights on the turbine and flow characteristics such as the evolution of tip vortices and wake meandering. Finally, the last study concerns the design and the performance analysis of a new three-bladed horizontal-axis miniature wind turbine with a rotor diameter of $15$ cm. Due to its small size, this turbine is particularly suitable for studies of wind farm flows and the interaction of the turbine with an incoming boundary-layer flow. Special emphasis is placed on accurate measurements of the mechanical power extracted by the miniature turbine from the incoming wind. In order to do so, a new setup is developed to measure the torque of the rotor shaft. The thrust and power coefficients of the miniature turbine are found to be around $0.8$ and $0.4$ in optimal conditions, respectively, which are close to the ones of large-scale turbines in the field.

This paper presents the results from numerical simulation of jet flow emanating from a cruciform orifice. OpenFOAM is used for the simulations with RANS standard k-e turbulence model. The results are validated with the experimental data of Quinn [1]. Mean flow quantities and turbulent quantities are discussed in detail. The evolution of cruciform shape to circular shape is described with various contours of mean flow and turbulent quantities. Possible reasons for the evolution of cross sectional shapes are discussed.

This textbook covers fundamental and advanced concepts of computational fluid dynamics, a powerful and essential tool for fluid flow analysis. It discusses various governing equations used in the field, their derivations, and the physical and mathematical significance of partial differential equations and the boundary conditions. It covers fundamental concepts of finite difference and finite volume methods for diffusion, convection-diffusion problems both for cartesian and non-orthogonal grids. The solution of algebraic equations arising due to finite difference and finite volume discretization are highlighted using direct and iterative methods. Pedagogical features including solved problems and unsolved exercises are interspersed throughout the text for better understanding. The textbook is primarily written for senior undergraduate and graduate students in the field of mechanical engineering and aerospace engineering, for a course on computational fluid dynamics and heat transfer. The textbook will be accompanied by teaching resources including a solution manual for the instructors. Written clearly and with sufficient foundational background to strengthen fundamental knowledge of the topic. Offers a detailed discussion of both finite difference and finite volume methods. Discusses various higher-order bounded convective schemes, TVD discretisation schemes based on the flux limiter essential for a general purpose CFD computation. Discusses algorithms connected with pressure-linked equations for incompressible flow. Covers turbulence modelling like k-ε, k-ω, SST k-ω, Reynolds Stress Transport models. A separate chapter on best practice guidelines is included to help CFD practitioners.

An experimental study was carried out to investigate the aeromechanics and wake characteristics of dual-rotor wind turbines (DRWTs) in either co-rotating or counter-rotating configuration, in comparison to those of a conventional single-rotor wind turbine (SRWT). The experiments were performed in a large-scale aerodynamic/atmospheric boundary layer (AABL) wind tunnel, available at Iowa State University with the oncoming atmospheric boundary-layer (ABL) airflows under neutral stability conditions. In addition to measuring the power output performance of DRWT and SRWT models, static and dynamic wind loads acting on those turbine models were also investigated. Furthermore, a high-resolution digital particle image velocimetry (PIV) system was used to quantify the flow characteristics in the near wakes of the DRWT and SRWT models. The detailed wake-flow measurements were correlated with the power outputs and wind-load measurement results of the wind-turbine models to elucidate the underlying physics to explore/optimize design of wind turbines for higher power yield and better durability.

Steadily increasing energy consumption, fluctuating fuel costs and concerns about global climate changes have led to the research and evaluation of alternative renewable energies. The wind turbine is among the promising alternative energy sources that have recently gained more attention. In this work, the challenging aspects involved in modelling the rotor aerodynamics and wakes behind the wind turbines are studied. This report covers the literature review of Blade Element Momentum (BEM) analysis of wind turbine, limitations of BEM method, effect of stall delay, wake aerodynamics, atmospheric boundary layer and its effects on the wake characteristics and previous different wake models of near and far wake regions. In this project, experimental data of NREL Phase VI Turbine (sequence S) were used to corroborate the results. There are two main objectives of this project. The first objective is to improve the BEM analysis to account for the three-dimensional (3D) effects due to the rotation of the turbine. The second objective is to contemplate on the effects of atmospheric boundary layers (ABL) on the wake characteristics. These two objectives act as a roadway to enhance coupled BEM-CFD analysis, which is left for the future works. In the coupled BEM-CFD analysis, the BEM method will be applied to calculate the aerodynamic forces of the aerofoil sections along the blade span. The main drawback of BEM analysis is the use of the twodimensional (2D) aerofoil characteristics (CL and CD ) which considers only the axial flow but not radial or spanwise flow along the blade span. This leads to a considerable difference in the lift coefficients between the rotating and non rotating blades, especially at inboard sections of the blade. This 3D phenomenon is called stall delay. The current study includes different proposals for the extrapolation of 2D aerofoil characteristics of the S809 aerofoil and their implementation in BEM analysis and comparison of power predicted with experimental results. Also, four existing stall delay correction models in BEM analysis are examined. In general, these models result in over-prediction of power, especially at high inflow wind speeds. An improved inverse BEM method is developed to compute 3D aerofoil characteristics at different radial locations along the blade span. In addition to five radial locations as described in the NREL/NASA Ames test analysis, 13 additional radial locations are considered for a better understanding of stall delay. A new BEM model with the local radius effect of aerofoil characteristics (other than as a function of Reynolds number and angle of attack only) is proposed. Implementation of the new model showed a good agreement with aerofoil characteristics distribution along the blade span with the 3D aerofoil characteristics computed from the CFD analyses using inverse BEM method. MATLAB code was developed for both BEM and Inverse BEM analyses. Most important in the wind farm analysis is the effect of the atmospheric boundary layer since the turbulence properties of the atmosphere affect the wake characteristics. In this work, the NREL Phase VI Turbine is virtually placed in different atmospheric boundary layers from open sea to city/forest. Simulations are performed with direct rotor modelling using sliding mesh analysis. Since the experiment results of wake characteristics of the NREL Phase VI Turbine was not available, different empirical models are used for comparison. It was evident that wake recovers at a faster rate as the roughness length of the ground increases. Also, it was noted that the turbulence intensity of the wake varies both laterally and vertically, but existing analytical wake turbulence intensity models provide only an averaged value The possible methods for indirect rotor modelling like Actuator Disk, Actuator Line and Actuator Surface methods that lead to coupled BEM-CFD analysis of wind turbine is discussed in brief. The possible ways of improving these indirect rotor models by using the aerodynamic forces computed from improved BEM analysis and wake aerodynamics are provided for the future works.

Investigation of the influence of swirl on a confined coannular swirl jet

The hydrodynamic effects of a jet in a swirling cross-flow problem, which is related to gas turbine blades film cooling, were numerically simulated using large eddy simulation with artificial inflow boundary conditions. The purpose of this study is to investigate the effects of swirling flow on a jet effusing from an inclined hole in a rotating channel. The finite volume method and the unsteady PISO algorithm were applied on a non-uniform staggered grid. The work is naturally divided into two main parts. The first part (the swirl flow generator), is a channel rotates axially to generate a turbulent swirling flow at different values of swirl number (SN) of 0.0, 0.15, 0.3, and 0.5 while the second part (test section), is a channel rotating about a parallel axis to investigate the interaction of a square jet with the turbulent swirling flow, generated by the first part, for the prediction of the film cooling under rotating conditions. Four different values of rotation number (Ro) were applied to the test section. The air jet was injected at 30 deg in the streamwise direction, at a velocity ratio of 1.0 and a jet Reynolds number of 4,700, based on the hole width and the jet exit velocity. It was found that the swirling flows primarily displayed the velocity profile of a forced vortex. Weak reverse flow was observed near the main vortex core, which moved in the direction of the swirl and deformed the kidney shape of the Counter Rotating Vortex Pair. As SN increases (SN > 0), the jet trajectory twists in an increasingly x-axis direction due to the centrifugal force effects of the swirl flow, and shifts from the centreline of the channel to the right-hand side (Z/D =+ 1.5). Also, it was shown that rotation has a strong impact on the mixing behaviour and film cooling effectiveness. Finally, it was concluded that the film cooling decreases rapidly as SN increases.

Lean premixed swirl combustion is widely used in gas turbines and many other combustion Processes due to the benefits of good flame stability and blow off limits coupled with low NOx emissions. Although flashback is not generally a problem with natural gas combustion, there are some reports of flashback damage with existing gas turbines, whilst hydrogen enriched fuel blends, especially those derived from gasification of coal and/or biomass/industrial processes such as steel making, cause concerns in this area. Thus, this paper describes a practical experimental approach to study and reduce the effect of flashback in a compact design of generic swirl burner representative of many systems. A range of different fuel blends are investigated for flashback and blow off limits; these fuel mixes include methane, methane/hydrogen blends, pure hydrogen and coke oven gas. Swirl number effects are investigated by varying the number of inlets or the configuration of the inlets. The well known Lewis and von Elbe critical boundary velocity gradient expression is used to characterise flashback and enable comparison to be made with other available data.Two flashback phenomena are encountered here. The first one at lower swirl numbers involves flashback through the outer wall boundary layer where the crucial parameter is the critical boundary velocity gradient, Gf. Values of Gf are of similar magnitude to those reported by Lewis and von Elbe for laminar flow conditions, and it is recognised that under the turbulent flow conditions pertaining here actual gradients in the thin swirl flow boundary layer are much higher than occur under laminar flow conditions. At higher swirl numbers the central recirculation zone (CRZ) becomes enlarged and extends backwards over the fuel injector to the burner baseplate and causes flashback to occur earlier at higher velocities. This extension of the CRZ is complex, being governed by swirl number, equivalence ratio and Reynolds Number. Under these conditions flashback occurs when the cylindrical flame front surrounding the CRZ rapidly accelerates outwards to the tangential inlets and beyond, especially with hydrogen containing fuel mixes. Conversely at lower swirl numbers with a modified exhaust geometry, hence restricted CRZ, flashback occurs through the outer thin boundary layer at much lower flow rates when the hydrogen content of the fuel mix does not exceed 30%. The work demonstrates that it is possible to run premixed swirl burners with a wide range of hydrogen fuel blends so as to substantially minimise flashback behaviour, thus permitting wider used of the technology to reduce NOx emissions.

Experimental measurements were carried out in an incompressible three-dimensional turbulent shear layer in the vicinity of an appendage mounted perpendicular to a flat plate. The thickness of the turbulent boundary layer as it approached the appendage leading edge was 76 mm or 1.07 times the maximum thickness of the appendage. As the oncoming boundary layer passed around the appendage, a strong secondary flow was formed which was dominated by a horseshoe root vortex. This secondary flow had a major effect in redistributing both the mean flow and turbulence quantities throughout the shear layer, and this effect persisted to a significant degree up to at least three chord lengths downstream of the appendage leading edge.

Experimental results are presented for the evolution of three turbulent quantities in the wake of a porous object, analogous to a wind-turbine wake. These are the mean velocity deficit, the turbulence intensity, and the characteristic wake width. It is noted that characteristic wake widths can be defined both in terms of the mean velocity deficit profile and the profile of turbulence intensity. Both definitions of wake width are observed to grow linearly, although not at the same rate, with that defined by turbulence intensity growing more rapidly than velocity deficit. The streamwise scaling of both wake width, and velocity deficit is found to conform to a non-equilibrium dissipation scaling in which the dissipation rate within the wake is out of equilibrium with the inter-scale energy flux within the mean cascade of turbulent kinetic energy. The cumulative effect of turbulence intensity produced by N upstream porous objects is also considered. It is shown that when the object spacing is sufficiently large that the wake-added turbulence decays substantially only consideration of the most immediately upstream wake is important. Contrastingly, when the spacing between adjacent objects is small then summing the contributions from all upstream wakes in the array is necessary.

Parabolic partial differential equation with small parameter in x direction and different small parameter in t direction is considered. This kind of problem leads to boundary layer phenomena in both side of x direction and bottom side of t direction. The analytical solution changes rapidly near three boundary layer. Firstly, the asymptotic solution with order one for all small parameter is studied. The analytical solution is approximated by the degenerate solution and three boundary layer functions. Secondly, non-equidistant mesh partitions both in x direction and t direction are constructed according to Shishkin's idea. The domain is divided into the outside boundary layer and the boundary layer. Thirdly, traditional finite volume method is applied by integrating the equation over the control volume. The discretized equation is derived. Asymptotic solution is used for the outside boundary layer, while finite volume method is applied for three boundary layers. Finally, numerical example is studied to demonstrate the accuracy of the present method.

The study of wind turbine wakes is very important for the layout of offshore wind farms. The technique of regulating the yaw angles of the upstream wind turbine to lessen the influence on the downstream turbines has attracted continual attention in recent years. In this study, the wake interactions between a yaw wind turbine and a downstream wind turbine are investigated using a numerical technique based on the openfoam solver in conjunction with an improved actuator line method. The Gaussian anisotropic body force projection method and the integral velocity sampling method are the two fundamental components of the improvement of the actuator line method. The NREL 5-MW wind turbine benchmark model is used to test the numerical accuracy. The simulation of the wake effects from the upstream turbine in non-yawed conditions that follows has good agreement with the results that have been published in the literature. Finally, this work presents a number of predictions about the power coefficients and wake characteristics of two tandem-arranged wind turbines at various yaw angles based on these precise verification efforts. The results of the analysis in yaw conditions are used to derive the yaw wake characteristics and the optimal yaw angle range. As the yaw angle increases, the total power of the wind turbine increases and then decreases, and the upstream wake area decreases significantly. The total power reaches its maximum at 20–30 deg. The research content of this paper will provide an important reference for wind farm scheduling.

Floating offshore wind turbines (FOWTs) may experience six degree of freedom (DoF) movements under the influence of environmental conditions. Different combinations of platform movements with the same amplitude and frequency may have distinct influences on the aerodynamic characteristics of the wind turbine. In this study, a detailed, full-scale CFD model of NREL 5 MW wind turbine is developed to investigate the specific aerodynamic and near wake characteristics under the influence of surge, pitch, and coupled surge–pitch platform motion based on the OpenFOAM tool box. It is clearly noted that different platform movements led to varying relative velocities of the blade, which affected the aerodynamic performance of wind turbines such as thrust, torque, and angle of attack (AOA). On the other hand, when the wind turbine was subjected to combined surge–pitch motion with the same phase, the wake velocity field fluctuated greatly, and the velocity at the center of the wake even exceeded the free flow velocity. Moreover, the platform movement affected the gap between the shed vortices. When the wind turbine moved forward, the gap between the vortices increased, while when the wind turbine moved backward, the gap between the vortices decreased or even converged, resulting in vortex–vortex interaction.

Several previous investigations of the near field of swirling jets have shown that these jets grow at a faster rate than non-swirling jets and experience significant changes in the turbulence quantities (c.f.\ Gilchrist, Naughton). A recent study by Shiri et al., however, showed that the growth rate enhancement does not persist in the far-field of a swirling jet flow with moderate swirl numbers (0.15 and 0.25). The results were shown to be consistent with the equilibrium similarity theory of Ewing in which the mean swirl velocity was argued to decrease downstream as $1/(x-x_o)^2$, while the mean stream-wise velocity decreased as $1/(x-x_o)$. In fact the only statistically significant effect of the swirl on the mean velocity for even the highest swirl number was a shift in the virtual origin (to $x/D_* = 0.75$ from $-2.9$). The present investigation extends the previous study to include all three velocity components of the turbulence quantities at a swirl number of $S=0.25$. Since only a two-component LDA was available, this was accomplished by making traverses in both the vertical and horizontal directions. All moments to third order were obtained, excepting those involving both the azimuthal and radial components simultaneously. Some of the results show the earlier measurements of Hussein et al. in the same jet (but without swirl). The second and third-order moments are quite close to the earlier non-swirling results. But unlike the mean velocity and spreading rate (which were nearly identical), the differences may be significant and a consequence of the swirl. As noted by George, if there were an effect of the source conditions on the similarity profiles, it is in the second and higher moment profiles where it would be expected to appear. On the other hand, the differences in second-order moments near the centerline could also be accounted for by a slight angular misalignment in either experiment ($<0.5\deg$).