Reynolds number dependence of turbulence statistics in the wake of wind turbines

Wind Energy ◽  
2011 ◽  
Vol 15 (5) ◽  
pp. 733-742 ◽  
Author(s):  
Leonardo P. Chamorro ◽  
R.E.A Arndt ◽  
F. Sotiropoulos
Keyword(s):  
Reynolds Number ◽  
Wind Turbines ◽  
Turbulence Statistics ◽  
Reynolds Number Dependence

scholarly journals Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Itzhak Fouxon ◽  
Joshua Feinberg ◽  
Petri Käpylä ◽  
Michael Mond
Keyword(s):  
Reynolds Number ◽  
Lyapunov Exponents ◽  
Fluid Particles ◽  
Reynolds Number Dependence

scholarly journals Aerodynamic improvement of Darrieus wind turbine

2021 ◽  
Vol 897 (1) ◽  
pp. 012001
Author(s):  
Oleg Goman ◽  
Andrii Dreus ◽  
Anton Rozhkevych ◽  
Krystyna Heti
Keyword(s):  
Reynolds Number ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Structural Reliability ◽  
Vertical Axis ◽  
Vertical Wind ◽  
Integral Approach ◽  
Vertical Axis Wind Turbine ◽  
Calculation Algorithm ◽  
Vertical Axis Wind Turbines

Abstract Until recently, vertical-axis wind turbines are less extensively developed in wind energetics. At the same time, there are a number of advantages in turbines of such type like their independence from the change of wind direction, lower levels of aerodynamic and infrasound noises, higher structural reliability (compared to horizontal engines), etc. With these advantages, vertical-axis wind turbines demonstrate promising capacities. Inter alia, the productiveness of such turbines can be refined through the aerodynamic improvement of the structure and comprehensive optimization of the rotor geometry. The main purpose of the presented paper is to aerodynamically improve vertical wind turbine in order to increase the efficiency of wind energy conversion into electricity. Within the framework of the classical theory of impulses, this article presents a study of the effect of variation in Reynolds number on the general energy characteristics of a vertical-axis wind turbine with two blades. The integral approach makes it possible to use a single-disk impulse model to determine the main specific indicators of the system. The power factor was calculated based on the obtained value of the shaft torque factor, which in turn was determined by numerically integrating the total torque generated by the wind turbine. To calculate the test problem, we used the classic NACA airfoils: 0012, 0015, 0018 and 0021. The proposed calculation algorithm makes it possible not to indicate the Reynolds number and corresponding aerodynamic coefficients at the beginning of the calculation, but to recalculate it depending on the relative speed, position of the airfoil and the linear speed of the airfoil around the circumference. Proposed modern design techniques can be helpful for optimization of vertical wind turbines.

Reynolds-number dependence of line and surface stretching in turbulence: folding effects

2007 ◽  
Vol 586 ◽  
pp. 59-81 ◽  
Author(s):  
SUSUMU GOTO ◽  
SHIGEO KIDA
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Turnover Time ◽  
Material Object ◽  
Material Objects ◽  
Short Time Scale ◽  
Kolmogorov Scale ◽  
Reynolds Number Dependence

The stretching rate, normalized by the reciprocal of the Kolmogorov time, of sufficiently extended material lines and surfaces in statistically stationary homogeneous isotropic turbulence depends on the Reynolds number, in contrast to the conventional picture that the statistics of material object deformation are determined solely by the Kolmogorov-scale eddies. This Reynolds-number dependence of the stretching rate of sufficiently extended material objects is numerically verified both in two- and three-dimensional turbulence, although the normalized stretching rate of infinitesimal material objects is confirmed to be independent of the Reynolds number. These numerical results can be understood from the following three facts. First, the exponentially rapid stretching brings about rapid multiple folding of finite-sized material objects, but no folding takes place for infinitesimal objects. Secondly, since the local degree of folding is positively correlated with the local stretching rate and it is non-uniformly distributed over finite-sized objects, the folding enhances the stretching rate of the finite-sized objects. Thirdly, the stretching of infinitesimal fractions of material objects is governed by the Kolmogorov-scale eddies, whereas the folding of a finite-sized material object is governed by all eddies smaller than the spatial extent of the objects. In other words, the time scale of stretching of infinitesimal fractions of material objects is proportional to the Kolmogorov time, whereas that of folding of sufficiently extended material objects can be as long as the turnover time of the largest eddies. The combination of the short time scale of stretching of infinitesimal fractions and the long time scale of folding of the whole object yields the Reynolds-number dependence. Movies are available with the online version of the paper.

scholarly journals New airfoils for micro horizontal-axis wind turbines

2021 ◽  
Author(s):  
Manoj Kumar Chaudhary ◽  
◽  
S. Prakash ◽  
Keyword(s):  
Reynolds Number ◽  
Wind Turbines ◽  
Low Reynolds Number ◽  
Horizontal Axis ◽  
Speed Ratio ◽  
Maximum Output ◽  
Horizontal Axis Wind Turbine ◽  
Horizontal Axis Wind Turbines ◽  
Low Reynolds ◽  
Bem Theory

In this study, small horizontal-axis wind turbine blades operating at low wind speeds were optimized. An optimized blade design method based on blade element momentum (BEM) theory was used. The rotor radius of 0.2 m, 0.4 m and 0.6 m and blade geometry with single (W1 & W2) and multistage rotor (W3) was examined. MATLAB and XFoil programs were used to implement to BEM theory and devise a six novel airfoil (NAF-Series) suitable for application of small horizontal axis wind turbines at low Reynolds number. The experimental blades were developed using the 3D printing additive manufacturing technique. The new airfoils such as NAF3929, NAF4420, NAF4423, NAF4923, NAF4924, and NAF5024 were investigated using XFoil software at Reynolds numbers of 100,000. The investigation range included tip speed ratios from 3 to 10 and angle of attacks from 2° to 20°. These parameters were varied in MATLAB and XFoil software for optimization and investigation of the power coefficient, lift coefficient, drag coefficient and lift-to-drag ratio. The cut-in wind velocity of the single and multistage rotors was approximately 2.5 & 3 m/s respectively. The optimized tip speed ratio, axial displacement and angle of attack were 5.5, 0.08m & 6° respectively. The proposed NAF-Series airfoil blades exhibited higher aerodynamic performances and maximum output power than those with the base SG6043 and NACA4415 airfoil at low Reynolds number.

Mixed velocity–passive scalar statistics in high-Reynolds-number turbulence

2003 ◽  
Vol 475 ◽  
pp. 173-203 ◽  
Author(s):  
L. MYDLARSKI
Keyword(s):  
Reynolds Number ◽  
Transverse Velocity ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Inertial Range ◽  
Scaling Exponents ◽  
Local Isotropy ◽  
Exponential Tails ◽  
Reynolds Number Dependence ◽  
Scalar Fluctuation

Statistics of the mixed velocity–passive scalar field and its Reynolds number dependence are studied in quasi-isotropic decaying grid turbulence with an imposed mean temperature gradient. The turbulent Reynolds number (using the Taylor microscale as the length scale), Rλ, is varied over the range 85 [les ] Rλ [les ] 582. The passive scalar under consideration is temperature in air. The turbulence is generated by means of an active grid and the temperature fluctuations result from the action of the turbulence on the mean temperature gradient. The latter is created by differentially heating elements at the entrance to the wind tunnel plenum chamber. The mixed velocity–passive scalar field evolves slowly with Reynolds number. Inertial-range scaling exponents of the co-spectra of transverse velocity and temperature, Evθ(k1), and its real-space analogue, the ‘heat flux structure function,’ 〈Δv(r)Δθ(r)〉, show a slow evolution towards their theoretical predictions of −7/3 and 4/3, respectively. The sixth-order longitudinal mixed structure functions, 〈(Δu(r))2(Δθ(r))4〉, exhibit inertial-range structure function exponents of 1.36–1.52. However, discrepancies still exist with respect to the various methods used to estimate the scaling exponents, the value of the scalar intermittency exponent, μθ, and the effects of large-scale phenomena (namely shear, decay and turbulent production of 〈θ2〉) on 〈(Δu(r))2(Δθ(r))4〉. All the measured fine-scale statistics required to be zero in a locally isotropic flow are, or tend towards, zero in the limit of large Reynolds numbers. The probability density functions (PDFs) of Δv(r)Δθ(r) exhibit roughly exponential tails for large separations and super-exponential tails for small separations, thus displaying the effects of internal intermittency. As the Reynolds number increases, the PDFs become symmetric at the smallest scales – in accordance with local isotropy. The expectation of the transverse velocity fluctuation conditioned on the scalar fluctuation is linear for all Reynolds numbers, with slope equal to the correlation coefficient between v and θ. The expectation of (a surrogate of) the Laplacian of the scalar reveals a Reynolds number dependence when conditioned on the transverse velocity fluctuation (but displays no such dependence when conditioned on the scalar fluctuation). This former Reynolds number dependence is consistent with Taylor’s diffusivity independence hypothesis. Lastly, for the statistics measured, no violations of local isotropy were observed.

Reynolds number dependence of an orifice plate

2013 ◽  
Vol 30 ◽  
pp. 123-132 ◽  
Author(s):  
Oliver Büker ◽  
Peter Lau ◽  
Karsten Tawackolian
Keyword(s):  
Reynolds Number ◽  
Orifice Plate ◽  
Reynolds Number Dependence
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