Wake meandering of a model wind turbine operating in two different regimes

The flow behind a model wind turbine under two different turbine operating regimes (region 2 for turbine operating at optimal condition with the maximum power coefficient and 1.4-deg pitch angle and region 3 for turbine operating at suboptimal condition with a lower power coefficient and 7-deg pitch angle) is investigated using wind tunnel experiments and numerical experiments using large-eddy simulation (LES) with actuator surface models for turbine blades and nacelle. Measurements from the model wind turbine experiment reveal that the power coefficient and turbine wake are affected by the operating regime. Simulations with and without a nacelle model are carried out for each operating condition to study the influence of the operating regime and nacelle on the formation of the hub vortex and wake meandering. Statistics and energy spectra of the simulated wakes are in good agreement with the measurements. For simulations with a nacelle model, the mean flow field is composed of an outer wake, caused by energy extraction by turbine blades, and an inner wake directly behind the nacelle, while for the simulations without a nacelle model, the central region of the wake is occupied by a jet. The simulations with the nacelle model reveal an unstable helical hub vortex expanding outward toward the outer wake, while the simulations without a nacelle model show a stable and columnar hub vortex. Because of the different interactions of the inner region of the wake with the outer region of the wake, a region with higher turbulence intensity is observed in the tip shear layer for the simulation with a nacelle model. The hub vortex for the turbine operating in region 3 remains in a tight helical spiral and intercepts the outer wake a few diameters further downstream than for the turbine operating in region 2. Wake meandering, a low-frequency large-scale motion of the wake, commences in the region of high turbulence intensity for all simulations with and without a nacelle model, indicating that neither a nacelle model nor an unstable hub vortex is a necessary requirement for the existence of wake meandering. However, further analysis of the wake meandering and instantaneous flow field using a filtering technique and dynamic mode decomposition show that the unstable hub vortex energizes the wake meandering. The turbine operating regime affects the shape and expansion of the hub vortex, altering the location of the onset of the wake meandering and wake meander oscillating intensity. Most important, the unstable hub vortex promotes a high-amplitude energetic meandering which cannot be predicted without a nacelle model.

Figure 1

Overall view of the G1 model, reproduced from Ref. [50]. Added for completeness.

Figure 2

Blade chord and twist angle.

Figure 3

G1 power (left) and thrust (right) experimental (solid lines) and BEM (dashed lines) coefficients, as function of TSR and blade pitch. The line color indicates the blade pitch in degrees.

Figure 4

Experimental setup in the wind tunnel.

Figure 5

(a) Sketch of the wind tunnel domain with spires at the inlet $(x/D=-20.5)$ and turbine located at ($x/D=0$ and $z/D=-2.5$). Comparison of the vertical profiles at $x/D=3.5$ from a precursor simulation (solid lines) with measurements (circles) for an empty wind tunnel for (b) mean streamwise velocity and (c) rms (root-mean-squared) of streamwise velocity fluctuations.

Figure 6

Comparisons of the computed and measured spanwise profiles for the region 2 case for (a) streamwise velocity deficit, (b) vertical velocity, (c) spanwise velocity, and (d) streamwise rms velocity $u^{\prime }$. The horizontal dotted lines at $z/D=\pm 0.5$ are the tip positions. The velocity is nondimensionalized by $U_{\infty }$, the mean free-stream velocity.

Figure 7

Comparisons of the computed and measured spanwise profiles for the region 3 case for (a) streamwise velocity deficit, (b) vertical velocity, (c) spanwise velocity, and (d) streamwise rms velocity $u^{\prime }$. The horizontal dotted lines at $z/D=\pm 0.5$ are the tip positions. The velocity is nondimensionalized by $U_{\infty }$, the mean free-stream velocity.

Figure 8

Comparisons of vertical center-plane contours between simulations with (left images) and without (right images) a nacelle model for turbines operating in region 2 for [(a), (e)] time-averaged downwind velocity, [(b), (f)] turbulence kinetic energy, [(c), (g)] time-averaged spanwise (rotational) velocity, and [(d), (h)] downwind vertical Reynolds shear stress. Notations demarcating the inner wake (formed by the nacelle) and outer wake (created by rotor blades) are shown on panels (a), (d), and (h). Open circles in panels (b) and (f) indicate the location of maximum turbulence kinetic energy in the far wake.

Figure 9

Comparisons of vertical center-plane contours between simulations with (left images) and without (right images) a nacelle model for turbine operating in region 3 for [(a), (e)] time-averaged downwind velocity, [(b), (f)] turbulence kinetic energy, [(c), (g)] time-averaged spanwise (rotational) velocity, and [(d), (h)] downwind vertical Reynolds shear stress. Notations demarcating the inner (formed by the nacelle) and outer (created by rotor blades) wakes are shown in panel (a). Open circles in panels (b) and (f) indicate the location of maximum turbulence kinetic energy in the far wake.

Figure 10

Vertical profiles of the turbulence variances for (a) $\overline{u^{\prime }{u}^{\prime }}/u_{\tau }^2$, (b) $\overline{v^{\prime }{v}^{\prime }}/u_{\tau }^2$, and (c) $\overline{w^{\prime }{w}^{\prime }}/u_{\tau }^2$ non-dimensionalized $u_{\tau }^2$, where $u_{\tau }$ is the friction velocity of the incoming turbulent boundary layer flow. The horizontal dotted line show the bottom and top tip position at $y/D=0.23$ and 1.23, respectively.

Figure 11

Contours of the instantaneous streamwise velocity normalized by $U_{\mathrm{hub}}$ at four successive time instances for (a) turbine operating in region 2 (R2-BN) and (b) turbine operating in region 3 (R3-BN).

Figure 12

Contours of the instantaneous streamwise velocity normalized by $U_{\mathrm{hub}}$ without a nacelle model at four instantaneous time instances for (a) turbine operating in region 2 (R2-B) and (b) turbine operating in region 3 (R3-B).

Figure 13

Comparisons of the Fourier power spectral density of the streamwise component of the velocity fluctuations ${\mathrm{\Phi }}_{11}$ with that from measurements, with the top images and bottom images in regions 2 and 3, respectively, along the tip position $y/D=0.72$ and $z/D=1$ for (a) at $x/D=2$, (b) at $x/D=4$, (c) at $x/D=6$, and (d) at $x/D=9$.

Figure 14

Contours of the Fourier power spectral density of the streamwise component of the velocity fluctuations premultiplied by frequency $f\mathrm{\Phi }$ as a function of the axial direction, $x/D$ at several radial positions: [(a), (d)] $y_h/D=0$, [(b), (e)] $y_h/D=0.2$, and [(c), (f)] $y_h/D=0.44$. Left column (a)–(c), R2-BN, and right column (d)–(f), R3-BN.

Figure 15

Instantaneous vorticity magnitude, $\left|\omega \right|D/Uh$, with velocity minima (dot) and meander profile (line) for (a) R2-BN, (b) R2-B, (c) R3-BN, and (d) R3-B. Average meander profile (e) amplitude, $\overline{A}$, and (f) wavelength $\overline{\lambda }$ with respect to distance from rotor plane, $x/D$, nondimensionalized by the diameter $D$.

Figure 16

Probability density function of the amplitude, $A/D$ (first row), and wavelength, $\lambda /D$ (second row), of the meander profiles at (a) $x/D=2$, (b) $x/D=4$, (c) $x/D=6$, and (d) $x/D=8$.

Figure 17

Validation of dynamic mode decomposition. (a) Residuals norm $\epsilon$ of DMD modes as number of modes $N$ increases. Dynamic mode energy spectrum $d_k^2$ (circle), energy spectrum at $x/D=2$ (solid), and energy spectrum at $x/D=5$ (dashed) for (b) R2-BN and (c) R3-BN.

Figure 18

Selected dynamic modes visualized by contours of the streamwise velocity and two-dimensional ($x\text{−}z$) plane vector field. (a) R2-BN, $\text{St}=0.29$; (b) R3-BN, $\text{St}=0.3$; (c) R2-BN, $\text{St}=0.73$; and (d) R3-BN, $\text{St}=0.74$.

Figure 19

Dynamic mode meander profiles created from hub vortex and wake meandering mode (h+m), dynamic mode meander profile from wake meandering mode (m), and meander profile from complete flow field overlaid on contours and velocity minima (white dots) of the sum of the average velocity and selected hub vortex and wake meandering modes, $U+u_k$, nondimensionalized by the hub velocity $U_{\mathrm{hub}}$ for (a) R2-BN and (b) R3-BN. For reference, the corresponding temporally averaged wake meander profile is shown (dash-dotted line). Characteristics of dynamic mode meander profiles (c) amplitude, $\overline{A}$, and (d) wavelength $\overline{\lambda }$ with respect to distance from rotor plane. Probability density function of amplitude, $A/D$, at (e) $x/D=3$ and (f) $x/D=6$.

Figure 20

Ratio of (a) the averaged amplitude and (b) the averaged wavelength of the dynamic mode meander profiles to those from the complete flow field as the number of employed frequency modes in ascending order are increased at $x/D=8$.