In this paper we investigate linear transient growth of perturbation energy in Taylor-Couette flow of a Bingham fluid. The effects of yield stress on transient growth and the structure of the optimal perturbation are mainly considered for both the wide-gap case and the narrow-gap case. For this purpose we complement the linear stability of this flow subjected to axisymmetric disturbances, presented by Landry et al. [M. P. Landry, I. A. Frigaard, and D. M. Martinez, J. Fluid Mech. 560, 321 (2006)], with the transient growth characteristics of both axisymmetric and nonaxisymmetric perturbations. We obtain the variations of the relative amplitude of optimal perturbation with yield stress, analyze the roles played by the Coriolis force and the additional stress in the evolution of meridional perturbations for the axisymmetric modes, and give the explanations for the possible change of the optimal azimuthal mode (featured by the maximum optimal energy growth $G_{\mathrm{opt}})$ with yield stress. These results might help us in the understanding of the effect of fluid rheology on transient growth mechanism in vortex flows.

The wind turbine with a variable-pitch vertical axis is a novel type of small wind turbine with great development potential in the field of wind power generation. This study assessed the aerodynamic performance of a two-dimensional variable-pitch vertical-axis wind turbine (VAWT) under fluctuating wind conditions (sinusoidal-type fluctuations with an average velocity of 6 m/s) using the finite-volume method and the $RNGk-\epsilon$ turbulence model. The effects of the fluctuating inflow amplitude ($U_{amp}$), frequency ($f_c$), and mean tip speed ratio (${\lambda }_{mean}$) on the power coefficient of the wind turbine are analyzed. The results show that a maximum power coefficient of 0.33 is obtained when the inflow amplitude reaches 50% of the average velocity. The power coefficient initially increases and then decreases with the increase in the fluctuating inflow frequency, reaching a maximum value of 0.32 at $f_c=0.45\mathrm{H}\mathrm{z}$. Furthermore, the power coefficient reaches its maximum value of 0.372 at ${\lambda }_{mean}$= 0.5. Proper orthogonal decomposition (POD) is used to decompose and reconstruct the flow field under both fluctuating and uniform inflow conditions. A comparison of the POD analysis between the two conditions shows that the energy distribution is more dispersed under the fluctuating inflow condition and reconstructing the flow field under fluctuating inflow conditions requires more POD modes than that under uniform inflow conditions.

This work is devoted to the studies of optimal perturbation and its transient growth characteristics in the Poiseuille flow with Reynolds number R = 1000 and with crossflow. The crossflow Reynolds number R _v , based on the uniform velocity in the negative normal direction, is varied from 0 to 200. The numerical result shows that the crossflow enhances the transient growth for three-dimensional disturbance case when R v < 17.9 . Seen from the contours of optimal energy growth in the wave number plane, the optimal perturbation that corresponds to the peak value of optimal growth becomes oblique perturbation, when crossflow is introduced. The corresponding streamwise wave number α _P increases continuously with increasing R _v , while spanwise wave number β _P drops firstly with increasing R _v and later increases. The comparison of exponential growth and transient growth is performed. It is observed that exponential growth becomes profound and even predominant over transient growth after a short period when the crossflow is sufficiently strong. Moreover, the mechanism of transient growth is discussed and it is found that the uniform crossflow can not cause transient growth in the absence of shear in basic flow. With increasing R _v , the Orr mechanism becomes more and more important relative to lift-up mechanism for the transient growth of optimal perturbation.

Numerical simulations are conducted to study the effects of wind gusts on the aerodynamic performance of a two-dimensional variable-pitch vertical-axis wind turbine. The influence of gust period, gust amplitude, and average tip speed ratio on the aerodynamic performance and the power coefficient of wind turbines is systematically analyzed. Results show that under gust conditions, the power coefficient of the wind turbine initially increases and then decreases as the gust period increases, reaching its maximum value at a gust period of 5. The maximum power coefficients for both standard gust and negative gust are achieved at a gust amplitude of 8 m/s. The power coefficient attains its maximum value at a mean tip speed ratio of 0.5, corresponding to values of 0.37 and 0.30 for the standard gust and negative gust, respectively. Proper orthogonal decomposition is employed to perform modal decomposition of the flow field under both gust and uniform flow conditions, which reveals that gust-induced unsteadiness increases flow complexity compared to uniform inflow.