Graduate Seminar in Fluid Mechanics
4:10 pm Presentation
“An Improved Generalized Model of Wind Turbine Wakes”
Presented by CARL SHAPIRO (Advisers: Profs. Meneveau & Gayme)
Simple wake models are needed to develop improved wind farm designs and for use in operational controllers to regulate wind farm power production and reduce structural loads. From the Reynolds-averaged Navier-Stokes, we derive a one-dimensional partial differential equation model. We apply a mixing-length model for the eddy viscosity in the wake that leads to linear downstream wake expansion, with a rate specified using a top-down model for a developing wind turbine array boundary layer (Meneveau 2012, J. Turbulence) where the friction velocity evolves non-monotonically downstream. The streamwise velocity deficits are distributed using a super-Gaussian function that smoothly transitions from a top-hat profile close to the turbine to a Gaussian profile farther downstream. Finally, large-eddy simulations are used to validate the improved wake model.
4:35 pm Presentation
“Turbulent Boundary Layer Over a Compliant Surface”
Presented by JIN WANG (Adviser: Prof. Katz)
Previous simultaneous time-resolved measurement of the 3D flow structure and deformation of a compliant wall by a turbulent channel flow involved wall stiffness too high to affect the flow, resulting in one-way coupling between flow and deformation. The current experiments focus on cases with deformations extending to several wall units aimed at generating two-way coupling. Guided by theoretical analysis, the required Young’s Modulus (0.15Mpa), shear speed (6m/s), and thickness (5mm) of the compliant surface is achieved. The large field of view (70×35 mm^2) deformation measurements elucidate that the advection speeds are fixed at 0.66 U0. Corresponding deformation amplitudes range from sub-micron to serval wall units with U0 increasing from 1 m/s to 6 m/s. The scale of deformation fits well with the predictions of the Chase model. The boundary layer flow is measured using high resolution 2D PIV which can resolve the viscous sublayer. The mean velocity profiles of flow over the compliant wall deviates slightly from the rigid wall at viscous sublayer and buffer region for low flow speeds when the deformation is smaller than the wall unit. At higher flow speeds, the influence of compliant wall deformation extends to the log layer, resulting a decrease of velocity magnitude.