Piezoelectric structures are widely used in engineering designs including sensors, actuators, and energy-harvesting devices. In this paper, we present the development of a three-dimensional finite element model for simulations of piezoelectric actuators and quantification of their responses under uncertain parameter inputs. The implementation of the finite element model is based on standard nodal approach extended for piezoelectric materials using three-dimensional tetrahedral and hexahedral elements. To account for electrical-mechanical coupling in piezoelectric materials, an additional degree of freedom for electrical potential is added to each node in those elements together with their usual mechanical displacement unknowns. The development was validated with analytical and experimental data for a range of problems from a single-layer piezoelectric beam to multiple layer beams in unimorph and bimorph arrangement. A more detailed analysis is conducted for a unimorph composite plate actuator with different design parameters. Uncertainty quantification was also performed to evaluate the sensitivity of the responses of the piezoelectric composite plate with an uncertain input of material properties. This sheds light on understanding the variations in reported responses of the device; at the same time, providing extra confidence to the numerical model.

Patient-specific computational fluid dynamics (CFD) modelling of the left ventricle (LV) is a promising technique for the visualisation of ventricular flow patterns throughout a cardiac cycle. While significant progress has been made in improving the physiological quality of such simulations, the methodologies involved for several key steps remain significantly operator-dependent to this day. This dependency limits both the efficiency of the process as well as the consistency of CFD results due to the labour-intensive nature of current methods as well as operator introduced uncertainties in the modelling process. In order to mitigate this dependency, we propose a semi-automated method for patient-specific computational flow modelling of the LV. Using magnetic resonance imaging derived coarse geometry data of a patient's LV endocardium shape throughout a cardiac cycle, we then proceed to refine the geometry to eliminate rough edges before reconstructing meshes for all time frames and finally numerically solving for the intra-ventricular flow. Using a sample of patient-specific volunteer data, we demonstrate that our semi-automated, minimal operator involvement approach is capable of yielding CFD results of the LV that are comparable to other clinically validated LV flow models in the literature.

Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2-D) and three-dimensional (3-D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over from 3-D to 2-D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at $Re=10\,000$ . It is found that even for highly anisotropic geometries, 3-D small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalise those structures if the span is 50 % of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3-D small-scale structures and 2-D Kármán vortices result in 2-D and 3-D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.

An oscillating spanwise pressure gradient is imposed numerically to control the flow separation and reduce the drag of a turbulent flow in a channel with square bars. The transverse flow produces a maximum drag reduction of 25 %, due to lower pressure and skin-friction drag forces. The pressure drag reduction reaches a maximum of 22 % and is due to a decrease of the positive high pressure in front of the bars and an increase of the low negative pressure behind the bars. The skin-friction drag reduction is caused by a lower wall-shear stress along the cavity between the bars where the flow is fully attached, while the wall-shear stress on the crest of the bars and in the separated region behind the bars is unaffected. The spanwise laminar flow obtained by neglecting the nonlinear terms involving the turbulent velocity fluctuations is used to compute the power spent for oscillating the fluid along the spanwise direction and an excellent agreement is found with the power spent obtained by the averaged turbulent flow. A marginal or negative net power saved is found by subtracting the power employed for controlling the flow from the power saved thanks to the transverse flow. The control reduces the total drag as the integral of the Reynolds stresses along the horizontal line connecting the corners of two consecutive bars is decreased, which in turn impacts the pressure and wall-shear stress reductions.