Unsteady forcing of turbulence by a randomly actuated impeller array

We investigate the unsteady forcing of turbulent flow in a well-stirred reactor using opposing arrays of pitched-blade impellers which randomly and independently reverse rotation. We systematically explore the dependence of the large-scale motions and the homogeneity and isotropy of the turbulence upon the forcing. We identify three dimensionless control parameters: the source fraction (the fraction of time spent in clockwise motion), the dimensionless forcing period and an impeller Reynolds number. We find the timescale of unsteady motion corresponds to the forcing period T, the average period of impeller reversal, independently of the impeller angular speed $$\varOmega$$ Ω and source fraction. As in jet-stirred tanks, unsteady forcing substantially increases the unsteady kinetic energy, energy dissipation, integral length scale and Taylor microscale Reynolds number ($$R_\lambda$$ R λ ) and improves the homogeneity and isotropy of the flow, provided the source fraction is chosen optimally and the forcing period is sufficiently large ($$\varOmega T > 10^3$$ Ω T > 10 3 ); impeller Reynolds number has a relatively small influence. The forcing period must be matched to angular speed: decreasing the forcing period below this threshold results in a less intense, more inhomogeneous turbulent flow. Spectra of two-point velocity increments demonstrate that unsteady energy injection is dominated by axial shear generated across impellers and becomes less prominent at smaller scales. However, even at $$R_\lambda \approx 354$$ R λ ≈ 354 , the signature of this unsteady forcing can still be detected in near-dissipation-range statistics. These observations provide insight into optimisation of forcing and the mechanism of energy transfer when using unsteady forcing to generate turbulence in confined vessels. Graphical abstract

Dynamics-Based Piecewise Constant Control of Omni-Vehicle

In this paper, we consider the dynamics of a mobile vehicle moving under control on a perfectly rough horizontal plane. The vehicle consists of a horizontal platform and three omni-wheels that can rotate independently. An omni-wheel has freely rotating rollers on its rim [1]. We use its simplest model: an omni-wheel on a perfectly rough plane is modelled as a rigid disk with a constraint that its contact point velocity directed perpendicular to the disk's plane. The vehicle is controlled by three direct current motors in wheels' axes. Two terms model torques generated by motors: the rst one is proportional to the voltage, the second one is proportional to the value of the angular velocity of a wheel (counter-electromotive force). We study constant voltage dynamics and boundary-value problems for arbitrary initial and nal mass center coordinates, course angles and their derivatives using a piecewise constant control with one switching point. This problem is reduced to a system of algebraic equations for some specific (symmetric) vehicle model. We numerically model the system and analyze the possibility of optimization. For another vehicle configuration, we get the solution as numerical parametric continuation starting from the solution for the symmetric vehicle.

On the Use of a Single Beam Acoustic Current Profiler for Multi-Point Velocity Measurement in a Wave and Current Basin

Harnessing the energy of tidal currents has huge potential as a source of clean renewable energy. To do so in a reliable and cost effective way, it is critical to understand the interaction between tidal turbines, waves, and turbulent currents in the ocean. Scaled testing in a tank test provides a controlled, realistic, and highly reproducible down-scaled open ocean environment, and it is a key step in gaining this understanding. Knowledge of the hydrodynamic conditions during tests is critical and measurements at multiple locations are required to accurately characterise spatially varying flow in test tank facilities. The paper presents a laboratory technique using an acoustic velocimetry instrument, the range over-which measurements are acquired being more akin to open water applications. This enables almost simultaneous multi-point measurements of uni-directional velocity along a horizontal profile. Velocity measurements have been obtained from a horizontally mounted Single Beam Acoustic Doppler (SB-ADP) profiler deployed in the FloWave Ocean Energy Research Facility at the University of Edinburgh. These measurements have been statistically compared with point measurements obtained while using a co-located Acoustic Doppler Velocimeter (ADV). Measurements were made with both instruments under flow velocities varying from 0.6 ms−1 to 1.2 ms−1, showing that flow higher than 1 ms−1 was more suitable. Using a SB-ADP has shown the advantage of gaining 54 simultaneous measurement points of uni-directional velocity, covering a significant area with a total distance of 10 m of the test-tank, at a measurement frequency of 16 Hz. Of those measurement points, 41 were compared with co-located ADV measurements covering 8 m of the profile for a tank nominal flow velocity of 0.8 ms−1, and four distributed locations were chosen to to carry out the study at 0.6 ms−1, 1.0 ms−1, and 1.2 ms−1. The comparison with the ADV measurement showed a 2% relative bias on average.