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Alternating waveforms
Published in W. Bolton, Mathematics for Engineering, 2012
Consider the line OA in Figure 17.11 rotating in an anticlockwise direction about O with a constant angular velocity ω (note that the unit of angular velocity is radians/second). A constant angular velocity means that the line rotates through equal angles in equal intervals of time. The line starts from the horizontal position and rotates through an angle θ in a time t.
Entropy optimization of non-Newtonian hybrid nanofluid EMHD flow by numerical and Levenberg–Marquardt backpropagation approach over a rotating disk
Published in Waves in Random and Complex Media, 2023
A. Divya, P. Bala Anki Reddy, Raja Das
Over a spinning (rotating) disk of porous media, an incompressible, time-dependent 3D Casson hybrid nanofluid flow is investigated. In reality, this disk is centered at and rotates at a constant angular velocity. The rotation and stretching of the disk causes the fluid to move about. The Hall effect's influence on the disk is generally investigated due to the enormous magnetic field. Figure 1 depicts the problem's geometry in cylindrical coordinates together with EMHD. Because z-axis is navigated by a uniform magnetic field , the surface temperature of the disk is assumed to be , whereas the temperature away from the disk is presumed to be . For the reorganization of the problem, we assumed the following assumptions: This flow includes various types of nanoparticles such as titanium dioxide and silver, which were detected in the blood's base fluid. The Hall current is presumed to be triggered by a sufficiently strong magnetic field and the simplified Ohm's law in the presence of an electric field is phrased as [5, 21]:
Synchronized PIV and pressure measurements on a model Francis turbine during start-up
Published in Journal of Hydraulic Research, 2020
Rahul Goyal, Michel J. Cervantes, Bhupendra K. Gandhi
The flow in the draft tube cone increases during the turbine start-up. Initially, the flow is increased to obtain the synchronous speed of the runner, then turbine-generator synchronization is achieved by the magnetization of the generator at synchronous speed. As a result, the turbine starts to operate at a constant angular velocity. The turbine is operating at off-design condition under transient operation until steady-state operation is reached at the BEP. The model Francis turbine is designed to operate at BEP condition where the high axial flow is available around the centreline of the draft tube (Fig. 9c). The off-design conditions of Francis turbine are normally observed to develop some unsteadiness in the flow such as vortex rope and torch-like vortex core in the draft tube (Dorfler et al., 2013). Therefore, the variation in instantaneous axial velocities during turbine start-up is presented in Figs 11–14. The time scale is maintained same according to the synchronized measurements (Figs 4–8) and the right side axis represents the percentage GVO. The horizontal axis is made dimensionless using runner radius (R = 174.5 mm). Both phases (I and II) of start-up with different schemes (I–III) are considered to investigate the unsteadiness in the flow downstream of the runner.
Hysteresis behaviour in spanwise rotating plane Couette flow at Re w = 2600
Published in Journal of Turbulence, 2021
Yuhan Huang, Zhenhua Xia, Shiyi Chen
RPCF is one of the benchmark problems for studying the rotating wall-bounded turbulence [28] and it has been widely studied, both experimentally and numerically, in the past [20,29–41]. In RPCF, the two planes, which are separated by , move towards opposite directions with a constant velocity difference . The system rotates in z-direction with a constant angular velocity . The system is determined by two control parameters, the Reynolds number (ν is the kinematic viscosity) and the rotation number . Gai et al. [37] numerically showed that the large-scale streamwise roll cells exist in RPCF and these roll cells can take a great share of the turbulent kinetic energy at different Ro. Xia et al. [20,22] reported that multiple states exist in RPCF at and the turbulent statistics at different states show obvious differences. Huang et al. [21] further found that hysteresis loops can be observed in RPCF at when Ro increases or decreases in the range . When , the number of roll cells in the computation domain is influenced by its history. when Ro increases from 0.01 in steps, there are two pairs of roll cells in the computational domain. When Ro decreases from 0.6 in steps, three pairs of roll cells were observed in the domain.