High-Performance Discrete-Vortex Algorithms for Unsteady Viscous-Fluid Flows near Moving Boundaries
A high-performance Discrete-Vortex Method (DVM) is successfully developed and implemented to directly simulate two-dimensional low to medium-Reynolds number flows around multiple arbitrarily shaped bodies undergoing either prescribed or free motions. The deterministic Viscous-Vortex-Domain (VVD) formulation is adopted to simulate vorticity diffusion. Through the use of CPU and Graphics-Processing-Unit (GPU) parallel computing, significant speedup of the simulation compared to a serial implementation on a CPU is achieved. The validity of the present DVM simulation is confirmed by comparing the present results with published ones for a variety of test cases. The current implementation of DVM has been used to study two novel flow problems of practical interest and has led to significant findings.
First, the full and partial ground effects on the lift generation of a flapping (air)foil in normal hovering mode are investigated. To achieve full ground effect, the foil of chord c is made to hover above the center of a finite-sized platform of length 10c. The computed force-enhancement, force-reduction, and force-recovery regimes at low, medium, and high ground clearances are observed to be in line with existing literature. This research puts special focus on partial ground effects when the foil is hovering near the edge of the platform. Lift-modifying mechanisms not previously observed under full ground effect have been discovered. When stroke reversal of the flapping occurs near the edge of the platform, a relatively stationary strong vortex may form above the platform edge. This strong vortex can either increase or decrease the instantaneous lift force on the foil depending on the position of the foil relative to the platform edge. Further, the platform edge may lead to the formation of an additional vortex pair which increases the instantaneous lift force as the foil sweeps past the edge under certain suitable conditions. Lastly, the platform edge can lead to the formation of a reverse von Kármán vortex street that extends well below the stroke plane under suitable geometric arrangements.
Second, the flow past a Bach-type vertical-axis wind or current turbine is simulated using the DVM at a Reynolds number of 1,500. The main purpose of the study is to evaluate the suitability of Bach-type turbines for use as micro-scale energy harvesters that can be applied to power, for example, sensor nodes of a Wireless Sensor Network. Through simulations, the maximum power coefficient of the turbine operating at a prescribed constant tip-speed ratio is found to be 0.18, which is comparable to the performance of a turbine of the same geometry at much higher Reynolds numbers. This indicates that there is only minimal performance penalty for miniaturization. The angular velocity of the turbine has a strong influence on the evolution of vortical flow structures. A new wake-capturing mechanism that boosts the performance of the turbine is discovered from the simulations for a certain range of tip-speed ratios where the vortex shed by the advancing blade helps drive the returning blade. In addition to the condition of prescribed rotation, free rotation of a steel Bach-type turbine under a steady current in water is also investigated. Significant fluctuation in angular velocity over one period of rotation is observed. This speed fluctuation is found to be detrimental to energy extraction, reducing the maximum power coefficient to approximately 0.16. This level of power-generation capability implies that such micro-scale turbines can significantly extend the life expectancy of a wireless sensor node or even maintain the node in a low-power state indefinitely.