Hairpin vortex solution in planar Couette flow: a tapestry of knotted vortices

A numerical continuation method has been carried out seeking solutions for two distinct flow configurations, planar Couette flow (PCF) and laterally heated flow in a vertical slot (LHF). We found that the spanwise vortex solution in LHF identifies a new solution in PCF. The vortical structure of our new solution has the shape of a hairpin observed ubiquitously in high-Reynolds-number turbulent flow, and we believe this discovery may provide the paradigm for a hierarchical organization of coherent structures in turbulent shear layers.

Characterization of the hairpin vortex solution in plane Couette flow

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

Development of an integrated reverse osmosis-greenhouse system driven by solar photovoltaic generators

The development of a system that integrates reverse osmosis (RO) with a horticultural greenhouse has been advanced through laboratory experiments. In this concept, intended for the inland desalination of brackish groundwater in dry areas, the RO concentrate will be reduced in volume by passing it through the evaporative cooling pads of the greenhouse. The system will be powered by solar photovoltaics (PV). Using a solar array simulator, we have verified that the RO can operate with varying power input and recovery rates to meet the water demands for irrigation and cooling of a greenhouse in north-west India. Cooling requires ventilation by a fan which has also been built, tested and optimised with a PV module outdoors. Results from the experiments with these two subsystems (RO and fan) are compared to theoretical predictions to reach conclusions about energy usage, sizing and cost. For example, the optimal sizing for the RO system is 0.12–1.3 m2 of PV module per m2 of membrane, depending on feed salinity. For the fan, the PV module area equals that of the fan aperture. The fan consumes <30 J of electrical energy per m3 of air moved which is 3 times less than that of standard fans. The specific energy consumption of the RO, at 1–2.3 kWh ?m-3, is comparable to that reported by others. Now that the subsystems have been verifi ed, the next step will be to integrate and test the whole system in the field.

Modelling vortex formation in an unbaffled stirred tank reactors

Agitating liquids in unbaffled stirred tank leads to the formation of a vortex in the region of the impeller shaft when operating in the turbulent flow regime. A numerical model is presented here that captures such a vortex. The volume of fluid model, a multiphase flow model was employed in conjunction with a multiple reference frame model and the shear stress turbulence model. The dimensions of the tank considered here, were 0.585 m for the liquid depth and tank diameter with a 0.2925 m diameter impeller at a height of 0.2925 m. The impeller considered was an eight-bladed paddle type agitator that was rotating with an angular velocity of 7.54 rad s (72 rpm) giving a Reynolds number of 10 and Froude number of 0.043. Preliminary results of a second investigation into the effect of liquid phase properties on the vortex formed are also presented. © 2006 Elsevier B.V. All rights reserved.

Vortex shedding from a row of square bars

Interactions of wakes in a flow past a row of square bars, which is placed across a uniform flow, are investigated by numerical simulations and experiments on the tassumption that the flow is two-dimensional and incompressible. At small Reynolds numbers the flow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric flow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the flow is obtained.

A new sensorless speed control scheme for doubly-fed reluctance generators

This paper presents the development and experimental validation of a novel angular velocity observer-based field-oriented control algorithm for a promising low-cost brushless doubly fed reluctance generator (BDFRG) in wind power applications. The BDFRG has been receiving increasing attention because of the use of partially rated power electronics, the high reliability of brushless design, and competitive performance to its popular slip-ring counterpart, the doubly fed induction generator. The controller viability has been demonstrated on a BDFRG laboratory test facility for emulation of variable speed and loading conditions of wind turbines or pump drives.

Developing a new SVPWM control strategy for open-winding brushless doubly fed reluctance generators

In this paper, a new open-winding control strategy is proposed for a brushless doubly fed reluctance generator (BDFRG) used for stand-alone wind turbine or ship generators. The BDFRG is characterized with two windings on the stator: a power winding and a control winding. The control winding is fed with dual two-level three-phase converters, and a vector control scheme based on space vector pulsewidth modulation is designed. Compared with traditional three-level inverter systems, the dc-link voltage and the voltage rating of power devices in the proposed system are reduced by 50% while still greatly improving the reliability, redundancy, and fault tolerance of the proposed system by increasing the switching modes. Its performance is evaluated by simulation in MATLAB/Simulink and an experimental study on a 42-kW prototype machine.

A note on the propagation of quantized vortex rings through a quantum turbulence tangle:energy transport or energy dissipation?

We investigate quantum vortex ring dynamics at scales smaller than the inter-vortex spacing in quantum turbulence. Through geometrical arguments and high-resolution numerical simulations, we examine the validity of simple estimates for the mean free path and the structure of vortex rings post-reconnection. We find that a large proportion of vortex rings remain coherent objects where approximately 75% of their energy is preserved. This leads us to consider the effectiveness of energy transport in turbulent tangles. Moreover, we show that in low density tangles, appropriate for the ultra-quantum regime, ring emission cannot be ruled out as an important mechanism for energy dissipation. However at higher vortex line densities, typically associated with the quasi-classical regime, loop emission is expected to make a negligible contribution to energy dissipation, even allowing for the fact that our work shows rings can survive multiple reconnection events. Hence the Kelvin wave cascade seems the most plausible mechanism leading to energy dissipation

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Vortex-density fluctuations, energy spectra, and vortical regions in superfluid turbulence

Measurements of the energy spectrum and of the vortex-density fluctuation spectrum in superfluid turbulence seem to contradict each other. Using a numerical model, we show that at each instance of time the total vortex line density can be decomposed into two parts: one formed by metastable bundles of coherent vortices, and one in which the vortices are randomly oriented. We show that the former is responsible for the observed Kolmogorov energy spectrum, and the latter for the spectrum of the vortex line density fluctuations.

Kelvin-wave cascade in the vortex filament model

The small-scale energy-transfer mechanism in zero-temperature superfluid turbulence of helium-4 is still a widely debated topic. Currently, the main hypothesis is that weakly nonlinear interacting Kelvin waves (KWs) transfer energy to sufficiently small scales such that energy is dissipated as heat via phonon excitations. Theoretically, there are at least two proposed theories for Kelvin-wave interactions. We perform the most comprehensive numerical simulation of weakly nonlinear interacting KWs to date and show, using a specially designed numerical algorithm incorporating the full Biot-Savart equation, that our results are consistent with the nonlocal six-wave KW interactions as proposed by L'vov and Nazarenko.

Direct power control with common mode voltage elimination for open-winding brushless doubly-fed wind power generators

In this paper, a new open-winding control strategy is proposed for a brushless doubly-fed reluctance generator (BDFRG) applicable for wind turbines. The BDFRG control winding is fed via a dual two-level three-phase converter using a single dc bus. Direct power control based on maximum power point tracking with common mode voltage elimination is designed, which not only the active and reactive power is decoupled, but the reliability and redundancy are all improved greatly by increasing the switching modes of operation, while DC-link voltage and rating of power devices decreased by 50% comparing to the traditional three-level converter systems. Consequently its effectiveness is evaluated by simulation tests based on a 42-kW prototype generator.