Any device aiming to harness the abundant clean and renewable energy from ocean and other water resources must have high energy density, be unobtrusive, have low maintenance, be robust, meet life cycle cost targets, and have a 10-20 year life. The vortex induced vibration aquatic clean energy (VIVACE) converter-invented by Bernitsas and Raghavan, patent pending through the University of Michigan-satisfies those criteria. It converts ocean/river current hydrokinetic energy to a usable form of energy such as electricity using VIV successfully and efficiently for the first time. VIVACE is based on the idea of maximizing rather than spoiling vortex shedding and exploiting rather than suppressing VIV. It introduces optimal damping for energy conversion while maintaining VIV over a broad range of vortex shedding synchronization. VIV occurs over very broad ranges of Reynolds (Re) number Only three transition regions suppress VIV. Thus, even from currents as slow as 0.25 m/s, VIVACE can extract energy with high power conversion ratio making ocean/river current energy a more accessible and economically viable resource. In this paper, the underlying concepts of the VIVACE converter are discussed. The designs of the physical model and laboratory prototype are presented. A mathematical model is developed, and design particulars for a wide range of application scales are calculated. Experimental measurements on the laboratory prototype are reported in the sequel paper and used here for preliminary benchmarking.

VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A New Concept in Generation of Clean and Renewable Energy From Fluid Flow

In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consi...

Direct numerical simulation of the turbulent channel flow of a polymer solution

The coupling of the plasma sheet to the solar wind is studied statistically using measurements from various satellite pairs: one satellite in the solar wind and one in either the magnetotail central plasma sheet or the near-Earth plasma sheet. It is found that the properties of the plasma sheet are highly correlated with the properties of the solar wind: specifically that (1) the density of the plasma sheet is strongly correlated with the density of the solar wind, (2) the temperature of the plasma sheet is strongly correlated with the velocity of the solar wind, (3) the particle pressure and total pressure of the plasma sheet are strongly correlated with the ram pressure of the solar wind, (4) B y in the plasma sheet is strongly correlated with the B y in the solar wind, (5) B z in the plasma sheet is weakly correlated with the B z in the solar wind, (6) E y in the plasma sheet is weakly correlated with the E y in the solar wind, and (7) plasma sheet earthward-tailward flow velocity is weakly anticorrelated with the solar wind velocity. After removing these solar wind dependencies, the dependencies of the properties of the plasma sheet on geomagnetic activity are reduced and changed. The time lags between the solar wind density and the plasma sheet density are investigated statistically and on a case-by-case basis; it is found that solar wind material reaches the midtail plasma sheet in ∼2 hours, reaches the near-Earth nightside plasma sheet in ∼4 hours, and reaches the dayside plasma sheet in ∼15 hours. The pathway for mass transport into the plasma sheet is explored; it is suggested that solar wind material is transported rapidly up the tail to the near-Earth region via the plasma sheet boundary layer, followed by poloidal transport via E x B convection in the near-Earth (low β) plasma sheet or followed by eddy diffusion in the not-too-distant (high β) plasma sheet. Analogies are drawn between the high Reynolds number plasma sheet and a high Reynolds number fluid wake.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97JA02986

The driving of the plasma sheet by the solar wind

[1] It is argued here that the inner heliosphere is filled with a network of entangled magnetic flux tubes and that the flux tubes are fossil structures that originate at the solar surface. 65,860 flux tubes are collected from seven years of measurements with the ACE spacecraft at 1 AU by spotting the flux tube walls with large changes in the magnetic field direction and the vector flow velocity. The tube walls are associated with large changes in the ion entropy density and the alpha-to-proton ratio. The median size of the flux tubes at 1 AU is 4.4 x 10 5 km. The tubes are larger in slow wind than in fast wind. The tubes are on-average aligned with the Parker spiral, with a large spread in orientations. This large spread may be caused by slight misalignments of tubes in the corona. The flux tubes map to granule and supergranule sizes on the Sun. The amounts of magnetic flux in the tubes at 1 AU correspond to the amounts of magnetic flux in field concentrations in the magnetic carpet. It is argued that the flux tubes do not reconnect during the ∼ 100-h advection to 1 AU owing to the expansion of the solar wind. The flux tube texture impacts the flow properties of the solar wind, turbulence in the solar wind, energetic-particle propagation in the inner heliosphere, and the driving of the Earth's magnetosphere. A method for using measurements of the flux tube walls for the remote sensing of magnetic field dynamics in the magnetic carpet is suggested.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2007JA012684

Flux tube texture of the solar wind: Strands of the magnetic carpet at 1 AU?

Measurements of turbulence properties of solutions of polymers have been made over a large range of drag-reduction, in a fully-developed channel flow. At flows close to maximum drag-reduction the Reynolds stresses were approximately zero over the whole cross section of the channel. Added mean polymer stresses were observed in the viscous wall region for small drag-reduction and over the whole cross-section for large drag-reduction. Even though the Reynolds stresses are zero, the velocity profile is not parabolic because of the presence of these mean stresses. We interpret the results by arguing that the interaction of turbulence with the polymers introduces mean and fluctuating polymer stresses which can create turbulence. The observation that the turbulence modification depends on the manner by which the polymers are introduced into the flow supports the notion that the polymers need to form aggregates in order to be effective.

Influence of drag-reducing polymers on turbulence: effects of Reynolds number, concentration and mixing

In this study the evolution of initially homogeneous and isotropic turbulence in the presence of a free surface was investigated. The Navier–Stokes equations were solved via direct pseudo-spectral simulation with a resolution of 963. The Reynolds number based on the volume-averaged turbulence kinetic energy and dissipation rate was 147. Periodic boundary conditions were used in two dimensions, and the top and bottom sides of the domain were flat and shear-free. A random, divergence-free velocity field with a prescribed spectrum was used as the initial condition. An ensemble of sixteen separate simulations was used to calculate statistics.Near the surface, the Reynolds stresses are anisotropic and the anisotropy extends a distance from the surface roughly equal to the turbulent lengthscale. The tangential vorticity fluctuations also vanish near the surface, owing to the no-shear condition, causing a corresponding decrease in the fluctuating enstrophy. The thickness of the region in which the surface affects the vorticity distribution is roughly one-tenth the turbulent lengthscale. The stress anisotropy near the surface appears to be maintained by reduced dissipation for the tangential velocity fluctuations, reduced pressure–strain transfer from the tangential to surface-normal velocity fluctuations, and rapid decay of the surface-normal velocity fluctuations due to dissipation. The turbulence kinetic energy rises in the near-surface region owing to a decrease in dissipation at the surface. This decrease in dissipation results from the local reduction in enstrophy owing to the vanishing of the tangential vorticity fluctuations at the surface. At the free surface, the mean pressure rises. This is also due to the reduction in enstrophy.While the tangential vorticity must vanish at the free surface, the flow is fully three-dimensional up to the surface and the production of surface-normal vorticity by vortex stretching attains a maximum at the free surface. The contribution to the total enstrophy by the surface-normal vorticity fluctuations remains relatively constant over depth. The production of the surface-normal enstrophy component due to vortex stretching is roughly balanced by turbulent transport of enstrophy away from the surface. Near the surface, there are elevated levels of production of tangential vorticity by both vortex-stretching and fluctuating shear strains.

Shear-free turbulence near a flat free surface

Two-component laser velocimeter measurements in a fully developed turbulent water channel flow with polymer injection were used to examine the effect of polymer injection on the Reynolds stresses and the production terms in the Reynolds stress transport equations. These measurements show that while the root-mean-square fluctuation level of the streamwise velocity was increased, the r.m.s. of the wall-normal velocity and the Reynolds shear stress were reduced.

Turbulent structure in a channel flow with polymer injection at the wall

In this study the surface features and the radar backscatter associated with breaking waves generated by a uniform flow past a stationary submerged hydrofoil were examined. The level of energy dissipation due to breaking was varied by changing the foil angle of attack. Time series of surface elevation profiles were obtained for the breaking crest region and the following waves. Radar backscatter (X-band) was also measured for an incidence angle of 45° with the radar looking both upwave and downwave for HH and VV polarizations. These measurements were compared to model predictions of radar backscatter using the surface elevation data as inputs to the model. The breaking crest region exhibited the largest surface disturbances, as measured by the temporal variance of the surface elevation. The maximum in the variance was associated with large low-frequency disturbances in the ‘toe’ region. Downstream-moving waves appear just ahead of the crest and, due primarily to interaction with the spatially varying current set up by the stationary wave, decrease in amplitude by an order of magnitude as they propagate downstream. These surface disturbances remain at a low level thereafter. A maximum radar cross-section per unit area of about 0.5 was observed near the breaking crest, for both HH and VV polarization in the upwave look direction. The maximum value for the upwave look direction was about twice as large as for the downwave look direction. Downstream of the breaking crest, the radar cross-section decreased rapidly and then leveled off, and an increasing difference between the VV and HH backscatter was observed as the overall backscatter level decreased. Near the second crest, there was a small increase in the height variance and in the radar cross-section. The surface-elevation measurements were used as inputs for a Bragg-scattering model and the expected radar backscatter was calculated. The variations in the observed radar cross-section downstream of the breaking crest are satisfactorily explained by the Bragg model when surface-tilt effects are taken into account. However, the backscatter from the breaking crest itself is not accurately predicted since, in this region, the small-scale surface roughness exceed the limits of validity for the Bragg model.

Radar backscatter and surface roughness measurements for stationary breaking waves

Results of an experimental study of the interaction of a turbulent jet with a free surface when the jet issues parallel to the free surface are presented. Three different jets, with different exit velocities and jet-exit diameters, all located two jet-exit diameters below the free surface were studied. At this depth the jet flow, in each case, is fully turbulent before significant interaction with the free surface occurs. The effects of the Froude number (Fr) and the Reynolds number (Re) were investigated by varying the jet-exit velocity and jet-exit diameter. Froude-number effects were identified by increasing the Froude number from Fr = 1 to 8 at Re = 12700. Reynolds-number effects were identified by increasing the Reynolds number from Re = 12700 to 102000 at Fr = 1. Qualitative features of the subsurface flow and free-surface disturbances were examined using flow visualization. Measurements of all six Reynolds stresses and the three mean velocity components were obtained in two planes 16 and 32 jet diameters downstream using a three-component laser velocimeter. For all the jets, the interaction of vorticity tangential to the surface with its ‘image’ above the surface contributes to an outward flow near the free surface. This interaction is also shown to be directly related to the observed decrease in the surface-normal velocity fluctuations and the corresponding increase in the tangential velocity fluctuations near the free surface. At high Froude number, the larger surface disturbances diminish the interaction of the tangential vorticity with its image, resulting in a smaller outward flow and less energy transfer from the surface-normal to tangential velocity fluctuations near the surface. Energy is transferred instead to free-surface disturbances (waves) with the result that the turbulence kinetic energy is 20 YO lower and the Reynolds stresses are reduced. At high Reynolds number, the rate of evolution of the interaction of the jet with the free surface was reduced as shown by comparison of the rate of change with distance downstream of the local Reynolds and Froude numbers. In addition, the decay of tangential vorticity near the surface is slower than for low Reynolds number so that vortex filaments have time to undergo multiple reconnections to the free surface before they eventually decay.

Turbulent structure in free-surface jet flows

Radar backscatter measurements from stationary breaking waves were used to examine how the surface roughness generated by wave breaking affects radar backscatter at moderate incidence angles. Stationary breaking waves were generated by submerging a stationary hydrofoil in a uniform flow. X band radar backscatter measurements were made at numerous streamwise positions along the stationary breaking waves from an incidence angle of 45° for horizontal transmit and receive polarization (HH) and vertical transmit and receive polarization (VV) looking both upwave and downwave. The radar returns increased substantially, and the HH-to-VV polarization ratio approached unity near the breaking crests. This radar signature is consistent with those observed in the field. Detailed optical measurements of the breaking surfaces revealed that the observed radar returns near the breaking crests were the result of increased incoherent backscatter from the small-scale surface roughness generated by the breaking waves, although surface tilt effects also modified the radar return. Scattering models based upon the small perturbation solution performed well in the wake of the stationary breaking crest, but they significantly underestimated the HH-to-VV polarization ratio near the breaking crest. More advanced scattering solutions such as the integral equation method produced more accurate results in regions containing the largest surface roughness. These findings suggest that incoherent backscatter from surface disturbances produced by deep water breaking waves may be the source of the high radar returns and small polarization ratios observed from the ocean at moderate incidence angles.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JC900223

David T. Walker

Papers

Shear-free turbulence near a flat free surface

Turbulent structure in a channel flow with polymer injection at the wall

Radar backscatter and surface roughness measurements for stationary breaking waves

Turbulent structure in free-surface jet flows

Radar backscatter from stationary breaking waves