Free Vortex Rings, Analogies and Differences Between Vorticity and a Passive Scalar

Passive scalar mixing in vortex rings

Journal of Fluid Mechanics ◽

10.1017/s0022112007006349 ◽

2007 ◽

Vol 582 ◽

pp. 449-461 ◽

Cited By ~ 32

Author(s):

RAJES SAU ◽

KRISHNAN MAHESH

Keyword(s):

Numerical Simulation ◽

Direct Numerical Simulation ◽

Vortex Ring ◽

Nozzle Exit ◽

Passive Scalar ◽

Rate Of Change ◽

Vortex Rings ◽

Ambient Fluid ◽

Stroke Length ◽

Formation Number

Direct numerical simulation is used to study the mixing of a passive scalar by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’ (Gharibet al. J. Fluid Mech.vol. 360, 1998, p. 121), is found to be 3.6. Simulations are performed for a range of stroke ratios (ratio of stroke length to nozzle exit diameter) encompassing the formation number, and the effect of stroke ratio on entrainment and mixing is examined. When the stroke ratio is greater than the formation number, the resulting vortex ring with trailing column of fluid is shown to be less effective at mixing and entrainment. As the ring forms, ambient fluid is entrained radially into the ring from the region outside the nozzle exit. This entrainment stops once the ring forms, and is absent in the trailing column. The rate of change of scalar-containing fluid is found to depend linearly on stroke ratio until the formation number is reached, and falls below the linear curve for stroke ratios greater than the formation number. This behaviour is explained by considering the entrainment to be a combination of that due to the leading vortex ring and that due to the trailing column. For stroke ratios less than the formation number, the trailing column is absent, and the size of the vortex ring increases with stroke ratio, resulting in increased mixing. For stroke ratios above the formation number, the leading vortex ring remains the same, and the length of the trailing column increases with stroke ratio. The overall entrainment decreases as a result.

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Implementation, Optimization and Validation of a Nonlinear Lifting Line Free Vortex Wake Module Within the Wind Turbine Simulation Code QBlade

Volume 9: Oil and Gas Applications; Supercritical CO2 Power Cycles; Wind Energy ◽

10.1115/gt2015-43265 ◽

2015 ◽

Cited By ~ 8

Author(s):

David Marten ◽

Matthew Lennie ◽

Georgios Pechlivanoglou ◽

Christian Navid Nayeri ◽

Christian Oliver Paschereit

Keyword(s):

Cfd Simulation ◽

Unsteady Aerodynamics ◽

Momentum Balance ◽

Vortex Rings ◽

Vortex Wake ◽

Computationally Efficient ◽

Simulation Code ◽

Free Vortex ◽

Institute Of Technology ◽

Lifting Line

The development of the next generation of large multi-megawatt wind turbines presents exceptional challenges to the applied aerodynamic design tools. Because their operation is often outside the validated range of current state of the art momentum balance models, there is a demand for more sophisticated, but still computationally efficient simulation methods. In contrast to the Blade Element Momentum Method (BEM) the Lifting Line Theory (LLT) models the wake explicitly by a shedding of vortex rings. The wake model of freely convecting vortex rings induces a time-accurate velocity field, as opposed to the annular averaged induction that is computed from the momentum balance, with computational costs being magnitudes smaller than those of a full CFD simulation. The open source code QBlade, developed at the Berlin Institute of Technology, was recently extended with a Lifting Line - Free Vortex Wake algorithm. The main motivation for the implementation of a LLT algorithm into QBlade is to replace the unsteady BEM code AeroDyn in the coupling to FAST to achieve a more accurate representation of the unsteady aerodynamics and to gain more information on the evolving rotor wake and flow-field structure. Therefore, optimization for computational efficiency was a priority during the integration and the provisions that were taken will be presented in short. The implemented LLT algorithm is thoroughly validated against other benchmark BEM, LLT and panel method codes and experimental data from the MEXICO and NREL Phase VI tests campaigns. By integration of a validated LLT code within QBlade and its database, the setup and simulation of LLT simulations is greatly facilitated. Simulations can be run from already existing rotor models without any additional input. Example use cases envisaged for the LLT code include; providing an estimate of the error margin of lower fidelity codes i.e. unsteady BEM, or providing a baseline solution to check the soundness of higher fidelity CFD simulations or experimental results.

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Implementation, Optimization, and Validation of a Nonlinear Lifting Line-Free Vortex Wake Module Within the Wind Turbine Simulation Code qblade

Journal of Engineering for Gas Turbines and Power ◽

10.1115/1.4031872 ◽

2015 ◽

Vol 138 (7) ◽

Cited By ~ 34

Author(s):

David Marten ◽

Matthew Lennie ◽

Georgios Pechlivanoglou ◽

Christian Navid Nayeri ◽

Christian Oliver Paschereit

Keyword(s):

Cfd Simulation ◽

Unsteady Aerodynamics ◽

Momentum Balance ◽

Vortex Rings ◽

Vortex Wake ◽

Computationally Efficient ◽

Simulation Code ◽

Free Vortex ◽

Institute Of Technology ◽

Lifting Line

The development of the next generation of large multimegawatt wind turbines presents exceptional challenges to the applied aerodynamic design tools. Because their operation is often outside the validated range of current state-of-the-art momentum balance models, there is a demand for more sophisticated, but still computationally efficient simulation methods. In contrast to the blade element momentum method (BEM), the lifting line theory (LLT) models the wake explicitly by a shedding of vortex rings. The wake model of freely convecting vortex rings induces a time-accurate velocity field, as opposed to the annular-averaged induction that is computed from the momentum balance, with computational costs being magnitudes smaller than those of a full computational fluid dynamics (CFD) simulation. The open source code qblade, developed at the Berlin Institute of Technology, was recently extended with a lifting line-free vortex wake algorithm. The main motivation for the implementation of an LLT algorithm into qblade is to replace the unsteady BEM code aerodyn in the coupling to fast to achieve a more accurate representation of the unsteady aerodynamics and to gain more information on the evolving rotor wake and flow-field structure. Therefore, optimization for computational efficiency was a priority during the integration and the provisions that were taken will be presented in short. The implemented LLT algorithm is thoroughly validated against other benchmark BEM, LLT, and panel method codes and experimental data from the MEXICO and National Renewable Energy Laboratory (NREL) Phase VI tests campaigns. By integration of a validated LLT code within qblade and its database, the setup and simulation of LLT simulations are greatly facilitated. Simulations can be run from already existing rotor models without any additional input. Example use cases envisaged for the LLT code include: providing an estimate of the error margin of lower fidelity codes, i.e., unsteady BEM, or providing a baseline solution to check the soundness of higher fidelity CFD simulations or experimental results.

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Passive scalar transport mediated by laminar vortex rings

Fluid Dynamics Research ◽

10.1088/1873-7005/aa5b59 ◽

2017 ◽

Vol 49 (2) ◽

pp. 025514 ◽

Cited By ~ 1

Author(s):

R H Hernández ◽

G Rodríguez

Keyword(s):

Passive Scalar ◽

Scalar Transport ◽

Vortex Rings ◽

Passive Scalar Transport

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Collision of two vortex rings

Journal of Fluid Mechanics ◽

10.1017/s0022112091000903 ◽

1991 ◽

Vol 230 ◽

pp. 583-646 ◽

Cited By ~ 80

Author(s):

S. Kida ◽

M. Takaoka ◽

F. Hussain

Keyword(s):

Energy Dissipation ◽

Initial Conditions ◽

Power Laws ◽

Passive Scalar ◽

High Energy ◽

Navier Stokes ◽

Vortex Rings ◽

Navier Stokes Equation ◽

Developed Turbulence ◽

High Energy Dissipation

The interaction of two identical circular viscous vortex rings starting in a side-by-side configuration is investigated by solving the Navier–Stokes equation using a spectral method with 643 grid points. This study covers initial Reynolds numbers (ratio of circulation to viscosity) up to 1153. The vortices undergo two successive reconnections, fusion and fission, as has been visualized experimentally, but the simulation shows topological details not observed in experiments. The shapes of the evolving vortex rings are different for different initial conditions, but the mechanism of the reconnection is explained by bridging (Melander & Hussain 1988) except that the bridges are created on the front of the dipole close to the position of the maximum strain rate. Spatial structures of various field quantities are compared. It is found that domains of high energy dissipation and high enstrophy production overlap, and that they are highly localized in space compared with the regions of concentrated vorticity. The kinetic energy decays according to the same power laws as found in fully developed turbulence, consistent with concentrated regions of energy dissipation. The main vortex cores survive for a relatively long time. On the other hand, the helicity density which is higher in roots of bridges and threads (or legs) changes rapidly in time. The high-helicity-density and high-energy-dissipation regions overlap significantly although their peaks do not always do so. Thus a long-lived structure may carry high-vorticity rather than necessarily high-helicity density. It is shown that the time evolution of concentration of a passive scalar is quite different from that of the vorticity field, confirming our longstanding warning against relying too heavily on flow visualization in laboratory experiments for studying vortex dynamics and coherent structures.

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