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Swimming
Published in Malcolm S. Gordon, Reinhard Blickhan, John O. Dabiri, John J. Videler, Animal Locomotion, 2017
John O. Dabiri, Malcolm S. Gordon
Equation 3.136 is the Helmholtz equation. It states that the vorticity of a fluid particle can change either due to the forces applied by the animal on the fluid (via ∇ × fl) or due to velocity gradients aligned with the local vorticity vector [giving a nonzero scalar product in (ω ⋅ ∇)u]. This latter effect is known as vortex stretching. Conceptually, the velocity field stretches the local vortex tubes; being divergence free, the vortex tubes narrow and elongate in response (in close analogy to the behavior of an incompressible mass of fluid that is stretched). To conserve angular momentum, the fluid particles in the narrower, stretched vortex tube must rotate faster, leading to stronger vorticity in the tube (Figure 3.27).
Turbulence
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
Vortex stretching mechanism transfers fluctuating energy and vorticity to smaller and smaller scales via non-linear interactions until velocity gradients become so large that the energy is converted to heat. The stretching is in the direction of motion, implying that vortices will become thinner in the direction normal to flow. Continued turbulence requires a continuous supply of energy to make up for the loss of energy.
Modelling Procedures
Published in Vanesa Magar, Sediment Transport and Morphodynamics Modelling for Coasts and Shallow Environments, 2020
The last two turbulence closure schemes considered are the vortex stretching and the energy cascade schemes. Both methods are fundamental to how energy is passed between different turbulence scales. Vortex stretching produces a change in vorticity in the direction of the stretching, in order to conserve angular momentum. Vortex stretching also produces energy cascading from large to small eddies, because the small eddies are exposed to the rate of strain of the large eddies, and therefore a change in vorticity, and a flux of energy from large eddies to small eddies. Most of the energy taken by an eddy of a given size is taken from the next largest eddy in size and passed to the next smallest eddy in size. This is equivalent to a cascading waterfall, where a filling pool overflows into the next pool, and this explains the energy cascade term so commonly used in turbulence dynamics. As the eddies become smaller and smaller, viscous stresses become more and more important until they completely dominate the dynamics and the eddy energy is dissipated as heat. The smallest scale known is the Kolmogorov microscale and is denoted here as ηk. Thus, the turbulent energy spectrum, E(k), can be divided into three regions, each dependent on the size of the wavenumber. The range of small wavenumbers is the energy production subrange, which contains most of the energy and is dominated by large eddies. The range of intermediate wavenumbers is the dissipation subrange, and in this range, energy cascading occurs from large to small eddies. This is the inertial subrange, and the energy decays with increasing wavenumber at a rate that is inversely proportional to k5/3, where k is the wavenumber, and proportional to ϵ2/3, where ϵ is the energy dissipation rate: E(k)=αϵ2/3k−5/3.
Static turbulence promoters in cross-flow membrane filtration: a review
Published in Chemical Engineering Communications, 2020
Chiranjit Bhattacharjee, V. K. Saxena, Suman Dutta
In membrane filtration processes, turbulence is defined as the process of increasing the flow rate of the feed or changing the flow path or to create additional mixing to disrupt the boundary layer which enhances the mass transfer rate in the module. In cross-flow systems this disruption leads to minimal accumulation of rejected particles over the membrane surface and hence results in increased permeate flux. This can be achieved by incorporating static inserts in membrane modules. In literature, these static inserts are referred to as static mixers or static turbulence promoters. Static turbulence promoters effectively change the hydrodynamics conditions of the module without significantly increasing energy consumption and investment costs. The intensity of turbulence plays an important role in changing the fluid dynamics in the system. Turbulent intensity is a measure of extent of turbulence dissipation which is used to signify the strength of turbulence in promoter-filled channels. One characteristic of turbulent flows is their irregularity or randomness. Stretching of three-dimensional vortices plays an important role in turbulence. This mechanism is also known as vortex stretching. Turbulence enhances the mixing of fluid and generates an additional diffusive effect termed as eddy diffusion. This diffusive effect of turbulence is the driving force for rapid mixing and simultaneous increase in momentum and mass transfer.
Numerical investigation and experimental observation of unsteady tip leakage cavitating flow for the axial waterjet pump
Published in Ships and Offshore Structures, 2023
Shun Xu, Xin-ping Long, Bin Ji, Gui-bin Li, Yong-liang Xiong
According to Wu’s theory (Wu 1993), the vortex stretching weakens the inertia moment of fluid, increases angular momentum, and promotes vorticity production. in Figure 26, the circumferential vorticity generation rate is negative at the TLV core and the intensity of local vorticity decreases consequently. Compared with other regions, the circumferential vortex stretching term in the unsteady cavitation region has the largest magnitude as the effect of cavitation shedding and collapsing. As shown in Figure 27, distributions of viscous diffusion in the circumferential direction are consistent with that in the axial direction.
The Role of Flame–flow Interactions on Lean Premixed Lifted Flame Stabilization in a Low Swirl Flow
Published in Combustion Science and Technology, 2023
Mohammad Shahsavari, Mohammad Farshchi, Mohammad Hossein Arabnejad, Bing Wang
in which and represents vorticity production terms due to the vortex tilting, and is produced due to the vortex stretching. Figure 12 compares these terms at Z = 30 mm, which indicates that the vortex stretching is several orders of magnitude larger than the tilting term. Therefore, vorticity production is dominated by vortex stretching.