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Ideal fluid flow
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
Vorticity is a vector that describes the local rotation of a point in the fluid, as seen by an observer moving along with it (recall Lagrangian approach of flow description). Mathematically, the vorticity is defined as the curl (or rotation) of the velocity field of the fluid, usually denoted by ω which should not be confused with the angular velocity vector of that portion of the fluid with respect to the external environment or to any fixed axis. Vortex line is related to the vorticity in the same way as streamline is related to the velocity as shown by their respective equations: dxu=dyv=dzw(streamline)dxωx=dyωy=dzωz(vortexline)
Multidimensional Effects, Potential Functions, and Fields
Published in Joel L. Plawsky, Transport Phenomena Fundamentals, 2020
To force the separation of variables solution to be exactly like that developed using the complex variables approach, we must specify that the circulation be zero or that c1 = 0. c1 represents the vorticity of the flow at the center of the cylinder, or the rate of angular deformation of a fluid element. Thus, the circulation about a closed curve is equal to the vorticity enclosed by it. We can get a better picture of the magnitude of c1 by assuming our cylinder rotates about its axis with a frequency of ω s−1. At the surface of the cylinder, vθ is just the perimeter of the circle of radius, ro, multiplied by the frequency of rotation. Thus, vθ=2πroω=−c1roc1=−2πro2ω
Turbulence
Published in Wioletta Podgórska, Multiphase Particulate Systems in Turbulent Flows, 2019
Turbulence is a three-dimensional motion characterized by a high level of fluctuating vorticity. The production of vorticity is increased by vortex filaments stretching, which is also a mechanism of energy transport from larger to smaller eddies. Moreover, turbulence is dissipative, so when energy is not supplied, the turbulence decays. Turbulence involves a wide range of spatial wave lengths. The properties of the largest eddies characterized by the lowest frequencies are determined by the mean flow that supplies the energy. This energy is transported to smaller and smaller eddies through inertial interactions. The smaller the eddy size the larger velocity gradient in the eddy and, therefore, the larger tangential stresses that counteract rotational motion. Simultaneously, at a higher wavenumber range, the dependence on external conditions decreases and the influence of viscosity increases, leading to energy dissipation in the region of smallest scales (Hinze, 1975).
Low-cost field particle image velocimetry for quantifying environmental turbulence
Published in Journal of Ecohydraulics, 2023
Eddies are parameterized here using eddy diameter and circulation. Eddy diameter plays a significant role in flow effects on fish, as swimming capability is largely affected by eddies on the same order of magnitude of size as the fish (Cada and Odeh 2001; Nikora et al. 2003; Lupandin 2005; Tritico and Cotel 2010; Cotel and Webb 2015). Therefore, with respect to fish conservation and understanding the environment’s impact on fish populations, being aware of the distribution of eddy sizes within the flow is important. Further, eddy diameter’s impact on fish is affected by the circulation contained within that eddy. Circulation can be thought of as the “strength” of an eddy, and is defined as the surface integral of vorticity (Wu et al. 2015). In this paper, eddy diameter is determined through calculating circulation along concentric circles centered on a local maxima of vorticity magnitude, and the eddy diameter is the diameter of the circle with the greatest circulation, following Drucker and Lauder (1999). Besides its connection to eddy diameter, circulation itself is an important parameter to evaluate fish performance; high circulation has been shown to have a significant impact on aquatic animals (Tritico 2009), affecting their swimming form and stability.
Vortex generators as a passive cleaning method for solar PV panels
Published in International Journal of Sustainable Energy, 2022
M. Mekawy Dagher, Hamdy A. Kandil
Vorticity is the curl of the velocity vector, as shown in Equation (5) where is the air velocity vector and , , and are the fluid velocity components in x, y, and z directions, respectively (ANSYS 2013). To better visualise the induced vortices, vorticity is calculated from Equation (5) and vorticity contours are plotted over the surface of a horizontal PV panel with installed VGs. Figure 9 shows the vorticity contours on the surface of a horizontal PV panel with three VGs. It can be seen from Figure 9 that the VGs induce vortices on the surface of the panel and these vortices become weaker as the distance from the VGs increases. In Figure 9, VGs are also installed facing the air flow direction, which is in the positive x direction.
Experimental Investigation on Flow Past an Isolated Micro Pin Fin Embedded in a Microchannel
Published in Nanoscale and Microscale Thermophysical Engineering, 2021
Can Ji, Zhigang Liu, Mingming Lv, Jichao Li
As Reynolds number increases from 10 to 350, vorticity intensifies with its maximum absolute value increased from 4.5 to 8. Meanwhile, vorticity extends further downstream. As can be seen, high vorticity region is confined only adjacent to the pin fin at low Reynolds number but extends to around 2.5 D downstream when Reynolds number is high, with a reduction in its width. These behavior could be explained as follows. As is known, the thickness of the boundary layer depends on the relationship between inertia and viscous forces, i.e. the Reynolds number. The larger the Reynolds number is, the thinner the boundary layer is. The effect of the thinning of the pin fin’s boundary layer is two-fold. On one hand, under the combined effect of the increasing Reynolds number and decreasing boundary layer thickness, velocity gradient in the boundary layer rises, which leads to an intensification of vorticity. On the other hand, the thinning of the boundary layer results in a reduction in the width of the high vorticity region. Besides, the narrowing of the high vorticity region also attributes to the increasing kinetic energy of main flow, which restricts the diffusion of vorticity in the cross-streamwise direction.