I understand that circulation is an integral quantity (i.e. it gives a number over an control volume), and it represents how much does a flow rotate along a contour.
But what is that number signify physically ? What insight can one achieve with that number?
Or why should one bother about a separate quantity dealing with flow rotation, when the velocity and pressure field information is available ?
Any answer from an engineering (practical) perspective would be much appreciated.
Thank you for your consideration and time.
I would rather go one step back and ask what is fluid anyway! Well, by definition, fluid is something that cannot stay at rest when subjected to external shear stress. So what happens when shear is applied....well it moves. The next question arises how does it move - does it translate or rotate?
Probably, you now already see why circulation or rotation is just an integral parameter of fluid dynamics.The applied shear stress has two components - symmetric and asymmetric. The symmetric part leads to stretching of a fluid element (imagine a rectangular box) while the asymmetric part produces a moment on the fluid element which results in rotation. The behavior is often expressed as vorticity determined as curl of the velocity field.
But isn't there something called irrotational flow where vorticity is considered to be zero? Sure it is and this type flow is a great simplification of the real life flow where velocity field is considered to be obtained from gradient of a potential (energy conserving) function by neglecting viscosity (causes friction hence energy loss). If wall effect can be ignored i.e. flow in the bulk away from any solid surface, potential flow is still a good approximation of the fluid flow.
In practical situations, circulation inevitably occurs whenever there's a flow separation from a solid surface i.e. boundary layer separation from a bluff body at higher Reynolds number which leads to turbulence characterized by the chaotic rotating flow structures involving eddies and vortices. Flow around the wings of aircraft, flow around impeller (pump, ship, mixer), cyclones are just few examples of circulatory nature of fluid flow which occurs at different length scales (integral to Kolmogorov scale). Due to turbulent nature of most of the flows in real life, it is essential to consider the rotational behavior of fluid.
I would rather go one step back and ask what is fluid anyway! Well, by definition, fluid is something that cannot stay at rest when subjected to external shear stress. So what happens when shear is applied....well it moves. The next question arises how does it move - does it translate or rotate?
Probably, you now already see why circulation or rotation is just an integral parameter of fluid dynamics.The applied shear stress has two components - symmetric and asymmetric. The symmetric part leads to stretching of a fluid element (imagine a rectangular box) while the asymmetric part produces a moment on the fluid element which results in rotation. The behavior is often expressed as vorticity determined as curl of the velocity field.
But isn't there something called irrotational flow where vorticity is considered to be zero? Sure it is and this type flow is a great simplification of the real life flow where velocity field is considered to be obtained from gradient of a potential (energy conserving) function by neglecting viscosity (causes friction hence energy loss). If wall effect can be ignored i.e. flow in the bulk away from any solid surface, potential flow is still a good approximation of the fluid flow.
In practical situations, circulation inevitably occurs whenever there's a flow separation from a solid surface i.e. boundary layer separation from a bluff body at higher Reynolds number which leads to turbulence characterized by the chaotic rotating flow structures involving eddies and vortices. Flow around the wings of aircraft, flow around impeller (pump, ship, mixer), cyclones are just few examples of circulatory nature of fluid flow which occurs at different length scales (integral to Kolmogorov scale). Due to turbulent nature of most of the flows in real life, it is essential to consider the rotational behavior of fluid.
Circulation helps at quantifying the actual strengh of a vortex. For example, let's consider two vortices with the same circulation. Because they have the same circulation, they will have the same strength, meaning that the force they will exert on surrounding fluid particles will be the same. This is very important, as if you model your vortices as vortex core lines, they will show as identical. It is a macroscopic description of a vortex.
However, the actual topology of the vortex can be different for the two vortices. Vortex 1 can have vorticity concentrated at its core, like the tip vortex observed at the tip of a wing, right where it is formed. Vortex 2 can have a more spread vorticity distribution, which often happens after the diffusion process. Vortex 2 could be for example Vortex 1 further downstream the wing; the vorticity is not anymore concentrated at the core but spread around it. However the circulation is still the same for both (without accounting for energy dissipation through viscous effects).
Vorticity is a microscopic description of a vortex.
https://www.researchgate.net/profile/J_Dgheim/publication/274735872_International_Journal_of_Heat_and_Fluid_Flow_August_2013_Vol42224-235_doi101016jijheatfluidflow201304001_Evaporation_phenomenon_past_a_rotating_hydrocarbon_droplet_of_ternary_components
Look forward the above article may be you find your answer.
Article International Journal of Heat and Fluid Flow August 2013, Vo...
Circulation determines the fluid dynamic force acting on a thin object like a wing or rotating rod. It is needed for explaining why such an object exerts lift force. Although the distributions of pressure and velocity provide lift calculation, they do not tel WHY there is the lift force. Please check Kutta–Joukowski theorem.
https://en.wikipedia.org/wiki/Kutta%E2%80%93Joukowski_theorem
Circulation means also presence of vorticity. Vorticity stretching is one of the main mechanism in the onset of turbulence.
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