[FluidKo]

Hello
I'm confused whether reciculating flow is free vortex or forced vortex?
I've thought there won't be exterior force in recirculating flow so I've thought recirculating flow is usually free vortex.
(Example of recirculating flow: Flow separation in curved pipe or sudden expansion/contraction pipe)
But I'm not sure.
Because I've searched this question at google, but nobody has uploaded about this question before.
Thank you

[FluidKo]

Oh I've solved it.
Now I think recirculating flow is forced vortex because in free vortex, there must be sink.
But in recirculating flow, there is no sink.
So recirculating flow is forced vortex.
Confusion whether recirculating flow is free vortex or forced vortex is caused by maelstrom in ocean.
I've though maelstrom in ocean is free vortex because it looks like there is a sink.
But it wasn't sink.
It just looks like cup of tea with rotation.

[LuckyTran]

A recirculation zone is its own category, circulating flows generally are not considered vortex flows at all. Consider a coiled water hose with water flowing in it, it's simply water flowing in a circular path and not suddenly a vortex. Circulation zones don't advect with the flow at the advection velocity, they just sit in their own isolated space.

[FluidKo]

Originally Posted by LuckyTran

A recirculation zone is its own category, circulating flows generally are not considered vortex flows at all. Consider a coiled water hose with water flowing in it, it's simply water flowing in a circular path and not suddenly a vortex. Circulation zones don't advect with the flow at the advection velocity, they just sit in their own isolated space.

Hello LuckyTran~!
Long time no see~!

But in my opinion, I think eventhough fluid is flowing in coiled pipe, there can be vortex.
(I was just wondering motion of recirculating flow)
We can consider it from concept of circulation.

I've uploaded picture that I describe the reason that I've thought why we can consider vortex of circulating flow in coiled pipe.

And also, in 9th page of below paper
(https://www.researchgate.net/publica...t_in_Crossflow)

We can see there is a reciculating region with forced vortex.
(Figure 9 and Figure 10)
If we look streamline, then we can tell vortex is forced vortex not free vortex.
(As far from the center, circumferential velocity is increased.)

I'm not sure but the reason why I think recirculating flow is forced vortex is following.
1. There is a main flow that will be separated at reagion with recirculating flow.
2. There will be shear stress between main flow and recirculating flow by molecule viscosity
3. That shear stress can work as exterior force to recirculating flow.
4. Cause of exterior force, recirculating flow has forced vortex.

This is what I've thought.
What do you think about it?
Thank you

[LuckyTran]

That picture is very misleading. There is no recirculation zone (in the traditional sense) behind a jet in crossflow. A jet in crossflow produces multiple kidney-shaped vortices and many other attached vortices and there is no zone of isolated fluid underneath.

I don't consider flow in a circular loop a vortex in the sense that I don't consider flow through a straight pipe to be a vortex flow. It's just flow in a straight pipe. You've seen already the difference between flow in a straight pipe and a bend, the primary flow is the same for both of them. There's just a small centrifugal force for the bend which if strong enough can produce a secondary flow. But that secondary flow is not what we are talking about for recirculation zones. Recirculation zones are large-scale separated shear layers.

Stoke's theorem is simply a calculus identity for calculating the circulation from a volume integral. It's not a statement about what the circulation is or ought to be, whether it is zero, positive, or negative. A flow in a circular loop has circulation but circulation by itself is not the sole characteristic of a vortex. Otherwise, everything is a vortex flow. And since everything is a vortex flow, it can simply be called flow. Clearly there's something more needed to make this leap from flow to tornado-like structure.

Originally Posted by FluidKo

1. There is a main flow that will be separated at reagion with recirculating flow.
2. There will be shear stress between main flow and recirculating flow by molecule viscosity
3. That shear stress can work as exterior force to recirculating flow.
4. Cause of exterior force, recirculating flow has forced vortex.

1-3 describes all separated shear layers. And 4 is not a reasoning, but your conclusion that all shear layers are vortex's. Specifically concerning 3, the shear stress is purely an internal force for any fluid particle in the interior of the domain, until you reach the walls then you have a boundary force there (the wall shear stress). But you can do CFD of a viscous fluid with slip walls where there is no wall shear stress at all and still get recirculation zones. So, the wall shear stress is not the cause of the recirculation zone either and so the recirculation zone occurs without any external force.

[FluidKo]

Originally Posted by LuckyTran

That picture is very misleading. There is no recirculation zone (in the traditional sense) behind a jet in crossflow. A jet in crossflow produces multiple kidney-shaped vortices and many other attached vortices and there is no zone of isolated fluid underneath.

I don't consider flow in a circular loop a vortex in the sense that I don't consider flow through a straight pipe to be a vortex flow. It's just flow in a straight pipe. You've seen already the difference between flow in a straight pipe and a bend, the primary flow is the same for both of them. There's just a small centrifugal force for the bend which if strong enough can produce a secondary flow. But that secondary flow is not what we are talking about for recirculation zones. Recirculation zones are large-scale separated shear layers.

Stoke's theorem is simply a calculus identity for calculating the circulation from a volume integral. It's not a statement about what the circulation is or ought to be, whether it is zero, positive, or negative. A flow in a circular loop has circulation but circulation by itself is not the sole characteristic of a vortex. Otherwise, everything is a vortex flow. And since everything is a vortex flow, it can simply be called flow. Clearly there's something more needed to make this leap from flow to tornado-like structure.




1-3 describes all separated shear layers. And 4 is not a reasoning, but your conclusion that all shear layers are vortex's. Specifically concerning 3, the shear stress is purely an internal force for any fluid particle in the interior of the domain, until you reach the walls then you have a boundary force there (the wall shear stress). But you can do CFD of a viscous fluid with slip walls where there is no wall shear stress at all and still get recirculation zones. So, the wall shear stress is not the cause of the recirculation zone either and so the recirculation zone occurs without any external force.

Oh yes I think that I was forgotten that circulation() is considering secondary flow not primary flow.
But eventhough we are dealing with primary flow for recirculation flow, isn't there can be forced vortex?

The reason that I've guessed there will be forced vortex is following.

1. First in below paper, streamline of recirculating flow is representing forced vortex. As far from the center of recirculating flow, circumferential velocity is increased.(Figure 9 and Figure 10)
https://www.researchgate.net/publica...zOWs50A&_iepl=

2. And also I think there will be forced vortex in terms of physical point.
Please refer to my cartoon for explanation of occurence of forced vortex.

A. If main flow meets recirculating flow, there will be shear stress between them because there is a velocity difference between them. Main flow will get friction(Shear stres) by recirculating flow and also recirculating flow will get friction(Shear stress) by main flow. This is just law of action-reaction.

* Because reciculating flow has higher pressure, it will have lower velocity than main flow by Bernoulli's equation.

B. Forced votex occurs when flow get exterior force.

C. Recirculating flow get exterior force which means shear stress
by main flow.

D. So in recirculating flow, forced vortex will occur.

Upper is my guess as far as I've thought.
What do you think about it?
If there is something wrong in my deduction, then what is the difference between forced vortex in uploaded figure and recirculaing flow in uploaded paper?

Thank you

Forced Vortex
https://upload.wikimedia.org/wikiped...nal_vortex.gif

Free Vortex
https://upload.wikimedia.org/wikiped...nal_vortex.gif

[LuckyTran]

I would advise you to look at other examples of vortex flows and not get overly fixated on why a recirulation zone should instead be classified as a vortex and rather familiarize yourself with characteritics of vortex flows.

A jet issuing into a quiescent flow can induce a toroidal vortex (a vortex ring). A jet in crossflow does produce many other types of vortices (like the horseshoe vortex). A separated flow behind an airfoil can generate a vortex street. The difference is that all of these vortices advect downstream stream. A recirculation bubble is anchored and lacks this really important key property and that's why (at least in my opinion) it deserves its own special treatment. In particular, not moving means that the 3D vortex stretching mechanism is not present (or at least does not apply) and the recirculation zone does not behave like a vortex should. The vortex stretching mechanism (at least in the classical sense) is a result of the Helmholtz and Kelvin's circulation theorems. Helmholtz's theorem is in layman's terms, that vortex tubes move with the fluid. Recirculation zones don't move. Even in the case of a maelstrom which is a notable stationary vortex, there is a flow along the vortex axis. Recirculation zones also don't exhibit this property.

[FluidKo]

Originally Posted by LuckyTran

I would advise you to look at other examples of vortex flows and not get overly fixated on why a recirulation zone should instead be classified as a vortex and rather familiarize yourself with characteritics of vortex flows.

A jet issuing into a quiescent flow can induce a toroidal vortex (a vortex ring). A jet in crossflow does produce many other types of vortices (like the horseshoe vortex). A separated flow behind an airfoil can generate a vortex street. The difference is that all of these vortices advect downstream stream. A recirculation bubble is anchored and lacks this really important key property and that's why (at least in my opinion) it deserves its own special treatment. In particular, not moving means that the 3D vortex stretching mechanism is not present (or at least does not apply) and the recirculation zone does not behave like a vortex should. The vortex stretching mechanism (at least in the classical sense) is a result of the Helmholtz and Kelvin's circulation theorems. Helmholtz's theorem is in layman's terms, that vortex tubes move with the fluid. Recirculation zones don't move. Even in the case of a maelstrom which is a notable stationary vortex, there is a flow along the vortex axis. Recirculation zones also don't exhibit this property.

Sorry I don't understand what are you meaning.

1. Recirculation bubble lacks this really important key property and that's why (at least in my opinion) it deserves its own special treatment.

What is the meaing of 'lack this really imporatant key property'?
What does 'really important key property' mean?

2. In particular, not moving means that the 3D vortex stretching mechanism is not present (or at least does not apply) and the recirculation zone does not behave like a vortex should.

A. What is the correlation between vortex stretching and fact that recirculation zone does not behave like a vortex? Vortex stretch that I know is one of process in energy casacade in turbulence.
Are you meaning that there is energy casacade(vortex stretching) in vortex(Ex: Karman Vortex) shedding contrary to recirulating flow? And also 'Helmholtz and Kelvin's circulation theorem' that I know is if there is irrotational flow, then the flow maintain irrotational flow forever. That's all what I know.

Thank you

[LuckyTran]

A vortex filament or vortex tube (i.e. a free vortex) has a bulk flow along the vortex axis. This property is actually a consequence of the same Stoke's theorem you already cited. If you integrate the circulation around a closed curve and the circulation is not zero, then there must be a flux of vorticity along the axis.

The classical recirculation zone behind a backward facing step in 2D does not have an out of plane velocity component. That's an important missing feature.

A forced vortex requires an external vorticity source. Think about all the boundary conditions. You have stationary walls and a uniform velocity inlet. You don't have an external vorticity source. There could be an external vorticity source if the walls were rotating but that requires you to have a washing machine with a motor attached, not just a simple duct. A recirculation zone is definitely not a forced vortex. It might deceptively look like a rotating cup of tea, except you know it's not a rotating cup.

A maelstrom is a free vortex, but there is a net flow down in the center of the vortex. Also you can see that the angular velocity in a maelstrom increases towards the center and yields the spiral shape. A forced vortex doesn't produce these spirals because the relative angular velocity of all fluid particles is the same. A maelstrom is a special case of a stationary free vortex because the convective speed is 0. It satisfies the property that it advects downstream because the advection speed is 0.

Recirculation zones occur even without washing machines and rotating cups, they don't have the flow along the vortex line, and they don't advect with the advection speed.

[FluidKo]

Originally Posted by LuckyTran

A vortex filament or vortex tube (i.e. a free vortex) has a bulk flow along the vortex axis. This property is actually a consequence of the same Stoke's theorem you already cited. If you integrate the circulation around a closed curve and the circulation is not zero, then there must be a flux of vorticity along the axis.

The classical recirculation zone behind a backward facing step in 2D does not have an out of plane velocity component. That's an important missing feature.

A forced vortex requires an external vorticity source. Think about all the boundary conditions. You have stationary walls and a uniform velocity inlet. You don't have an external vorticity source. There could be an external vorticity source if the walls were rotating but that requires you to have a washing machine with a motor attached, not just a simple duct. A recirculation zone is definitely not a forced vortex. It might deceptively look like a rotating cup of tea, except you know it's not a rotating cup.

A maelstrom is a free vortex, but there is a net flow down in the center of the vortex. Also you can see that the angular velocity in a maelstrom increases towards the center and yields the spiral shape. A forced vortex doesn't produce these spirals because the relative angular velocity of all fluid particles is the same. A maelstrom is a special case of a stationary free vortex because the convective speed is 0. It satisfies the property that it advects downstream because the advection speed is 0.

Recirculation zones occur even without washing machines and rotating cups, they don't have the flow along the vortex line, and they don't advect with the advection speed.

Hum...Okay.
Then to summarize,
Recirculating flow can't be classified as free vortex because there is no sink that represents vortex line.
Recirculating flow can't be classified as forced vortex because there is no exterior force.
Eventhough in slip condition which means there is no shear stress, recirculating flow can occur and that means recirculating flow doens't require exterior force.
Although streamline of recirulating looks like forced vortex, because there is no exterior force, recirculating flow can't be classified as forced vortex.
So we have to classify recirulating flow as just reculating flow.

I've thought all of flows that deceptively looks like rotation must be classified to free vortex or forced vortex.
But it was not always. There was a another type of flow that deceptively
looks like rotation which means recirulating flow.
Then flow that looks like rotation in this world are only free vortex, forced vortex and recirculating flow?(except for turbulence)
Can we classify flow that looks like rotation to only 3 types?(except for turbulence)
Or there can be other many types of flow that looks like rotation?
Thank you

[LuckyTran]

Free and forced vortex are the two canonical examples of vortex flows obtained by examining solutions to the vorticity transport equation without viscosity. Real vortex flows with viscosity fall somewhere in between. For example, a free vortex like solution with viscosity is the Lamb-Oseen vortex. A forced vortex placed into a viscous fluid yields the Rankine vortex. Because vortices are advection phenomenon with some sort of rotation imparted, they are often categorized by their dynamic behavior: their initiation, growth, propagation, and eventual decay processes. How a vortex is born, how it lives, and how it dies–these processes contain far more details than simply "fluid is rotating."

Furthermore, these are derived from 2D or 2.5D consideration and no attention has been given to the ends of the vortex filament. Vortices are also classified by where their ends terminate. If the vortex filament is a closed loop then it becomes a extremely stable vortex ring. When the two end are attached to a solid body at different points, hairpin vortices form. The ends of the filament can also terminate in the interior due to viscous effects overcoming the inertial effects (i.e. horseshoe vortex or a wingtip vortex). There's many many many more named vortex phenomenon not even accounting for vortex phenomenon driven by external forces (like coriolis forces or E&M forces in magnetohydrodynamics or in stellar winds). There are also vortex systems. Some vortex systems always give counter-rotating vortex pairs that interact with the background flow and each other.

[FluidKo]

Originally Posted by LuckyTran

Free and forced vortex are the two canonical examples of vortex flows obtained by examining solutions to the vorticity transport equation without viscosity. Real vortex flows with viscosity fall somewhere in between. For example, a free vortex like solution with viscosity is the Lamb-Oseen vortex. A forced vortex placed into a viscous fluid yields the Rankine vortex. Because vortices are advection phenomenon with some sort of rotation imparted, they are often categorized by their dynamic behavior: their initiation, growth, propagation, and eventual decay processes. How a vortex is born, how it lives, and how it dies–these processes contain far more details than simply "fluid is rotating."

Furthermore, these are derived from 2D or 2.5D consideration and no attention has been given to the ends of the vortex filament. Vortices are also classified by where their ends terminate. If the vortex filament is a closed loop then it becomes a extremely stable vortex ring. When the two end are attached to a solid body at different points, hairpin vortices form. The ends of the filament can also terminate in the interior due to viscous effects overcoming the inertial effects (i.e. horseshoe vortex or a wingtip vortex). There's many many many more named vortex phenomenon not even accounting for vortex phenomenon driven by external forces (like coriolis forces or E&M forces in magnetohydrodynamics or in stellar winds). There are also vortex systems. Some vortex systems always give counter-rotating vortex pairs that interact with the background flow and each other.

Wow~!
Thank you for your sincere answer.
I had no idea for vortex, but I've heard lots of important things for vortex from you.
Thank you