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jv11
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- TL;DR
- Doublet (dipole)flow- flow between two spheres or cylinders - is it good example of doublet flow with distance of 0m between source and sink ?
Here is explanation of doublet (dipole)flow I have found on the web.
Doublet flow in fluid dynamics refers to the flow pattern created by combining a source and a sink (an inflow point) placed very close to each other. When these two singularities are brought infinitesimally close while maintaining a constant product of their strength and separation distance, they form a doublet. This configuration creates streamlines that resemble the flow around a cylinder in two dimensions or a sphere in three dimensions.
When two spheres move close to each other inside a fluid, the flow pattern between them can be approximated by a Rankine oval. This is because the combination of source and sink flows, induced by the moving spheres, can be superposed to create a closed streamline shape resembling an oval. The shape and characteristics of this "Rankine oval" are influenced by the relative size and separation distance of the spheres, as well as the fluid's velocity.
The statement "sphere moving inside fluid is reversed bernoulli pipe" refers to a thought experiment or a way to visualize the relationship between fluid pressure and velocity, as described by Bernoulli's principle. It's not a literal reversed Bernoulli pipe, but rather a conceptual analogy. In a typical Bernoulli pipe, a fluid speeds up in a narrower section, causing a pressure drop. In this conceptualization, a sphere is used to create a local constriction in a fluid flow, similar to how a narrower pipe section would. This constriction, according to Bernoulli's principle, would cause a localized increase in fluid velocity and a corresponding decrease in pressure. The "reversal" refers to the fact that the sphere's presence is causing the pressure drop, not the pipe's geometry itself.
In a fluid system, the fluid's speed is fastest when flowing through the smallest diameter section. This is due to the principle of continuity, which states that the volumetric flow rate (volume of fluid passing a point per unit time) must remain constant in a closed system if the fluid is incompressible.
Two spheres (white circles) in the center in a picture above are positioned in wind tunnel
The flow of wind(fluid ) is marked lines with arrows.
The space in between spheres is acting like source and sink- and doublet flow is created - the wind travels in concentric circles in direction opposite of main flow.
These concentric circles have different speed and consequently pressure is different.
This can be called waves .
The flow of waves can be described with wave function .
The point where main flow “wraps” around waves(concentric circles) is called stagnation Point.
The main flow traveling around stagnation point “circle “ is layered and has different speed (and pressure ) in each layer .
This is perceived as distortion of fluid field .
The attractive forces crated between two spheres are product of static and dynamic pressures of wind (potential and kinematic energy of moving fluid (wind).
Here is theoretical example ,how I understand this:
Two cylinders with diameter of d=1m
And height h=1m are positioned at distance of r1=1m.
Speed of wind moving against the cylinders is V2=0.4m/s
At this distance measured speed in between cylinders is V1=3m/s
At distance r2= 2.75 m between cylinders measured speed V2=0.4m/s
Doublet flow has two concentric circles moving around each cylinder.
In cylinder to the left the direction is CWand for cylinder to the right the direction is CCW.
The radius of first concentric circles is
Cr1=1m(from the center of cylinders)
Cr2=1.875m
The Average angular speed of fluid traveling in Cr1 is
Av1=V1x Cr1
Av1=3x1 = 3rad/s
Av2=V2xCr2
Av2=0.4x1.875 = 0.75rad /s
The stagnation pressure - the speed in “hollow “sphere is not 0,so we can calm it pressure P1 is calculated :
Po=Ps+0.5 x D x V^2
D=1kg/m3 density of air
V=V2=3m/s
Po=10^5Pa
P1=100000-4.5=99995.5
This pressure is uniformed through Cr1
The pressure P2
P2=100000-0.16=99999.84Pa
This pressure is uniformed in area around Cr2
From difference between Po,P1 and P2 (potential energy of fluid)we can calculate force difference between the Force at distance r1 compared to force at distance r2.
The cylinders are balloons with plastic skin of negligible mass filled with air .
The mass of cylinder is
Mc1=Mc2=v(volume )cad
Mc1=3.14kg=Mc2
The wind tunnel is positioned inside the diving aircraft so gravitational force of earth is not involved.
The pressure difference P3:
P3=P2-P1=E
E=99999.84-99995.5
E=4.34J
E-energy(work ) which creats the force difference between Cr1 and Cr2.
E=Fxs
S=2.75-1=1.75m
F=E /s=4.34/1.75 = 2.48N
This is the force which can be created by different potential energy of moving fluid between Cr1 and Cr2.
Negative acceleration
a=(V1-V2)/t
F=mxa
F=Mc1x(V1-V2)/t
t=F/Mc1x(V1-V2)
t=2.48/2.6=0.95 sec
The force needed to “push” cylinders apart has to be minimum 2.48N and it would push the cylinders apart in 0.95sec.
Now if we put two of these “new bigger hollow cylinders “ at distance Lx
The same doublet flow will happen
And we can call it fractal nature of doublet flow .
Or dipole flow .
Is this a good way to understand doublet(dipole) flow ?
Doublet flow in fluid dynamics refers to the flow pattern created by combining a source and a sink (an inflow point) placed very close to each other. When these two singularities are brought infinitesimally close while maintaining a constant product of their strength and separation distance, they form a doublet. This configuration creates streamlines that resemble the flow around a cylinder in two dimensions or a sphere in three dimensions.
When two spheres move close to each other inside a fluid, the flow pattern between them can be approximated by a Rankine oval. This is because the combination of source and sink flows, induced by the moving spheres, can be superposed to create a closed streamline shape resembling an oval. The shape and characteristics of this "Rankine oval" are influenced by the relative size and separation distance of the spheres, as well as the fluid's velocity.
The statement "sphere moving inside fluid is reversed bernoulli pipe" refers to a thought experiment or a way to visualize the relationship between fluid pressure and velocity, as described by Bernoulli's principle. It's not a literal reversed Bernoulli pipe, but rather a conceptual analogy. In a typical Bernoulli pipe, a fluid speeds up in a narrower section, causing a pressure drop. In this conceptualization, a sphere is used to create a local constriction in a fluid flow, similar to how a narrower pipe section would. This constriction, according to Bernoulli's principle, would cause a localized increase in fluid velocity and a corresponding decrease in pressure. The "reversal" refers to the fact that the sphere's presence is causing the pressure drop, not the pipe's geometry itself.
In a fluid system, the fluid's speed is fastest when flowing through the smallest diameter section. This is due to the principle of continuity, which states that the volumetric flow rate (volume of fluid passing a point per unit time) must remain constant in a closed system if the fluid is incompressible.
Two spheres (white circles) in the center in a picture above are positioned in wind tunnel
The flow of wind(fluid ) is marked lines with arrows.
The space in between spheres is acting like source and sink- and doublet flow is created - the wind travels in concentric circles in direction opposite of main flow.
These concentric circles have different speed and consequently pressure is different.
This can be called waves .
The flow of waves can be described with wave function .
The point where main flow “wraps” around waves(concentric circles) is called stagnation Point.
The main flow traveling around stagnation point “circle “ is layered and has different speed (and pressure ) in each layer .
This is perceived as distortion of fluid field .
The attractive forces crated between two spheres are product of static and dynamic pressures of wind (potential and kinematic energy of moving fluid (wind).
Here is theoretical example ,how I understand this:
Two cylinders with diameter of d=1m
And height h=1m are positioned at distance of r1=1m.
Speed of wind moving against the cylinders is V2=0.4m/s
At this distance measured speed in between cylinders is V1=3m/s
At distance r2= 2.75 m between cylinders measured speed V2=0.4m/s
Doublet flow has two concentric circles moving around each cylinder.
In cylinder to the left the direction is CWand for cylinder to the right the direction is CCW.
The radius of first concentric circles is
Cr1=1m(from the center of cylinders)
Cr2=1.875m
The Average angular speed of fluid traveling in Cr1 is
Av1=V1x Cr1
Av1=3x1 = 3rad/s
Av2=V2xCr2
Av2=0.4x1.875 = 0.75rad /s
The stagnation pressure - the speed in “hollow “sphere is not 0,so we can calm it pressure P1 is calculated :
Po=Ps+0.5 x D x V^2
D=1kg/m3 density of air
V=V2=3m/s
Po=10^5Pa
P1=100000-4.5=99995.5
This pressure is uniformed through Cr1
The pressure P2
P2=100000-0.16=99999.84Pa
This pressure is uniformed in area around Cr2
From difference between Po,P1 and P2 (potential energy of fluid)we can calculate force difference between the Force at distance r1 compared to force at distance r2.
The cylinders are balloons with plastic skin of negligible mass filled with air .
The mass of cylinder is
Mc1=Mc2=v(volume )cad
Mc1=3.14kg=Mc2
The wind tunnel is positioned inside the diving aircraft so gravitational force of earth is not involved.
The pressure difference P3:
P3=P2-P1=E
E=99999.84-99995.5
E=4.34J
E-energy(work ) which creats the force difference between Cr1 and Cr2.
E=Fxs
S=2.75-1=1.75m
F=E /s=4.34/1.75 = 2.48N
This is the force which can be created by different potential energy of moving fluid between Cr1 and Cr2.
Negative acceleration
a=(V1-V2)/t
F=mxa
F=Mc1x(V1-V2)/t
t=F/Mc1x(V1-V2)
t=2.48/2.6=0.95 sec
The force needed to “push” cylinders apart has to be minimum 2.48N and it would push the cylinders apart in 0.95sec.
Now if we put two of these “new bigger hollow cylinders “ at distance Lx
The same doublet flow will happen
And we can call it fractal nature of doublet flow .
Or dipole flow .
Is this a good way to understand doublet(dipole) flow ?
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