Flow over a cylinder
Aim : To investigate the behaviour of fluid while in motion over the surface of the cylinder.
Theory
The problem at hand is of external flow condition, this problem provides a very rudimentary case for understanding the nature of the flow which in further cases becomes more and more complex. The complexity is majorly due to the geometry, nature of geometry(symmetric or asymmetric), surface roughness, temperture of the object over which the flow takes place.
The Reynold's Number (Re) = `(rho *V*D)/mu`
The nature of flow determined using Reynold's number,
`Re < 2*10^5` - Laminar Flow
`2*10^5< Re<2*10^6` - Transition Flow
`Re>2*10^6` - Turbulent Flow
Simulation
For the simulaton purpose the base value of Reynold's Number is - Diameter = 8 m and velocity = 2 m/s. the value turns out `1.024*10^6`
| Simulation No. | Reynold's No. (`10^6`) | Diameter (m) | Velocity (m/s) |
| 1 | 1.2288 | 9.6 | 2 |
| 2 | 1.4336 | 4.48 | 5 |
| 3 | 2.048 | 3.2 | 10 |
Simulation Flow 1: The flow is considered to be along the x-axis, For the simulation length is 10 metre, the flow through for this case becomes 5 seconds and hence the animation of 10 seconds.
It has been observed that for this case the value of pressure is highest at a point which coincides with the horizontal drawn through the cenrte of cylinder. In the Pressure disribution diagram it a dumble shape is seen and strength of distribution ranging from low to moderate pressure distribution.
On the contrary in the velocity profile diagram, the velocity is low at the point along line passing through centre of cylinder and behind the cylinder the velocity is zero which increases as the distance from the cylinder increases and reaches the free stream velocity. At the surface, along the vertical line passing through the centre of cylinder the velocity has the maximum value and decreases as the flow takes place farther than farther from the cylinder surface.
Animation-1 Pressure distribution plot for Re1
Animation-2 Velocity distribution plot for Re1
Simulation flow 2 : The flow is considered to be along the x-axis, For the simulation length is 20 metre, the flow through for this case becomes 4 seconds and hence the animation of 8 seconds.
In the Pressure distribtuion diagram it was observed that the dumbbell were reduced in size as also with the passage of time there happen to be distortion in its shape. The maximum pressure can be found to have formed a small zone in front of cylinder which evolves with time.
In the velocity diagram, the flow seems to waver compared to Re1 with time. There is a longer distance over which the velocity drop is substantial in this case. The free stream flows almost tangentially to the cylindrical surface hence there exist a large zero velocity zone behind the cylinder.
Animation-3 Pressure distribution plot for Re2
Animation-4 Velocity distribution plot for Re2
Simulation flow 3 : The flow is considered to be along the x-axis, For the simulation length is 30 metre, the flow through for this case becomes 3 seconds and hence the animation of 6 seconds.
In the Pressure distribution diagram, the pressure intially is lower and it increases as the flow proceeds in the direction of cylinder. The increment isn't large but the dumbbell observed previously is diminshed
In the velocity distribution diagram, the flow has maximum values near the separation points. The zone of zero and low velocity lies behind the cylinder and exhibits a dynamic nature analogous to slythering of a snake. The velocity of free stream shows more tangential nature than the previous results.
Animation-5 Pressure distribution plot for Re3
Animation-6 Velocity distribution plot for Re3
Further when attempt was made to increase Reynold's Number to turbulent flow it was observed that increment in both diameter and velocity doesn't affect the pressure and velocity distribution much, however increment in velocity and subsequent decrement in the diameter gives rise to instability to the flow. Diameter = 8 m, Velocity = 20 m/s, Re4 = `1.088* 10^7`
Animation-7 Pressure Distribution plot for Re4
Animation-8 Velocity Distribution plot for Re4
It can thus be concluded from the observations that the flow stablizes if both the diameter and velocity are increased by a proportional amount. It follows an inverse relation, meaning if diameter is reduced and velocity is increased the flow may become turbulent depending upon the factor by which there is increment in the velocity.