Flow over a cylinder
This Project will deal with the transient flow simulation over a cylinder with varying Reynolds Number of the fluid taken.
THEORY:
Reynolds Number as we know is defined as the ratio of inertial force by viscous force.
The Reynolds number is defined as:
Re = rho*U_inlet*D/mu
ρ(rho) is the density of the fluid (SI units: kg/m3)
U_inlet is the velocity of the fluid with respect to the object (m/s)
D is a characteristic linear dimension (m)
μ(mu) is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/m·s)
- Here for the simulation,the fluid taken is water.
- Its dynamic viscosity is taken as 8.89*10^-4 N.s/m^2 at 25 degree celsius.
- The diameter over which the flow will occur is taken as 0.2m.
- The length is taken as 0.5m.
- Density of water is taken as 1000kg/m^3.
- The mesh level selected is 4 and advance channel refinement is being done.
- The domain is the x-direction is taken as 2m for each case.
SIMULATION CALCULATIONS:
Now, for the first case where Re=20:
The inlet velocity came out to be 8.89x10^-5 m/s
This value came from the reynolds no. equation.
Then i have calculated the flow through time and the end time.Before that I will just brief out on both the terms;
If the inlet velocity is 1m/s and if the length of the domain is 5 m then the flow through time is 5 seconds.
That is, it takes 5 seconds for the flow from the inlet to go to the outlet.This 5 seconds is called the flow through time.
While the end time should always be twice or thrice the flow through time so that the simulation can occur till the fluid exits the domain.
Therefore, in this case:
Flow through time= 22500s
End time= 68570s
Output time step=10s
Here are the RESULTS for the above simulation:
Velocity plot:
Pressure Plot:
Link for the simulation:
Now, for the second case where Re=40:
The inlet velocity came out to be 1.778x10^-4 m/s.
Therefore, in this case:
Flow through time= 11250s
End time= 22500s
Output time step=10s
Here are the RESULTS for the above simulation:
Velocity Plot:
Pressure Plot:
Link for the simulation:
Now, for the third case where Re=100:
The inlet velocity came out to be 4.445x10^-4 m/s.
Therefore, in this case:
Flow through time= 4500s
End time= 9000s
Output time step=10s
Here are the RESULTS for the above simulation:
Velocity Plot:
Pressure Plot:
Link for the simulation:
Now, what I have done is in order to calculate the drag coefficient for the different case scenarios, I have calculated the drag force(F) which is exerted on the cylinder surface.
Case 1:
F=8.832x10^-7N
Case 2:
F=2.45x10^-6N
Case 3:
F=9.6492x10^-6N
We know that,
Cd= 2*F/(rho*u^2*A)
where, F= Drag force in the direction of the flow
rho= density of the fluid
u= fluid velocity
A= reference area
Case 1:
Cd=2.235
Case 2:
Cd=1.55
Case 3:
Cd=0.976
CONCLUSION:
The flow past the cylinder is very wide in the first case.As, the velocity of flow is increases the wideness decreases and the flow becomes more converging type.The low velocity region just behind the cylinder is also reduced as the velocity increases and vortex formation occurs.
At the leading edge of the cylinder a stagnation point is formed where the oncoming flow is brought to rest. The pressure here is equal to the stagnation pressure. To either side of the stagnation point the flow accelerates around the forward surface of the cylinder producing a drop in the pressure .
Immediately adjacent to the cylinder surface a thin boundary layer is formed. The boundary layer is a region where the velocity drops rapidly to zero to satisfy the no slip condition at the cylinder surface. The direct effects of viscosity are felt only within the boundary layer.
If ReD is less than about 400,000 the boundary layer remains laminar from the stagnation point at the front of the cylinder to the point where it separates.
The resulting flow pattern termed sub-critical, is associated with a high drag on the cylinder, which can be observed from the above datas.
The laminar boundary layer separates just upstream of the maximum thickness. Separation occurs because the boundary layer anticipates the deceleration of the flow (and therefore positive pressure gradient) that would otherwise occur on the rearward face of the cylinder. Downstream of separation the flow quickly becomes turbulent and a broad wake is formed. The wake as a whole is unstable and rolls up into vortices that are shed antisymmetrically at regular intervals from the cylinder. This type of wake is called a von Kármán vortex street. Because of separation, the pressure remains low and approximately constant over the rearward face of the cylinder.
As the velocity/Re no. increases the drag coefficient decreases.