Flow over a cylinder
Objective: To simulate the flow over a cylinder for the given conditions.
Problem Statement:
Calculate the baseline case Reynolds number.
- Re = rho*U_inlet*D/mu
- D = cylinder diameter
- mu = dynamic viscosity
- rho = density
Run a baseline simulation and then calculate the Reynolds number. Then increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation.
Simulation end time should be calculated properly. Create animations for pressure-velocity for all the three Reynolds numbers. Explain your observations.
Theory:
External flows past objects have been studied extensively because of their many practical applications. For example, airfoils are made into streamline shapes in order to increase the lifts, and at the same time, reducing the aerodynamic drags exerted on the wings. On the other hand, flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body. In certain Reynolds number range, a periodic flow motion will develop in the wake as a result of boundary layer vortices being shed alternatively from either side of the cylinder.
Calculations:
Re = 1000
rho = 1.225 kg/m3
D = 0.04 m
mu = 1.81 × 10-5 kg/(m·s)
Length of the domain = 0.1 m
V = (Re*mu)/(rho*D) m/s
Flow through time = (length of the domain)/(inlet velocity)
End time = Flow through time * 2
Case 1:
V = (1000*1.81 × 10-5)/(0.04*1.225)
V= 0.369 m/s
Flow through time = 0.1/0.369 = 0.2710 s
End time = 0.2710*2 = 0.5420 s
Case 2:
V = (1200*1.81 × 10-5)/(0.04*1.225)
V= 0.443 m/s
Flow through time = 0.1/0.443 = 0.2257 s
End time = 0.2257*2 = 0.4515 s
Case 3:
V = (1400*1.81 × 10-5)/(0.04*1.225)
V= 0.517 m/s
Flow through time = 0.1/0.517 = 0.1934 s
End time = 0.1934*2 = 0.3868 s
Case 4:
V = (2000*1.81 × 10-5)/(0.04*1.225)
V= 0.739 m/s
Flow through time = 0.1/0.739 = 0.1488 s
End time = 0.1488*2 = 0.2977 s
Case Setup:
The cylinder is created with the following dimesions.
For each case, the value of the total analysis time changes and the output time step remains the same.
Then the Air is chosen as the fluid in all the cases as shown above.
The Velocity in the X direction is changed by referring to the calculations for each case.
Procedure:
- Create the cylinder with the dimensions mentioned above.
- Then we start the wizard for the flow simulation and select all the default options in each step, making an exception for the ones which are provided in the case study, and changes are made for each case.
- Later the cut plots are added for both pressure and velocity.
- Then adjust the mesh size is adjusted to the desired value.
- Later run the program to get the results after the solver completes the execution.
- Create animations for both pressure and velocity in each case and then they are saved.
Results:
Case 1:
This plot describes the velocity heat map when case 1 is simulated.
This plot describes the pressure heat map when case 1 is simulated.
This animation describes the velocity heat map when case 1 is simulated.
This animation describes the pressure heat map when case 1 is simulated.
Case 2:
This plot describes the velocity heat map when case 2 is simulated.
This plot describes the pressure heat map when case 2 is simulated.
This animation describes the velocity heat map when case 2 is simulated.
This animation describes the pressure heat map when case 2 is simulated.
Case 3:
This plot describes the velocity heat map when case 3 is simulated.
This plot describes the pressure heat map when case 3 is simulated.
This animation describes the velocity heat map when case 3 is simulated.
This animation describes the pressure heat map when case 3 is simulated.
Case 4:
This plot describes the velocity heat map when case 4 is simulated.
This plot describes the pressure heat map when case 4 is simulated.
This animation describes the velocity heat map when case 4 is simulated.
This animation describes the pressure heat map when case 4 is simulated.
Conclusion:
It can be observed from each case there is a progression in the Reynolds number as the velocity also increases along with it. Although there isn't much difference in the pressure variation which is evident from the animations and the plots shown above. The maximum pressure acts on the point where the fluid(air) is in complete contact with its surface. The end results can be made more accurate by making the mesh a lot more finer in order to improve the final solution. The velocity of the fluid halfway through as it passes the cylinder is at the peak due to the deflection made by the air and then it deviates from it.
The simulation has been successfully run and the plots and animations were created and demonstrated.
References:
http://www.eng.fsu.edu/~shih/succeed/cylinder/cylinder.htm
Project Link: