Flow over a cylinder using Solidworks
Objective- To Simulate the flow over a cylinder
- Calculate the baseline case Reynolds number.
- Re = rho*U_inlet*D/mu
- D = cylinder diameter
- mu = dynamic viscosityrho = 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.
Inputs :
- Diameter of Cylinder = 0.04m
- Length of the Cylinder= 0.05m
- Air density = 1.2047(kg/m3)
- Dynamic viscosity of air (at 20 degree celcius & 1 atm pressure)= 1.825⋅10-5 (N-s/m^2)
Theory-
Reynolds Number
The Reynolds number is the ratio of inertial forces to viscous forces. The Reynolds number is a dimensionless number used to categorize the fluids systems in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid. Mathematically, the Reynolds number, Re, is defined as
Re=ρ⋅v⋅dμRe=ρ⋅v⋅dμ
rho = density
v = velocity
d = diameter
mu= viscocity
Inputs :
Diameter of Cylinder = 0.04m
Length of the Cylinder= 0.05m
Air density = 1.2047(kg/m3)
Dynamic viscosity of air (at 20 degree celcius & 1 atm pressure)=1.825⋅10−51.825⋅10-5 (N-s/m2)
Calculation
- Calculation of Reynolds number & Velocity
Reynolds number = (rho x Velocity x D)/Dynamic visosity
Re = (1.2047*10*0.04)/(1.825*10^(-5)) = 26404.3835
Case1- When Reynolds number increased by 20%
Re = 1.2*26404.3835
Re = 31685.26
Velocity for (Re = 31685.26) = 12 m/s
Case2- When Reynolds number increased by 40%
Re = 1.4*26404.3835
Re = 36966.1369
Velocity for (Re = 36966.1369) = 14 m/s
Case3- When Reynolds number increased by 100%
Re = 2*26404.3835
Re = 52808.767
Velocity for (Re = 52808.767) = 20 m/s
- Calculation of Simulation end time
Length of domain (X-direction) = 0.22+0.14 = 0.36m
Case1- When Reynolds number increased by 20%
Velocity for (Re = 31685.26) = 12 m/s
Flow Through Time = (Length of domain)/(Velocity)
Flow Through Time = 0.36/12 = 0.03s
Simulation end time = 2*Flow Through Time = 0.06s
Case2- When Reynolds number increased by 40%
Velocity for (Re = 31685.26) = 12 m/s
Flow Through Time = (Length of domain)/(Velocity)
Flow Through Time = 0.36/14 = 0.02571s
Simulation end time = 2*Flow Through Time = 0.05143s
Case3- When Reynolds number increased by 100%
Velocity for (Re = 52808.767) = 20 m/s
Flow Through Time = (Length of domain)/(Velocity)
Flow Through Time = 0.36/20 = 0.018s
Simulation end time = 2*Flow Through Time = 0.036s
Procedure
1)Create a new part model.
2)Make a circle of 0.04m clameter and extrude it to 0.05m to make a cylinder.
3)Click on wizard in flow simulation toolbar for base line simulation and name the project and after it select time-dependent analysis and enter the simulation end time as total analysis time.
4)In Fluids, select air in gas as project fluid, and in initial conditions pressure as 101325 Pa, temperature as 293.2 K and velocity as 10m/s foe base line simulation and for other cases use Velocity for (Re increased by 20%) = 12 m/s, Velocity for (Re increased by 40%) = 12 m/s & Velocity for (Re increased by 100%) = 20 m/s.
5)Right click on Gloal Mesh and select edit definitions, change mesh to point 4.
6)Right click on cut plot for velocity & pressure in normal to the plane direction (Z-direction) at mid of cylinder and than run. After the solver is finished in the results select on the animation and save it for the cut plots in all the cases.
7)Now after base line simulation create new project & change the inlet velocity according to Reynolds number and click on run and get the animation for cut plot of pressure-velocity.
Results
- Base line simulation
- A) Pressure cut plot
B) Velocity cut plot
- Case1- When Re increased by 20%
- A) Pressure cut plot
B) Velocity cut plot
- Case2- When Re increased by 40%
- A) Pressure cut plot
B) Velocity cut plot
- Case3- When Re increased by 100%
- A) Pressure cut plot
B) Velocity cut plot
Conclusion-
- Inlet velocity in x direction increases with the increase in reynolds number, thus increasing the flow of air over the cylinder and when air flowing through the x axis hits the surface of the cylinder facing the inlet velocity, a high pressure region and velocity decreases at that region. The velocity increases and is at its maximum at the the top and bottom surface as a low pressure region is created there and at the beck region which is shielded by the cylinder the velocity is minimum.
- If we compare velocity plots for the 1st two cases (when re increased by 20% & 40%) both are similar in some ways, But we see there is significant difference in the velocity plot for the 3rd case (when re increased by 100%) as air passes over cylinder, if we closely look at the blue colour region's length is increasing in X-direction. There is a significant increase in the velocity which us shown by red colour region.
- From above plots we can also say that as the velocity or Renold’s number increase the flow over the cylinder becomes steady and the velocity plot at 20% and 40% exhibit slight unsteady plot whereas at 100% the
flow is steady.