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AIM: SIMULATION OF FLOW OVER A CYLINDER TO CAPTURE THE PHENOMENON OF KARMAN VORTEX STREET PART-I Simulation of the flow with the steady and unsteady case and calculation of the Strouhal Number for Re= 100. PART-II Calculation of the coefficient of drag and lift over a cylinder by setting the Reynolds number…
Naveen Gopan
updated on 14 Jul 2020
AIM:
SIMULATION OF FLOW OVER A CYLINDER TO CAPTURE THE PHENOMENON OF KARMAN VORTEX STREET
PART-I
PART-II
OBJECTIVES:
GOVERNNG EQUATONS:
Naiver Stokes Equation:
Reynolds Number (Red):
Red = ρ×V×dμ
ρ = Density of fluid
V = Inlet velocity of fluid
d = Diameter of the cylinder
μ = Dynamic viscosity
KÁRMÁN VORTEX STREET
A Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies.
It is named after the engineer and fluid dynamicist Theodore von Kármán and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds. Red range (47<Red<105 for circular cylinders; reference length is d: diameter of the circular cylinder) eddies are shed continuously from each side of the circle boundary, forming rows of vortices in its wake.
This formula will generally hold true for the range 40 < Red < 150:
where:
FLOW DOMAIN:
2D geometry constructed using ANSYS SpaceClaim.
Cylinder: Diameter(D) = 2m
BASELINE MESH:
REFINED MESH:
Method: All triangles method
Edge sizing:
Given to the cylinder to get accurate simulation results.
Type: Number of Divisions
Number of Divisions = 36
Inflation Layer:
BOUNDARIES:
MONITOR POINT:
Monitor point created at x=4D downstream. In this wake, flow over the cylinder would help us to analyze and check the occurrence of vortex shedding by capturing velocity or pressure variation at this point.
SOLVER AND SETUP (FOR ALL SIMULATIONS):
Material for all simulation:
Material Assigned to cell Zone (surface): User Defined Material (properties below)
Red = ρ×V×dμ
ρ = Density of fluid = 1 kg/m3
V = Inlet velocity of fluid
d = Diameter of the cylinder = 2m
μ = Dynamic viscosity = 0.02kg/m-s
Therefore, Red = 1×V×20.02
Red = 100 x V
Varying ‘V’ to get the desired Reynolds number
Solution Method:
The solver used is ANSYS Fluent (Double precision).
Type: Pressure-based
Velocity Formulation: Absolute
Physics Model: Laminar and standard wall functions. (will be used for the entirety of this project since the desired Reynolds numbers are all in the laminar range)
Solution Initialization: Hybrid Initialization
PART 1 (Red = 100):
Steady Simulation
Time: Steady
Boundary Conditions:
Inlet: velocity magnitude (normal to boundary) = V = 1m/s
Outlet: Gauge Pressure (Pascal) = 0
Wall: Stationary wall
Shear Condition = No slip
Convergence Plot: Number of Iterations given to run = 1500
Number of Iterations to converge = 390
Velocity Variation at Monitor Point:
Velocity Contour:
Drag Coefficient Variation: Drag Coefficient = 1.3352895
Here, Strouhal number cannot be calculated since we can’t determine the Vortex Shedding Frequency.
Unsteady Simulation
Time: Transient
Boundary Conditions:
Inlet: velocity magnitude (normal to boundary) = V = 1m/s
Outlet: Gauge Pressure (Pascal) = 0
Wall: Stationary wall
Shear Condition = No slip
Convergence Plot: Number of Time steps = 1500
Time Step Size = 0.1 s
Velocity Variation at Monitor Point:
Velocity Contour:
Drag Coefficient variation: Drag Coefficient = 1.45
From above velocity and lift coefficient variation we can observe that the flow simulation has converged at flow time 110 s.
From the Lift Coefficient Plot, Vortex Shedding Frequency = 1.5140−120 = 0.075
To calculate Strouhal Number:
From Hand Calculation: For Red = 100, this formula will generally hold true for the range 40 < Red < 150
St = 0.198⋅(1−(19.7100))
St = 0.158994
From Simulation:
St = 0.075⋅21
St = 0.15 (equal to the hand calculated value)
PART 2 (Red = 10, 50, 150, 200, 250, 300):
Steady Simulation
Time: Steady
Boundary Conditions:
Inlet: velocity magnitude (normal to boundary) = V = 0.1m/s (Red = 10), 0.5m/s (Red = 50), 1m/s (Red = 100), 1.5m/s (Red = 150),
2m/s (Red = 200), 2.5m/s (Red = 250), 3m/s (Red = 300)
Outlet: Gauge Pressure (Pascal) = 0
Wall: Stationary wall
Shear Condition = No slip
Convergence Plot: Number of Iterations given to run = 1500
Red = 10, V = 0.1m/s
Convergence Plot: Number of Iterations given to run = 600
Number of Iterations to converge = 500
Drag Coefficient = 3.3264739
Velocity Contour:
Red = 50, V = 0.5m/s
Convergence Plot: Number of Iterations given to run = 700
Number of Iterations to converge = 50
Drag Coefficient = 1.5944976
Velocity Contour:
Red = 150, V = 1.5m/s
Convergence Plot: Number of Iterations given to run = 700
Number of Iterations to converge = 400
Drag Coefficient = 1.1992105
Velocity Contour:
Red = 200, V = 2m/s
Convergence Plot: Number of Iterations given to run = 700
Number of Iterations to converge = 350
Drag Coeffcient = 1.09292
Velocity Contour:
Red = 250, V = 2.5m/s
Convergence Plot: Number of Iterations given to run = 700
Number of Iterations to converge = 300
Drag Coeffcient = 1.0325197
Velocity Contour:
Red = 300, V = 3m/s
Convergence Plot: Number of Iterations given to run = 700
Number of Iterations to converge = 350
Drag Coeffcient = 0.94617954
Velocity Contour:
OBSERVATIONS:
Red (Reynolds Number) |
Drag Coefficient (CD) |
10 |
3.3264739 |
50 |
1.5944976 |
100 |
1.3352895 |
150 |
1.1992105 |
200 |
1.09292 |
250 |
1.0325197 |
300 |
0.94617954 |
INFERENCE:
Values of Reference Material:(https://www.sciencedirect.com/science/article/pii/S0307904X08000243)
Recently Zdravkovich, in an excellent monograph, has compiled almost all the experimental, analytical and numerical simulation data on flow past cylinders, available since 1938 and systematically classified this challenging flow phenomenon into five different flow regimes based on the Reynolds number. In the present study, the computation is restricted only to the first few regimes designated by Zdravkovich as (1) creeping laminar state (L1) of flow ð0 < Re < 4Þ, (2) laminar flow (L2) with steady separation ð4 < Re < 48) forming a symmetric contra-rotating pair of vortices in the near wake, (3) laminar flow (L3) with periodic vortex shedding ð48 < Re < 180Þ and finally (4) part of the transition-in-wake (TrW) regime ð180 < Re < 400Þ when the three-dimensional instabilities lead to the formation of streamwise vortex structure. Computations are carried out in the present work in the range of 1 < Re < 400 for comparison with available measurement data or other computation results for both steady and unsteady flow situations. All the computations use an implicit pressure-based finite volume Navier–Stokes algorithm (RANS3D) for time-accurate prediction of the flow.
As we can see the trend of variation is same for both materials. The values of drag coefficient keeps decreasing as the value of Reynolds number increases. As the value of drag coefficient also converges at high enough velocities the phenomenon of Karman vortex street also disappears. The case where Karman vortex street was captured at ts entirety was at Reynolds number 100. But this also depends on the size of the cylinder also, if we would have increased the size of cylinder as we increased the Reynolds number, vortex shedding could have been observed at those high values.
CONCLUSION:
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