Steady Vs Unsteady flow over a cylinder using Ansys Fluent
Steady Vs Unsteady flow over a cylinder
Objective: Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street and study of the vortex sheddings.
PART-I
- Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
PART-II
- Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)
- Discuss the effect of Reynolds number on the coefficient of drag. [ Results should be validated with any standard literature and error should be within 5 %]
Expected results:-
- In both approaches, show that the flow has converged. That is, what quantities or plots need to be looked at to determine that the flow has converged?
- Plots of the coefficient of drag and lift.
- Plots to show vortex shedding behind the cylinder.
- Mention the preferred material at the end of the challenge submission page.
Theory:
Application:
The flow over a cylinder found its importance in various practical applications, like heat exchangers, in a submarine, chimneys, etc.
The phenomenon of Karman vortex street:
The von Kármán vortex street is a direct result of boundary layer seperation over bluff bodies. Immersed in fluid flow, any body of finite thickness will force the surrounding fluid to flow in curved streamlines around it. Towards the leading edge this causes the flow to speed up in order to balance the centripetal forces created by the curved streamlines. This creates a region of falling fluid pressure, also called a favourable pressure gradient. Further along the body, where the streamlines straighten out, the opposite occurs and the fluid flows into a region of rising pressure, an adverse pressure gradient. The increasing pressure gradient pushes against the flow and causes the slowest parts of the flow, those immediately adjacent to the surface, to reverse direction. At this point the boundary layer has separated from the body. and the combination of flow in two directions induces a wake of turbulent vortices.
For example, consider the flow past an infinitely long cylinder protruding out of your screen (as shown in the figure above). For very low Reynolds number flow (Re < 10) the inertial forces are negligible and the streamlines connect smoothly behind the cylinder. As the Reynolds number is increased into the range of Re = 10-40 (by, for example, increasing the free stream velocity ), the boundary layer separates symmetrically from either side of the cylinder, and two eddies form that rotate in opposite directions. These eddies remain fixed and do not “peel away” from the cylinder. Behind the vortices the flow from either side rejoins and the size of the wake is limited to a small region behind the cylinder. As the Reynolds number is further increased into the region Re > 40, the symmetric eddy formation is broken and two asymmetric vortices form. Such an instability is known as a symmetry-breaking bifurcation in stability theory and the ensuing asymmetric vortices undergo periodic oscillations by constantly interchanging their position with respect to the cylinder. At a specific critical value of Reynolds number (Re ~ 100) the eddies start to peel away, alternately from either side of the cylinder, and are then washed downstream.
This condition of alternately shedding vortices from the sides of the cylinder is known as the von Kármán vortex street.
Strouhal Number:
The Strouhal Number is a dimensionless value useful for analyzing oscillating unsteady fluid flow dynamics problems.
The Strouhal Number can be expressed as
St = ω l / v
where
St = Strouhal Number
ω = oscillation frequency
l = characteristic length
v = flow velocity
The Strouhal Number can be important when analyzing unsteady, oscillating flow problems. The Strouhal Number represents a measure of the ratio of the inertial forces due to the unsteadiness of the flow or local acceleration to the inertial forces due to changes in velocity from one point to an other in the flow field.
The vortices observed behind a stone in a river, or measured behind the obstruction in a vortex flow meter, illustrates these principles.
The Strouhal Number is a function of Reynolds number.
Reynolds Number:
The type of flow in the wake depends on the Reynolds number of the flow impinging on the body,
Re = rho*v*d/mu
where rho is the density of the fluid, v is the impinging free stream flow velocity, d is a characteristic length of the body, e.g. the diameter for a sphere or cylinder, and mu is the viscosity or inherent stickiness of the fluid. The Reynolds number essentially takes the ratio of inertial forces rho*v*d to viscous forces mu, and captures the extent of laminar flow (layered flow with little mixing) and turbulent flow (flow with strong mixing via vortices).
Drag and Lift:
Drag is the force, which acts along the direction of motion of force on the body.
Lift is the force that acts at a right angle to the motion of force through the air. Lift is created by the Pressure Difference.
The top of Airfoil is shaped to provide a longer path than the bottom. Air molecules have farther to go over the top. Air molecules must move faster over the top to meet the molecules at the trailing edges that have gone underneath. From Bernoulli’s equation, higher velocity produces lower pressure on the top.
Steps in Simulation:
Open Ansys Workbench. Drag and drop Fluid Flow (Fluent) onto Project Schematic.
Here, we will see Steps we need to follow to solve a particular engineering system from a CFD standpoint.
- Geometry: Spaceclaim, where we import the geometry.
- Mesh: Ansys Mesh, where Boundary naming, element sizing and mesh generation with required grid size will be done.
- Setup: Ansys Fluent, where actual case setup will be done.
- Solution: Ansys Fluent, where runtime results visualization done.
- Results: CFD-Post, where Post Processing of Results will be done.
CAD Cleanup:
Import Short Tee geometry into Spaceclaim, Spaceclaim is CAD cleanup software that can be used to prepare CAD models for simulation setup. It could be for CFD or FEA.
As we can see above figure is the Solid model. We are using 2D approximation. Here we are going to simulate the flow past an infinitely long cylinder of 2metre diameter protruding out of the screen. The size of the computational domain is 20metre*60metre.
Mesh generation:
- Convert the Quadrilateral dominant mesh into triangular mesh.
- Improve the circumference of the circle by assigning more no of division say 36.
- Provide inflation layer at the wall of the cylinder to get the smooth flow at the surface of the cylinder.
- Naming the Mesh as inlet, outlet, symmetry and wall (surface of cylinder).
- Update the Mesh.
Fluent Setup:
- Setting up physics: Select laminar model
- Material Selection: Custom Material.
Properties of Material:
Density = 1 kg/m^3
Viscosity = 0.02 kg/m.s
- Setting Boundary Condition:
Inlet= 1m/s
Outlet= 0 Pascal. (Ambient Pressure)
Wall = wall (No slip boundary condition)
Symmetry = symmetry
- Assigning different Flow quantities:
- Create Velocity Monitor Point
- Create Pressure and Velocity contour
- Create the report Plot for drag and Lift Coefficient.
- Add Animation for Pressure and Velocity.
- Initialize and run the Simulation.
PART-I
- Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
Steady Flow Simulation:
Re = 100
Inlet Velocity = 1m/s
Material Density = 1kg/m^3
viscosity = 0.02 kg/m.s
Residual Plot
Vertex-average-velocity:
There is vortex shedding as well as von Karman Street Effect takes place because Reynold Number is more than 40.
Drag Coefficient(cd):
The Drag Coefficient is 1.3363
Lift Coefficient(cl):
The Lift Coefficient is 0.181
Velocity Contour:
Pressure Contour:
The Solution is converged at 250 iterations as in Residuals plot is use to check convergence criteria which is giving constant value.
UNSTEADY STATE:
Timestep size = 0.1 second
Timesteps = 2200
Residual Plot
The Solution is converged at 40,000 iterations as in Residuals plot is use to check convergence criteria which is giving constant value.
Vertex-average-velocity:
Drag Coefficient(cd):
The Drag Coefficient is 1.3363
Lift Coefficient(cl):
The Lift Coefficient is 0.179
Velocity Contour:
Pressure Contour:
The Strouhal Number = Oscillation/mean Speed = (f*L)/Velocity = (0.08*2) = 0.16
where, f = Number of cycle/Time of cycle = 2/25 = 0.08
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PART-II
- Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. (Run with steady solver)
Steady Flow Simulation:
Material Density = 1kg/m^3
viscosity = 0.02 kg/m.s
Case 1:
Re = 10
Inlet Velocity = 0.1m/s
Residual Plot
The Solution is converged at 1400 iterations as in Residuals plot is use to check convergence criteria which is giving constant value.
Vertex-average-velocity:
There is no vortex shedding as well as no von Karman Street Effect takes place because Reynold Number is less than 40.
Drag Coefficient(cd):
The Drag Coefficient is 3.391
Lift Coefficient(cl):
The Lift Coefficient is 0.0069
Velocity Contour:
Pressure Contour:
Case 2:
Re = 100
Inlet Velocity = 1m/s
This Case is done above in Part -1 Steady-State Simulation.
Case 3:
Re = 1000
Inlet Velocity = 10m/s
Residual Plot
The Solution is converged at 175 iterations as in Residuals plot is use to check convergence criteria which is giving constant value.
Vertex-average-velocity:
There is vortex shedding as well as von Karman Street Effect takes place because Reynold Number is more than 40.
Drag Coefficient(cd):
The Drag Coefficient is 0.64 (Approximately)
Lift Coefficient(cl):
The Lift Coefficient is 0.02631(Approximately)
Velocity Contour:
Pressure Contour:
Case 4:
Re = 10000
Inlet Velocity = 100m/s
Residual Plot
The Solution is converged at 200 iterations as in Residuals plot is use to check convergence criteria which is giving constant value.
Vertex-average-velocity:
There is vortex shedding as well as von Karman Street Effect takes place because Reynold Number is more than 40.
Drag Coefficient(cd):
The Drag Coefficient is 0.54 (Approximately)
Lift Coefficient(cl):
The Lift Coefficient is 0.2875(Approximately)
Velocity Contour:
Pressure Contour:
Case 5:
Re = 100000
Inlet Velocity = 1000m/s
Residual Plot
The Solution is converged at 300 iterations as in Residuals plot is use to check convergence criteria which is giving constant value.
Vertex-average-velocity:
There is vortex shedding as well as von Karman Street Effect takes place because Reynold Number is more than 40.
Drag Coefficient(cd):
The Drag Coefficient is 0.48 (Approximately)
Lift Coefficient(cl):
The Lift Coefficient is 0.249(Approximately)
Velocity Contour:
Pressure Contour:
The effect of Reynolds number on the coefficient of drag:
|
Reynolds Number |
Coefficient of Drag (cd) |
Coefficient of Lift(cl) |
|
10 (Steady-state) |
3.391 |
0.00689 |
|
100 (Steady-state) |
1.351 |
0.181 |
|
100 (Transient-state) |
1.37 |
0.179 |
|
1000 (Steady-state) |
0.64 |
0.02631 |
|
10000 (Steady-state) |
0.54 |
0.2875 |
|
100000 (Steady-state) |
0.48 |
0.249 |
Conclusion
As the Reynold number increases, the coefficient of drag decreases. Because when the Reynold Number is large (Re>4000), then there is turbulent flow, in which laminar flow is very small, hence the viscosity effect also small, leads to lower skin friction drag.
Similarly, on the other hand, when Reynold number decreases (Re<2300), the flow becomes laminar, friction increases, hence the coefficient of drag also increases.
Animation