Simulation of fluid flow over a cylinder
Objective: To Simulate the two-dimensional flow past a circular cylinder in different laminar flow regimes with the steady and unsteady case.
Software used: Ansys 2019 R3.
Description:
Consider a stream of fluid flow past a circular cylinder. As fluid passes the topmost point of the cylinder, it finds itself unable to negotiate the rear half of the cylinder where there is an uphill pressure gradient. Hence the fluid separates from the leading surface and the flow is seperated individually with highly organised and typically consists of two sequences of vortices, one from each side of the body, with circulations of opposite signs. Depending on the shape and motion of the body more complicated patterns of vortices may arise.
In the wake of the cylinder, the flow pattern consists of an alternating system of vortices or regions of rotation, as shown in Figure is 'shed'. This repeating pattern of swirling vortices at the wake of the cylinder is known as Karman vortex street.
It is important to note that even if the incoming flow is steady (i.e, does not change with time), the unsteadiness is intrinsically generated and the Karman street is formed downstream of the body.
A vortex street can be observed only over a given range of Reynolds numbers (Re), normally one finds that for Re <ReS≈5 the flow is steady and attached to the cylinder. At ReS the flow separates and two symmetric recirculation zones are formed but the flow remains steady. Beyond Recrit ≈46 the flow becomes unsteady and the Kármán vortex street appears. At sufficiently large Reynolds number the vortex street persists for many cylinder diameters but it can break down far downstream and reorganise itself into a secondary structure.
The Reynolds number is a measure of the ratio of inertial to viscous forces in the flow of a fluid and may be defined as:
Re = ρVD/ µ
where:
ρ = Density,
D = the diameter of the cylinder around which the fluid is flowing,
V = the steady velocity of the flow upstream of the cylinder and
µ = the kinematic viscosity of the fluid.
Strouhal made the first measurements of the frequencies associated with the shedding of vortices by defining a Strouhals number (S)
S = fD/U
S = 0.212*(1 - 21.2/Re)
where, diameter (D), speed (U), frequency (f)
Note: As Strouhal Number deals with frequency, it can be only obtained for transient type problems
Both Renolds number and Strouhals number are nondimensional numbers.
On the practical side, the Karman street can lead to unwanted noise or even cause failure of structures when the vortex shedding frequency coincides with the natural frequency of structure. This type of vortex-induced oscillations can occur in a variety of situations such as chimneys, bridges, heat exchanger tubes, overhead power cables and marine structures. Therefore understanding the physics of the Karman vortex street is crucial to avoid disasters in these situations.
Procedure:
Step1: Geomtery along with dimensions
Step2: Meshing with Mesh size = 200mm
Note: Mesh insertions and Named selections are necessary to define boundary conditions.
Step3: Setup & Solution
Set-up details:
*Viscous Model: Laminar
*Solver type: Pressure-based
*Solving method scheme: Simple
*Initializing Method: Hybrid for Steady case
Standard for unsteady case (transient)
*Number of itterations: 800
Solution:
We shall consider 2 cases during simulation
Case1: Comparing the fluid at steady and unsteady case with same Re number
Case2: Comparing the fluid at steady case with different Re no.s(i.e. 10,100,103,104,105)
**Note: For Re number above 1000, use Viscous model as Turbulent (i.e. K-epsilon or K-omega)
Case1: Comparing the fluid at steady and unsteady case with same Re number
*Re = 100
*Material: User defined fluid with ρ=1kg/m3 and µ=0.02kg/m-s
*Inlet Velocity : 1m/s
i. Steady Case:
Drag-Coefficient Lift-Coefficient
Velocity Vs Itteration Pressure Vs Itteration
Velocity Contour Pressure Contour
ii. Unsteady Case:
*Time step: 0.1
Drag-Coefficient Lift-Coefficient
Velocity Vs Itteration Pressure Vs Itteration
Velocity Contour Pressure Contour
Residuals Strouhals number
From the above plot of Strouhals number we can observe that the curve is converged at 0.16
We know that,
S = 0.212*(1 - 21.2/Re) = 0.212*(1 - 21.2/100) = 0.167
Therefore, we have done the correct simulation without any input errors.
Case2: Comparing the fluid at steady case with different Re numbers
*Material: User defined fluid with ρ=1kg/m3 and µ=0.05kg/m-s
i. Re @ 10
*Inlet Velocity : 0.25m/s
Drag-Coefficient Lift-Coefficient
ii. Re @ 100
*Inlet Velocity : 2.5m/s
Drag-Coefficient Lift-Coefficient
iii. Re @ 1000
*Inlet Velocity : 25m/s
Drag-Coefficient Lift-Coefficient
iv. Re @ 10,000
*Inlet Velocity : 250m/s
Drag-Coefficient Lift-Coefficient
v. Re @ 1,00,000
*Inlet Velocity : 2500m/s
Drag-Coefficient Lift-Coefficient
Step4: Result
Case 1: Re @ 10 Case 2: Re @ 100
Case 3: Re @ 1000 Case 4: Re @ 10,000
Case 5: Re @ 1,00,000
Animation video of above case
Effect of Re number on Drag (For Cylinder):
Case 1 (Re@10): At very slow flow in which we have neglected viscosity entirely. So there will be no separation of flow and no viscous wake downstream of the cylinder. Because the flow is symmetric from upstream to downstream, there is no drag on the cylinder.but this type of flow does not occur in nature where there is always some small amount of viscosity present in any fluid.
Case 2 (Re@100): A stable pair of vortices are formed on the downwind side of the cylinder. The flow is separated but steady and the vortices generate a high drag on the cylinder.
Case 3 (Re@1000): In this, flow velocity is increased. The downstream vortices become unstable, separate from the body and are alternately shed downstream. The wake is very wide and generates a large amount of drag.
Case 4 (Re@10,000): The flow velocity is increased even more. The periodic flow breaks down into a chaotic wake. The flow in the boundary layer on the windward side of the cylinder is laminar and orderly and the chaotic wake is initiated as the flow turns onto the leeward side of the cylinder. The wake is not quite as wide as for Case 3, so the drag is slightly less.
Case 5 (Re@1,00,000): flow is even at higher velocity. The boundary layer transitions to chaotic turbulent flow with vortices of many different scales being shed in a turbulent wake from the body. The separation point is initially slightly downstream from the laminar separation point, so the wake is initially slightly smaller and the drag is less than the corresponding laminar drag (Case 4).
Conclusion:
Increasing velocity eventually brings the turbulent drag up to and even higher than the laminar drag value, but there is a range of Reynolds numbers, during transition from laminar to full turbulent, for which the turbulent drag is less than the laminar drag.
Reference:
https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html
Link for zip file:
https://drive.google.com/open?id=1EY-RbhvUsz9mGEVdR8-s5PsZk8by7bgp
Attachments:
Part-1 and Part-2 required plots.