Steady Vs Unsteady flow over a cylinder
Objective:
In this challenge the objective is to simulate flow over cylinder using ANSYS Fluent and observe the vortex shedding phenomenon. The simulation is done with both steady and transient solver and Strouhal number was calculated for Transient case.
In the second part it is required to see the effect of Reynolds number on vortex shedding and observe the variation of Drag and Lift co-efficient. For all the cases a user defined material was used with density = 1 kg/m^3 and viscousity = 0.02 kg/m-s.
One of the most complex phenomena in the field of fluid dynamics is the Von Karman vortex shedding, the periodic oscillation developed at the wake region. In order to study the same using computational simulation, the bluff body under consideration is a circular cylinder. Using suitable boundary conditions and Reynolds number = 100, the flow is simulated for both steady and unsteady state. The velocity profile is plotted to capture the vortex shedding and the corresponding Strouhal number is determined. The study is further extended to calculate the force coefficients - drag and lift- for the range of Reynolds number – 10 to 10^5.
Vortex shadding:
In a fluid flow past a bluff body, due to the resistance to flow at the walls, vortex or region of flow with revolving fluid flow takes place at the back of the body. These vortices are shed periodically from the wake region to form periodically oscillating fluid flow known as Von Karman Vortex Street. However, vortex street formation is dependent on several factors including the Reynolds number (Re) of the fluid flow.
At a critical Re>47, there is development of vortex street at the street. Von Karman Vortex Street can be observed in real life applications such as the pattern of clouds in the sky etc. It is to be noted that for vortex shedding the flow separation has to occur at the back. This explains the absence of Vortex Street in the wake region of a streamlined body where the flow separation is less significant.
With the advances in the field of computational fluid dynamics, we are able to capture the periodic oscillation of the velocity profile by defining a user-defined wind tunnel and simulating with the bluff body inside. By altering the initial and boundary conditions, the fluid flow can be studied for a range of Re. However, the accuracy of these results with the experimental results has noted to be poor as we increase the Reynolds number and the fluid flow transitions to turbulent flow. This is due to several reasons such as the aspect ratio of the mesh geometry under consideration, the three dimensional nature of the vortices at higher fluid velocity which are not captured in the 2D simulation.
The impact of the vortex shedding can be studied by determining the force exerted in the wake region behind the body. In fluid flow, the force parameters predominantly used are the coefficient of drag Cd and the coefficient of lift CL. A general trend observed is that at lower velocity where the flow separation is less significant the drag force is very high. At higher velocities and Re, the drag force decreases and there is increase in the lift force acting on the wall of the body.
Geometry:
Consider a circular body of diameter D= 2 m. For the simulation, the surface of dimensions 10 D x 30 D is considered with symmetry along the z axis and offset of 5D along x axis from the mid-point
Mesh:
Type: Triangle Dominant
Element Size: 0.25 m
Inflation: 5 mm with 6 layers growth 1.2
Steady Solver with Re 100
Convergence residual plot:
No. of Iterations to converge = 375
Drag coefficient:
Drag coefficient = 1.3432
Lift coefficient:
Lift coefficient = 0.1266
Velocity monitor point contour:
Vertex average of velocity:
Unsteady Solver(Transient) with Re 100
Step Size: 0.1 sec
No. of Time Step = 2000
Flow time: 200 sec
Convergence residual plot:
No. of Iterations to converge = 37000
Drag coefficient:
Drag coefficient = 1.3697
Lift coefficient:
Lift coefficient = -0.0238
Velocity monitor point contour:
Vertex average of velocity:
Calculation of Strouhal Number:
From the plot we can see that there are 3.5 cycles between flow time of 120 s and 140 s
This gives the frequency = 3.5/(140-120) = 0.175 cycles/sec
Characteristic length = Diameter of Cylinder = 2 m
Inlet velocity = 1 m/s
St=0.175*2/1
= 0.35
Part 2: Simulation using Steady Solver for Different Reynolds Number
Case 1: Velocity inlet = 0.1 m/s Re = 10
Convergence residual plot:
Drag coefficient:
Drag coefficient = 3.3242
Lift coefficient:
Lift coefficient = 9.323e-4
Velocity monitor point contour:
Vertex average of velocity:
Case 2: Velocity inlet = 10 m/s Re = 1000
Convergence residual plot:
Drag coefficient:
Drag coefficient = 1.0899
Lift coefficient:
Lift coefficient = -5.37e-1
Velocity monitor point contour:
Vertex average of velocity:
Case 3: Velocity inlet = 100 m/s Re = 10000
Convergence residual plot:
Drag coefficient:
Drag coefficient = 0.9447
Lift coefficient:
Lift coefficient = 0.5707
Velocity monitor point contour:
Vertex average of velocity:
Case 4: Velocity inlet = 1000 m/s Re = 100000
Convergence residual plot:
Drag coefficient:
Drag coefficient = 0.7321
Lift coefficient:
Lift coefficient = 0.2922
Velocity monitor point contour:
Vertex average of velocity:
Effect of Reynolds Number on Drag Coefficient
On comparing the simulations done for different reynolds number it can be said that the Drag coefficient values decreases with increase in Reynolds Number. The formula for drag coefficient is
Cd = Drag Force/(0.5*ρ*A*v^2)
The Drag coefficient is inversely propotional to square of velocity which causes a decrease in the value with increase in Reynolds Number. The Drag coefficient remains almost constant in the Range 10^3 to 10^5 due to formation of turbulent wake.
A decrease in coefficient of drag doesn't neccesarily means a decrease in Drag Force.
For validation of the result, Experimental Data available in the literature was used
Drag coefficient of laminar flow past circular cylinder by B.N. Rajani and others and available on books such as Cengel , White.
|
Re |
Simulation |
Experiment |
Error (%) |
|
10 |
3.32 |
3.35 |
0.90 |
|
100 |
1.34 |
1.34 |
0 |
|
1000 |
1.089 |
1.19 |
8.48 |
|
10000 |
0.944 |
1.02 |
7.45 |
|
100000 |
0.732 |
0.65 |
12.61 |
Reference paper link: https://www.sciencedirect.com/science/article/pii/S0307904X08000243