Steady vs unsteady simulations of flow over a 2D cylinder
In this project, flow over a 2D cylinder is studied for both steady and transient state using simulations done through Ansys. In order to study vortex shedding a customized fluid is set having density as 1kg/m3 and viscosity as 0.02 kg/ms so as to get a reynolds number of 100. To observe fluctuations due to vortex shedding a point is set at distance of four times the diameter of the hole from its center i.e., 8m from the center of the hole to monitors velocity. The simulation of flow over a 2D cylinder in conducted both in steady and transient states. SIMPLE method is used in the simulations. The simulation is considered to be converged when the velocity fluctuation becomes constant.
Geometry:
A computational domain of 60x20m is set up with a hole i.e., 2D cylinder having a diameter of 2m. The image of the geometry is given below
Mesh:
A computational mesh is set up which is made up of triangular elements, the element size being 0.25m.
Since the part surrounding the hole is highly significant an edge sizing having 36 divisons is made to make the hole more perfect in shape, then 6 inflation layers are added to capture intricate details using first layer thickness method with first layer height as 5e-3m and growth rate of 1.2. The respective image is shown below:
Mesh metrics:
Even though the geometry is meshed with all triangles method, adding inflation layers have added some quad mesh elements.
Steady state simulation:
Convergence plot:
Monitor point velocity magnitude:
The simulation is converged when the velocity fluctuations becomes constant as shown below
From the above image we can see that the solution becomes converged at 500 iteration where the fluctuation of velocity becomes constant.
Screen capture during simulation:
Animation file demonstrating vortex shedding in steady state:
Transient state simulation:
For the transient state simulation a time step of 0.1s is used with 20 iterations for each time step.
Convergence plot:
Monitor point velocity magnitude:
The simulation is converged when the velocity fluctuations becomes constant as shown below
From the above image we can see that the solution becomes converged at 23,750 iteration where the fluctuation of velocity becomes constant.
Screen capture during simulation:
Animation file demonstrating vortex shedding in transient state:
Strouhal number calculation:
Strouhal number cannot be calculated in steady state simulation as in steady simulation only end results are given importance. So, to calculate Strouhal number a transient simulation is required. In transient simulation once the velocity fluctuations become constant, the frequency of fluctuation is calculated by varying time steps. From the frequency value obtained, the Strouhal number is calculated. The Strouhal number is calculated using the formula given below:
`Sr = (fL)/U`
where, f is the frequency of velocity fluctuations
L is the hydraulic diameter
U is the free stream velocity.
In this simulation the free stream velocity U is taken as 1m/s, hydraulic diameter is the diameter of the 2D cylinder which is 2m and f is 1/T, where the T is found as 5.8s through transient simulation, from this the Strouhal number obtained is 0.344.