Week 2 - Flow over a Cylinder.

AIM: The aim of the simulation can briefly be described as follows:

         1.Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100. 

         2. Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000. Also discussing the effects of Reynolds number on drag.

THEORY: 1. The flow over a cylinder is a very common kind of situation that we encounter in everyday lives, this particular problem has been worked on by people over a long period of time. Common places where we encounter such flows are heat exchange pipes ( for air-conditioning in Hospitals and hotels), flow over submarine components ( both internal-external), flow over chimneys ( mainly to assess the aerodynamic or hydrodynamic forces being imparted on the structure.)

2. On looking into experimental and computational results, we see that there is an instability of the wake at the critical Reynolds number, this flow is periodic and has definite frequencies know as the Von-Karmann vortex sheet. The flow past the cylinders can be systematically classified into a Creeping laminar state (0<Re<4), laminar state (4<Re<48), one with periodic vortex shedding (48<Re<180) and the transition wake  (180<Re<400).

3. The mechanism of flow separation over a cylinder is critical to understand the Von-Karman vortex shedding. The flow-on encountering a finite thickness body tends to go over the body in curved streamlines. On negotiating the body curvature, the flow experiences acceleration to counteract the centripetal acceleration. Due to this acceleration, there is a pressure drop, hence generating a region called the favorable pressure gradient. As soon as the pressure becomes adverse in the other side of cylinder, the flow is no longer able to negotiate the gradients and it separates tangentially, once this occurs there is a combination of flow reversal and wake, which are primarily low pressure regions.

4. On look at low Reynolds number i.e Re<10, the viscous forces are dominant, hence the flow passes the cylinder still being attached to the surface. Between numbers of 10<Re<40, flow separates from two points symmetrically apart, forming contra-rotating eddies, it is at Re>40, we see asymmetric vortices, undergoing periodic oscillations, with a switch in position w.r.t the cylinder. Its at Re>100 the 3-D instabilities creep in and there is streamwise vortcies which peel off alternately from either side of the cylinder, this phenomenon is called the Vonn- Karman shedding, this region is called the Von-Karman vortex sheet. 

5. The shedding of vortices is periodic and occurs at a particular frequency, also important to note is that, this shedding of vortices generate pressure differentials at the surface of the cylinder giving rise Aerodynamic loading which can impart structural stresses, hence a quantity is required to address the oscilatory phenomenon, hence introducing the Stouhaul Number. 

6. The Strouhal number is defined as Sr=fL/V,where f is the frequency, L is the length of playing field, and V is the velocity of the flow. It is basically a ratio of inertial forces due to local flow acceleration to inertial forces due to changes in velocity from one point to another.

7. Fluid has two methods of interaction pressure and shear, hence they are distributed in all directions, there are necessarily two directions which are important to us the one perpendicular to the flow and the one in the direction opposite to the flow, hence all the components resolved in these specific directions contribute e to Lift and Drag Respectively.

SETUP & SIMULATION

1. We start with opening the ANSYS work bench by dragging out the Fluent in the workspace. 

2. We open space claim and we set-up the model for the analysis, the model used here:

 This is a 2-D surface, with the rectangular part acting as the body enclosure with a circular cut-out indicating a cylinder, The dimensions of the enclosure are 60D X 40D, with the cylinder positioned at 20D from the front face and 40D from the back face, here D is the cylinder dia (D=2m).

The geometry can be created from basic shape commands, once done the pull-out options have to be used so that it becomes a 2-D surface.

3. Once the CAD cleanup is done, we proceed for meshing, the mesh used for this simulation is:

  The method used here is triangular elements, with element size as 0.25m, rounding the circular edges using by edge sizing, also creating a Body-Fit mesh using inflation layer, with the first layer height as 5e-3 with a growth rate of 1.2.

SIMULATION & SET-UP

On completing meshing we proceed with, setup as follows:

1. General settings- Transient or Steady depending on case.

2. Viscous Model- Laminar (No turbulence)

3. Fluid settings- Air, Density-1, Kinematic viscosity depending on Flow velocity & Reynolds Number.

4. Boundary conditions- Velocity 1m/s for all cases, no-slip condition, pressure outlet ( gauge pressure=0).

5. Residuals- Uncheked for Convergence Criteria.

6. Method- Coupled for transient & SIMPLE for steady.

7. Report Definitions- Lift, Drag,velocity plot (create monitor point).

8. Refrence Values- Area=2m^2, Depth=1m, Length=2m, other conditions set as inlet.

9. Initilization- Standard used, inlet conditions.

10. Calculation settings- a) Transient settings-no time steps=2000, 0.1s per step.

                                     b) Steady settings- no of iterations= 500.

SIMULATIONS

CASE-I

a)

REYNOLDS NUMBER-100, STEADY STATE.

b)

PRESSURE PLOT RE-100.

TRANSIENT CASE

a)

RE-100, TRANSIENT 

b)

PRESSURE CONTOURS RE-100 TRANSIENT.

CASE-II

For RE-10 ( RESIDUAL, DRAG, VELOCITY PLOT, LIFT, CONTOURS)

b) RE-100

RE-1000

RE-10000

RE-100000

RESULTS AND INFERENCES

CASE-I

Lift (Cl)= 0.207

Drag (Cd)=1.339

Strohaul number=0.2 [ fD/v, frequency=2/20, D=2, V=1]

CASE-II

STEADY CASE FOR DIFFERENT REYNOLDS NUMBER

INFERENCES:

As we can see that as Reynolds increases there is decrease in the drag co-efficient.