Flow over a Circular Cylinder: Study of pressure profile on the cylinder surface

Aim

To study the flow characteristics during a flow over a Circular Cylinder with Reynolds numbers of 100, 200 and 250 using Fluent software package.

Theory

1. Fluid Properties:Medium: AirDensity: 1 kg/ m3Density is the amount of matter present per unit volume of space.Dynamic Viscosity: 0.01 kg/ msDynamic viscosity is the internal resistance offered by the fluid to its motion.The value of 0.01 kg/ ms is assumed to ease the calculation. Since the Reynolds number is the deciding factor for laminar or turbulent flows, the assumed viscocity value does not affect the flow behavior.

2. Reynolds number and proof for laminar flow:Reynolds numbers cases simulated are for 100, 200 and 250. For the case of flow over a circular cylinder, the critical Reynolds number where the transition from laminar to turbulent regime takes place at 4 x105. And so the Re cases of 100, 200 and 250 are in the laminar region.

3. Mesh Creation Structured:Figure-1

4. Grid spacing Variable grid spacing:Figure-2

5. Dimensions of Flow domain:Figure-3

6. Position of cylinder:To ensure the fully developed flow at the cylinder surface, the flow domain chosen is 30D in the upstream of the cylinder and to study the effect of cylinder and its wake, downstream domain is extended to 50D. The same is shown in Figure-3. 7. Boundary condition:Cylinder surface: WallFar field: Symmetry, because to neglect the wall effect on the flow domain near the cylinder Inlet: Uniform Velocity inlet, to achieve the required Reynolds numberOutlet: Outflow with unit flow rate weighting to satisfy mass conservation

8. Coefficients (Cd, Cl, Cp):

The lift, drag of awingdepend not only on the airfoil shape and its associated velocity distribution, but also on wing planform and on the wing area. Experiments show, that doubling the wing area or the fluid density also doubles lift and drag, but doubling the air speed yields four times as much lift. The forces and moments also depend on the density of the air and on the shape of the wing. It is possible to compare the aerodynamic properties of differently sized airfoils or wings, if all forces and moments are normalized. These dimensionless properties (coefficients) aredefined as followsLift Coefficient

Drag Coefficient

Where, L is the lift force, D is Drag force, is fluid density, v is airspeed, S is plan form area.Knowing these coefficients for a certain airfoil section at a certain angle of attack, makes it possible to calculate the forces acting on wing sections of different sizes, mounted between walls at different flow velocities and air densities, but at the same angle of attack.

Coefficient of Pressure: Velocity and pressure are dependent on each other -Bernoulli's equationsays that increasing the velocity decreases the local pressure and vice versa. Thus the higher velocities on the upper airfoil side result in lower than ambient pressure whereas the pressure on the lower side is higher that the ambient pressure. It is possible to plot apressure distributioninstead of the velocity distribution, usually not the pressure, but the ratio of the local pressure to the stagnation pressure is plotted and called pressure coefficientCp.Coefficient of pressure Cp is found from,

of zero indicates the pressure is the same as the free stream pressure. of one indicates the pressure isstagnation pressureand the point is astagnation point.9. Theoretical prediction of velocity and pressure:

Irrotational incompressible flow past a circular cylinder without circulation is the potential flow. Such a flow can be generated by adding a uniform flow, in the positive x direction to a doublet at the origin directed in the negative x direction. According to the potential flow theory of flow over a cylinder, in the two intersections of the x-axis with the cylinder, the velocity will be found to be zero. These two points are thus called stagnation points, which are highlighted in Figure below. And Maximum velocity occurs on the sides of the cylinder at 90 and -90.

Figure: Stream lines past a cylinderOn the surface of the cylinder, the equation of velocity is

Interest here is also the pressure coefficient distribution predicted by the theory, given by the expressionCp=1-4sin2,

where is angle measured from the back of the cylinder. This inviscid pressure distribution is unrealistic in because it implies a zero drag.

Results and discussion:

1. Time step details: For all three Reynolds number cases following time step details are considered for simulation,S. No.Time step size: 0.02 sec

1Number of Time steps: 75, 000 numbers

2Time stepping method: Fixed

3Max iterations per Time step: 200

2. Error criteria:Absolute error criterion used for convergence is 0.01 for continuity, x-momentum and y-momentum equations. Error plots:Re 100

Re 200

Re 250

Stream function plots:Re 100

Re 200

Re 250

Velocity (Vx) contour plots:Re 100

Re 200

Re 250

Velocity (Vy) contour plots:Re 100

Re 200

Re 250

Pressure contour plots:Re 100

Re 200

Re 250

Cd variation with time:Re 100

Re 200

Re 250

Cl variation with time:Re 100

Re 200

Re 250

Cp on cylinder surface:Re 100

Re 200

Re 250

Vorticity Contours:Re 100

Re 200

Re 250

Wake velocity profile:Re 100

Re 200

Re 250

The vortices are not visible at the wake region for all the Re range because of which there is no appreciable variation in Drag coefficient. The possible reasons could be the mesh quality is not sufficient to capture the separation and vorticity generation or the chosen solving algorithm of 2nd order implicit may not be appropriate or the pressure velocity coupling algorithm of SIMPLE and Momentum Discretization method of Second order Upwind is not capturing the vortices with the mesh combination. So the mesh independence study could be carried out.