Flow over a cylinder

Aim -

1) Simulating the flow over the cylinder and observing effect of increasing Reynolds number on flow.

Introduction -

Reynolds number is an important parameter in fluid mechanics. This describes fluid, geometry and flow this allows us to compare different fluid systems.

Generally flow pattern can observe as follows-

Unstable flow results into moving wake and increases drag. Wakes form because at wall fluid is steady and pressure increases as wall falls away. If momentum is insufficient, the fluid reverses and separates from the wall. The separation of boundary layer can distinguish the wake. The further upstream separation occurs the more drag is experienced by the cylinder.

The conditions for separation are –

1)Wall-fluid Contact(no-slip)

2)Adverse pressure gradient

3)Insufficient Momentum

Sucking a small amount of fluid through the wall removes the low momentum particles and they are replenished by high momentum particles from surrounding.the strength of suction to eliminate separation is relatively constant.

Non-uniform profiles improved significantly upon uniform suction.the location of suction has great effect and varies predictably with reynolds number.

Case setup –

We first calculate reynolds number for base setup and then increase it by factor of 20%,40%,100% and see effect on flow trajectory.

Take initial contitions as –

Diameter of cylinder(D) -40mm

Length of cylinder (L)-50 mm

Flow velocity (V)- 0.001478 m/s

Density of air(ρ) -1.225 kg/cu.m

Dynamic viscosity(µ) -1.81*10^-5

Reynolds number calculated as –

`Re=(ρ*v*D)/μ=(1.225*0.001478*0.04)/(1.81*〖10〗^(-5) )=4.001215`

Flow through time(Ft) is given as,

`Ft=(distance)/(flow velocity)=0.3/0.001478=202.976 s`

End time should be at least twice the Ft hence endtime will be 406s

Results –

Pressure contour-

Velocity streamlines –

Velocity Contour –

We will now consider that only velocity of flow varies as we increase the Reynolds number keeping all other parameters constant.

Case1) Re increased by factor of 20%

`Re=20/100*4.001215+4.001215=4.801458`

Velocity is given as,

`V=(Re*μ)/(ρ*D)=(4.801458*1.81*〖10〗^(-5))/(1.225*0.04)=0.001774 m/s`

Flow through time considering length of computational domain be 300mm

`Ft=(Distance)/(flow velocity)=0.3/0.001774=169.1s`

Results-

Pressure contour –

Velocity contours-

Case2) Re increased by factor of 40%

`Re=40/100*4.001215+4.001215=5.601701`

Velocity is given as,

`V=(Re*μ)/(ρ*D)=(5.601701*1.81*〖10〗^(-5))/(1.225*0.04)=0.002069 m/s`

Flow through time considering length of computational domain be 300mm

`Ft=(Distance)/(flow velocity)=0.3/0.002069=144.99s`

Results-

Pressure contour –

Velocity contours-

Case3) Re increased by factor of 100%

`Re=100/100*4.001215+4.001215=8.00243`

Velocity is given as,

`V=(Re*μ)/(ρ*D)=(8.00243*1.81*〖10〗^(-5))/(1.225*0.04)=0.002955 m/s`

Flow through time considering length of computational domain be 300mm

`Ft=(Distance)/(flow velocity)=0.3/0.002955=101.522s`

Results-

Pressure contour –

Velocity contours-

Case4) Re increased by factor of 1000%

`Re=1000/100*4.001215+4.001215=40.4122`

Velocity is given as,

`V=(Re*μ)/(ρ*D)=(40.4122*1.81*〖10〗^(-5))/(1.225*0.04)=0.01492 m/s`

Flow through time considering length of computational domain be 300mm

`Ft=(Distance)/(flow velocity)=0.3/0.01492=20.1s`

Results-

Pressure contour –

Velocity contours-

Conclusion -

from above cases it can be concluded that as reynolds number increases flow starts seperating and wake formation eases which results in increase in drag force