Flow over a cylinder

Aim:To simulate the flow over a cylinder(i.e. Transient Flow).

Introduction:Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions.CFD is applied to a wide range of research and engineering problems in many fields of study and industries, including aerodynamicsand aerospace analysis, weather simulation,natural science and environmental engineering, industrial system design and analysis,biological engineering, fluid flows and heat transfer, and engine and combustion analysis.

Reynolds Number:The Reynolds number (Re) is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents).

The Reynolds number is defined as

where:

• ρ is the density of the fluid (SI units: kg/m³)
• u is theflow speed (m/s)
• D is the diameter of the tube (m)
• μ is the dynamic viscosity of the fluid(Pa·s or N·s/m² or kg/(m·s))
• ν is the kinematic viscosity of the fluid (m²/s).

Problem Statement:First of all we have to done a baseline simulation and the find a reynolds no, and after that increasng it by some factor and with that velocity we have to do the transient analysis of all cases.

• Calculate the baseline case Reynolds number.
  • Re = rho*U_inlet*D/mu
  • D = cylinder diameter
  • mu = dynamic viscosity
  • rho = density
• Run a baseline simulation and then calculate the Reynolds number. Then increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation.

Geometry of Model: Dimensions: Diameter=0.05m

Length=0.100m

Baseline Simulation Study:First baseline study is done in which the fluid is 'Air' whose velosity on x-direction is taken with a magnitude of 10m/s.

And with the help of this Reynolds number is calculated but before that the values which is considered in this are:

Inputs	Values
Diameter	0.05m
Velocity (x-direction)	10m/s
Density	1.225kg/m^3
Dynamic Viscosity	1.81e-05kg/(ms)

Now with the reynolds no. formula the value is calculated:

Re = rho*U_inlet*D/mu

where,

• D = cylinder diameter
• mu = dynamic viscosity
• rho = density
• U_inlet=velcoity at inlet

The Reynolds no. value obtained in this is :Re=33839.78

Now we have increase this reynolds no. by 20%,40%,100% and these are:

Increasing 20% means 1.2*Re i.e. equal to 40607.73

Increasing 40% means 1.4*Re i.e. equal to 47375.692

Increasing 100% means 2*Re i.e. equal to 67679.59

After that with these Reynolds no. valocities are calculated and also the simulation end time:

At 1.2*Re the velocity is 12m/s

At 1.4*Re the velocity is 14m/s

At 2.0*Re the velocity is 20m/s

In this the length of compuatational domain along x-axis is .7m

And we know Velocity=Distance/Time

So, time=Distance/speed

The simulation end time at 10m/s=.7/10=0.07*2=0.14sec

The simulation end time at 12m/s=0.7/12=.0583*2=0.1167sec

The simulation end time at 14m/s=0.7/14=.05*2=0.100sec

The simulation end time at 20m/s=.7/20=.035*2=0.07sec

From this we can see that with the increase in velocity the simulation end time is decreasing.

For Baseline Simulation the conditions are:

Inputs	Values
Analysis Type	External Flow
Fluid	Air
Time Dependent	Total Analysis time:0.1sec
	Output time setup:0.01sec
Inlet Velocity	10m/s
Global Mesh Level	4

Results:For flow over cylinder at 10m/s : (i.e. Baseline Simulation)

Pressure Cut Plot:

Animation:

Velocity Cut Plot:

Animation:

For flow over cylinder at 12m/s:

Pressure cut plot:

Animation:

Velocity cut plot:

Animation:

For flow over cylinder at 14m/s:

Pressure cut plot:

Animation:

Velocity cut plot:

Animation:

For flow over cylinder at 20m/s:

Pressure cut plot:

Animation:

Velocity cut plot:

Animation:

Conclusion: 1.As can be seen in the result that the pressure is almost constant in all cases.But with the increase in Reynolds No. the velocity value also increases.

2. The simulation end time is decreasing with increase in velocity .

3.The velocity profile variation is also increasing with the increase in velocity as can be seen in the result at 20m/s the velocity profile is longer as compared to other.