Steady Vs Unsteady flow over a cylinder

OBJECTIVE

To simulate the flow over cylinder and explain the phenomenon of Karmen Vortex street

Part – I

• Simulate the phenomenon for Re = 100 using steady and transient solver. Calculate the value of Strouhal number.

Part – II

• Calculate the drag and lift coefficient over a cylinder for Re = 10, 100, 1000, 10000, 100000 using steady solver.
• Discuss the effect of Reynolds number on drag coefficient.

THEORY

In fluid dynamics, a Karmen vortex street is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid.

In the wake region of a body, the flow consists of an alternating system of vortices. If the vortices on the top region are rotating clockwise then in the bottom the vortices are rotating counter clockwise and vice versa.

The phenomenon is significant with increase in Reynolds number of the flow.

PROCEDURE

Brief procedure followed to setup different simulations

Geometry setup – creating the cylinder and then defining the surrounding region

Mesh – different mesh option are used to get a refined mesh.

• Insert -> method -> trias. To get the tria elements
• Insert -> edge sizing -> select cylinder walls -> no of elements = 36 (10 degrees for each element)
• Insert -> inflation -> select geometry -> select boundary -> first layer thickness = 0.005m -> no of inflation layers -> 6

• Mesh element size = 0.1 m

Nodes - 23885

Elements - 46718

Setting up physics – different steps involved in setting up simulation

• General -> Steady/Transient -> pressure based solver (incompressible flow)
• Model -> Laminar (low Reynolds no)
• Material – We will control the Reynolds number using the viscosity of the flow. So new material is created defining density =1 and viscosity.
• Boundary Condition -> inlet velocity = 1 m/s, outlet = pressure -> gauge pressure =0
• Definition -> Drag coefficient, Lift coefficient and vertex averaged velocity
• Initialization -> Hybrid initialization (to create initial conditions in our geometry)
• Activity -> solution animation (to setup velocity animation to track the vortex shedding phenomenon)

Solve -> Run calculation (enter no of iteration/timestep)

PART – I Run a simulation for Re = 100 using Steady and transient solve. Calculate Strouhal number

Steady Solver - Input – Velocity – 1m/s, Re = 100, D = 2, density = 1 so viscosity = 0.02

The solution starts to converge at around 500 - 600 iteration. Vortices are formed beyond the cylinder

drag coefficient: 1.6048

lift coefficient: 0.0197

residual plots

Drag and lift coefficients

Vertex velocity average

Velocity and pressure contour

Transient Solver - Input – Velocity – 1m/s, Re = 100, D = 2, density = 1 so viscosity = 0.02

Time step = 0.1

Drag coefficient = 2.08005

lift coefficient = 0.11160

Residual Plot

Drag and lift coefficient

Vertex velocity average

Velocity and Pressure Contour

STROUHAL Number

The Strouhal number is a dimensionless number describing oscillating flow mechanisms. The Strouhal number represents the ratio of inertial forces due to the local acceleration of the flow to the inertial forces due to the convective acceleration.

f= frequency, L = length, U = Free stream velocity

Since this is a time dependent quantity, the value for strouhal number is only possible in case of transient simulation. So for Transient simulation with Re = 100 and time step = 0.1, the strouhal number gives the value of strouhal no.

Strohal Number = 0.016

Part - 2 Calculate drag and lift coefficient for Re = 10, 100, 1000, 10000, 100000

RE = 10, viscosity = 0.2

residual plots

Drag and Lift coefficients

Velocity and pressure contour

It can be seen from above images that although the residual are way below the convergence criteria, solution has not converge. Even Value of drag coefficient is very high and thus vortex shedding doesn't take place at such low reynolds number.

RE= 100, viscosity = 0.02

discussed above

Re = 1000, viscosity = 0.002

The solution starts to converge at around 300 iteration. Vortices are formed beyond the cylinder

residual plots

vertex velocity average

Drag and lift coefficients

Velcoity and pressure contour

Re = 10000, viscosity = 0.0002

The solution starts to converge at around 200 iteration. Vortices are formed beyond the cylinder

residual plot

Drag and lift coefficients

vertex velocity average

Velocity and pressure contour

Re = 100000, viscosity = 0.00002

The solution starts to converge at around 150 - 200 iteration. Vortices are formed beyond the cylinder

residual plot

lift and drag coefficient

vertex velocity average

velocity and pressure contour

Re	cd	cl	velocity
10	5.4318007	-0.001292089	0.42371792
100 steady	1.6048	0.019703128	0.64222336
1000	1.5367994	0.53125112	0.73625898
10000	1.5233681	-0.61685817	0.8689456
100000	1.4566432	-1.2129731	0.81473446

From the above results we can say that as the reynolds number increases the value of drag coeffcient decreases. This is due to the dominance of inertia forces over viscous force and as a result the formation of vortices is more dominant

NOTE: the value of lift varies between the negative and positive values as the inlet flow is symmetric along the axis of the object and upon contact with cylinder is dispersed in two similar components one acting downward and one acting upward. Thus negative value signifies that the force is acting downward

CONCLUSION

• Both steady and transient solver are used in the study. It shows that the results obtained by transient solver are more detailed as compared to steady
• Vortex shedding becomes dominant with increase in reynolds number. At lower reynolds number, the convergence is very difficult (in case of Re =10)
• Drag coefficient devreases with increases in reynolds number
• As the reynolds number increase, in this case the convergence is faster.