Week 2 - Flow over a Cylinder.

Aim: To simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

Conditions:

i)To calculate the strouhal number @ reynolds number, Re=100 , in steady and unsteady case.

ii)To calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000 using steady solver.

iii)To discuss the effect of Reynolds number on the coefficient of drag

Solution:

Strouhal Number: It is a dimensionless number describing oscillating flow mechanisms.

Reynolds number: A dimensionless number used in fluid mechanics to indicate whether fluid flow past a body or in a duct is steady or turbulent.

CASE-1

Strouhal number for the Steady case having conditions

density = 1

viscosity= 0.05

velocity= 1

Diameter of the cylinder = 5 m

strouhal number = 0.5 (max) @ magnitude= 0.0000071547565

Strouhal number for the Unsteady case having conditions

density = 1

viscosity= 0.05

velocity= 1

Diameter of the cylinder = 5 m

Strouhal number = 0.5(max) @ magnitude= 0.00023033109

CASE-2

Coefficient of Lift and drag for given reynolds number

S.no	Reynolds number	Lift coefficient	Drag coefficient	Lift/Drag Ratio
A	10	0.00027945299	0.18142748	1.5403x10^-3
B	100	0.10623703	6.2688864	0.01694
C	1000	24.302005	545.71896	0.044532
D	10000	58431.369	21443.52	0.36698
E	100000	1993156.5	3279770.9	0.60771

Plots for the given reynolds number

Plots for Lift coefficient

lift coefficient graph for reynolds number Re=10

lift coefficient graph for reynold number Re=100

lift coefficient graph for reynolds number Re=1000

lift coefficient graph for reynolds number Re=10000

lift coefficient graph for reynolds number Re=100000

Plots for Drag coefficient

Drag coefficient graph for reynolds number Re=10

Drag coefficient graph for reynolds number Re=100

Drag coefficient graph for reynolds number Re=1000

Drag coefficient graph for reynolds number Re=10000

Drag coefficient graph for reynolds number Re=100000

Plots of Vertex average of Velocity

Vertex average of Velocity graph for reynolds number Re=10

Vertex average of Velocity graph for reynolds number Re=100

Vertex average of Velocity graph for reynolds number Re=1000

Vertex average of Velocity graph for reynolds number Re=10000

Vertex average of Velocity graph for reynolds number Re=100000

Contours

Contour for reynolds number Re=10

Contour for reynolds number Re=100

Contour for reynolds number Re=1000

Contour for reynolds number Re=10000

Contour for reynolds number Re=100000

Results and conclusions:

• as the reynolds number, increases the Lift/Drag ratio increases gradually.
• Drag also increases as the reynolds number is increasing.
• vortex shedding begins to happen when the reynolds number of the fluid hits 100

References:

• Hurst, E., Yang, Q., & Chung, Y. (2014). The effect of Reynolds number on turbulent drag reduction by streamwise travelling waves. Journal of Fluid Mechanics, 759, 28-55. doi:10.1017/jfm.2014.524
• B.N. Rajani, A. Kandasamy, Sekhar Majumdar,Numerical simulation of laminar flow past a circular cylinder,Applied Mathematical Modelling,Volume 33, Issue 3,2009.