Flow over a cylinder

Aim: Simulate the flow over a cylinder

Objective:

• To run baseline simulation and calculate reynold number
• To Increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation.
• Do the analysis of result

Therotical background:

External flows past objects have been studied extensively because of their many practical applications. For example, airfoils are made into streamline shapes in order to increase the lifts, and at the same time, reducing the aerodynamic drags exerted on the wings. On the other hand, flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body. In certain Reynolds number range, a periodic flow motion will develop in the wake as a result of boundary layer vortice being shed alternatively from either side of the cylinder. This regular pattern of vortices in the wake is called a Karman vortex street. It creates an oscillating flow at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations, especially when the shedding frequency matches one of the resonant frequencies of the structure.

flow separation:

The presence of the fluid viscosity slows down the fluid particles very close to the solid surface and forms a thin slow-moving fluid layer called a boundary layer. The flow velocity is zero at the surface to satisfy the no-slip boundary condition. Inside the boundary layer, flow momentum is quite low since it experiences a strong viscous flow resistance. Therefore, the boundary layer flow is sensitive to the external pressure gradient (as the form of a pressure force acting upon fluid particles). If the pressure decreses in the direction of the flow, the pressure gradient is said to be favorable. In this case, the pressure force can assist the fluid movement and there is no flow retardation. However, if the pressure is increasing in the direction of the flow, an adverse pressure gradient condition as so it is called exist. In addition to the presence of a strong viscous force, the fluid particles now have to move against the increasing pressure force. Therefore, the fluid particles could be stopped or reversed, causing the neighboring particles to move away from the surface. This phenomenon is called the boundary layer separation.

wake:

Consider a fluid particle flows within the boundary layer around the circular cylinder. From the pressure distribution measured in an earlier experiment, the pressure is a maximum at the stagnation point and gradually decreases along the front half of the cylinder. The flow stays attached in this favorable pressure region as expected. However, the pressure starts to increase in the rear half of the cylinder and the particle now experiences an adverse pressure gradient. Consequently, the flow separates from the surface and creating a highly turbulent region behind the cylinder called the wake. The pressure inside the wake region remains low as the flow separates and a net pressure force (pressure drag) is produced.

vortex shedding:

The boundary layer separates from the surface forms a free shear layer and is highly unstable. This shear layer will eventually roll into a discrete vortex and detach from the surface (a phenomenon called vortex shedding). Another type of flow instability emerges as the shear layer vortices shed from both the top and bottom surfaces interact with one another. They shed alternatively from the cylinder and generates a regular vortex pattern (the Karaman vortex street) in the wake . The vortex shedding occurs at a discrete frequency and is a function of the Reynolds number. The dimensionless frequency of the vortex shedding, the shedding Strouhal number, St = f D/V, is approximately equal to 0.21 when the Reynolds number is greater than 1,000.

Governing equation:

1] Reynold Number:

`Re=(ρ .u.D)/μ=(u.D)/v=(Q.D)/(v.A)`

where:

D is the hydraulic diamete of the pipe (m);

Q is the volumetric flow rate (m³/s);

A is the pipe's cross-sectional area (m²);

u is the mean speed of the fluid (SI units: m/s);

μ is the dynamic viscosity of the fluid (Pa·s = N·s/m² = kg/(m·s));

ν is the kinematic viscosity of the fluid, ν = μ/ρ (m²/s);

ρ is the density of the fluid (kg/m³).

Probelm :

Fluid:Air

Flow type: External flow

x-domain = 0.6(m)

density of air = 1.225 (kg/m^3)

diameter of pipe = 0.02(m)

length of pipe = 0.05(m)

dynamic viscosity = 1.81e-5 (pa-s)

total flow time = 2*(distance/velocity)

Cases	Reynold number	Velocity	Total flow time
baseline	13535.91	10	0.12
120% of baseline	16243.09	12	0.1
140% of baseline	18950.27	14	0.086
200% of baseline	27071.82	20	0.06

Geometry:

:

plot:

1. Baseline simulation :https://drive.google.com/drive/folders/1gJZ1xsj6Z4hQ0rDW6ahDiGtM2y4xu3we?usp=sharing
2. Re=120%of baseline reynold numberhttps://drive.google.com/drive/folders/1NcVvtSNKi7NC2LA4WcMz4veY_wEq9Bqx?usp=sharing
3. Reynold number = 140% of baseline reynold numberhttps://drive.google.com/drive/folders/1mG6tbqrKKGLJUG_50ISp2ExsmiaMoc3N?usp=sharing
4. Reynold number = 200% of base line reynold numberhttps://drive.google.com/drive/folders/1ARS2L-zaafhFXS6FYI153sBxXqdpSagr?usp=sharing

Conclusion:

• velocity of flow increases with reynold number
• there is not large variation in relative pressure
• high pressure is created on surface facing velocity
• as velocity increases velocity profile is behind the cylinder for longer time

Result:

• CFD analysis of flow over cylinder has been done successfully.