TACOMA BRIDGE - Flow over cylinder

INTRODUCTION

Studying the external flow past a body has been the major significance, as they contribute to studying the aerodynamic behaviour of cars, aeroplane, bridges or any other objects which are submerged in fluids. The shape of the objects has significant impact as they present various behaviours, in some shapes, the flow gets attached to the body without separating called as streamlined bodies, in others, flows starts separating, formation of wake regions, which are referred to as the blunt bodies. Classic example of such bodies are Cylinders and plates.

NATURE OF FLOW

As the particle comes in contact with the blunt body, the particles in center of the flow which comes in contact with blunt body comes to virtual stop and velocity is almost equal to zero and the pressure is maximum, this point is referred as the stagnation point. By the conditon of No-Slip, velocity of particles closer to body moves slowly and this region is referred as the boundary layer. Boundary layer is referred as the zone from the wall of cylinder to a point where velocity is 0.95 times the freestream velocity.

BOUNDARY LAYER SEPARATION AND WAKE

Flow has to go through against the viscosity and favorable pressure gradient. That is the pressure has to decrease in direction of flow. However, with the adverse pressure gradient condition that is when dp/dx>0, flow has to work against the pressure, hence the particles starts detaching from the body to take low resistance path. This results in the boundary layer separation. Post the boundary layer separation, zone behind the cylinder is subjected to highly turbulent region where the pressure is low, pressure drag is produced in the region.

KARMAN VORTEX SHEET AND TACOMA BRIDGE

Free shear layer which are formed by the boundary layer separation shed vortices from top and bottom alternatively. This vortex shedding pattern is referred to as the karman vortex sheet. This comes into play in the downstream of wake region behind the cylinder. This is pronounced at the particular frequeny which is the function of the Reynolds number. This also results in the uneven pressure distribution and strong oscillations

In 1940s, Tacoma narrow bridge collapsed to the same reason, osciallation induced by the karman sheet matched the resonant frequency of the bridge at one of the node. The karman sheet was induced due to air blowing at 19.4m/s.

Momentum imnbalance also induces the force in the cylinder which is commonly referred to as the drag force.

The tacoma bridge collapse footage can be found in this link https://www.youtube.com/watch?v=XggxeuFDaDU

CFD SIMULATION

Geometry: Cylinder with Diameter of 0.04m and length of 0.05m is taken as the geometry of interest of study.

Meshing: Automatic meshing feature is utilised with the mesh level of 4 with Automatic refinement. Local mesh is also inserted in the region where solid is in contact with the fluid

Initial conditions and case setup:

Air is taken as the fluid at 101325pa, 288.2K, Time dependency is enabled. The simulation end time is deided by 2*L/u where L is the length of the computational domain and u is the inlet velocity which is initialised. The reynolds number is changed by changing the velocity of the flow.

Reynolds number is calculated using

The length of the computational domain is as follows

Length = Length of the upstream section + Cylinder diameter + Length in downstream section

Length = 0.16 + 0.04 + 0.4 = 0.6m

Condition	Velocity	Reynolds Number	Sim end time
Base Re	10	27071	0.12
1.2Re	12	32486	0.1
1.4Re	14	37900	0.0857
2Re	20	54143	0.06
Check	0.0369	100	32.52

RESULTS AND PLOTS

Case 1: Base Reynolds number, Re = 27071, Reynolds number being high, formation of wake region and recircualation could be noticed.

Flow trajectory clearly shows formation of wake behind the cylinder

Case 2: 1.2 times Base Re

This one shows the intialisation of karman sheets, wake zone stretched

Case 3: 1.4 times base Re

Case 4: 2 times Base Re

Case 5: Since all the four cases have very high Reynolds number, this case was executed at Re=100, where some portion of the flow would still be attached to the surface.

DISCUSSION AND OBSERVATIONS

1) Tacoma bridge collapsed because, the bridge base had no space for air to flow through, Bridge acted as a blunt body, Reynolds number in order of magnitude of 10^6, resulted in formation of karman sheets in downstream, oscillation of which matched the natural frequency of the bridge resulting in forming resonance and collapse,

2) This gave an important changes to Bridge construction and civil engineering in general, Aeroelasticity was accounted, even Burj Khalifa has an opening for unobstructed air passage

3) At lower reynolds number, flow is attached to the surface (Re<1), post this small wake region is formed (Re<100), wake zone grows(Re<1000), Vortex shedding starts (Re>10000).

4) Momentum imbalance creates the pressure drag in the system

5)Wake zone is an highly turbulent region behind the cylinder

6) Animated videos can be found in the link https://youtu.be/1xBhXjOssck