Analysis of wind flow over a truss bridge

Problem Statement:

There is a truss bridge, the modelling wind is flowing over it at a high velocity. Find out the variations of velocity around the bridge.

CFD:

Computational Fluid Dynamics (CFD) is the process of mathematically modelling a physical phenomenon involving fluid flow and solving it numerically using the computational process.

In a CFD software analysis, the examination of fluid flow in accordance with its physical properties such as velocity, pressure, temperature, density and viscosity is conducted. To virtually generate an accurate solution for a physical phenomenon associated with fluid flow, those properties have to be considered simultaneously.

A mathematical model of the physical case and a numerical method are used in a CFD software tool to analyze the fluid flow. For instance, the Navier-Stokes (N-S) equations are specified as the mathematical model of the physical case. This describes changes in all those physical properties for both fluid flow and heat transfer. A mathematical model varies in accordance with the content of the problem such as heat transfer, mass transfer, phase change, chemical reaction, etc. Moreover, the reliability of a CFD analysis highly depends on the whole structure of the process. 

Theory:

Causes of Oscillation 

Oscillation of bridge under wind load can be different due to the variation of wind's magnitude, direction and steadiness. Essentially, the wind is the flow of air, therefore theories of fluid mechanics should be applied to analyze this kind of problem. However, the real flow pattern of wind is not always easy to describe by a graph and or a simple equation because most of the time wind is not steady. Usually, we use mean wind speed along with fluctuating wind to represent the flow. For a certain problem, we make different assumptions. Three common models of bridge vibration under wind effect are vortex-shedding, flutter and buffeting. Fundamental knowledge for aerodynamics will be introduced first. Then the detail of the of mechanism for each vibration pattern is illustrated afterwards.

Aerodynamics 

When wind passes through a bridge, it will react in the vertical direction, wind direction along with torsional deflection. Therefore, the bridge deck should follow equations in aerodynamics. Concerning the problem of dynamics, equation of motion is the basic rule for all the analyses. When it comes to the problem of bridges, often we pick up a cross-section of the bridge and let the wind flow from one direction. The wind can be viewed separately into two parts, which is mean wind speed U and fluctuation u(t) and w(t). The fluctuation part of the wind varies with time. Reactions induced by wind are horizontal force D, lift force L and moment M. 

Vortex- Shedding 

As we all know, an object with a certain mass and stiffness has its own natural frequency, which is defined as the square root of stiffness over mass. When this object A interfaces with low-pressure object B which is vibrating at A's natural frequency, resonance will occur. The phenomenon is very common in nature and is familiar to everybody. Also, this is the basic mechanism of vortex shedding. When wind flows through a bridge deck at a particular speed, vortex shedding will be generated at the downwind side. The figure shows the vortex when flow passes through a cylinder. A low-pressure region is generated at the downstream side of the cylinder. As upper and downflow move to the low pressure region alternatively, a vortex is created. Then certain vortex pattern here is called Von Karman Vortex Street. 

Computational Geometry:

Meshing:

Boundary Conditions:

• An rectangular enclosure is made of the bridge to simulate airflow

over the bridge. One end is named as an inlet and the other as an outlet.

• Viscous model (K-epsilon (2 equations), Realizable Model, Scalable Wall

Functions) was taken.

• Velocity Magnitude 15 km/h from the inlet.
• Zero gauge pressure is kept In the outlet.
• No-Slip condition is applied on the wall.

Solution Methods:

• Pressure velocity coupling scheme was kept at ‘Coupled’.
• In spatial discretization,

            →The gradient was set to ‘Green-Gauss Node Based’.

            →The pressure was kept at ‘Second Order’.

            →Momentum, Turbulent kinetic energy and Turbulent Dissipation

                The rate was set to ‘Second Order Upwind’.

• Pseudo Transient was also selected.
• 500 iterations are done for the calculation.

Solution:

Velocity Contours:

Velocity Vectors:

Simulation Video:

Conclusion:

With the help of ANSYS Fluent, the variations of velocity around the bridge were simulated and observed.

I've studied the method and compared the result with that from software. Wind engineering is not a new subject, on the contrary, theories on this field have been greatly developed already. However, there will always be requirements for engineering work on the subject because bridge construction is always going on. Therefore, after handling all the knowledge of wind effects on a bridge, we can move further to design, such as optimization and damage prevention, etc. instead of just making an analysis.