If you are designing a tall, slender, structure and it is subject to wind (such as a derrick/mast or communication tower), you need to consider vortex shedding.
In this post we cover:
- What is vortex shedding?
- Why does vortex shedding matter?
- How to calculate vortex shedding?
What is Vortex Shedding?
Vortex shedding happens when wind hits a structure, causing alternating vorticies to form at a certain frequency. This in turn causes the system to excite and produce a vibrational load. Historically, it has been very difficult to calculate by hand. Today, with modern technology and new engineering practices, completing a vortex shedding analysis is a valuable tool used in the design of tall equipment and structures.
Why does Vortex Shedding Matter?
The frequency of the vortices is dependent on the shape of the blunt body, and the velocity of the fluid flow or wind hitting this body. The vortices create low pressure zones on the downwind side of the object on alternate sides. As the fluid flows to fill the low pressure zone, it produces a vibration at a specific calculable frequency. This vibration is only a major concern if it happens to coincide with the natural frequency of the structure. For structures that are tall and uniform in size and shape, the vibrations can be damaging and ultimately lead to fatigue failure. Masts or towers are highly susceptible to vibrations induced by vortex shedding. By completing a vortex shedding analysis of structures under realistic wind loading, engineers can evaluate whether more efficient structures can and should be developed.
How to Calculate Vortex Shedding:
Step 1: Determine the Strouhal number
The vortex street frequency is calculated using the Reynolds number (which describes the fluid flow characteristics) and the Strouhal number (which describes the oscillations of a fluid). The Reynolds number is calculated using viscosity, density, flow velocity, and some geometry from the object in the fluid. It is calculated over a range of flow speeds (or wind velocities). The Strouhal number is then calculated from those Reynolds numbers, although for laminar flow situations a Strouhal of 0.2 is often used. The frequency of the vortex street is then calculated using the Strouhal number, the width of the body, and the flow speed. It is helpful to chart this calculation over a range of wind speeds.
Step 2: Find the natural frequencies of the mechanical system
Many times, especially in the case of derrick/mast design or bridges, the structure in question can have a complex geometry of gussets, cross members and varying thickness and material. In the past, finding the correct mathematical model of such a structure in order to find the natural frequency would be difficult and inaccurate. Today, with the advancement of technology and engineering practice, calculating the natural frequency can be done fairly efficiently. Sparta Engineering exclusively uses SolidWorks 3D CAD software to model projects. When it comes time to do an analysis such as determining if vortex shedding is a problem or not, the geometry is already in the computer ready for analysis. A Finite Element Analysis software such as SolidWorks’ Simulation Package, can be used to calculate the natural frequency of a very complex system. The output of such analysis is the frequencies of each harmonic (usually only the first 5 are applicable), the displacement caused by the vibration, as well as a graphical representation of the deflection.
Step 3: Comparing Natural frequencies to calculated frequencies
Now that we have the natural frequencies of the mechanical system from the simulation software, we can compare these frequencies to those calculated in step 1. If the natural frequency from the computer model line up to the frequencies calculated in stage 1 and the wind speed scenarios, it is highly likely you could have a problem. It is important to apply sound engineering judgment at this stage when interpreting the results. The formulas used in this calculation are only good for a certain rage of wind speeds and to some degree are based on experimental data. The accuracy of the analysis also depends on how accurate of a model you chose to do your analysis with. If you decide there is a problem or just want to be on the safe side there are several steps you can take in order to prevent vortex shedding.
Step 4: Fixing the problem
There are three main approaches that can be applied to prevent the structural failure from vortex shedding. The simplest is to address the fluid flow and create a disturbance on the structure so that the vortex street cannot form. This is commonly done by adding a spiral at the top of the structure (but any change to the body that disrupts the vortex would work). Another method is to design the structure itself so the natural frequencies are outside the operating frequencies. This can be done by varying the cross-section along the length of the structure or by adding or changing supports. There are also dynamic systems such as dampeners that can successfully be applied to absorb vibration.
While vortex shedding is a common phenomenon that can lead to structural failure, it is one that is often overlooked because of the complexity of modeling the situation correctly. Using the steps outlined above, vibrational problems can be easily identified and a few hypothesis can be tested. Design changes can be made before any real problem arises. The key point to remember is if you are designing a tall slender mechanical system exposed to wind loading, make sure the engineer is considering vortex shedding vibrations and conducts the appropriate analysis.