Flow Induced Vibration Part 2: Using CFD to find the forcing frequencies

Combining CFD with FEA can provide a powerful method to investigate flow induced vibration. In Part 1 of this post, the use of FEA to find the natural frequency of the spray lance was discussed. In this post, the use of CFD to find the frequencies found in the velocity fluctuations as the fluid flows across the spray lance.

The spray lance shown in the previous post was designed to be inserted into a vertical column with a turbulent airflow. An important question that had to be answered was whether the flow across the spray lance would induce vibrations within the spray lance that would lead to vibration or even to failure. Since the system was in the design phase, it was necessary to use computer simulations to investigate the expected performance of the system. A transient CFD analysis was performed to estimate the velocities that would be found within the system during normal operation.

The plot below shows the fluctuation in the average velocity along the length the spray lance as determined from the transient CFD analysis. This plot shows that significant fluctuations in the velocity can be expected and, as a result, fluctuations in the forces acting on the spray lance. 

A Fourier analysis of this velocity signal yielded a frequency spectrum for this velocity profile as shown in the figure below. This plot shows that the primary frequencies of the velocity are found below 10 Hz, with the two main frequencies at approximately 2-4 Hz.

This second look shows that there are no strong forcing frequencies found at the first or second natural frequencies of the spray lance. Like the results from the velocity analysis, these results also suggest that the configuration is unlikely to experience vibration due to the flow across the spray lance.

The method outlined in these two posts is a simple approach to looking at flow induced vibration. A complete analysis is far more complicated and takes more factors into account. This method however can be used as a screening tool to find potential problems. For example, if the velocity were at or near the critical velocity or if the frequencies in the velocity were found to be near the natural frequency of the spray lance, it would indicate that there was a strong possibility that excessive vibration would exist when the system was started. In this were indeed the case, more investigation or a redesign of the spray lance would be required.

Flow Induced Vibration Part 1: Using FEA to determine the natural frequency

In a recent project I had to design a spray lance to be inserted into a large vertical column. In an early design iteration, it was necessary to determine if the spray lance would suffer from flow induced vibration once the system was started. Since the system did not exist and there was no data about how it actually worked, a computer study of the system was performed to investigate the possibility of flow induced vibration. 

One of the useful tools in most FEA packages is the ability to determine the natural frequency of a part very quickly. Using FEA to determine the natural frequency rather than a using a hand calculation can help reduce the time and effort required to study the dynamics of a system. This is especially true if a part undergoes many design changes and the FEA package is linked to or part of the CAD package.

Knowing the natural frequency of a part is important when dealing with turbulent fluid flow or rotating machinery because if the natural frequency of a part happens to be close to the frequency of some forcing function that exists within a system the part is likely to fail at loads far below what a static analysis predicts. This occurs due to the fact that if the forcing function matches the natural frequency, the amplitude of the deflection due to the forcing function is magnified with each cycle, eventually leading to failure. This behavior is called resonance and in almost all engineering cases, is a very bad thing.

In the video example above, the first five calculated natural frequencies for the spray lance are 12.7 Hz, 14.7 Hz, 79.1 Hz, 90.4 Hz, and 218.4 Hz. 

As fluids flow across cylinders and other shapes, they can create a regular vortex pattern downstream of the shape. The frequency of these vortices can be expressed using the Strouhal Number which varies primarily as a function of shape and Reynolds number. In this case, the average fluid properties and velocity were used to calculate the Reynolds number across the spray lance to see if it falls within the zone (below Re<300,000) where vortex shedding occurs. In this case, the Reynolds number is approximately 3,600 which is in the vortex shedding zone. At this Reynolds number, the Strouhal Number is approximately 0.21. As a result, the critical velocity where the frequency of the vortex shedding equals the first two natural frequencies are 15.1 ft/s for the first natural frequency and 17.5 ft/s for the second natural frequency. The average velocity along the spray lance was found to be approximately 4.6 ft/s. At this velocity, the frequency of vortex shedding is approximately 3.9 Hz, which is well below the first natural frequency of 12.7 Hz. The fact that the average velocity is well below the first critical velocity suggests that the likelihood for vibration due to the vortex shedding is low.

I'm being overly dramatic, right?

So my last statement was rather extreme: "...there is one rule that MUST NOT be forgotten..." OK, I admit, it does seem rather extreme, but before you rush to judgment, consider two cases:

Case 1: Several years ago, I was involved in modeling a pollution control system. The system was part of a gas turbine power plant and was located after the gas turbine and was designed to remove NOx from the exhaust gas stream. The company where I worked was selling one component of the system and I was using CFD to demonstrate the effectiveness of our equipment. At the same time, the engineering firm designing the system had hired an independent consulting firm to use CFD to model the entire system to help ensure the effectiveness of the finished design. I supplied 3D models of our equipment to the consultant who included my equipment in his model and performed the analysis. When I reviewed the results of the modeling, I discovered that the consultant had incorrectly used a "symmetry" boundary condition. The use of this incorrect boundary condition completely changed the results of the analysis.

OK, the results of this error weren't too bad; it resulted in more time to fix the boundary condition and to rerun the analysis and modify the design. The only cost in this case was money. But what if more than money were at stake?

Case 2: In Chapter 15 of his book To Engineer Is Human, Henry Petroski relates the following incident:

"The two and a half acres of roof covering the Hartford Civic Center collapsed under snow and ice in January 1978, only hours after several thousand fans had filed out following a basketball game..."

Subsequent investigations revealed that the FEA model used to design the structure did not accurately represent the combination of the dead weight of the roof plus the live loads (snow and ice load and other loads) acting on the roof and its supporting structure. This was the result of an incorrect boundary condition being used to model the loading. In the post accident analysis, a computer model showed the failure when the correct boundary conditions were used. Petroski puts in this way: "The computer provided the answer to the question of how the accident happened because it was asked the right question explicitly..." (italics mine). Unfortunately the right question was only known after the accident. If the failure had happened a few hours earlier with the arena filled with spectators, the cost of the failure would possibly have included deaths and injuries to many people.

So once again, I will repeat my statement: There is one rule that MUST NOT be forgotten:

GABAGE IN = GARBAGE OUT

(To read more about this failure: http://matdl.org/failurecases/Building%20Cases/Hartford%20Civic%20Center/hartford.htm)

Never forget GIGO

The field of engineering has been radically changed by the development of the computer. Over the last 50 years computers have shrunk from being the size of a large room to being the size of a deck of cards. Even while the size of computers has continued to shrink, the processing power of computers has increased dramatically. Programs which used to require a super computer can now be performed on a small desktop, or even laptop, computer. As computing power increased, engineers moved from using slide rules to using electronic calculators and then to desktop computers to perform their routine work. 

Today these computers are running advanced software that can solve complex problems that
 were virtually impossible to solve in the past. Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) software are examples of these advanced software packages. Many of these packages include advanced simulation features such as Fluid Structure Interaction (FSI) where stresses and deformations within solids created by a fluid flowing around the solid are calculated and then the effect of the solid upon the fluid is calculated. There are many other examples of sophisticated software being used today to design advanced machines and structures.

No matter how fast a computer can perform operations or how sophisticated the software is or how "pretty" the output from these programs is, there is one rule that MUST NOT be forgotten:

GARBAGE IN = GARBAGE OUT

Keith D. Robinson, P.E.

Welcome to the blog of Keith D. Robinson, P.E., a engineering consultant in Colorado Springs, Colorado. The goal of this blog is to discuss issues that arise in the engineering world and to hopefully provide some useful information to the readers. In general the information will come from the main areas in which I practice engineering but occasionally I will bring in information from outside my usual areas. These main areas will be Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA), Industrial Ventilation, and Process/System simulation.

For more information about me and what I do, please check out my website at www.kdrobinsonpe.com