# CFD Vortex Shedding for Performance: Simulations and Analysis of Induced Vibrations

### Key Takeaways

• What vortex shedding is.

• An overview of vortex shedding and fluid-structure interactions (FSI).

• Applying CFD vortex shedding techniques. Vortex formed in a fluid

Vortices are one of Mother Nature’s fairly common creations that still invoke wonder and awe. Although we know what these occurrences are, we are often surprised and unprepared when they formulate. We can readily identify hurricanes, tornadoes, and even black holes; however, pinpointing exactly where they will materialize is a bit more elusive. Being able to prevent their effects--in the case of earth-borne vortices--is even more daunting.

Unpreparedness in systems design, however, can lead to disastrous results, as vortex-induced vibrations (VIVs) at or near the resonant frequency of a structure may cause degradation or even failure. Therefore, it is important to understand these phenomena that occur within fluid systems. The best means for performing this is by employing CFD vortex shedding analysis that necessitates advanced functionality and capabilities.

## What Is Vortex Shedding?

An example of a vortex shedding simulation is shown in the figure below. CFD vortex shedding simulation streaklines example

As shown, the vortex was formed by the fluid flowing past a square object or opening in the flow medium. The introduction of this barrier to normal flow causes a vortex to form temporarily around an axis line--that may be a straight line or curved. As flow continues beyond the barrier, the vortex begins to shed, which can cause oscillations within the fluid that creates pressure, velocity differences, and vibrations within the medium. These vortex-induced vibrations (VIVs) can be harmful and, if severe enough, may even cause structural deformation.

## CFD Vortex Shedding and Fluid-Structure Interactions

For the case of a flow around a circular cylinder, vortex formulation and behavior can be somewhat predicted according to the Reynolds number for the fluid, as shown in the figure below. Vortex behavior vs. Reynolds number. Image source: Fundamentals of Vortex-Induced Vibration

Knowing whether the fluid flow is laminar or turbulent is important. However, it is also important to understand what happens at the boundaries between fluids and structures. This fluid-structure interaction (FSI) can be defined as follows:

 Fluid-structure interaction (FSI) refers to the activity that occurs when a moving fluid surrounds or flows through a non-rigid and/or elastic structure. These interactions, which may be oscillatory, can cause structural fatigue and early system failure.

FSIs due to vortex shedding may introduce shear stress and strains in the fluid and have the effects listed in the table below.

 EFFECTS OF FLUID-STRUCTURE INTERACTIONS Structure Deformation Time Variations Effects Analysis Small Slow Minimal deformation Structural stress Small Fast Pressure waves and sound vibrations Acoustic-structure interaction analysis Large Fast Pressure and velocity field changes Multi-dimensional: fluid flow and pressure on deformations and deformations on fluid flow and pressure

As shown in the table above, the type of analysis necessary varies according to the degree of deformation and time variation--not to mention the material properties of the structure. However, it is also important to know the properties--pressure, viscosity, velocity, etc.--of the fluid to develop and/or design a solution for the system.

## CFD Vortex Shedding Analysis Techniques

In most cases, the best tool for analysis of fluid flow systems is the Navier-Stokes equation, given below for a compressible Newtonian fluid.

F(i) = F(p) + F(v) + F(e)

Note that F(i) are the internal forces, F(p) are the pressure forces, F(v) are the viscous forces, and F(e) are the external forces.

In mathematical symbol form, the equation is: Navier-Stokes equation

Typically, this equation is solved with the continuity equation: Continuity equation

Together, the Navier-Stokes and continuity equations serve to uphold the important concepts of conservation of momentum and conservation of mass, respectively. When solving the Navier-Stokes equations, the objective is to determine the fluid velocity, pressure, and other properties all around and upon the system geometry. For simple systems, such as a circular pipe or parallel plate, determining these parameters is fairly straightforward. However, for more complex fluid analysis, software tools are typically invoked to find solutions.

Performing CFD vortex shedding analysis necessitates that you utilize an advanced solver with the ability to solve complex mathematical models accurately, such as from Cadence’s Omnis. CFD analysis tree capabilities with Cadence tools

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