When Theodor von Kármán first discovered vortex shedding in 1911, he likely had no idea how pivotal his work would become for modern engineering, particularly in heat exchanger design. Vortex shedding, a phenomenon in fluid dynamics, has since emerged as a critical factor in maintaining the structural integrity and efficiency of these essential systems. Despite its importance, many remain unaware of the significant risks it poses.

At DRG, through extensive analysis of heat exchangers across multiple projects, we’ve consistently identified a common yet often overlooked challenge: the impact of vortex shedding. As fluid flows around the tubes in a heat exchanger, oscillating forces are generated, leading to flow-induced vibrations (FIV). If not properly accounted for, these vibrations can cause excessive tube displacement, ultimately leading to fatigue-related failures, unplanned downtime, and costly repairs.

In this article, we explore the technical aspects of vortex shedding and its impact on heat exchanger design. We will expand on the key parameters that influence vortex shedding frequency, such as the Strouhal number, fluid velocity, and tube diameter, while also examining the complexities of analyzing these effects in real-world applications. By understanding these dynamics, you will better mitigate the risks and enhance the reliability of heat exchanger systems.

## Vortex Shedding Frequency and Its Role

*V*, the characteristic size of the object (in this case, the diameter

*D*of the tube), and the Strouhal number through the following relationship:

- ${f}_{s}$ is the vortex shedding frequency,
- ${S}_{t}$ is the Strouhal number (typically between 0.2 and 0.3 for cylindrical tubes),
- $V$ is the fluid velocity past the tube,
- $D$ is the diameter of the tube.

**natural frequency**$f{n}_{}$ of the tubes, which can be calculated as:

- ${f}_{n}$ is the natural frequency of the tube,
- $k$ is the stiffness of the tube,
- $m$ is the mass per unit length of the tube.

**resonance**can occur, amplifying the vibrations to dangerous levels.

## Complexities of Vortex Shedding Analysis in Heat Exchangers

Analyzing vortex shedding in heat exchangers presents significant challenges due to the complex flow patterns and interactions involved. Several key factors contribute to the complexity of vortex shedding analysis:

**Tube Bundles and Interactions**: In most heat exchangers, tubes are organized in bundles, and as fluid passes through, it generates irregular vortex shedding, often leading to tube-to-tube interactions. These interactions can induce vibrations, particularly in tightly packed tube bundles, increasing the potential for damage**Cross-flow and Mixed-flow Configurations**: Heat exchangers often have different flow configurations (cross-flow, parallel flow, or counter-flow). In**cross-flow**, for example, fluid passes perpendicular to the tubes, enhancing the vortex-shedding effect. Multiple rows of tubes increase flow disturbances and the likelihood of**fluid-elastic instability**, where feedback between the fluid and tube vibrations causes escalating oscillations.**Non-linear Effects**: In real-world applications, fluid-structure interactions are highly non-linear. Damping mechanisms, turbulence, and variations in flow velocity introduce complexities that make vortex shedding difficult to predict accurately with basic models. Computational fluid dynamics simulations are often used to capture these non-linear interactions and predict the risk of failure.**Thermal Expansion and Tube Wear**: Over time, tubes in a heat exchanger can undergo thermal expansion, corrosion, and wear, which alters their stiffness and mass distribution. This, in turn, affects their natural frequency and susceptibility to vortex shedding-induced vibrations.

Accurate prediction of vortex shedding behavior is essential to avoid system failures. CFD simulations play a crucial role in understanding these complex interactions and ensuring the long-term reliability of heat exchangers.

## Simulation Approaches for Vortex Shedding in Heat Exchangers

To accurately predict vortex shedding and assess its potential to cause failures in heat exchangers, engineers at DRG rely on Computational Fluid Dynamics. CFD plays a crucial role in modeling the behavior of fluid as it flows around the tubes, allowing engineers to predict where and how vortices will form. By solving the complex partial differential equations of fluid mechanics, CFD provides detailed insights into flow patterns, turbulence, pressure distribution, and the forces acting on the tubes.

One of the major advantages of CFD is its flexibility in simulating various design conditions. Engineers can easily adjust parameters such as the number of tubes, their arrangement, and the spacing between them. These variations are critical because the configuration of the tubes significantly influences how the fluid interacts with the structure, which in turn affects the likelihood and intensity of vortex shedding.

After identifying the forces generated by fluid flow, engineers perform a comprehensive stress analysis to evaluate whether the loads on the tubes are within acceptable limits. This analysis helps determine whether the system has the necessary structural integrity to withstand the forces and prevent potential failures caused by excessive vibrations. CFD simulations, therefore, provide engineers with both the predictive capabilities and the design flexibility needed to ensure the safe and reliable operation of heat exchangers.

*Author: Uri Peker, Engineer at Dynaflow Research Group*