Training case study: Vibration concern in U-tube reactor effluent cooler—beyond initial screening

Andy Mountford, Senior Technical Lead, Training
Peter Joosten, Manager, Technical Support

In this case study, a TEMA DEU heat exchanger design must cool high pressure reactor effluent from 180 °C to 40 °C. The corrosive reactor gas is assigned to the tube side, with cooling water on the shell side. The cooling water inlet nozzle is located at the U-bend. A circular impingement plate is specified in accordance with TEMA ρV² guidelines. The bundle has parallel-cut double-segmental baffles to meet the shellside pressure drop limit, and sealing devices are specified in the baffle overlap regions to mitigate flow bypassing (Figure 1).

Figure 1. Geometry of reactor gas cooler and Xist^® 2D Tube Layout drawing showing Xvib^® velocity states

A positive overdesign is calculated for the proposed geometry, and the Xist Vibration Analysis shows a clean bill of health (Figure 2). A natural frequency of 74.8 Hz is reported for the U-bend. However, the program considers the lowest straight span natural frequency (225.2 Hz) in all vibration checks, resulting in a calculated FEI of 0.286 in the bundle entrance region (i.e., at the U-bend).

Figure 2. Sections of Xist Vibration Analysis: Tube natural frequencies and bundle and shell entrance/exit checks

Based on these results, the design appears to be acceptable. However, a runtime warning (Figure 3) signals that the longest unsupported span is in the U-bend, reducing confidence in the Xist vibration screening. If the geometry cannot be modified, assessment with Xvib is recommended.

Figure 3. Xist runtime warning regarding longest unsupported span

Figure 1 shows the Xvib velocity states in the Xist 2D Tube Layout.¹ This bundle configuration features fourteen unique combinations of velocity and tube support. New functionality in Xist 9.3 permits single-click consolidation of multiple Xvib analyses into a single Xvib file for simultaneous analysis of all velocity state combinations. Figure 4 shows the Xvib Output Summary for this case. Tubes 5, 7, 8, and 11 have velocity to critical gap velocity (FEI) ratios greater than 1, and tubes 8 and 11 have vortex shedding amplitudes greater than half the tube gap.

Figure 4. Xvib Output Summary for the reaction gas cooler

The higher vibration potential for tubes 8 and 11 (FEI > 2.5) is due to their proximity to the impingement plate edge. Applying a scaled Xist nozzle velocity to the bundle entrance span of these tubes captures possible flow jetting at the plate edges. Tubes 5 and 7 are also expected to suffer vibration damage (FEI = 1). None of the four highlighted tubes are (fully) supported in the first baffle, and the resultant unsupported span length is the longest in the bundle. The calculated fundamental natural frequency for these tubes is the lowest in the bundle at 54 Hz—significantly below the 225 Hz used in the Xist analysis. This lower frequency results in a higher log decrement (0.1 vs. 0.038 in Xist) due to increased squeeze film damping from the longer time available for liquid compression in the tube-baffle gap. For a water exchanger, a log decrement near 0.1 appears more realistic.

The results of this case study indicate that more support should be added to the U-bend region, or a full support should be installed at the U-bend tangent with the cooling water inlet nozzle relocated to the straight portion of the bundle. If the Xist warning regarding the longest unsupported span is ignored or the Xvib analysis is not conducted, the design might proceed to manufacturing, potentially leading to costly tube failures in the U-bend region.

Footnote

¹ Definitions of each velocity state (i.e., each tube color) are given in the legend of the 2D Tube Layout Drawing in Xist.