All predictive methods for flow-induced vibration require an input of the velocity. The stream analysis method (Palen, 1969 and Grant, 1975) provides a procedure for determining the fraction of the total flow in each of five shell-side streams. These streams are the main cross flow, the bundle-to-shell leakage, the baffle-to-shell leakage, the tube-to-baffle leakage, and the bypass stream in any lane due to tube pass partitions parallel to the cross- flow velocity. In most industrial heat exchangers the main cross flow is between 65 and 80% of the total flow. Further, as the shell-side fluid flows through the bundle of tubes, the velocity is constantly changing in magnitude and direction.

A. Cross-flow velocities

The definition of cross-flow velocity u_c used by most investigators of flow-induced vibration is based on the minimum flow area through a tube row perpendicular to the primary direction of flow. See Figure 1. For an ideal tube bank this velocity is well defined. However, for a shell-and-tube heat exchanger it is somewhat ambiguous. As can be seen in Figure 2, the number of tubes in each row varies from baffle tip to baffle tip. In order to be consistent and conservative, the cross-flow velocity for vibration prediction will be based on 80% of the total flow and the minimum gap flow area in a tube row at the position of the exchanger lo be analyzed. This is usually near the baffle tips, where the velocities are highest.

Figure 1 Cap area of cross-flow velocity u_c for various tube field geometries

Figure 2 Cross-flow velocity in segmentally baffled bundle