Experimental estimation of equivalent loads on upward two-phase crossflow in tube bundles via Kalman filtering

Abstract

Tube bundles of heat exchangers are permanently exposed to flow-induced forces, which may lead to high amplitude vibrations compromising the lifetime. In this context, Flow-induced vibration (FIV) is the most crucial dynamic issue to deal with in the design and operation of shell-and-tube heat exchangers. The experimental investigation of FIV requires determining the nature of flow-induced forces and their consequences, which are given by the characteristics of tube vibration. However, the measurement of flow-induced forces is challenging due to space restrictions within a tube bundle and their intrinsic spatially-distributed nature, often represented by equivalent point forces. The present work aims to estimate the equivalent flow-induced forces in tube bundles due to two-phase crossflow using Virtual Sensing principles. In order to do that, a device is designed and constructed to replace a tube within a normal triangular (transversal pitch to diameter ratio of 1.26) tube bundle, which is subjected to two-phase flow with void fractions ranging from 30% to 95% and a wide range of mass velocities. The device is instrumented with two couples of accelerometers and strain sensors, aligned with drag and transverse directions. The measured dynamic responses are discussed in terms of void fraction, mass velocities, and flow patterns. The results confirm the severity of FIV under Intermittent-type flow patterns. Further, the equivalent force estimation is performed via the Augmented Kalman Filter (AKF), which requires a model approximation (based on EMA techniques) and the system’s outputs. The values of the input covariance matrix are determined through the L-curve regularization method. Finally, the quality of the estimated equivalent force is tested by simulating system accelerations, whose RMS values are compared with measured data. The results suggest better acceleration predictions in the transverse direction than in the main flow direction for relatively low mass velocities and Bubbles flow pattern.