A new criterion for the instability threshold of a square tube bundle subject to an air–water cross-flow

In this paper, we investigate the fluid-elastic instability of a square tube bundle subject to two-phase cross-flow. A dimensional analysis is carried out, leading to a new criterion of instability. This criterion establishes a direct link with the instability thresholds in single-phase flows. In parallel to the dimensional analysis, experimental work is carried out to i) determine the instability thresholds in single-phase flows (new relation between the Scruton, Stokes and Reynolds number), ii) to test the validity of the two-phase flow instability criterion, derived from the dimensional analysis. The experiments are carried out on a square tube bundle (pitch ratio of 1.5) consisting on 5 rows of 3 tubes (plus two end-rows of half tubes). The central tube is mounted on two flexible blades allowing a vibration in the transverse direction only, whereas all the other tubes are rigid. The instability threshold in single-phase (water) flow is obtained from a method of direct measurement of the fluid-elastic forces, in which the motion of the central tube is imposed. The instability threshold in two-phase (air–water) flow is obtained from a method of indirect measurement, with an active system stability control, of the fluid-elastic forces, in which the central tube vibrates freely. Three sets of blades with different stiffnesses are tested to investigate the stability of the central tube. The criterion of instability is in very good agreement with air–water experiments, predictive for all homogeneous void fractions, and so for all flow regimes (identified in our experiments with an optical probe). This new criterion is of theoretical interest for the understanding of complex two-phase flow excitations, as well as of practical significance for the predictive analysis of industrial components.