Development of Models Correlating Vibration Excitation Forces to Dynamic Characteristics of Two-Phase Flow in a Tube Bundle

Abstract

Recent experiments reveal that somewhat unexpected but significant quasi-periodic forces in both the drag and lift directions existed in a rotated triangular tube bundle subjected to two-phase cross flow. The quasi-periodic drag forces appear to be related to the momentum flux fluctuations in the main flow path between the cylinders. The quasi-periodic lift forces, on the other hand, are mostly correlated to the oscillation in the wake of the cylinders. The objective of this work is to develop semi-analytical models for correlating vibration excitation forces to dynamic characteristics of two-phase flow in a rotated triangular tube bundle and understanding the nature of vibration excitation forces. The relationships between the lift or drag forces and the dynamic characteristics of two-phase flow are established through fluid mechanics momentum equations. A model has been developed to correlate the void fraction fluctuation in the main flow path and the dynamic drag forces. A second model has been developed for correlating the oscillation in the wake of the cylinders and the dynamic lift forces. Although still preliminary, each model can predict the corresponding forces relatively well.

Two-phase flow induced vibration in piping systems

“…Proposed correlations were comparable to the experimental data obtained in the range specified by the authors. Study performed by Zhang et al (2008) also compared the relationship between two-phase momentum flux and flow induced vibration. Authors conducted two-phase FIV experiment on cylindrical rod arrays placed within the rectangular flow channel.…”

Correlation Between Vibration Excitation Forces and the Dynamic Characteristics of Two-Phase Flow in a Rotated Triangular Tube Bundle

“…Detailed flow and vibration excitation force measurements in tube bundles subjected to two-phase cross flow are required to understand the underlying vibration excitation mechanisms. Some of this work has already been done by Pettigrew et al [12] and Zhang et al [13][14][15][16]. The distributions of both void fraction and bubble velocity in rotated-triangular tube bundles were measured and somewhat unexpected but significant quasi-periodic forces in both the drag and lift directions were observed [12].…”

“…recently, as in Refs [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. However the understanding of the physical mechanism that induces these forces is not yet reached.…”

“…The first one, F Blbm , rs (t)is due to momentum change at the surface (inlet and outlet), and the second one, F ElbowYV {t) is due to momentum change within the volume of the elbow. sm(-+-r)dt (7)(8)(9)(10)(11)(12)(13)(14) We now define the Fourier Transform of F ElbowYS {t) as F Elb<mrs (co), where ^o., ra (^) = 7^w,n(0^^ = ^^C/ 2^( «)(ie -^) (7)(8)(9)(10)(11)(12)(13)(14)(15) and F*<co) is the complex conjugate of F EI , rs (m), thus ^W,«(«) =^/7 i t/^«*(fl,)(l-^) (7)(8)(9)(10)(11)(12)(13)(14)(15)(16) The PSD of F ElbowJS (t), s F (f ± )can be expressed as: -or(^K(w)(l-e-^)(l-e^)…”

“…f) 3U (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) Similarly, the Fourier Transforms of F Elbowjy (t) ^F m<mjr (co). F* Elbow , YV {co) is the conjugate of F Elbowjr <<o).…”