Equivalent Theodorsen Function for Fluidelastic Excitation in a Normal Triangular Array

Fluidelastic instability (FEI) remains the most important mechanism of flow-induced vibrations, which can potentially cause large amplitude vibrations and early failure of nuclear steam generator tubes. In this study, experimental tests are conducted to measure the unsteady and quasi-static fluid forces acting on a normal triangular tube array of $P/D=1.5$ subjected to single-phase (water) cross-flow. The unsteady and quasi-static fluid forces are then used together to estimate the time delay between the central tube motion and fluid forces on the tube itself. The time delay effect for the quasi-steady fluidelastic instability model is derived in the frequency domain in the form of an Equivalent Theodorsen Function. The results are compared to the first Equivalent Theodorsen Function developed for rotated triangular array by Li and Mureithi (2017, “Development of a Time Delay Formulation for Fluidelastic Instability Model,” J. Fluids Struct., 70, pp. 346–359). Using the Equivalent Theodorsen Function, a stability analysis is carried out to predict the critical velocity for fluidelastic instability in a normal triangular array subjected to single-phase flow. The predicted stability threshold is consistent with previous published experimental data. The results show that the normal triangular array is more stable than the rotated triangular array.