Nusselt and Reynolds numbers correlation for oscillatory flow of thermoacoustics over heated tube banks

The back-and-forth motion characteristic of the oscillatory flow brings complexity in predicting the heat transfer nature for thermoacoustic wave conditions. Investigating this is crucial as the flow forms the backbone for the thermodynamic cycles of its operation. Often, the steady approximation in calculating heat transfer leads to ambiguity in designing the system. This concern is addressed in this paper via an in-depth analysis of the fluid dynamic behavior and heat transfer characteristics of oscillatory flow within a thermoacoustic framework, spanning experimental works for Reynolds numbers ranging from 300 to 24,000. The investigation focused on a tube bank heat exchanger composed of nine tubes arranged in inline and staggered configurations. Experiments were conducted at constant tube surface temperatures treated at 40 °C and 80 °C, respectively. The distinguishing difference in heat transfer behaviors for oscillatory flow is visualized by the Computational Fluid Dynamics (CFD) models, employing the Reynolds-Averaged Navier Stokes equation with the k-omega turbulence shear stress transport model. The flow never leaves the system, and it cyclically crosses the tubes back and forth with a travel distance that depends on the drive ratio of the flow. The unique nature of the flow forms the foundation for the experimental findings that show a linear relationship between the Nusselt and Reynolds numbers regardless of the configuration of tube banks and tube bank temperature. The Pearson ruler regression analysis was conducted using Matlab R2022b and a Nusselt correlation, Nu = 0.000853RePr⅓, is proposed with a confidence level of 95 %. Notably, the correlation aligns with the constant value known as the Colburn-j factor, with a value of 0.00083. The small Colburn-j value is shown to be the influence of the log-mean temperature difference characteristic of oscillatory flow. It shows a consistent heat transfer process between the heated tubes and surrounding fluid, which is important to sustain the thermoacoustic effect in the system. For future thermoacoustic design, the use of steady heat transfer correlation should be avoided or at least used with caution as the comparative analysis with published works concluded that the Nusselt and Reynolds correlation for steady flow tends to overpredict the heat transfer by two to threefold.