Generalized optimization of cross-flow staggered tube banks using a subscale model

Finding a general optimum arrangement of the cross-flow staggered tube banks causes a significant decrease in using available energy resources due to their extensive use in industrial applications. This paper presents a numerical optimization study by generalized pattern search algorithm (GPSA) to investigate optimum longitudinal and transverse pitches of the staggered tube banks in turbulent flow regime. Symmetric and periodic boundary conditions are employed to simulate all the tube banks without considering the entire volume. Using these boundary conditions, the optimization process can be directly performed by simulating the flow and heat transfer through tube banks with a CFD code and the previous researchers' correlations are not employed in this process. The “goodness factor” which takes into consideration the effects of both heat transfer and pressure drop simultaneously in a proper order is used as the objective function. In the first part of the study, optimum pitches are calculated for specific inlet Reynolds and Prandtl numbers. Subsequently, the effect of both inlet Reynolds and Prandtl numbers are separately investigated on the optimum pitches in the turbulent regime. Results show that the optimum dimensionless longitudinal and transverse pitches of the staggered tube banks are independent of the inlet Reynolds and Prandtl numbers in the turbulent regime and equal to PL, opt ≅ 1 and PT, opt ≅ 1.3, respectively. As a result, a general compact arrangement for staggered tube banks is proposed that is applicable in practical applications due to its high efficiency and compactness.