The development of heat transfer correlations from CFD predictions of the thermal performance in complex, non-isothermal horizontal tube bundle geometries

A commercial Computational Fluid Dynamics, CFD, code has been used to compute the thermal performance of a complex tube bundle consisting of a large horizontal constant temperature outer tube containing nitrogen gas and four inner horizontal tubes of different diameters and at different temperatures. The complex nature of the problem means that all modes of heat transfer (conduction, buoyancy driven convection and radiation) are important. Further, the non-linear coupling of the between fluid flow, heat transfer and the imposed thermal boundary conditions results in complex relationships between heat transfer and imposed tube operating temperatures. There are numerous examples, for example, electric power cable bundles and hydrocarbon recovery tube bundles, where there is a need to obtain quick reliable estimates for heat transfer performance, however, CFD computations are non-trivial and time consuming to undertake for these geometries. The work presented in this paper takes the CFD generated thermal performance data and uses them to develop engineering correlations. The parameters in the correlations contain the standard dimensionless numbers (Nusselt, Prandlt and Rayleigh) and dimensionless geometric length scale ratios. It is shown that by careful choice and development of the correlation form, it is possible to achieve a simple (correlation based) predictive method that is capable of providing estimates for the thermal performance of the complex tube bundles which are within 10% of the CFD computed values, irrespective of the thermal boundary conditions imposed. The resultant correlations and their associated standard deviations from the CFD data are presented and discussed. The use of these correlations means that sound engineering calculations can be undertake on a hand calculator or a spread sheet, enabling preliminary designs to be examined and ranked quickly and efficiently, allowing the specialist, expensive and time consuming CFD computations to focus on optimisation of the final tube bundle design.