The influence of thermal boundary conditions on turbulent forced convection pipe flow at two Prandtl numbers. (December 2019)

• Record Type: Journal Article
• Authors: Straub, Steffen; Forooghi, Pourya; Marocco, Luca; Wetzel, Thomas; Vinuesa, Ricardo; Schlatter, Philipp; Frohnapfel, Bettina
• Is Part Of: International journal of heat and mass transfer. Volume 144(2019)
• Publication Date: 2019-12
• Subjects: Thermal boundary conditions -- Low Prandtl number -- Forced convection -- Pipe -- Turbulence; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2019.118601
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Strong effect of boundary condition on Nusselt number for low Prandtl number fluids. Nusselt Number decomposition for forced convection pipe flow. Database of first- and second-order thermal statistics. Abstract: Different types of thermal boundary conditions are conceivable in numerical simulations of convective heat transfer problems. Isoflux, isothermal and a mixed-type boundary condition are compared by means of direct numerical simulations (for the lowest Reynolds number) and well-resolved large-eddy simulations of a turbulent forced convection pipe flow over a range of bulk Reynolds numbers from Re b = 5300 to Re b = 37700, at two Prandtl numbers, i.e. Pr = 0.71 and Pr = 0.025 . It is found that, while for Pr = 0.71 the Nusselt number is hardly affected by the type of thermal boundary condition, for Pr = 0.025 the isothermal boundary condition yields ≈ 20 % lower Nusselt numbers compared to isoflux and mixed-type over the whole range of Reynolds numbers. A decomposition of the Nusselt number is derived. In particular, we decompose it into four contributions: laminar, radial and streamwise turbulent heat flux as well as a contribution due to the turbulent velocity field. For Pr = 0.71 the contribution due to the radial turbulent heat flux is dominant, whereas for Pr = 0.025 the contribution due to the turbulent velocity field is dominant. Only at a moderately high Reynolds number, such as Re b = 37700, both turbulent contributions are of similar magnitude. A comparison of first- and second-order thermal statistics between the different types of thermal boundary conditions shows that the statistics are not only influenced in the near-wall region but also in the core region of the flow. Power spectral densities illustrate large thermal structures in low-Prandtl-number fluids as well as thermal structures located right at the wall, only present for the isoflux boundary condition. A database including the first- and second-order statistics together with individual contributions to the budget equations of the temperature variance and turbulent heat fluxes is hosted in the open access repository KITopen (DOI:https://doi.org/10.5445/IR/1000096346 ).