The influence of pipe length on thermal statistics computed from DNS of turbulent heat transfer

We present results from direct numerical simulation of turbulent heat transfer in pipe flow at a bulk flow Reynolds number of 5000 and Prandtl numbers ranging from 0.025 to 2.0 in order to examine the effect of streamwise pipe length (πδ ≡ πD/2 ⩽ L ⩽ 12πδ) on the convergence of thermal turbulence statistics. Various lower and higher order thermal statistics such as mean temperature, rms of fluctuating temperature, turbulent heat fluxes, two-point auto and cross-correlations, skewness and flatness were computed and it is found that the value of L required for convergence of the statistics depends on the Prandtl number: larger Prandtl numbers requires comparatively shorter pipe length for convergence of most of the thermal statistics.

► Study of effects of streamwise periodicity on turbulent heat transfer in pipe flow.
► Streamwise periodic length for convergence depends on the type of statistics and Pr.
► Explain the reasons for variation of thermal statistics in published literature.
► All statistics seem to converge with DNS carried out with a pipe length of 8πδ.