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a b s t r a c tFully developed turbulent flows of power-law fluids in a cylindrical stationary pipe are investigated numerically by the use of large eddy simulation (LES) for various power law index (0:5 6 n 6 1:4) at different Reynolds numbers (4000 6 Re s 6 12,000). To validate the present computations, the predictions are compared to the results reported in the archival literature for laminar and turbulent flows. The LES predictions agree reasonably favourably with the findings of the literature. The log-region of the mean axial velocity profile expands with increasing Re s and decreasing power-law index n. The predicted friction factor for n 6 1 at Re s ¼ 4000 is slightly overestimated in comparison with Dodge and Metzner correlation, and is better interpolated by Gomes correlation. With increasing n the apparent viscosity increases close to the wall and decreases for y þ > 30. This implies that the turbulent fluctuations develop and are more intense further from the wall when n > 1 and closer to the wall when n < 1. The influence of Re s and n on the higher-order statistics (skewness and flatness) is analyzed. Visualizations of the instantaneous filtered velocity fields exhibit turbulent patterns which develop more as n increases.

The Large Eddy Simulation (LES) of two-phase flows with resolved scale interfaces is investigated through the a priori filtering of Direct Numerical Simulations (DNS) of one-fluid and multifield models. A phase inversion benchmark [1][2][3][4] is considered highlighting many coalescence and interface rupture events in a kind of atomization process. The order of magnitude of specific two-phase subgrid LES terms is first considered with the two modeling approaches. Then, different existing models such as Smagorinsky [5], Wall-Adapting Local Eddyviscosity (WALE) model [6], Bardina [7], Mixed [8] and Approximate Deconvolution Model (ADM) [9] are used to account for two-phase subgrid effects. These models are compared to filtered DNS results. The main conclusion concerning a priori LES filtering is that the inertia term is not predominant in two-phase flows with fragmentation and rupture of interface. This conclusion is different from that of the studies of [3,[10][11][12][13]. concerning LES models, functional modeling do 1 not correlate to filtered DNS results whereas structural approaches do. Bardina and ADM are clearly the good LES framework to consider for two-phase flows with resolved scale interfaces. ADM is clearly better than Bardina in our study. The authors greatly acknowledge the reviewer for its comments and remarks that have guided us in improving the technical and editorial aspects of the manuscript. From a general point of view, all the comments and remarks recommended by the reviewer have been taken into account. They are highlighted in the text in red. More specifically, we can detail them as follows: COMPUTERS & FLUIDS 1) I would recommend to add the main conclusions to the abstract and to add a separate section conclusions to the paper.In agreement with reviewer remark and in order to improve the fast reading and understanding of the paper, we have included a conclusion part in the abstract. In addition, the last section have been extended to "Summary, conclusion and future work", with addition of conclusions in order to highlight the originality and main results of the work. 2) Abstract : DNS and ADM should be defined.Done. The same has been achieved for the Wall-Adapting Local Eddy-viscosity (WALE) model. 3) A streak of the interface points towards the upper left corner of the box. Is that physical?Yes, this a physical feature of the interface. As we are dealing with liquid-liquid twophase flows, when the light fluid (blue surface) goes to the top part of the cavity under gravity effects, heavy liquid can be trapped near vertical walls or vertical corners, inducing this king of interface topology.4) The sentence "Among the few existing …" seems to have a grammar mistake. Detailed Response to ReviewersThis sentence has been rewritten as follows "Among the few existing references, it is worth mentioning the work on LES formulation for the one-fluid model and subsequent a priori LES filtering of DNS simulations for the estimate of new specific two-phase contributions in the mass, momentu...

Heat flux ratio effect Turbulent heat transfer Fully developed annular pipe flow a b s t r a c t Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, d ¼ ðr 2 À r 1 Þ=2, and the laminar maximum velocity is Re d ¼ 3500. A Prandtl number Pr ¼ 0:71 and a radius ratio r à ¼ 0:1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q à ¼ q 1 =q 2 , on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q à ¼ 1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q à on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q à varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q à from 1 to 100, lead to opposite trends.