Longitudinal and transverse structure functions in decaying nearly homogeneous and isotropic turbulence

Streamwise evolution of longitudinal and transverse velocity structure functions in a decaying homogeneous and nearly isotropic turbulence is reported for Reynolds numbers Reλ up to 720. First, two theoretical relations between longitudinal and transverse structure functions are examined in the light of recently derived relations and the results show that the low-order transverse structure functions can be well approximated by longitudinal ones within the sub-inertial range. Reconstruction of fourth-order transverse structure functions with a recently proposed relation by Grauer et al. is comparatively less valid than the relation already proposed by Antonia et al. Secondly, extended self-similarity methods are used to measure the scaling exponents up to order eight and the streamwise evolution of scaling exponents is explored. The scaling exponents of longitudinal structure functions are, at first location, close to Zybin's model, and at the fourth location, close to She–Leveque model. No obvious trend is found for the streamwise evolution of longitudinal scaling exponents, whereas, on the contrary, transverse scaling exponents become slightly smaller with the development of a steamwise direction. Finally, the stremwise variation of the order-dependent isotropy ratio indicates the turbulence at the last location is closer to isotropic than the other three locations.

Fully Developed Turbulence of Power⁃Law Fluids in Circular Pipe Based on Large Eddy Simulation

In this study,Large eddy simulation(LES)of the fully developed turbulence of power⁃law fluids in a circular pipe was performed using the dynamic subgrid⁃scale model.Under a specific Reynolds number,the flow information of three fluids with a range of power⁃law indexes was obtained.The trends of the mean axial velocity and the normalized apparent viscosity were analyzed.Simulation results show that shearing⁃thinning fluid displayed more noticeable non⁃Newtonian characteristics than shear⁃thickening fluid.The predicted friction factors were approximately equal to the Dodge and Metzner correlation and Gomes correlation.The peak values of root mean squares(RMS)and Reynolds stress increased as the power⁃law index increased.The turbulence statistics(skewness and flatness)from the wall to the pipe center were calculated.From the calculated results,the velocity fluctuation near the wall had strong intermittent and asymmetry.As demonstrated by the contours of the normalized instantaneous axial velocity and viscosity,the turbulence was more developed as the power⁃law index increased.It is concluded that the LES is feasible to predict the turbulence of pipe flow under higher Reynolds numbers.

THE APPLICATION AND DEVELOPMENT OF TURBULENCE MODELS IN BUOYANT RECIRCULATING FLOWS

In this paper, a modified κ-ε turbulence model, a simplified algebraic stress model and a developed two-fluid model have been presented based on numerical modeling of turbulent buoyant recirculating flows. The calculated results by these models are in good agreement with experiments. However, the last model is much better for simulating gravity-stratified flows.

THE NUMERICAL PREDICTION OF DEVELOPING TURBULENT FLOW IN 3-D RECTANGULAR DUCTS

Comparisons are made between experimental data and numerical predictions based on the k-e turbulent model of low Reynolds number applicable to developing turbulent flow in rectangular ducts of arbitrary aspect ratio.The numerical procedure utilizes the separated-layers finite-analytical method.The merits of the k-e turbulent model of low Reynolds number and the computation procedure are assessed by means of comparison with results,referred to that of the length-scale model and the full-Reynolds-stress model used in recent years.