Session G11: Boundary Layers: General

Numerical simulation of spiral vortices on sphere rotating around axis parallel to mean flow

Flow characteristics and fluid force on a sphere rotating around an axis parallel to mean airflow were investigated using Large Eddy Simulation at around critical Reynolds numbers of 200,000. As a result of the simulation, a decrease in the numbers of spiral vortices and striped pressure distributions on the sphere were visualized depending on the rotation speed of the sphere even though the sphere is exposed to the same Reynolds number condition. Also, as the rotation speed of the sphere is increased, the relative velocity between the mean flow and the surface of the sphere increased, subsequently, the length of the spiral vortex decreased due to the boundary layer transition on the surface of the sphere. The shift of the separation point depending on the rotation speed is also discussed from the viewpoint of this boundary layer transition on the surface.   

New formulations for the mean wall-normal velocity and Reynolds shear stress in turbulent boundary layer under zero pressure gradient

In this talk, we present a novel analytical solution for the mean wall-normal velocity in a turbulent boundary layer (TBL) under zero pressure gradient (ZPG). The analytical equation is rigorously derived without relying on any ``a priori" assumptions regarding the mean streamwise velocity. By neglecting the higher order terms in the exact solution, an approximate formulation for the mean wall-normal velocity is obtained. The accuracy of this approximation is then validated through a comparison with data from direct numerical simulations (DNS). Drawing upon the distinct behaviors of force balance in the inner and outer regions of ZPG TBL, simplified approximate mean momentum equations are derived by decomposing the Reynolds shear stress into inner and outer parts. The inner and outer Reynolds shear stresses are then obtained through integration of the corresponding approximate mean momentum equations. The outer Reynolds shear stress is revealed to exhibit a strong connection to the mean wall-normal velocity. Specifically, it is observed that $R_{uv-mathrm{out}}/u^2_ au approx 1 - UV/(U_e V_e)$, where $u_ au$ represents the friction velocity, and $U_e$ and $V_e$ denote the mean streamwise and wall-normal velocities at the boundary layer edge, respectively. Finally, an approximate formulation for the Reynolds shear stress across the entire TBL is developed by synthesizing the inner and outer parts. Extensive validation against both DNS and experimental data, spanning a wide range of Reynolds numbers, demonstrates the excellent agreement achieved.   

Large-scale motions of thermal transport in high Reynolds number wall-bounded turbulent flows

Previous studies have found that there is a close correlation between the large-scale motions (LSMs) that mainly contribute to the momentum transport and the LSMs that transport most of the scalar fluxes. In our previous work, we found that LSMs that are responsible for momentum transport are similar to LSMs that transport heat. However, the study was done at a low-Reynolds number turbulent channel flow which does not closely represent actual cases. The proposed study investigates the shape and the size of LSMs in turbulent channel flows for a range of Reynolds. Particular emphasis is given to the physical size of the LSMs that carry most of the heat fluxes. A direct numerical simulation (DNS) databases of a turbulent channel flows up to friction Reynolds number (Re_τ) =5000 are used to visualize the structures. The LSMs are educed by using the three-dimensional iso-surfaces of cross-correlation coefficients of velocity and temperature fluctuations. Three-dimensional structures are computed at the different regions of the boundary layer to observe how the volume of the structures varies with the wall coordinate. This information is important for developing turbulence models and techniques for controlling flow and heat transfer in wall-bounded turbulent flows.   

DNS-informed formulas for temperature distributions and heat fluxes in forced thermal convection

We carry out DNS of forced thermal convection in turbulent pipe flow in a wied range of Reynolds and Prandtl numbers. The observed universaility of the thermal eddy diffusion coefficient is leverage to derive explicit formulas for the mean temperature distribution across the radial direction, and in turn explicit formulas for the heat transfer coefficients, which reproduce the DNS results with great accuracy. The resulting formulas are manipulated to a form similar to the classical form developed by Kader & Yaglom, however providing clear predictive improvement at low Prandtl numbers.