Session Q38: Turbulence Theory of Wall Bounded Flows

Scale-resolving PANS simulations of turbulent boundary layers

Scale-resolving simulation (SRS) of the turbulent flat-plate boundary layer (TFPBL) is performed using the partially averaged Navier-Stokes (PANS) approach. The focus of the current study is to examine the ability of PANS method to accurately capture turbulent structures and two-point correlations in wall-bounded flows. The dependence of simulated statistics and flow structure effect on inflow boundary conditions is also examined.  Wall-resolved PANS (WR-PANS) method has already been shown to effectively capture flow structure in turbulent channel flows when periodic boundary conditions are employed. The current study demonstrates that PANS in conjunction with recycling/rescaling inflow field not only accurately recover the lag-law behavior but also captures  higher-order statistics and flow structures of TFPBL. The development of Tollmien-Schlichting (TS) waves and  transport of momentum through the ejection and sweep mechanisms are reasonably simulated in the near-wall region. Overall, it is shown that PANS performs well in wall-bounded turbulent flows at a reasonable computational expense.   

On the log law and the hydraulic diameter

We develop predictive formulas for friction resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress nonuniformities. The traditional hydraulic diameter naturally emerges from the analysis as the controlling length scale for common duct shapes as triangles and regular polygons. The analysis also suggests that a new effective diameter should be used in more general cases, yielding corrections of a few percent to friction estimates based on the traditional hydraulic diameter. Fair but consistent predictive improvement is shown for duct geometries of practical relevance, including rectangular and annular ducts, and circular rod bundles.

Wall-attached and wall-detached motions in wall-bounded turbulent flows

The Townsend's attached eddies hypothesis (AEH) has received a lot of attentions in recent years. While wall-attached eddies are responsible for a number of important processes in wall-bounded turbulence, the detailed statistical behavior and many flow quantities can not be explained using only the AEH and only wall-attached eddies. A decomposition of the flow to wall-attached and wall-detached motions is useful in this context. This study presents a decomposition methodology, where inner motions are separated from outer motions. Wall-attached motions are "small-scale" outer motions, whose sizes are bounded by the local distance from the wall and the boundary layer height. The "large-scale" outer motions, on the other hand, are wall-detached motions, whose statistical behaviors are not modeled by the AEH. The decomposition methodology is used for channel, boundary layer and atmospheric surface layer flows. While there is no general theory for the outer, wall-detached motions, the statistical behaviors of wall-attached motions are very well captured by the AEH.   

Skin friction measurements and predictive correlations for systematically-varied roughness

Skin-friction, roughness functions and predictive correlations are presented for random roughness that have a Guassian distribution of roughness scales. The root-mean-square (rms) roughness height and the skewness of the probability distribution function are parametrically changed to investigate the role of these parameters in the creation of frictional drag. Results are presented for all roughness regimes, from hydraulically-smooth to fully-rough. Most surfaces follow a roughness function similar to the one developed by Nikuradase for uniform sand-grain. Predictive engineering correlations for the equivalent sandgrain roughness height indicate that the rms roughess height and skewness are important scales, however, different correlations are needed for surface roughness with positive, negative and zero skewness.   

Exact coherent states of attached eddies in channel flow

Exact coherent states in shear flows take the form of a travelling wave, and their unstable manifolds are believed to form a skeleton for the dynamics of turbulence.  We present a new set of exact coherent states that we have numerically continued up to Re=30000, and which show several properties associated with Townsend's attached eddy hypothesis.  These states are wall-attached, show self-similar scaling with spanwise wavelength, and asymptotic scaling with wall-units as Re is increased.  For large Re these states appear via a saddle-node bifurcation with spanwise wavelength $L_z^+\approx 50$ and phase speed $c^+\approx 11$.  These results suggest that as Re is increased, new sets of self-sustaining structures are born in the near-wall region, while those that emerged earlier continue into self-sustaining structures in the logarithmic region.