Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to 13650

Abstract

A numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range 3060 Re θ 13 650. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately 5δ to 6δ long which are meandering with a lateral amplitude of 0.3δ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted C f ,2 , is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that C f ,2 is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength λ x > δ contribute to more than 60 % of C f ,2 , and that those larger than λ x > 2δ still represent approximately 45 % of C f ,2 .

High-fidelity simulations of unsteady civil aircraft aerodynamics: stakes and perspectives. Application of zonal detached eddy simulation

“…They are called very-large-scale motions (VLSM) or superstructures. The role played by these structures in the boundary layer dynamics is still unclear, but Deck et al [11,52] have recently emphasized how significant the contribution of the VLSM to mean wall shear stress is. The computational cost of a WRLES (or quasi-DNS) is extremely expensive because of the very small Figure 9.…”

Riblets Induced Drag Reduction on a Spatially Developing Turbulent Boundary Layer

“…Using the notation of Deck et al [6], the friction coefficient is split as c f = c f ,1 + c f ,2 + c f ,3 . Because of the geometric complexity of our flow, the original FIK's formulation cannot be applied as is.…”

“…The production term 3 and the turbulent diffusion term 6 exhibit profiles almost identical between flat and ribbed plates. The main difference between flows is an enhancement of the dissipation (term 2) in the y + ∈ [6,12] layer. To balance the budget, a tiny downward shift of the production level (term 3) in the viscous sublayer (y + < 6) provides the additional energy.…”

“…Term 1 accounts for the convection by the mean flow. Terms 2 through 5 are production terms: term 2 represents the gradient production and is the enstrophy analogue for the kinetic energy budget term 3 in equation (6). Terms 3 and 4 denote the production (or removal) caused by the stretching of vorticity fluctuations by the turbulent and the mean strain rate.…”

“…A new equilibrium establishes with a weaken turbulence activities. All levels of the turbulent budget (6) are dumped in absolute terms, including the dissipation which has been initially enhanced. As long as the riblets maintain an important level of enstrophy production, the flow budget remains balanced with small turbulence levels.…”