Simulations of zero pressure-gradient turbulent boundary layers over riblets

TL;DR

This work investigates how zero-pressure-gradient turbulent boundary layers respond to streamwise step changes between smooth walls and riblets, focusing on drag-increasing triangular riblets with $s^+ \approx 50$. It employs large-eddy simulations with a novel grid-generation strategy for unstructured spectral-element codes and an inflow precursor to realize a ZPG TBL over riblets, enabling controlled step-change experiments. The study reveals that the internal equilibrium layer thickness $\delta_{IEL}$ grows to $0.4\delta_0$ within $4$–$12\delta_0$ depending on transition direction, but the wake remains history-locked (frozen) and the skin-friction coefficient $C_f$ does not reach its equilibrium value even at $\sim 45\delta_0$. These findings highlight persistent history effects in riblet-textured boundary layers and inform both drag predictions and the modeling of texture transitions in engineering applications, with implications for riblet design and flow-control strategies. $Re_{\theta,0} \simeq 680$ and $Re_\tau \simeq 283$ characterize the upstream state, while the flows evolve toward $Re_{\theta} \sim 1000$ downstream.$

Abstract

We computationally study the response of zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs) to streamwise step changes from a smooth wall to riblets (S-R), and vice versa (R-S). We consider triangular riblets with tip angle $90^o$ (T9), that increase drag, with viscous-scaled spacing $50$. A novel grid-generation approach is developed for unstructured spectral-element codes, consistent with the size of turbulent scales across the TBL. We generate a ZPG TBL upstream of the step change (with thickness $δ_0$) with momentum thickness Reynolds number $Re_{θ_0} \simeq 680$. The TBL departure from equilibrium due to the step change, and its subsequent relaxation, recall previous studies on step changes in surface roughness. Downstream of the R-S step change, the internal equilibrium layer thickness $δ_{IEL}$ reaches $0.4 δ_0$ within $12δ_0$. However, downstream of the S-R step change $δ_{IEL}$ reaches $0.4 δ_0$ within $4δ_0$. In all cases, $δ_{IEL}$ does not reach the boundary layer thickness, even up to a distance of $45δ_0$ downstream of the step change, owing to persistent history effects within the frozen wake region.

Figures (7)

• Figure 1: Mean velocity profiles for the cases from Table \ref{['tab:channel']} compared with the reference data of Endrikat et al. (2021). The shaded region ($y^+ > 100$) is discarded from comparison, as the profiles of Endrikat et al. (2021) are from a reduced-domain channel flow simulation.
• Figure 2: (a) Flow setup and visualization for the case T9_SM. (b) Mean velocity profiles upstream of the step change ($x = -4 \delta_0$) for the T9_SM and SM_T9 cases (lines); the profiles are compared with ones from the smooth-wall ZPG TBL of Schlatter et al. (2009), and T950_fine case from Table \ref{['tab:channel']}.
• Figure 3: Visualisation of the grid for the case T9_SM on an $yz$-plane as well as over the riblets and smooth surfaces near the step change. The viscous-scaled spanwise grid size $\Delta^+_z$ is reported at different viscous-scaled wall-normal distances $y^+$; $\delta^+_{400}$ is the viscous-scaled boundary layer thickness at $Re_\tau = 400$ (i.e. $\delta^+_{400} = 400$).
• Figure 4: Streamwise variations of (a) $Re_\theta$, and (b,c) $C_f$ for the T9-to-smooth step change. In (a,b) the smooth case (SM) is added as a reference. In (c), $C_f$ for T9_SM is normalized by $C_f$ from the smooth case ($C_{f_\mathrm{SM}}$) at matched $Re_\theta$; rough-to-smooth step change data of Rouhi et al. (2019) (Ref. DNS) and Li et al. (2019) (Ref. EXP).
• Figure 5: Same quantities as Figure \ref{['fig:fig4']} but for SM_T9 step change. In (a,b) the T9 case is added as a reference. In (c), $C_f$ for SM_T9 is normalized by $C_f$ from the T9 case ($C_{f_\mathrm{T9}}$) at matched $Re_\theta$; smooth-to-rough step change data of Rouhi et al. (2019) (Ref. DNS).