Session Q07: Boundary Layers: Turbulent Boundary Layers III

Spectral and Coherence Analyses of wind-LiDAR measurements collected in the Atmospheric Surface Layer for detecting the k-1 spectral region

In the realm of wall-bounded turbulence, the k^-1  law of the streamwise-velocity spectrum ( is the wavenumber) has been ascribed to the statistical presence of wall-attached eddies. However, previous investigations have shown puzzling results for the identification of the spectral boundaries of the k^-1 region, and their flow-based definition is still elusive. Investigations of coherent turbulent structures present in turbulent boundary-layer flows require a large scale-separation, and, thus, a high-Reynolds number flow, which makes the atmospheric surface layer (ASL) a unique environment to investigate wind-generated turbulence. In this work, wind-LiDAR measurements collected within the ASL are leveraged to estimate the spectral boundaries of the k^-1 region with two approaches: the first one is based on piece-wise modeling of the streamwise-velocity spectrum, while the second one is based on the coherence analysis of the streamwise velocity. The findings of this work include a generalized modeling of the linear coherence of the streamwise velocity, the estimate of the maximum height where the k^-1 region is detectable, and the vertical profiles of attached- and detached-eddy contributions to the streamwise turbulence intensity.    

An Experimental Investigation of the Influence of Superhydrophobic Surfaces on Turbulent Boundary Layer Separation

We investigate the separation of a turbulent boundary layer (TBL) in an adverse pressure gradient over a convex backward facing ramp coated with a superhydrophobic surface (SHS). Past research has shown that the location of TBL separation can be modified by the increased skin friction over a rough surface. SHSs in specific cases have been shown to also be effective in modifying the skin friction in a TBL. In our experiment, we investigate the influence of an air infused SHS-induced reduction in skin friction on the location of TBL separation. A TBL develops over a flat plate in a water tunnel, reaching a Reynolds number based on fetch distance on the order of Re_x ≈ 10⁶. The developed boundary layer then separates in an adverse pressure gradient as it flows over a diverging ramp with a constant radius of 127mm. The location of separation on the ramp is compared for the cases with and without an SHS coating, and the flow is characterized by particle image velocimetry (PIV).   

A novel mean shear stress model and its application in pressure gradient turbulent boundary layers

The mean shear stress is one of the most important quantities of interest in turbulent boundary layers (TBL). Kumar and Mahesh (Physical Review Fluids, 6(2), 024603, 2021) developed a model for the mean shear stress in a zero pressure gradient TBL using the governing equations for the mean flow. They derived a relation between the mean total stress and the mean velocity, containing an unknown term, which was modeled using existing TBL data. Their model requires the wall-normal mean velocity profile, which requires modeling if not available. Hence, they also provided a compact fit for the mean wall-normal velocity using scaling arguments and existing data. Both models showed good agreement with reference data for a range of Reynolds numbers. The present work incorporates pressure gradient effects in the mean shear stress and wall-normal velocity models. The proposed models show good agreement with a variety of existing pressure gradient TBL data. Finally, the shear stress model is used to devise a method to indirectly determine friction velocity without requiring any data from the bottom 20 percent of TBL. The accuracy of the proposed method is evaluated for a variety of zero and pressure gradient TBL.    

Streamline coordinate analysis of the flow past an axisymmetric body computed by large-eddy simulation

Turbulent boundary layers with streamline curvature are ubiquitous in engineering applications, and the flow around axisymmetric bodies is further complicated by transverse curvature. We analyze results of wall-resolved large-eddy simulation of an axisymmetric hull in an orthogonal coordinate system defined by streamlines and streamline-normal lines. The numerical algorithm used in the present work is based on the unstructured overset method developed by Horne and Mahesh [J. Comput. Phys (2019) 397: 108790]. Equations in the streamline coordinate frame reduce to the Bernoulli equation and the Euler equation for curved streamlines away from the body and provide insight into the momentum balance within the boundary layer.   

Non-equilibrium turbulent boundary layer with adverse pressure gradient and convex wall curvature

Direct numerical simulations (DNS) of flows over an airfoil (suction side) and a flat plate are compared to characterize the effect of wall curvature on a turbulent boundary layer and generate data for acoustic model development for fan applications. The two cases have matched adverse pressure gradient (APG) quantified by the acceleration parameter ($K=(ν/U_∞²)(dU_∞/dx_s)$). For the airfoil flow, an existing DNS carried out by Wu et al. {Journal of Fluid Mechanics}, 868:584-610 (2019) of the flow around a controlled-diffusion (CD) airfoil is used.  For the flat-plate flow, a separate simulation that matches the $K$ distribution in the APG region of the airfoil flow is carried out.

The differences between the two cases constitute the mild convex curvature effects found in a boundary layer on a CD airfoil. Specifically, in the region of weak APG, the curvature effect dominates and yields a lower friction coefficient. In the high-APG region (near the airfoil trailing edge) the effects of wall curvature and APG appear to interact.

Overall, the comparison between the two flows shows that the boundary layer developments are qualitatively similar, indicating that a flat-plate boundary layer can serve as a low-cost surrogate of an airfoil boundary layer in numerical studies of important features of an airfoil flow for fan applications   

Spatio-temporal statistics of a turbulent boundary layer under unsteady adverse pressure gradients : data from Time-Resolved Particle Image Velocimetry

An unsteady adverse pressure gradient turbulent boundary layer was created by rapidly deforming a 0.45 m long ceiling panel of a boundary layer wind tunnel to the shape of a convex bump. The spatial strength of pressure gradient and the rate of change of pressure gradient imposed were independently varied using an electropneumatic control mechanism for the ceiling panel. Time-Resolved Particle Image Velocimetry (TR-PIV) was used to capture the response of the boundary layer for a range of adverse pressure gradients. This talk will focus on the spatial and temporal evolution of single- and multi-point turbulent statistics obtained from phase-locked ensemble averages of the TR-PIV data for 3 rates of imposition of pressure gradients corresponding to non-dimensional times, t^* (defined as the ratio of convective time scale to imposed unsteady time scale), of 4.38, 1.53, and 0.61. The friction Reynolds number of the incoming flow, Re_τ, was 940 and the boundary layer thickness, δ, was 42 mm.   

Wall-modeled large-eddy simulations of flow over a Gaussian-shaped bump with a relaminarization sensor

Large-eddy simulations are conducted with an equilibrium shear-stress wall model to investigate the flow over a Gaussian-shaped bump geometry. Spanwise periodic simulation results are compared with Direct Numerical Simulations by Uzun & Malik (2020) and experimental data by Williams et al (2020). We consider configurations at two different Reynolds numbers Re_L=10⁶ and 3.41x10⁶ with a freestream Mach number M=0.2. The flow presents mild separation downstream of the bump apex for both Reynolds numbers, and a region of flow relaminarization around the apex for the lower Reynolds number configuration. Direct application of the wall model in the relaminarization region leads to a significant overprediction of the skin friction. A relaminarization sensor is developed to locally condition the application of the wall model based on simulation flow quantities. The predictive capabilities and robustness of the relaminarization sensor are assessed for both Reynolds numbers, along with previously developed laminar-to-turbulent transition sensors by Bodart & Larsson (2012) and Mettu & Subbareddy (2018). The proposed sensor correctly distinguishes the relaminarization region in the low Re_L case, leading to improved flow predictions.   

Large-Eddy Simulation of a Boundary Layer with Unsteady Pressure Gradient

Large-Eddy Simulation is used to study a turbulent boundary layer subject to a space- and time-dependent free-stream pressure gradient. Comparison is made with steady cases with fixed pressure gradients. The adverse pressure gradient is strong enough to cause flow separation. The pressure gradient is prescribed by an oscillating blowing and suction profile at the top boundary. Several cases have been investigated for a range of reduced frequencies k. For the highest k the separation bubble is not as thick as in an equivalent steady case, but its length remains comparable. The phase-averaged field shows that the flow is synchronized with the forcing throughout the domain. However, hysteresis occurs in the near wall region. As the reduced frequency decreases, the extent of the separation bubble in the wall-normal direction increases, but its length is reduced compared with the corresponding steady case. The region of slow-moving fluid generated by the flow reversal is advected downstream, causing a decorrelation between the forcing and the velocity and pressure in this region.   

Spectral analysis of a high-Reynolds-number near-equilibrium adverse-pressure-gradient turbulent boundary layer

The effects of adverse pressure gradients (APG) in high-Reynolds-numbers turbulent boundary layers (TBLs) is thoroughly assessed using both one- and two-dimensional spectra of the Reynolds stresses. The employed database was recently obtained through well-resolved large-eddy simulation (LES) of a near-equilibrium APG TBL with a moderate Rotta-Clauser pressure-gradient parameter β≈1.4, where the momentum-thickness-based and friction Reynolds numbers reach Re_θ=8,700 and Re_τ=1,900, respectively. The effects of the APG will be assessed by comparing the data with a zero-pressure-gradient (ZPG) TBL at similar Re_τ. The increase of energy in the outer region of the TBLs is partly linked with the presence of larger turbulent scales, but there is additional energy due to the rising of energetic smaller scales from the inner region close to the wall, as well as a new peak of production of TKE in the outer region. The two-dimensional spectra show longer spatial and temporal scales in the streamwise and spanwise Reynolds stresses near the wall and in the overlap region.   

Effect of wing-tip vortices on aerodynamic quantities of a NACA0012 wing

The present work aims at investigating the formation of wing-tip vortices in a finite-span wing, studying their effect on the flow and the turbulent boundary layers developing on both the suction and pressure sides, and understanding their effect on the aerodynamic quantities of the wing. This is done by performing high-resolution large-eddy simulations of a NACA0012 profile at a chord-based Reynolds number of Re_c=200,000, where many of the relevant quantities are compared between an infinite-span wing (i.e., periodic in the spanwise direction) and a finite-span wing with rounded wing-tip geometry. The simulations are performed using the high-order spectral-element code Nek5000 with adaptive-mesh-refinement (AMR) capabilities to achieve a high accuracy at an affordable computational cost. Our analysis will compare turbulence statistics around the wing and in the wake of both wings, power-spectral densities, as well as an assessment of the characteristics of the wing-tip vortices.