Session E10: Boundary Layers: Turbulent Boundary Layers Curvature and Pressure Gradient Effects (3:10pm - 3:55pm CST)

A novel installation to impose unsteady pressure gradients on a turbulent boundary layer

A $0.45 m$ long flexible ceiling panel located above a fully-developed flat plate turbulent boundary layer (TBL) is rapidly deformed using a mechanism with pneumatic actuators. The actuation results in a temporal deformation of the ceiling panel to the shape of a convex curve. This creates a temporally-strengthening pressure gradient (favorable and adverse in spatial sequence) on the flat plate TBL beneath. The changing curvature profiles of the ceiling panel in time are extracted from high-speed videos, and the resulting pressure gradient (PG) profiles imposed on the TBL are characterized using 5 unsteady pressure sensors flush-mounted on the flat plate. The range of unsteady time scales accessible with this installation are $0.05 - 0.3s$, corresponding to equivalent reduced frequencies, $k_{eq}$, of $0.15 - 0.9$. This range is relevant to the physics of dynamic stall, flow over turbomachinery, wind turbine blades, etc. The range of PG strengths accessible (in terms of acceleration parameter, $K$) are $3.5 \times 10^{-6} - 6 \times 10^{-6}$, which are classified as strong PGs relevant to engineering flows of interest. The effects of the resulting temporally- and spatially-varying PGs on coherent structures in the TBL will be studied using time-resolved PIV in future experiments.   

The re-laminarization of a supersonic boundary layer subject to a strong convex curvature

The relaminarization of supersonic, spatially developing, turbulent boundary layers (SSDTBL) subject to strong convex curvatures has many applications, but published studies on the subject are scarce. Early work by Luker, Bowersox and Buter (2000) explored the influence of such geometries experimentally at Mach 2.9. They found a sharp decrease of the turbulence intensity and Reynolds shear stress with respect to a reference zero-pressure gradient (ZPG) region in the near-wall region. Furthermore, large eddies where being annihilated by the FPG into small eddies. In the present work, we explore the effect of a very strong convex curvature (with the ratio of curvature radius to inlet boundary layer thickness around 6) on a SSDTBL through a high-resolution Direct Numerical Simulation (DNS). Preliminary results exhibit a similar behavior to the one previously described. Our focus for the present study will be the assessment of the impact of convex streamline curvature on large coherent structures via 3D two-point correlation. Furthermore, we also assess the impact on the energy cascade through the power spectrum. Lastly, we compare and contrast the present results with available experimental and computational results.   

Direct Numerical Simulations of a Separating Turbulent Boundary Layer Subjected to Zero-Net-Mass-Flux Actuation

The response of a turbulent separation bubble (TSB) to zero-net-mass-flux actuations is investigated via DNS. The TSB is formed by applying a suction-only velocity profile on the top boundary. Streamwise-oriented actuators are placed upstream of the TSB to produce perturbations mimicking the G\"{o}rtler vortices that cause a low-frequency unsteadiness of the TSB. The natural vortex-shedding frequency ($f_h$) and breathing/flapping frequency ($f_l=0.4f_h$) of the undisturbed TSB are examined, as well as another one at 10$f_l$. Compared with the undisturbed case, the TSBs under the actuation at $f_h$ and $f_l$ reattach earlier, leading to a 50\% reduction in length and improved pressure recovery. The low-frequency unsteadiness is amplified, showing as a periodic formation of clockwise-rotating large vortices at $f_l$. Actuation at $10f_l$ barely changes the TSB and even causes more pressure loss. The response preference of the TSB to certain actuation frequencies is further discussed by a spectral analysis of a harmonic resolvent operator performed to a base flow that consists of the mean and the low-frequency unsteady motion. The preferred perturbation and the receptivity of the mean flow to actuation at different frequencies suggested by analysis are consistent with the DNS.   

Estimating the Bounds of the Logarithmic Layer in Adverse Pressure Gradient Turbulent Boundary Layers

The location of the start and end of the logarithmic layer in a zero pressure gradient turbulent boundary layer (ZPG TBL) are well-established to be $\approx3\sqrt{\delta^+}$ and $\approx0.15\delta^+$ (where $\delta^+$ is the friction Reynolds number) Wei $et$ $al.$ ($J.$ $Fluid$ $Mech.$, vol. 522, 2005, pp. 303--327). The corresponding bounds for adverse pressure gradient (APG) TBLs are not known, as here the Clauser pressure gradient parameter $\beta\neq0$. In this talk, we employ various tools to describe how the bounds of the inertial sublayer may behave under APG conditions, such as whether the $\sqrt{\delta^+}$ dependence for the onset of the inertial region is maintained in modest APG TBLs. The bounds of the logarithmic layer will also be discussed relative to the behavior of the mean momentum balance. Low Reynolds number large eddy simulations and newly acquired higher Reynolds number ($7000\leq\delta^+\leq8000$) experimental data are used in this analysis. Hot-wire measurements are obtained at the Flow Physics Facility at the University of New Hampshire in the region of an APG ramp, where $\beta\leq2$. The behavior of the logarithmic layer will be compared to ZPG TBL data from low Reynolds number direct numerical simulation and high Reynolds number experiments.   

An adverse-pressure-gradient turbulent boundary layer with nearly-constant $\beta \simeq 1.4$ up to $Re_{\theta} \simeq 8,700$.

The results of a new well-resolved large-eddy simulation (LES) of an adverse-pressure-gradient (APG) turbulent boundary layer (TBL) are presented. Using a resolution of $13824 \times 301 \times 1920$ collocation points, the momentum-thickness-based and friction Reynolds numbers reach $Re_{\theta}=8,700$ and $Re_{\tau}=1,900$, respectively. We impose a freestream-velocity distribution following a power law, which leads to near-equilibrium conditions as discussed in previous studies. We obtain a long region where the Rotta-Clauser pressure-gradient parameter is nearly constant at 1.4. We perform detailed statistical and spectral analyses of the data and compare the results with those of a zero-pressure-gradient (ZPG) TBL at similar $Re_{\tau}$. We observe larger outer-region fluctuations in the APG, which are due to a combination of increased small-scale energy and a large-scale spectral peak far from the wall. Close to the wall, the spanwise premultiplied spectrum $k_z\phi_{uu}$ is very similar in the APG and ZPG, even for increasing Reynolds number. The spanwise premultiplied spectra $k_z\phi_{vv}$, $k_z\phi_{ww}$ and co-spectrum $k_z\phi_{-uv}$, exhibit noticeable differences between APG and ZPG, both close and far from the wall. This becomes more pronounced for increasing $Re$   

Quadrant Analysis of Zero and Adverse Pressure Gradient Turbulent Boundary Layers using High Spatial Resolution 2C-2D PIV Measurements

High spatial resolution particle image velocimetry (PIV) has been used in an experiment in a $2m$ wide, $1m$ high and $20m$ long LML boundary layer wind tunnel to measure the instantaneous velocity fields of ZPG-TBL at $Re_{\delta_2} = 7,750$ and APG-TBL at $Re_{\delta_2} = 9,840$ ($\beta = 2.01$) and $Re_{\delta_2} = 16,240$ ($\beta = 2.27$). High spatial resolution enables the capture of TBL from the viscous sublayer to the end of the log layer. We study the effect of mild APG on the individual contribution of the four quadrants of fluctuations in the streamwise and the wall-normal velocities towards Reynolds shear stress. It is found that near the wall ($y^+ < 30$), contributions of the first and third quadrants relative to the second quadrant are higher than relative to the fourth quadrant but in opposite direction in all three cases of TBL. Above $y^+ = 30$, these relative contributions are nearly 45\% in ZPG-TBL and 50\% in APG-TBL. Below $y^+ = 10$, all four quadrants contribute more towards the total Reynolds shear stress with increasing APG.   

Near equilibrium in intermittently turbulent oscillatory boundary layer flows

Direct Numerical Simulation results, produced using the spectral element solver Nek5000, have been used to examine the mean flow structure of oscillatory boundary layer flows in the intermittently turbulent regime. Comparison with unidirectional developing boundary layers results reveal similarities in the way that flow approaches a state that mimics the characteristics of the fully developed unidirectional turbulent boundary layer. The analysis of turbulence statistics revealed the existence of near-equilibrium conditions which result in the presence of a logarithmic velocity profile. The shape and defect parameter values are examined as diagnostics to reach the near-equilibrium conditions. The present analysis elucidates inconsistencies in the literature regarding the values of the velocity profile's slope and intersects in temporary accelerating boundary layers. In addition, the present analysis explains the presence of negative phase shift between free-stream velocity and bed shear maxima which is the result of a late and incomplete transition to a fully turbulent state.   

Turbulent statistics in subsonic and transonic open channel flow with a contraction

In this study, we have simulated an open channel flow at bulk Reynolds numbers of $11,000$ with a sinusoidal contraction to locally yield favorable-pressure-gradient (FPG), zero-pressure gradient (ZPG) and adverse-pressure-gradient (APG) effects, and investigate the effects of the resulting flow separation on the near-wall turbulent structure. Conditions up to transonic Mach numbers are considered to assess compressibility effects on the turbulent flow separation and reattachment. The adopted direct numerical simulations (DNS) framework relies on a block-spectral high-order unstructured code, H$^{3}$AMR. The dependency on the streamwise domain length is assessed as well as the effects on mesh resolution via a combined h- and p-refinement grid sensitivity analysis.   

Direct numerical simulation of a turbulent flow over a curved ramp using FastRK3

Flow separation, resulting from an adverse pressure gradient (APG), is encountered in many engineering applications. However, the physical mechanisms of separated turbulent boundary layers over curved walls are not yet fully understood. In order to provide the necessary statistics for the validation of RANS and LES models, and explain the physical mechanisms of such flows, we have performed direct numerical simulations (DNS) of a spatially developing turbulent boundary layer over a curved ramp with APG using our new pressure-correction method called FastRK3 (Aithal \& Ferrante, {\textit{J.~Comput.~Phy.}, 2020}). FastRK3 is a three-stage, Runge-Kutta based pressure-correction method for the incompressible Navier-Stokes equations in orthogonal curvilinear coordinates, and requires solving the Poisson equation for pressure only once per time step without loss of accuracy with respect to the standard RK3. In the current work, we focus our study on the dynamics of the turbulence kinetic energy of the flow in curvilinear coordinates.