Session U08: Boundary Layers: Pressure Gradient

Large-eddy simulation of the Boeing speed bump with slip-wall boundary conditions

Traditional wall models for large-eddy simulation (LES) rely on Reynolds-averaged Navier-Stokes (RANS) closure models to provide wall-stress boundary conditions to the LES equations. The slip wall boundary condition is derived explicitly from the LES constitutive equations and does not assume an attached boundary layer profile as is common in equilibrium boundary layer approximations (Bose & Moin, Phys. Fluids, 2014). This enables slip wall models to provide enhanced predictive capability in complex and separated flows where the thin boundary layer equations become invalid.

In this study, the high Reynolds number flow over a Gaussian bump (Boeing speed bump), with favorable and adverse pressure gradients, and turbulent separation and reattachment, is computed with a wall-modeled LES. Grid convergence of the solutions is achieved with the slip wall model for a spanwise-periodic domain section at Re=2M and simulations of a finite-span domain at Re=3.4M (aspect ratio ~ 1.0) are in agreement with recent experimental skin friction data (Gray et al., 2022). Results of the slip wall model predict a robust separation across grids while those of the equilibrium wall model with standard subgrid-scale models show a spuriously diminished separation on intermediate grid resolutions.

    

Frequency dependence of unsteady separation in a turbulent boundary layer

Large-Eddy Simulations were carried out to characterize the unsteady separation induced by a dynamic pressure gradient on a turbulent boundary layer. Mean and phase-averaged quantities were described in a previous meeting. Here we report about the behaviour of higher-order statistics. The turbulent kinetic energy (TKE) reveals peculiar differences between the medium (k=1) and low (k=0.2) frequency cases. For the lowest k, TKE matches well the steady case before the separation bubble at the most adverse pressure gradient phase, and its evolution in time is in-phase with the free-stream forcing. As the frequency increases, the lag generated by hysteresis effect causes the maximum of TKE to be shifted in phase, and the region of high TKE before the separation bubble is significantly smaller. Both at high and low frequency, the region of high TKE after the bubble is completely absent, due to the advection of the slow-moving fluid region as shown by the phase evolution of TKE. An advection-like phenomenon plays a significant role even at the lowest k. It was not captured by the phase-averaged flow analysis, and seems to be characterized by different dynamics compared to the medium frequency case.   

Comparison of statistics and structures for a turbulent boundary layer under steady and unsteady adverse pressure gradients

Spatially varying steady and unsteady pressure gradients of equal strengths were imposed at the end of a boundary layer wind tunnel using a 0.38 m long deforming plate. The exclusively accelerating unsteady pressure gradient had a k value, defined as the ratio of convective time scale to imposed unsteady time scale, of 2.78. Approximately 12,000 snapshots were collected at 0.1kHz using particle image velocimetry (PIV) for the steady case and 500 phase-locked ensembles were collected at 3.75 kHz using time-resolved PIV for the unsteady case. The friction-based Reynolds number, Re_τ, of the incoming flow was approximately 956 with a boundary layer thickness, δ, of approximately 47.5 mm at the middle of the field of view. This talk will focus on comparing single point statistics between the temporally-averaged steady and ensemble-averaged unsteady pressure gradients. Results from an extended version of classical Proper Orthogonal Decomposition, Scale-Dependent Proper Orthogonal Decomposition (SD-POD), will also be discussed to understand the differences in the flow features during the expansion and contraction of the separation bubble present in the field of view.  

       

Development and analysis of a turbulent boundary layer under spatially and temporally varying unsteady adverse pressure gradients

Unsteady adverse pressure gradients were imposed by an apparatus placed at the end of a boundary layer wind tunnel containing a 0.38 m long curving plate, rotary actuator, and pulley system. Varying pressure inputs to the actuator enabled achievable plate deflection speeds between 0.37 m/s and 0.97 m/s. The value k, a dimensionless unsteadiness parameter comparing the convective timescales to the imposed geometric timescales, was observed within the range of 0.29 to 3.42 when the freestream velocity was 7.5 m/s. Time-resolved planar particle image velocimetry (PIV) was used to analyze the behavior of the flow as the plate curved by collecting 500 phase-locked ensemble images at 3.75 kHz. This imaging was specifically done with a plate deformation speed of 0.74 m/s and k value of 2.78. The friction-based Reynolds number, Re_τ, of the incoming flow was approximately 956 in the center of the field of view with a boundary layer thickness, δ, of approximately 47.5 mm at the beginning of the field of view. This talk will primarily focus on the development and characterization of the experimental setup and preliminary PIV data. Opportunities for future work utilizing the full capabilities of the setup are also addressed.   

Wall-resolved large-eddy simulation of non-equilibrium turbulent boundary layers

Evolution of a turbulent boundary layer (TBL) under a streamwise varying pressure gradient is studied using wall-resolved large-eddy simulation (LES). The simulations are based on the experiments of Volino (Journal of Fluid Mechanics 897, A2, 2020) , who performed profile measurements at several streamwise stations in an initially zero pressure gradient TBL evolving through a region of favorable pressure gradient, followed by a zero pressure gradient recovery and a subsequent adverse pressure gradient region. The pressure gradient quantified by the acceleration parameter was held constant in each of these three regions. The simulation setup and the computational grid are carefully designed to mimic the experimental conditions without requiring a long development region for the incoming zero pressure gradient TBL. The profiles of mean velocity and Reynolds shear stress components obtained from LES show good agreement with the available experimental data at several stations in the domain. The response of TBL to changing pressure gradients is analyzed to understand the behavior of non-equilibrium TBL, common in many engineering applications.   

Spatio-temporal changes to coherent structures in a TBL caused by unsteady pressure gradients

A temporally-strengthening favorable-adverse pressure gradient sequence was imposed on a flat plate turbulent boundary layer (TBL). A series of steady pressure gradients that instantaneously matched the time-varying pressure gradients were also independently imposed. The TBL response was captured in the adverse pressure gradient region using time-resolved particle image velocimetry. Energetically-dominant structures of the flow and their spatio-temporal variations were extracted using space-time proper orthogonal decomposition (ST-POD) for the unsteady case and spectral proper orthogonal decomposition (SPOD) for the corresponding steady cases. Differences in modal changes in the TBL between the unsteady and steady pressure gradient impositions were quantitatively tracked as a function of time, accounting for differences in size, angle of inclination, height from the wall, etc. In this talk, we discuss the structural differences, make connections to differences in turbulent statistics previously identified by the authors, and likewise study the effect of timescale of pressure gradient imposition.   

Reynolds number and pressure gradient history effects on rough-wall turbulent boundary layers

In this study, we examine the effects of Reynolds number for different pressure gradient histories imposed on a rough-wall boundary layer. Measurements are carried out at the University of Southampton’s 1.2m x 1m cross-section, 12m long boundary layer wind tunnel with the freestream speed varied from 10m/s to 35m/s. A NACA0012 wing of chord 1.25m is mounted at the centreline of the test section (at 0.5 m above the bottom wall) and is used to exert a non-equilibrium pressure gradient history on the rough wall turbulent boundary layer developing on the bottom wall of a wind tunnel. Mean static pressure measurements were obtained in the rough-wall over a large streamwise distance to record the pressure gradient histories. Hot-wire measurements are taken in the boundary layer over the rough-wall at a location of one-chord length downstream of the trailing edge of the aerofoil. At this location, the local pressure gradient is almost zero regardless of the angle of attack of the wing in the freestream and this gives us data for different pressure gradient histories at the same Reynolds number and vice-versa. Using this data, mean and turbulence statistics as well as spectra will be presented allowing comparison of both pressure gradient history and Reynolds number effects.

    

Effect of wing-tip vortices on turbulent boundary layer and wake of a NACA0012 wing

Wing-tip vortices are formed at the tip of the finite-span lift-generating surfaces due to pressure difference between the suction and pressure sides. The current study aims at investigating, from a fundamental point of view, the effect of these wing-tip vortices on the turbulent boundary layer (TBL) and wake of a NACA0012 wing at a chord-based Reynolds number of 200,000 and at different angles of attack up to 10 degrees. This includes the effect of the imposed spanwise pressure gradient, velocity and rotation on the TBLs (specially on the suction side), the impact of the wing-tip vortices on the wake development and relaminarization due to imposed rigid-body rotation, the impact on the overall drag, and a number of additional flow quantities. The study is complemented by a direct comparison to infinite-span (periodic) wings at the same configurations, to allow for a better understanding of the effect of three dimensionality. Our numerical experiments take advantage of the AMR-capable (adaptive mesh refinement) version of the high-order code Nek5000 to perform a set of high-resolution large-eddy simulations (LES). The results are analyzed in terms of flow statistics, budgets, and energy spectra.   

Author not Attending

The drag-reduction effect of a traveling wavy surface has been a central topic since Kramer's research on dolphin skin suggested it as a possible solution to improve vehicle efficiency. However, many simulations and experimental works have focused on the wind-water wave interface, when the surface wave pattern on the solid surface usually follows the Rayleigh wave pattern. The Rayleigh wave, contrary to the prograde airy wave, has the particle traveling in the retrograde direction, i.e., traveling in the opposite direction of the wave transmitting direction at the surface. We performed a direct numerical simulation of turbulent Couette flows over waving Rayleigh wave surfaces with different wave slopes and material properties to study turbulence flow properties in the vicinity of compliant surfaces. The results show a very different pattern to the airy wave cases, which can guide the future design of surface actuators and explore a nonlocal technique to perform flow control.   

An experimental study of a turbulent boundary layer with favorable and adverse pressure gradients

A turbulent boundary layer is studied as it undergoes a favorable and adverse pressure gradient in sequence. A deformable ceiling panel is used (Parthasarathy & Saxton-Fox, 2022) to apply a range of pressure gradients on the boundary layer. This talk will focus on the turbulent statistics and structures within statically held but non-equilibrium pressure gradients. Planar PIV (particle image velocimetry) and preliminary stereo PIV data at will be reported. This data is collected using a mobile particle image velocimetry rig, which allows for 2100 mm of adjustment in the streamwise direction and 200 mm of adjustment in the spanwise direction. This was built to enable rapid data collection in the multiple fields of view with high degree of repeatability. The stereo PIV data will be reported from two planes: one in the favorable pressure gradient and one in the adverse pressure gradient region. The talk will also highlight the long-term plans to acquire data upstream of the pressure gradient imposition and at the side walls of the wind tunnel, to enable careful comparison with computation. This data will be compiled into a publicly available database for use in further research.   

Pressure gradient effects on the distribution of velocity fluctuations in turbulent boundary layers

This research investigates the wall-normal distribution of the streamwise and wall-normal velocity fluctuations in turbulent boundary layers with zero pressure gradient (ZPG) and a strong adverse pressure gradient (APG). High-spatial-resolution (HSR) two-component – two- dimensional (2C-2D) particle image velocity (PIV) measurements of the strong APG-TBL at Re_δ2 = 9, 650 and β = 30, are compared with the 2C-2D PIV measurements of the ZPG-TBL at Re_δ2 = 7,750 (where Re_δ2 is the momentum-thickness based Reynolds number and β is the Clauser’s pressure gradient parameter). The streamwise velocity fluctuations are skewed towards the larger values and the wall-normal velocity fluctuations towards the smaller values whereas this trend is reversed in the wake region. The extent of asymmetry in the near-wall and wake regions increases with an increase in the imposed APG. The locations of the zero skewness and the minimum flatness of the streamwise velocity fluctuations collapse with the location of the maximum Reynolds streamwise stress in both boundary layers, irrespective of the imposed pressure gradient. The same is observed for the wall-normal velocity fluctuations too.   

Numerical investigation on accelerating boundary layer subject to strong free-stream turbulence and Görtler instability

This research is based on the highly resolved large-eddy simulation database of a high-pressure turbine vane (Zhao & Sandberg, J. Fluid Mech., 2020), focusing on the boundary layer on the pressure side of the turbine blade, which is subject to combined effects of strong favorable pressure gradient (FPG), free-stream turbulence (FST) and Görtler instability due to the concave wall. On the one hand, the time- and spanwise-averaged flow remains laminar under the stabilizing effect of the FPG. The self-similar velocity boundary layer can be well described by the Falker-Skan equation, with a good estimation of the wall friction coefficient. On the other hand, the velocity fluctuation in the boundary layer is initially inhibited by the strong FPG while then amplifying significantly further downstream. The growth of the velocity fluctuation is presumably caused by the Görtler instability, as the Görtler number gradually increases and starts to play a leading role. In addition, small-scale vortices form in the near-wall region, inducing mushroom-like structures that spring up from the wall. The intense wall-normal transport caused by the vortical structures significantly enhances the heat flux to the wall.