Session Q04: Boundary Layers: General (3:55pm - 4:40pm CST)

Thin film flow along partially immersed rotating cylinder.

The steady-state withdrawal of a liquid film from a partially immersed horizontal rotating cylinder in a pool is examined theoretically. A boundary layer form of the Navier-Stokes Equations (NSE) is coupled with pressure variations induced by the interface. Following the approach of von-Karman and Polhausen, the equations are integrated to obtain an integro-differential equation with an assumed parabolic velocity profile to obtain an approximate first-order nonlinear-ordinary differential equation that governs the film thickness. A removable critical point singularity (Weinstein {\&} Ruschak 1999, Chem. Eng. Sci. 54) arises in the film equation at the location where inertia and gravitational effects balance, and removal of this singularity sets the volumetric flowrate and the height of the film as a function of azimuthal location along the cylinder. The azimuthal location of the critical point location is linked to the submerged depth of the roller. Although the film equation is designed to enable the interface profile to approach a horizontal pool surface away from the roller, the choice of parabolic profile precludes this limit. Full numerical solutions of the NSE are used to determine an alternative non-parabolic velocity profile that enables the horizontal pool limit.   

Underlying mathematical structure shared between boundary layers and the pandemic

As of yet, there is no exact analytic solution to the Blasius, Falkner-Skan, and Sakiadis boundary layer problems. However, for each of these, there exists asymptpotic expansions that can be used to construct approximate analytical solutions. The same can be said for the nonlinear systems of differential equations that are currently being used to model the pandemic. The authors show how a large parameter expansion of the Sakiadis boundary layer problem (Barlow et al., QJMAM 2017) is of the same form as the long-time expansion of the Susceptible-Infected-Recovered model of epidemiology (Barlow & Weinstein, Physica D 2020). The method of asymptotic approximants is used to find closed-form accurate analytic solutions for both of these problems, over the entire domain on which they are defined.   

A new scenario of the optimal route from free-stream perturbations to bypass transition in a boundary layer.

The optimal route from free-stream perturbations to bypass transition in a flat plate boundary layer is found by computing of the nonlinear optimal inflow perturbation evolution. This study fills the gap between secondary instability of velocity streaks and transition, and reveals that the transition is not the consequence of the saturation of the most unstable secondary instability as widely supposed, but of the interaction of multiple secondary modes, whose phase mismatch induces strong shears leading to a tertiary instability. The optimal route illustrates that free-stream perturbation components gradually enter the boundary layer and contribute to transition successively: the steady (and low-frequency) inflow perturbations induce near-wall velocity streaks; the sinusoidal meandering motion of streaks triggered by high-frequency perturbations generates helical vortex filaments; the filaments then undergo tertiary instability associated with higher-frequency perturbations, leading to an avalanche of breakdown into a tangle of numerous finer-scale vortices and thence to turbulence.   

Stream-wise statistical homogeneity in boundary layer resolvent analysis

Resolvent analysis is the natural extension of linear stability theory to statistically stationary turbulent flows and has been used to predict the dominant mode shapes for various spatiotemporal frequencies. However, extension of the method to boundary layers often requires assuming stream-wise statistical homogeneity even though the flow is non-homogeneous in the stream-wise direction. The current study investigates the validity of this assumption by leveraging boundary layer self-similarity to rescale the boundary layer in the wall-normal direction (Ruan {\&} Blanquart 2020). In the rescaled coordinates, the stream-wise direction is much more closely approximated as statistically homogeneous. Resolvent analysis is then applied to 1) the Cartesian (unscaled) system and 2) the rescaled system for a variety of spatiotemporal modes at Reynolds numbers of 1000, 2500 and 4000 with a constant kinetic energy norm. Both methods agree on mode shapes for inner layer spatiotemporal frequencies, but~differ~significantly on mode peak location and mode width for outer layer spatiotemporal frequencies. Finally, analytical expressions are provided~both to~explain the changes and to provide estimates of high Reynolds number behavior.~   

Experimental Assessment of Multi-Rotor Downwash Interaction

As the usage of small multi-rotor unmanned aircraft systems (UAS) continues to grow there is a need to understand the complex flow and its interactions with the propellers and the UAS airframe. This is particularly important to understand the interactions of the inflow and downwash with sensors mounted on the structure, such as chemical, thermodynamic, or wind sensors where interactions may contaminate the measurements. This effort maps the in-flow around a multirotor using multiple techniques including PIV, flow visualization, and sonic anemometers. These experiments determine the effectiveness of sensors onboard multi-UAV for atmosphere measurements. The study includes a single rotor analysis to isolate the effects of a single rotor plan proceeded by investigation of double and quad rotor systems. The rotors are placed in an open-jet wind tunnel to allow for the flow visualization without boundary layer interference. The resulting data is compared to the inflight data and tower mounted sensors to validate the experimental results. *Supported by the NSF NRI 2.0 program under grant 1925147.   

Five Hole Probe Sweeping Wake Surveys

As robotic aircraft are increasingly used for atmospheric measurements a cheap and accurate wind sensor is needed. Oklahoma State University has developed a 3D printed multi-hole probe to fill this need. The probes are mounted to a fixed wing aircraft to measure a 3D wind vectors, including transient phenomena such as gusts and turbulence. The probe is calibrated using non-nulling calibration in wind tunnels. A wake survey is conducted with the probe by sweeping in the wake of various objects, such as a cylinder or wing, similar to the flying hot-wire concept. These wake surveys serve as a method to explore and verify the limits of the probes. The results show a reasonable drag profile of the model, without the need for a traversing system. Of interest will be how the probe handles turbulence between the wake of the model and the tunnel free stream. These experiments provide a better understanding of the probe measurements and support the expansion of the probes use in field studies.   

Inner-outer decomposition and universal near-wall turbulent motions in turbulent channels

Near-wall turbulent velocities in turbulent channel flows are decomposed into small-scale and large-scale components at $y^+<100$, where $y^+$ is the viscous-normalized wall-normal height. The small-scale one is obtained by fully removing outer influences. On the other hand, the large-scale one represents the near-wall footprints of outer energy-containing motions. We present plenty of evidences that demonstrate the small-scale motions are Reynolds-number invariant with the viscous scaling, at friction Reynolds numbers between 1000 and 5200. At lower Reynolds numbers from 180 to 600, the small scales can not be scaled by the viscous units, and the vortical structures are progressively strengthened as Reynolds number increases, which is proposed as the main mechanism responsible for the anomalous scaling behavior. The finding of the universal small-scale motions in wall turbulence may be akin to the universal small scales in homogeneous and isotropic turbulence, possibly suggesting the universality of the existence of universal small-scales in different turbulent flows.   

Scalar Transport in Restricted Nonlinear Turbulence

Streamwise coherent structures have been shown to play an important role in momentum and energy transport in wall bounded shear flows. Studies regarding the transport of scalars, such as heat or chemical species, have revealed scalar fluctuations are highly correlated with streamwise velocity fluctuations, suggesting coherent structures also play a key role in scalar dynamics. We test this hypothesis by modeling scalar transport in the restricted nonlinear (RNL) framework. RNL models of wall-turbulence represent the flow as a large scale streamwise constant field that nonlinearly interacts with simplified streamwise varying perturbations. Our results show that a similar restriction of both the velocity and scalar fields to streamwise constant mean dynamics interacting with streamwise varying perturbation fields supported by a single non-zero wavenumber leads to a coupled model that accurately predicts low-order statistics. Furthermore, the quasi two-dimensional nature of the RNL system implies cross-plane features are largely responsible for mixing the scalars in wall-bounded turbulent flow. We further extend this model to demonstrate the utility of the RNL paradigm in investigating high Prandtl number and buoyancy effects in stably-stratified turbulence.   

Large-eddy simulations of rough-wall turbulent boundary layers: examining the logarithmic law for turbulence fluctuations

We study rough-wall turbulent boundary layers (TBLs) for their ability to represent the lower region of the atmospheric flow in which wind farms operate. In this region, the logarithmic law dictates that the streamwise and spanwise velocity variances $u'^2$ and $v'^2$ scale log-linearly and that the wall-normal variance $w'^2$ remains nearly constant. To date, all these predictions have been observed in experiments and direct numerical simulations, but only the $u'^2$ prediction has been observed in large-eddy simulations (LES). This is partly because most studies focus only on $u'^2$, which contains most of the turbulent kinetic energy in TBLs. In wind farms, however, $v'^2$ and $w'^2$ are also important because of their pronounced effect on wake meandering and hence turbulence generation. Here we perform LES using a finite-volume code in order to parametrically study the effects of (i) the grid resolution and grid-cell aspect ratio, (ii) the wall model and (iii) the subgrid-scale model. We find that although all of these factors affect the accuracy of LES, it is the grid-cell aspect ratio that affects $v'^2$ and $w'^2$ the most. In particular, we find that using nearly isotropic grid cells causes all three components of the velocity variance to agree with the logarithmic law.   

Investigation of Wall-Detached Turbulence in the Atmospheric Surface Layer through LiDAR and Sonic-Anemometer Measurements

In the context of wall-bounded turbulence, the enhanced measurements capabilities currently available to probe turbulence at very high Reynolds numbers have re-ignited investigations on Large- and Very Large-Scales of Motion (LSM and VLSM). Specifically, the contribution to the Reynolds stresses carried by detached eddies have been recently investigated for a wide range of Reynolds numbers $(Re_{\tau }={10}^{3}$ to ${10}^{6})$. In this scenario, the present work focuses on a high-Reynolds number atmospheric surface layer flow probed with scanning Doppler wind LiDARs, sonic anemometers and a ceilometer at the SLTEST facility in Utah. Based on these new experimental datasets, the presence of detached eddies has been quantified throughout the whole surface layer and a possible theoretical background is provided to motivate the observed wall-normal profiles of the streamwise Reynolds stress. The contribution of this work is dual: first, the capability of the LiDAR technology to probe near-wall atmospheric turbulence is assessed; second, a theoretical support to the knowledge about the physics underlying wall-detached eddies is provided   

Observations of the Urban Boundary Layer Using Autonomous Vehicles

As advanced aerial mobility (AAM) operations become a reality and navigate in both rural areas and cities, there is a better need to understand, observe, and report on the state of the Earth's Planetary Boundary Layer (PBL) and Urban Boundary Layer (UBL) required for safe navigation. Much of the current understanding of the PBL/UBL structures is limited to numerical predictions with limited scales and insufficient wind tunnel and ground/low altitude weather station validation, thus not providing substantiative information for of the high Re BL regime. Using sensors such as ultrasonic anemometers mounted to robotic aircraft more cohesive measurements are taken to provide improved observations in building wakes within the UBL. Comparisons are made with numerical models within an urban landscape. Through field experimentation optimized flight paths and measurement methods can be developed. These methods are valuable for creating a normalized PBL/UBL observations process that can improve wind and weather forecasting and improve climate models. In addition, experiments are conducted in the wakes of wind turbines to evaluate the impact of terrain on turbine in flow and the resulting, including wake interactions between wind turbine farms and associated surrounding structures.