Turbulent Boundary Layer Features via Lagrangian Coherent Structures, Proper Orthogonal Decomposition and Dynamic Mode Decomposition

High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Reθ of 9800 in order to elucidate the coherent structures. Snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to visualize the flow structure depending on the turbulent kinetic energy and frequency content. The first six POD and DMD modes show the largest and the lowest amount of energy and frequency, respectively. Lagrangian coherent structure (LCS) based on the algorithm developed using the variational theory is also applied to track the flow via attracting and repelling trajectories. The shapes and the length of the trajectories show variation with increasing advection time. LCS trajectories are overlayed with the individual POD and DMD modes. Repelling and attracting lines cover the structure of these modes. Reconstructed flow fields from individual POD modes are also used to generate new LCS trajectories. The energy and frequency content have a direct impact on the length of the trajectories, where the longest reconstructed trajectories associate with the higher energy and lower frequency modes, and vise verse. The multiple intersection points between the repelling and attracting lines marked the low momentum regions

Multicolor Dye-based Flow Structure Visualization for seal-whisker geometry characterized by computer vision

Pinniped vibrissae possess a unique and complex three-dimensional topography, which has beneficial fluid flow characteristics such as substantial reductions in drag, lift, and vortex induced vibration. To understand and leverage these effects, the downstream vortex dynamics must be studied. Dye visualization is a traditional qualitative method of capturing these downstream effects, specifically in comparative biological investigations where complex equipment can be prohibitive. High-fidelity numerical simulations or experimental particle image velocimetry (PIV) are commonplace for quantitative high-resolution flow measurements, but are computationally expensive, require costly equipment, and can have limited measurement windows. This study establishes a method for extracting quantitative data from standard dye visualization experiments on seal whisker geometries by leveraging novel but intuitive computer vision techniques, which maintain simplicity and an advantageous large experimental viewing window while automating the extraction of vortex frequency, position, and advection. Results are compared to direct numerical simulation (DNS) data for comparable geometries. Power spectra and Strouhal numbers show consistent behavior between methods for a Reynolds number of 500, with minima at the canonical geometry wavelength of 3.43 and a peak frequency of 0.2 for a Reynolds number of 250. The vortex tracking reveals a clear increase in velocity from roll-up to 3.5 whisker diameters downstream, with a strong overlap with the DNS data but shows steady results beyond the limited DNS window. This investigation provides insight into a valuable bio-inspired engineering model while advancing an analytical methodology that can readily be applied to a broad range of comparative biological studies

A Lacunarity-Based Index for Spatial Heterogeneity

Characteri zing spatial heterogeneity is fundamental in numerous areas, yet defining spatial patterns often depends on qualitative assessments or a priori knowledge. Lacunarity analysis is a popular occupancy-based method for identi fy ing relevant length scales in spatially heterogeneous systems. From lacunarity, we identify the ex istence of a point which encapsulates the spatial heterogeneity of a given system. This value sati sfies the conditions for the lac unarity cutoff function and forms the bas is of a heterogeneity index. We evaluate the behavior of both parameters in mono fractal, clustered, and periodic systems. ln addition, we demonstrate the broad utility of our approach to the scientific community by classifying the spati al heterogeneity of fractured sea ice and comparing our findings to ex isting measures. The heterogeneity index produced a linear correlation with the area fraction of open ocean to ice with an R2 of 0.967

Increased Panel Height Enhances Cooling for Photovoltaic Solar Farms

Solar photovoltaic (PV) systems suffer substantial efficiency loss due to environmental and internal heating. However, increasing the canopy height of these systems promotes surface heat transfer and boosts production. This work represents the first wind tunnel experiments to explore this concept in terms of array flow behavior and relative convective heat transfer, comparing model solar arrays of varied height arrangements - a nominal height, extended height, and a staggered height configuration. Analyses of surface thermocouple data show average Nusselt number () to increase with array elevation, where panel convection at double height improved up to 1.88 times that of the nominal case. This behavior is an effect of sub-array entrainment of high velocity flow and panel interactions as evidenced through flow statistics and mean kinetic energy budgets on particle image velocimetry (PIV) data. The staggered height arrangement encourages faster sub-panel flow than in the nominal array. Despite sub-array blockage due to the lower panel interaction, heat shedding at panel surfaces promotes improvements on over 1.3 times that of the nominal height case

Technoeconomic Analysis of Changing PV Array Convective Cooling Through Changing Array Spacing

Accuracy in photovoltaic (PV) module temperature modeling is crucial to achieving precision in energy performance yield calculations and subsequent economic evaluations of PV projects. While there have been numerous approaches to PV temperature modeling based on both the steady-state and transient thermal assumptions, there have been few attempts to account for changing convective cooling on PV module surfaces resulting from changes in the PV system layout. Changes in system row spacing, in particular, can have a meaningful impact on module electrical efficiency and subsequent economic performance, even when considering additional costs from the changes in row spacing. Using a heat transfer approach based on the spatial definition of a PV array, technoeconomic analyses of different plant configurations are presented here that show an improved system levelized cost of energy (LCOE) for fixed-tilt PV systems when increasing system row spacing. These LCOE improvements have been found to be as high as 2.15% in climates characterized by low ambient temperatures and higher average annual wind speeds in U.S. climates. While the LCOE improvements are primarily driven by incident irradiance changes for altered row spacing, the waterfall analysis of the different components of changing system LCOE show that modifications in the heat transfer dynamics have a 0.5% contribution to the LCOE reduction for the largest LCOE, compared with a 3.3% reduction from irradiance changes

A One-Dimensional Volcanic Plume Model for Predicting Ash Aggregation

During explosive volcanic eruptions, volcanic ash is ejected into the atmosphere, impacting aircraft safety and downwind communities. These volcanic clouds tend to be dominated by fine ash (μm in diameter), permitting transport over hundreds to thousands of kilometers. However, field observations show that much of this fine ash aggregates into clusters or pellets with faster settling velocities than individual particles. Models of ash transport and deposition require an understanding of aggregation processes, which depend on factors like moisture content and local particle collision rates. In this study, we develop a Plume Model for Aggregate Prediction, a one-dimensional (1D) volcanic plume model that predicts the plume rise height, concentration of water phases, and size distribution of resulting ash aggregates from a set of eruption source parameters. The plume model uses a control volume approach to solve mass, momentum, and energy equations along the direction of the plume axis. The aggregation equation is solved using a fixed pivot technique and incorporates a sticking efficiency model developed from analog laboratory experiments of particle aggregation within a novel turbulence tower. When applied to the 2009 eruption of Redoubt Volcano, Alaska, the 1D model predicts that the majority of the plume is over-saturated with water, leading to a high rate of aggregation. Although the mean grain size of the computed Redoubt aggregates is larger than the measured deposits, with a peak at 1 mm rather than 500 μm, the present results provide a quantitative estimate for the magnitude of aggregation in an eruption

Lagrangian Diffusion Properties of a Free Shear Turbulent Jet

A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. Measurements are conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. Stereoscopic particle tracking velocimetry results in three-component tracks of position, velocity and acceleration of the tracer particles within the vertically oriented jet with a Taylor-based Reynolds number Reλ≃230. Analysis is performed at seven locations from 15 diameters up to 45 diameters downstream. Eulerian analysis is first carried out to obtain critical parameters of the jet and relevant scales, namely the Kolmogorov and large (integral) scales as well as the energy dissipation rate. Lagrangian statistical analysis is then performed on velocity components stationarised following methods inspired by Batchelor (J. Fluid Mech., vol. 3, 1957, pp. 67–80), which aim to extend stationary Lagrangian theory of turbulent diffusion by Taylor to the case of self-similar flows. The evolution of typical Lagrangian scaling parameters as a function of the developing jet is explored and results show validation of the proposed stationarisation. The universal scaling constant C0 (for the Lagrangian second-order structure function), as well as Eulerian and Lagrangian integral time scales, are discussed in this context. Constant C0 is found to converge to a constant value (of the order of C0=3) within 30 diameters downstream of the nozzle. Finally, the occurrence of finite particle size effects is investigated through consideration of acceleration-dependent quantities

Data-Driven Modeling of the Wake Behind a Wind Turbine Array

The wake flow in a wind turbine array boundary layer is described using the Koopman operator. Dynamics of the flow are decomposed into the linear and forcing terms, and the low-energy delay coordinates are revealed. The rare events show the non-Gaussian long tails that capture the switching and bursting phenomena. The near-wake region shows the incoherent phase space region, where the dynamics are strongly nonlinear. The far-wake region is marked with the small non-Gaussian forcing term, and the dynamics are largely governed by linear dynamics. The data-driven predictive model is built based on the Hankel-based dynamic mode decomposition and treats the nonlinear state of forcing term as external actuation. The model forecasts the evolution of the flow field for short-term timescales. The mean relative errors between the predictive and test fluctuating velocities are approximately 15%

The Rough Favourable Pressure Gradient Turbulent Boundary Layer

Laser Doppler anemometry measurements of the mean velocity and Reynolds stresses are carried out for a rough-surface favourable pressure gradient turbulent boundary layer. The experimental data is compared with smooth favourable pressure gradient and rough zero-pressure gradient data. The velocity and Reynolds stress profiles are normalized using various scalings such as the friction velocity and free stream velocity. In the velocity profiles, the effects of roughness are removed when using the friction velocity. The effects of pressure gradient are not absorbed. When using the free stream velocity, the scaling is more effective absorbing the pressure gradient effects. However, the effects of roughness are almost removed, while the effects of pressure gradient are still observed on the outer flow, when the mean deficit velocity profiles are normalized by the U∞ δ∗/δ scaling. Furthermore, when scaled with U2∞, the 〈u2〉 component of the Reynolds stress augments due to the rough surface despite the imposed favourable pressure gradient; when using the friction velocity scaling u∗2, it is dampened. It becomes ‘flatter’ in the inner region mainly due to the rough surface, which destroys the coherent structures of the flow and promotes isotropy. Similarly, the pressure gradient imposed on the flow decreases the magnitude of the Reynolds stress profiles especially on the 〈v2〉 and -〈uv〉 components for the u∗2 or U∞2 scaling. These effects are reflected in the boundary layer parameter δ∗/δ, which increase due to roughness, but decrease due to the favourable pressure gradient. Additionally, the pressure parameter Λ found not to be in equilibrium, describes the development of the turbulent boundary layer, with no influence of the roughness linked to this parameter. These measurements are the first with an extensive number of downstream locations (11). This makes it possible to compute the required x-dependence for the production term and the wall shear stress from the full integrated boundary layer equation. The finding indicates that the skin friction coefficient depends on the favourable pressure gradient condition and surface roughness

Distribution of Mean Kinetic Energy Around an Isolated Wind Turbine and a Characteristic Wind Turbine of a Very Large Wind Farm

An isolated wind turbine and a very large wind farm are introduced into large-eddy simulations of an atmospheric boundary layer. The atmospheric flow is forced with a constant geostrophic wind and a time-varying surface temperature extracted from a selected period of the CASES-99 field experiment. A control volume approach is used to directly compare the transfer of mean kinetic energy around a characteristic wind turbine throughout a diurnal cycle considering both scenarios. For the very large wind farm case, results illustrate that the recovery of mean kinetic energy around a wind turbine is dominated by the vertical flux, regardless of atmospheric stratification. Contrarily, for an isolated wind turbine, the recovery is dependent on the background atmospheric stratification and it is produced by a combination of advection, vertical flux, and pressure redistribution. The analysis also illustrates that during the unstable stratification periods vertical entrainment of mean kinetic energy dominates, whereas during the stable regime horizontal entrainment is predominant. Finally, it is observed that in both scenarios, the single wind turbine and the large wind farm cases, turbulent mixing is driven by the background convective stratification during the unstable period and by the effect of the wind turbine during the stable regime