Lagrangian modeling of a non-homogeneous turbulent shear flow: Molding homogeneous and isotropic trajectories into a jet

Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics, practical turbulence is often non-homogeneous and anisotropic, leading to great modeling challenges. In this letter, an efficient model is proposed to predict turbulent jet statistics with high accuracy. The model leverages detailed knowledge of readily available velocity signals from idealized homogeneous turbulence and transforms them into Lagrangian trajectories of a turbulent jet. The resulting spatio-temporal statistics are compared against experimental jet data showing remarkable agreement at all scales. In particular the intermittency phenomenon is accurately mapped by the model to this inhomogeneous situation, as observed by higher-order moments and velocity increment probability density functions. Crucial to the advancement of turbulence modeling, the transformation is simple to implement, with possible extensions to other inhomogeneous flows such as wind turbine wakes and canopy flows, to name a few

Entrainment, Diffusion and Effective Compressibility in a Self-Similar Turbulent Jet

An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, ⟨Uφ⟩, is found to be essentially indistinguishable from the global mean velocity field of the jet, ⟨U⟩, for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which ∇⋅⟨Uφ⟩≠0 even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated to entrained fluid particles. By considering a classical advection-diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity KT) and momentum (through the turbulent viscosity νT) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of KT and νT (and hence of the turbulent Prandtl number σT=νT/KT) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets

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

Inertial particle clustering due to turbulence in an air jet

ABSTRACT: Explosive volcanic eruptions create turbulent plumes of fine ash particles. When these particles collide in the presence of moisture and electrostatic fields they combine into larger aggregates, which can significantly change the atmospheric residence time of the airborne cloud. Previous studies have suggested that turbulence may lead to preferential concentration—also known as clustering—of particles within the flow, increasing the likelihood of collisions and aggregation. Few experimental studies have quantified these processes for volcanic plumes. This behavior was investigated using a particle-laden air jet. By systematically varying the exit speed and the size, density, and concentration of particles, flows were produced with Reynolds numbers of 4940 to 19300, Stokes numbers of 1.0 to 17.4 (based on the convective scale), and particle mass loadings of 0.3 to 3.9%. Specific emphasis is placed on two Stokes numbers of 1.9 and 17.4, which differ by nearly an order of magnitude. Particle image velocimetry was employed to measure the velocity distribution within a two-dimensional rectangular region along the jet centerline in each experiment. Voronoï decomposition was used to quantify the extent of preferential concentration by measuring the distribution of cell sizes around each individual particle. Results show that particles exhibit clustering behavior when Stokes numbers are close to 1. We also measured the radial distribution functions (RDFs) to quantify the likelihood of particle collisions. At low Stokes number, the RDF magnitude was significantly higher, which corresponds to increased collision frequency in the particle-laden jet. Computational analysis finds that increasing the RDF by a factor of 20 results in a doubling of peak aggregate size. These findings demonstrate that preferential concentration due to turbulent structures could have important effects on collision frequencies, ash aggregation, and electrification in volcanic plumes

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

Reduced Order Description of Experimental Two-Phase Pipe Flows: Characterization of Flow Structures and Dynamics via Proper Orthogonal Decomposition

Multiphase pipe flow is investigated using proper orthogonal decomposition for tomographic X-ray data, where holdup, cross-sectional phase distributions and phase interface characteristics within the pipe are obtained. Six cases of stratified and mixed flow with water content of 10%, 30% and 80% are investigated to gain insight into effects of velocity and proportion of water on the flow fields. Dispersed and slug flows are separately analyzed to consider the added interface complexity of the flow fields. These regimes are also highly applicable to industry operational flows. Instantaneous and fluctuating phase fractions of the four flow regime are analyzed and reduced order dynamical descriptions are generated. Stratified flow cases display coherent structures that highlight the liquid-liquid interface location while the mixed flow cases show minimal coherence of the eigenmodes. The dispersed flow displays coherent structures for the first few modes near the horizontal center of the pipe, representing the liquid-liquid interface location while the slug flow case shows coherent structures that correspond to the cyclical formation and break up of the slug in the first 5 modes. The low order descriptions of the high water content, stratified flow field indicates that main characteristics can be captured with minimal degrees of freedom. Reconstructions of the dispersed flow and slug flow cases indicate that dominant features are observed in the low order dynamical description utilizing less than 1% of the full order model. POD temporal coefficients a1, a2 and a3 show a high level of interdependence for the slug flow case. The coefficients also describe the phase fraction holdup as a function of time for both dispersed and slug flow. The second coefficient, a2, and the centerline holdup profile show a mean percent difference below 9% between the two curves. The mathematical description obtained from the decomposition will deepen the understanding of multiphase flow characteristics and is applicable to long distance multiphase transport pipelines, fluidized beds, hydroelectric power and nuclear processes to name a few

Building a Turbulent Jet: Measuring/Modeling Lagrangian Dispersion, Particle Trajectory Dynamics and Intermittency

The mechanics of how particles diffuse, interact, eject, etc. within a fluid is applicable to numerous industrial and environmental applications. Unwanted products of combustion, dust contamination of solar panels, pathogen transport during a cough and ejections of particles during volcanic eruptions, are a few examples of flows in which increased knowledge of particle dynamics could result in substantial reduction of negative environmental and economic impacts. To better understand the tendencies of particles within shearing flows (such as jets), an extensive experimental campaign was conducted. Measurements of a turbulent round water jet were performed within an icosahedral tank. Particle tracking velocimetry was employed to create three-component, three-dimensional trajectories. Particles of varying size and weight were used to seed the flow in order to provide a range of inertial effects based on the particle interaction with the fluid. Numerous Eulerian and Lagrangian parameters were characterized and most notable, a trajectory stationarization technique was successfully implemented to address the inhomogeneity of the flow field. This approach could be extended to provide systematic methods to analyze complicated flow fields, enhancing knowledge of their dynamics. Alternatively, theoretical models of particle mechanics have been constructed, contributing to the baseline understanding of Lagrangian dynamics. Stochastic processes and phenomenological approaches are presented to accurately predict the low-order statistics of tracers, point particles which follow the motion of the fluid, for the idealized flow of homogeneous, isotropic and stationary turbulence (i.e. without the inclusions of external forces). In comparison to previous models, the proposed process is infinitely differentiable for finite Reynolds number and includes intermittent scaling properties. Furthermore, particle accelerations and velocities can be modeled based on the stochastic processes, providing full temporal information of the flow dynamics. The advancements made to homogeneous, isotropic and stationary turbulence are then exploited and used as an input to generate an inhomogeneous flow field based on self-similar relations within a jet to include, in a simple way, the intermittent behavior of the turbulence. Specifically, a model is proposed to compensate a stationary signal by the evolution of the Eulerian background properties of a jet to transform Lagrangian velocities in order to build up an ensemble of turbulent jet trajectories. The modeled jet, based on inputted signals from a stochastic process and direct numerical simulation are compared against the experimental data. Statistics show remarkable agreement for statistics of velocity increments and for higher-order moments, accurately capturing dissipative behavior within the non-homogeneous flow. With some additional study, the proposed model could be applied to modeling of particle velocity statistics during volcanic eruptions, pathogen transport during a cough and pollutant contamination from smokestacks

A generalized framework for reduced-order modeling of a wind turbine wake

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Hessian-based Topology of Two-phase Slug Flow

Experimental slug flow is analyzed through a topological method and proper orthogonal decomposition (POD). Local phase fractions of a pipe cross-section, acquired through X-ray tomographic reconstruction, are analyzed by extracting critical points via eigenvalues associated with the Hessian matrix. Based on the sign of the eigenvalues, three types of critical points are classified: local maxima, minima and saddle points. Reduced order descriptions (ROD), obtained as results of the POD, are examined to investigate the flow dynamics associated with the primary eigenfunctions with respect to critical point placement and frequency. Voronoï mapping is employed for visualization of the critical points as a function of cross-sectional location, and quantification of the spatial distribution of the critical points. For each classification, the sum of the respective critical point over the cross-section correlates to the temporal holdup of liquid within the pipe. The local maxima and minima display an increase in their occurrence that relates to the liquid slug passage while the local saddle points follow the profile of the liquid holdup as the bubble is forming after the passage of the liquid slug. The total number of local maxima per snapshot as a function of time peaks prior to the liquid holdup peak, displaying the instabilities present in the flow field preceding the liquid slug reaching the top of the pipe. Applying critical point theory to the RODs reveals that the first two modes capture the liquid-dominated slug body region and the Taylor bubble/liquid film region. The observed time lag between the total maxima and the liquid holdup provides opportunity for implementation of predictive control monitoring in fields where instabilities influence system mechanics

Barriers to Mass Timber Adoption Mid to High-Rise Buildings

Advancements in technology and manufacturing have provided the means to construct tal l wood buildings that are safe and cost effective while gaining the aesthetic and environmental benefits associated with mass timber. The objective of this research is to identify perceived barriers of the integration of mass timber as a desirable bui lding material for architects and structural engineers. Building on a previous study, surveys wi ll be distributed to professionals in the building science field to detect information gaps pertain ing to wood as a viable alternative to concrete in mid to high - rise applications.https://pdxscholar.library.pdx.edu/research_based_design/1074/thumbnail.jp