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Relevant bibliographies by topics / Wakes (Aerodynamics) Turbulence. Turbomachines

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Academic literature on the topic 'Wakes (Aerodynamics) Turbulence. Turbomachines'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Wakes (Aerodynamics) Turbulence. Turbomachines"

1

Abhari, R. S., and M. Giles. "A Navier–Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping." Journal of Turbomachinery 119, no. 1 (1997): 77–84. http://dx.doi.org/10.1115/1.2841013.

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An unsteady, compressible, two-dimensional, thin shear layer Navier–Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi-three-dimensional formulations is used to account for the stream-wise variation of streamtube height. The code uses Ni’s Lax–Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin–Lomax turbulence model. The computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triang

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2

Gundy-Burlet, K. L., M. M. Rai, R. C. Stauter, and R. P. Dring. "Temporally and Spatially Resolved Flow in a Two-Stage Axial Compressor: Part 2—Computational Assessment." Journal of Turbomachinery 113, no. 2 (1991): 227–32. http://dx.doi.org/10.1115/1.2929090.

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Fluid dynamics of turbomachines are complicated because of aerodynamic interactions between rotors and stators. It is necessary to understand the aerodynamics associated with these interactions in order to design turbomachines that are both light and compact as well as reliable and efficient. The current study uses an unsteady, thin-layer Navier–Stokes zonal approach to investigate the unsteady aerodynamics of a multistage compressor. Relative motion between rotors and stators is made possible by the use of systems of patched and overlaid grids. Results have been computed for a 2 1/2-stage com

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Zhang, Di, Ma Jiao-Bin, and Qi Jing. "Numerical study of unsteady flow and exciting force for swept turbomachinery blades." Thermal Science 20, suppl. 3 (2016): 669–76. http://dx.doi.org/10.2298/tsci160205199z.

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The aerodynamic performance of blade affects the vibration characteristics and stable operation of turbomachinery closely. The aerodynamic performance of turbine stage can be improved by using swept blade. In this paper, the RANS method and the RNG k-? turbulence mode were adopted to investigate the unsteady flow characteristics and excitation force of swept blade stage. According to the results, for the swept blade, the fluid of boundary layer shifts in radial direction due to the influence of geometric construction. It is observed that there is similar wake development for several kinds of s

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Yang, Xiaolei, Daniel Foti, Christopher Kelley, David Maniaci, and Fotis Sotiropoulos. "Wake Statistics of Different-Scale Wind Turbines under Turbulent Boundary Layer Inflow." Energies 13, no. 11 (2020): 3004. http://dx.doi.org/10.3390/en13113004.

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Subscale wind turbines can be installed in the field for the development of wind technologies, for which the blade aerodynamics can be designed in a way similar to that of a full-scale wind turbine. However, it is not clear whether the wake of a subscale turbine, which is located closer to the ground and faces different incoming turbulence, is also similar to that of a full-scale wind turbine. In this work we investigate the wakes from a full-scale wind turbine of rotor diameter 80 m and a subscale wind turbine of rotor diameter of 27 m using large-eddy simulation with the turbine blades and n

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Ames, F. E., and M. W. Plesniak. "The Influence of Large-Scale, High-Intensity Turbulence on Vane Aerodynamic Losses, Wake Growth, and the Exit Turbulence Parameters." Journal of Turbomachinery 119, no. 2 (1997): 182–92. http://dx.doi.org/10.1115/1.2841100.

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An experimental research program was undertaken to examine the influence of large-scale high-intensity turbulence on vane exit losses, wake growth, and exit turbulence characteristics. The experiment was conducted in a four-vane linear cascade at an exit Reynolds number of 800,000 based on chord length and an exit Mach number of 0.27. Exit measurements were made for four inlet turbulence conditions including a low-turbulence case (Tu ≈ 1 percent), a grid-generated turbulence case (Tu ≈ 7.5. percent) and two levels of large-scale turbulence generated with a mock combustor (Tu ≈ 12 and 8 percent

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O’Brien, J. E., and S. P. Capp. "Two-Component Phase-Averaged Turbulence Statistics Downstream of a Rotating Spoked-Wheel Wake Generator." Journal of Turbomachinery 111, no. 4 (1989): 475–82. http://dx.doi.org/10.1115/1.3262296.

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Measurements of the axial and tangential components of the unsteady turbulent flow downstream of a rotating spoked-wheel wake generator have been obtained. The results of this study have implications for the use of this type of wake generator to produce simulated turbine guide vane wakes. Instantaneous velocity information was phase averaged based on a signal synchronized with the bar-passing frequency. Mean velocity profiles and phase-averaged Reynolds stress results were found to be consistent with measurements obtained behind a stationary cylinder. Reynolds stresses were significantly highe

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7

Chow, Yi-Chih, Oguz Uzol, and Joseph Katz. "Flow Nonuniformities and Turbulent “Hot Spots” Due to Wake-Blade and Wake-Wake Interactions in a Multi-Stage Turbomachine." Journal of Turbomachinery 124, no. 4 (2002): 553–63. http://dx.doi.org/10.1115/1.1509078.

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This experimental study provides striking examples of the complex flow and turbulence structure resulting from blade-wake and wake-wake interactions in a multi-stage turbomachine. Particle image velocimetry (PIV) measurements are performed within the entire 2nd stage of a two-stage turbomachine. The experiments are performed in a facility that allows unobstructed view of the entire flow field, facilitated using transparent rotor and stator and a fluid that has the same optical index of refraction as the blades. This paper contains data on the phase-averaged flow structure including velocity, v

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Abramian, M., and J. H. G. Howard. "A Rotating Laser-Doppler Anemometry System for Unsteady Relative Flow Measurements in Model Centrifugal Impellers." Journal of Turbomachinery 116, no. 2 (1994): 260–68. http://dx.doi.org/10.1115/1.2928360.

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The behavior of the relative flow in centrifugal turbomachines is extremely complex due to the existence of various fluid dynamic phenomena and their interaction. At design and off-design operating conditions, the relative flow is subject to stationary unsteadiness, which includes the flow separation and wakes associated with passage pressure gradients, secondary flows, and boundary layer stability. It is also subject to periodic unsteadiness from the rotating stall and the cyclic flow phenomena induced by the casing. This paper describes the mechanical and optical design of a rotating laser-D

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Langtry, R. B., F. R. Menter, S. R. Likki, Y. B. Suzen, P. G. Huang, and S. Völker. "A Correlation-Based Transition Model Using Local Variables—Part II: Test Cases and Industrial Applications." Journal of Turbomachinery 128, no. 3 (2004): 423–34. http://dx.doi.org/10.1115/1.2184353.

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A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics (CFD) methods using unstructured grids and massive parallel execution. The model is based on two transport equations, one for the intermittency and one for the transition onset criteria in terms of momentum thickness Reynolds number. The proposed transport equations do not attempt to model the physics of the transition process (unlike, e.g., turbulence models), but form a framework for the implementatio

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Schobeiri, Meinhard T., Burak Öztürk, and David E. Ashpis. "On the Physics of Flow Separation Along a Low Pressure Turbine Blade Under Unsteady Flow Conditions." Journal of Fluids Engineering 127, no. 3 (2005): 503–13. http://dx.doi.org/10.1115/1.1905646.

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The present study, which is the first of a series of investigations dealing with specific issues of low pressure turbine (LPT) boundary layer aerodynamics, is aimed at providing detailed unsteady boundary flow information to understand the underlying physics of the inception, onset, and extent of the separation zone. A detailed experimental study on the behavior of the separation zone on the suction surface of a highly loaded LPT-blade under periodic unsteady wake flow is presented. Experimental investigations were performed at Texas A&M Turbomachinery Performance and Flow Research Laborat

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Dissertations / Theses on the topic "Wakes (Aerodynamics) Turbulence. Turbomachines"

1

Brock, Jerry S. "A modified Baldwin-Lomax turbulence model for turbomachinery wakes." Thesis, This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-09052009-040231/.

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Ali, Naseem Kamil. "Thermally (Un-) Stratified Wind Plants: Stochastic and Data-Driven Reduced Order Descriptions/Modeling." PDXScholar, 2018. https://pdxscholar.library.pdx.edu/open_access_etds/4634.

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Wind energy is one of the significant sources of renewable energy, yet a number of challenges preclude optimal operation of wind plants. Research is warranted in order to minimize the power losses and improve the productivity of wind plants. Here, a framework combining turbulence theory and data mining techniques is built to elucidate physics and mechanisms driving the energy extraction of the wind plants under a number of atmospheric/operating conditions. The performance of wind turbines is subjected to adverse effects caused by wake interactions. Therefore, it is crucial to understand wake-t

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Zhang, Di. "Turbulence Modeling and Simulation of Unsteady Transitional Boundary Layers and Wakes with Application to Wind Turbine Aerodynamics." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/81137.

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Wind energy industry thrived in the last three decades, environmental concerns and government regulations stimulate studies on wind farm location selection and wind turbine design. Full-scale experiments and high-fidelity simulations are restrictive due to the prohibitively high cost, while the model-scale experiments and low-fidelity calculations miss key flow physics of unsteady high Reynolds number flows. A hybrid RANS/LES turbulence model integrated with transition formulation is developed and tested by a surrogate model problem through joint experimental and computational fluid dynamics a

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Ghuge, Harshavardhan Roy Christopher J. "Detached eddy simulations of a simplified tractor-trailer geometry." Auburn, Ala., 2007. http://repo.lib.auburn.edu/2006%20Fall/Theses/GHUGE_HARSHAVARDHAN_18.pdf.

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Aseyev, Aleksandr Sergeyevich. "Vortex Identification in the Wake of a Wind Turbine Array." PDXScholar, 2015. https://pdxscholar.library.pdx.edu/open_access_etds/2217.

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Vortex identification techniques are used to analyze the flow structure in a 4 x 3 array of scale model wind turbines. Q-criterion, Δ-criterion, and λ2-criterion are applied to Particle Image Velocimetry data gathered fore and aft of the last row centerline turbine. Q-criterion and λ2-criterion provide a clear indication of regions where vortical activity exists while the Δ-criterion does not. Galilean decomposition, Reynolds decomposition, vorticity, and swirling strength are used to further understand the location and behavior of the vortices. The techniques identify and display the high mag

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Hamilton, Nicholas Michael. "Wake Character in the Wind Turbine Array: (Dis-)Organization, Spatial and Dynamic Evolution and Low-dimensional Modeling." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/3084.

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To maximize the effectiveness of the rapidly increasing capacity of installed wind energy resources, new models must be developed that are capable of more nuanced control of each wind turbine so that each device is more responsive to inflow events. Models used to plan wind turbine arrays and control behavior of devices within the farm currently make questionable estimates of the incoming atmospheric flow and update turbine configurations infrequently. As a result, wind turbines often operate at diminished capacities, especially in arrays where wind turbine wakes interact and inflow conditions

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Scott, Ryan. "Characterizing Tilt Effects on Wind Plants." PDXScholar, 2019. https://pdxscholar.library.pdx.edu/open_access_etds/5035.

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Tilting the nacelle of a wind turbine modifies entrainment into the wind plant and impacts total efficiency. Extreme angles can produce flying and crashing wakes where the wake either disrupts entertainment from the undisturbed flow above or is decimated on the ground. The effect of tilt angle on downstream wake behavior was investigated in a series of wind tunnel experiments. Scale model turbines with a hub height and diameter of 12 cm were arranged in a Cartesian array comprised of four rows of three turbines each. Nacelle tilt was varied in the third row from -15° to 15° in chosen 5° increm

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Subaschandar, N. "Turbulent Near Wake Behind An Infinitely Yawed Flat Plate." Thesis, Indian Institute of Science, 1995. http://hdl.handle.net/2005/146.

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Near wake is the region of wake flow just behind the trailing edge of the body where the flow is strongly influenced by the upstream flow conditions and also perhaps by the characteristics of the body. The present work is concerned with the study of the development of turbulent near wake behind an infinitely yawed flat plate. The turbulent near wake behind an infinitely yawed flat plate is the simplest of the three-dimensional turbulent near wake flows. The present study aims at providing a set of data on the turbulent near wake behind an infinitely yawed flat plate and also at understanding

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Books on the topic "Wakes (Aerodynamics) Turbulence. Turbomachines"

1

FEDERAL AVIATION ADMINISTRATION. Caution, wake turbulence. U.S. Dept. of Transportation, Federal Aviation Administration, 1995.

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2

Wake turbulence: An obstacle to increased air traffic capacity. National Academies Press, 2008.

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3

Dickinson, Wayne. A benthic chamber with electric stirrer mixing. Woods Hole Oceanographic Institution, 1992.

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4

Tatnall, Christopher Rhoads. An investigation of candidate sensor-observable wake vortex strength parameters for the NASA Aircraft Vortex Spacing System (AVOSS). National Aeronautics and Space Administration, Langley Research Center, 1998.

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5

Eldridge, Thomas Michael. The application of PDA to measure vaporizing droplets in a heated wake. 1994.

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6

Experimental study of vane heat transfer and aerodynamics at elevated levels of turbulence. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1994.

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Experimental study of vane heat transfer and aerodynamics at elevated levels of turbulence. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1994.

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8

J, Hall Edward, Delaney Robert A, and Lewis Research Center, eds. Follow-on low noise fan aerodynamic study: Task 15-final report. National Aeronautics and Space Administration, Lewis Research Center, 1999.

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J, Hall Edward, Delaney R. A, and Lewis Research Center, eds. Follow-on low noise fan aerodynamic study: Task 15-final report. National Aeronautics and Space Administration, Lewis Research Center, 1999.

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Follow-on low noise fan aerodynamic study: Task 15-final report. National Aeronautics and Space Administration, Lewis Research Center, 1999.

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Book chapters on the topic "Wakes (Aerodynamics) Turbulence. Turbomachines"

1

Neunaber, Ingrid. "Turbulence of Wakes." In Handbook of Wind Energy Aerodynamics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-05455-7_45-1.

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2

Ferrand, P., S. Aubert, G. Oliveira, and L. Smati. "A Numerical Analysis of Wakes Propagation in Inviscid Flow of Turbine." In Unsteady Aerodynamics and Aeroelasticity of Turbomachines. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5040-8_3.

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3

Wierciński, Z. "Nonlinear Critical Layer in the Unsteady Boundary Layer Induced on a Flat Plate by Wakes." In Unsteady Aerodynamics and Aeroelasticity of Turbomachines. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5040-8_2.

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Sentker, A., and W. Riess. "Unsteady Flow and Turbulence in a Low Speed Axial Compressor." In Unsteady Aerodynamics and Aeroelasticity of Turbomachines. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5040-8_18.

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Barnett, M., and J. M. Verdon. "Analysis of Blade Unsteady Boundary Layers and Wakes." In Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachines and Propellers. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4613-9341-2_19.

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Adachi, Tsutomu, and Yutaka Yamashita. "Passages of Preceding Blade Wakes and Their Effects in the Rotor Passages of a Single Stage Axial-Flow Fan." In Unsteady Aerodynamics and Aeroelasticity of Turbomachines. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5040-8_24.

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Conference papers on the topic "Wakes (Aerodynamics) Turbulence. Turbomachines"

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Nikparto, Ali, and Meinhard T. Schobeiri. "A New Physics Based Unsteady Transition Model Using the Universal Intermittency Function." In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/gt2019-90585.

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Abstract The flow inside a gas turbine engine has unique complexities. One of the important characteristics of such flow field is the existence of periodic unsteady wakes, originating from stator–rotor interaction. The unsteady wakes, with their highly vortical core, impinge on the downstream blade surfaces and cause an intermittent transition of the boundary layer from laminar to turbulent. The relative intermittency value corresponding to the wake vortical core and the calm region outside the wake, irrespective of freestream turbulence intensity and wake frequency, exhibits a universal behav

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2

Wolff, Torben, Florian Herbst, Oliver Freund, Le Liu, and Joerg R. Seume. "Validating the Numerical Prediction of the Aerodynamics of an Axial Compressor." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-25530.

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Numerical methods have become the basis for the aerodynamic design of turbomachinery in order to reduce the time for development cycles and associated cost. Designing modern axial compressors requires high confidence in the quality of numerical predictions. In terms of the aerodynamics, the loading of the blades as well as the efficiency targets constantly increase. Losses have to be predicted precisely and the impact of three-dimensional secondary flows, separation, and laminar-turbulent transition must be taken into account. In the present paper, the aerodynamic prediction quality of the sta

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Infantino, Daniele, Francesca Satta, Daniele Simoni, Marina Ubaldi, Pietro Zunino, and Francesco Bertini. "Phase-Locked Investigation of Secondary Flows Perturbed by Passing Wakes in a High-Lift LPT Turbine Cascade." In ASME Turbo Expo 2015: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/gt2015-42480.

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The present work describes the experimental investigations carried out at the Aerodynamics and Turbomachinery Laboratory of Genoa University aimed at characterizing the unsteady features of the secondary flows in a High-Lift Low Pressure Turbine cascade perturbed by incoming wakes. The investigations have been carried out at the nominal exit flow Reynolds number of 300000 in a 5-blade large-scale linear cascade. Hot-wire phase-locked ensemble-averaging technique has been applied to analyze in depth the time-dependent velocity and turbulence intensity distributions in a downstream tangential pl

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Nikparto, Ali, and Meinhard T. Schobeiri. "Numerical and Experimental Investigation of Aerodynamics on Flow Around a Highly Loaded Low-Pressure Turbine Blade With Flow Separation Under Steady and Periodic Unsteady Inlet Flow Condition." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56699.

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Understanding the behavior of flow field around a turbine blade is of importance in gas turbine engineering and it can affect the design and performance of engine elements. An important phenomena that can affect the flow regime is the effect that impinging wakes, originating from stator blades, have on the flow around rotor blades. Reynolds Averaged Navier-Stokes (RANS) equation, in conjunction with turbulence models enables us to model flow fields. This study numerically and experimentally investigates the behavior of the boundary layer development along the suction and pressure surfaces of a

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Dorney, Daniel J., Om P. Sharma, and Karen L. Gundy-Burlet. "Physics of Airfoil Clocking in a High-Speed Axial Compressor." In ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/98-gt-082.

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Axial compressors have inherently unsteady flow fields because of relative motion between rotor and stator airfoils. This relative motion leads to viscous and inviscid (potential) interactions between blade rows. As the number of stages increases in a turbomachine, the buildup of convected wakes can lead to progressively more complex wake/wake and wake/airfoil interactions. Variations in the relative circumferential positions of stators or rotors can change these interactions, leading to different unsteady forcing functions on airfoils and different compressor efficiencies. In addition, as the

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Abharl, Reza S., and Michael Giles. "A Navier Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping." In ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/95-gt-182.

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An unsteady, compressible, two dimensional, thin shear layer Navier Stokes solver is modified to predict the motion-dependent unsteady flow around oscillating airfoils in a cascade. A quasi 3-D formulation is used to account for the streamwise variation of streamtube height. The code uses Ni’s Lax-Wendroff algorithm in the outer region, an implicit ADI method in the inner region, conservative coupling at the interface, and the Baldwin-Lomax turbulence model. Computational mesh consists of an O-grid around each blade plus an unstructured outer grid of quadrilateral or triangular cells. The unst

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Elsner, Witold, Stephane Vilmin, Stanislaw Drobniak, and Wladyslaw Piotrowski. "Experimental Analysis and Prediction of Wake-Induced Transition in Turbomachinery." In ASME Turbo Expo 2004: Power for Land, Sea, and Air. ASMEDC, 2004. http://dx.doi.org/10.1115/gt2004-53757.

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The paper presents an experimental and numerical analysis of the interaction between wakes and boundary layers on aerodynamic blade profiles. The experiment revealed that incoming wakes interact with boundary layers and cause the significant increase of velocity fluctuations in the boundary layer and in consequence shift the transition zone towards the leading edge. The full time evolution of periodic wake induced transition was reproduced from measurements. The numerical simulation of the flow around the blade profile has been performed with the use of the adaptive grid viscous flow unNEWT PU

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Müller-Schindewolffs, Christoph, and Florian Herbst. "The Effect of Turbulent Scales on Low-Pressure Turbine Aerodynamics: Part A — An Optimized Turbulent Boundary-Condition." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75162.

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Exact inflow conditions for DNS and LES can be generated by resource-intensive precursor simulations of three-dimensional periodic boxes or infinite channels, in the case where a wall-bounded flow is investigated. A cheaper and much more flexible alternative is the use of synthetic boundary conditions. In the proposed paper, a modified synthetic-eddy-method will be presented, which suits the demands and specifications of turbo-machinery applications. It will further be extended to subsonic compressible flows by adding a mechanism to uncouple acoustic waves. It is applied to synthetically repro

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Persico, G., V. Dossena, B. Paradiso, L. Battisti, A. Brighenti, and E. Benini. "Three-Dimensional Character of VAWT Wakes: An Experimental Investigation for H-Shaped and Troposkien Architectures." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-57762.

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In this paper the aerodynamics and performance of two Vertical Axis Wind Turbines are discussed, on the basis of a wide set of experiments performed at Politecnico di Milano (Italy). A H-shaped and a Troposkien Darrieus turbine for micro-generation, characterized by the same swept area and blade section, are tested in real-scale. Performance measurements show that the Troposkien rotor outperforms the H-shaped turbine, mostly related to the larger midspan section of the Troposkien rotor (resulting by the constraint of constant swept area) and to the non-aerodynamic struts of the H-shaped rotor.

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Naskar, Souvik, and S. Sarkar. "Large Eddy Simulation of Wake-Shear Layer Interactions Over a Multi-Element Aerofoil." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-14115.

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Abstract Modern commercial airliners use multi-element aerofoils to enhance take-off and landing performance. Further, multielement aerofoil configurations have been shown to improve the aerodynamic characteristics of wind turbines. In the present study, high resolution Large Eddy Simulation (LES) is used to explore the low Reynolds Number (Re = 0.832 × 104) aerodynamics of a 30P30N multi-element aerofoil at an angle of attack, α = 4°. In the present simulation, wake shed from a leading edge element or slat is found to interact with the separated shear layer developing over the suction surface

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