On a Leray–α model of turbulence

2005 ◽  
Vol 461 (2055) ◽  
pp. 629-649 ◽  
Author(s):  
Alexey Cheskidov ◽  
Darryl D. Holm ◽  
Eric Olson ◽  
Edriss S. Titi
Keyword(s):  
Power Law ◽  
Upper Bound ◽  
Empirical Data ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Large Eddy Simulation Model ◽  
Eddy Simulation ◽  
Wide Range ◽  
Three Dimensional Models

In this paper we introduce and study a new model for three–dimensional turbulence, the Leray– α model. This model is inspired by the Lagrangian averaged Navier–Stokes– α model of turbulence (also known Navier–Stokes– α model or the viscous Camassa–Holm equations). As in the case of the Lagrangian averaged Navier–Stokes– α model, the Leray– α model compares successfully with empirical data from turbulent channel and pipe flows, for a wide range of Reynolds numbers. We establish here an upper bound for the dimension of the global attractor (the number of degrees of freedom) of the Leray– α model of the order of ( L / l d ) 12/7 , where L is the size of the domain and l d is the dissipation length–scale. This upper bound is much smaller than what one would expect for three–dimensional models, i.e. ( L / l d ) 3 . This remarkable result suggests that the Leray– α model has a great potential to become a good sub–grid–scale large–eddy simulation model of turbulence. We support this observation by studying, analytically and computationally, the energy spectrum and show that in addition to the usual k −5/3 Kolmogorov power law the inertial range has a steeper power–law spectrum for wavenumbers larger than 1/ α . Finally, we propose a Prandtl–like boundary–layer model, induced by the Leray– α model, and show a very good agreement of this model with empirical data for turbulent boundary layers.

scholarly journals Large Eddy Simulations of Turbulent and Buoyant Flows in Urban and Complex Terrain Areas Using the Aeolus Model

Atmosphere ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1107
Author(s):  
Akshay A. Gowardhan ◽  
Dana L. McGuffin ◽  
Donald D. Lucas ◽  
Stephanie J. Neuscamman ◽  
Otto Alvarez ◽  
...  
Keyword(s):  
Urban Areas ◽  
Complex Terrain ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Buoyant Plumes ◽  
Flow And Transport ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy ◽  
Radiological Dispersal

Fast and accurate predictions of the flow and transport of materials in urban and complex terrain areas are challenging because of the heterogeneity of buildings and land features of different shapes and sizes connected by canyons and channels, which results in complex patterns of turbulence that can enhance material concentrations in certain regions. To address this challenge, we have developed an efficient three-dimensional computational fluid dynamics (CFD) code called Aeolus that is based on first principles for predicting transport and dispersion of materials in complex terrain and urban areas. The model can be run in a very efficient Reynolds average Navier–Stokes (RANS) mode or a detailed large eddy simulation (LES) mode. The RANS version of Aeolus was previously validated against field data for tracer gas and radiological dispersal releases. As a part of this work, we have validated the Aeolus model in LES mode against two different sets of data: (1) turbulence quantities measured in complex terrain at Askervein Hill; and (2) wind and tracer data from the Joint Urban 2003 field campaign for urban topography. As a third set-up, we have applied Aeolus to simulate cloud rise dynamics for buoyant plumes from high-temperature explosions. For all three cases, Aeolus LES predictions compare well to observations and other models. These results indicate that Aeolus LES can be used to accurately simulate turbulent flow and transport for a wide range of applications and scales.

scholarly journals A comparison of Newtonian and non-Newtonian models for pulsatile blood flow simulations

2013 ◽  
Vol 21 (5-6) ◽  
pp. 147-153 ◽  
Author(s):  
Iqbal Husain ◽  
Fotini Labropulu ◽  
Chris Langdon ◽  
Justin Schwark
Keyword(s):  
Blood Flow ◽  
Power Law ◽  
Three Dimensional ◽  
Arterial Stenosis ◽  
Pulsatile Blood Flow ◽  
Blood Flows ◽  
Newtonian Model ◽  
Wide Range ◽  
Flow Effects ◽  
Three Dimensional Models

AbstractMathematical modeling of blood flows in the arteries is an important and challenging problem. This study compares several non-Newtonian blood models with the Newtonian model in simulating pulsatile blood flow through two three-dimensional models of an arterial stenosis and an aneurysm. Four non-Newtonian blood models, namely the Power Law, the Casson, the Carreau, and the Generalized Power Law, as well as the Newtonian model of blood viscosity, are used to investigate the flow effects induced by these different blood constitutive equations. The aim of this study is three-fold: firstly, to investigate the variation in wall shear stress in an artery with a stenosis or aneurysm at different flow rates and degrees of severity; secondly, to compare the various blood models and hence quantify the differences between the models and judge their significance; and lastly, to determine whether the use of the Newtonian blood model is appropriate over a wide range of shear rates.

On LES Methods Applied to Seal Geometries

2012 ◽  
Author(s):  
James Tyacke ◽  
Richard Jefferson-Loveday ◽  
Paul Tucker
Keyword(s):  
Maximum Error ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Final Solution ◽  
Complex Flow ◽  
Eddy Simulation ◽  
Wide Range ◽  
Large Eddy ◽  
Rans Models ◽  
Flow Through

Nine Large Eddy Simulation (LES) methods are used to simulate flow through two labyrinth seal geometries and are compared with a wide range of Reynolds-Averaged Navier-Stokes (RANS) solutions. These involve one-equation, two-equation and Reynolds Stress RANS models. Also applied are linear and nonlinear pure LES models, hybrid RANS-Numerical-LES (RANS-NLES) and Numerical-LES (NLES). RANS is found to have a maximum error and a scatter of 20%. A similar level of scatter is also found among the same turbulence model implemented in different codes. In a design context, this makes RANS unusable as a final solution. Results show that LES and RANS-NLES is capable of accurately predicting flow behaviour of two seals with a scatter of less than 5%. The complex flow physics gives rise to both laminar and turbulent zones making most LES models inappropriate. Nonetheless, this is found to have minimal tangible results impact. In accord with experimental observations, the ability of LES to find multiple solutions due to solution non-uniqueness is also observed.

The Extension of a Solution-Adaptive Three-Dimensional Navier–Stokes Solver Toward Geometries of Arbitrary Complexity

1993 ◽  
Vol 115 (2) ◽  
pp. 283-295 ◽  
Author(s):  
W. N. Dawes
Keyword(s):  
Guide Vane ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Wide Range ◽  
Nozzle Guide Vane ◽  
Recent Developments ◽  
Nozzle Guide

This paper describes recent developments to a three-dimensional, unstructured mesh, solution-adaptive Navier–Stokes solver. By adopting a simple, pragmatic but systematic approach to mesh generation, the range of simulations that can be attempted is extended toward arbitrary geometries. The combined benefits of the approach result in a powerful analytical ability. Solutions for a wide range of flows are presented, including a transonic compressor rotor, a centrifugal impeller, a steam turbine nozzle guide vane with casing extraction belt, the internal coolant passage of a radial inflow turbine, and a turbine disk cavity flow.

Large Eddy Simulation of Cross Flow in Pipe Junction

2018 ◽  
Author(s):  
Jiajun Chen ◽  
Yue Sun ◽  
Hang Zhang ◽  
Dakui Feng ◽  
Zhiguo Zhang
Keyword(s):  
Large Eddy Simulation ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cross Flow ◽  
Exciting Force ◽  
Navier Stokes ◽  
Pipe Network ◽  
Eddy Simulation ◽  
Large Eddy

Mixing in pipe junctions can play an important role in exciting force and distribution of flow in pipe network. This paper investigated the cross pipe junction and proposed an improved plan, Y-shaped pipe junction. The numerical study of a three-dimensional pipe junction was performed for calculation and improved understanding of flow feature in pipe. The filtered Navier–Stokes equations were used to perform the large-eddy simulation of the unsteady incompressible flow in pipe. From the analysis of these results, it clearly appears that the vortex strength and velocity non-uniformity of centerline, can be reduced by Y-shaped junction. The Y-shaped junction not only has better flow characteristic, but also reduces head loss and exciting force. The results of the three-dimensional improvement analysis of junction can be used in the design of pipe network for industry.

scholarly journals Representing the War. Early Twentieth Century Maps and Models in the Fonds of the Italian War History Museum in Rovereto

2021 ◽  
Vol 4 ◽  
pp. 1-8
Author(s):  
Elena Dai Prà ◽  
Valentina De Santi ◽  
Giannantonio Scaglione
Keyword(s):  
Twentieth Century ◽  
Three Dimensional ◽  
Field Surveys ◽  
History Museum ◽  
Early Twentieth Century ◽  
Wide Range ◽  
The First World War ◽  
Three Dimensional Models ◽  
The University ◽  
First World

Abstract. The representation of the areas in which some of the most significant events of the First World War took place has produced a wide range of materials, such as cartography, aerial and terrestrial photos, textual descriptions and field surveys. In addition, war events were also represented through three-dimensional models. Topographic maps and models constitute composite figurations, which are rich in informative data useful for the preservation of the memory of places and for increasing the knowledge of cultural heritage. Hence, these sources need to be studied, described, interpreted and used for future enhancement. The focus of this paper are archival materials from the collections kept at the Italian War History Museum of Rovereto (Museo Storico Italiano della Guerra), in the Trentino-Alto Adige region. Firstly, we will investigate the cartographic fond in order to assess the composition and origin of its materials. Secondly, we will present the Museum’s collection of Early-Twentieth Century models. Such precious heritage is not yet part of an exhibition, and is kept in the Museum’s warehouses. The paper constitutes the occasion to present the initial results of a still ongoing project by the Geo-Cartographic Centre for Study and Documentation (GeCo) of the University of Trento on the study and analysis of two archival complexes preserved in the abovementioned Museum. In particular, the paper focuses on the heuristic value of such representational devices, which enable an analysis of the different methods and languages through which space is planned and designed, emphasizing the complementarity between different types of visualization.

Laminarization of Internal Flows Under the Combined Effect of Strong Curvature and Rotation

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
K. M. Guleren ◽  
I. Afgan ◽  
A. Turan
Keyword(s):  
Secondary Flows ◽  
Combined Effect ◽  
Navier Stokes ◽  
Duct Flow ◽  
Internal Flows ◽  
Square Duct ◽  
Eddy Simulation ◽  
Numerical Predictions ◽  
Wide Range ◽  
Strong Curvature

The laminarization phenomenon for the flow under the combined effect of strong curvature and rotation is discussed based on numerical predictions of large-eddy simulation (LES). Initially, the laminarization process is presented for the fully developed flow inside a spanwise rotating straight square duct. LES predictions over a wide range of rotation numbers (Ro=0–5) show that the turbulent kinetic energy decreases monotonically apart from 0.2<Ro<0.5. Subsequently, a spanwise rotating U-duct flow is considered with Ro=±0.2. The interaction of curvature and Coriolis induced secondary flows enhances the turbulence for the negative rotating case, whereas this interaction ensues strong laminarization for the positive rotating case. Finally, the laminarization is presented in the impeller of a typical centrifugal compressor, rotating at a speed of Ω=1862rpm(Ro=0.6). The resulting LES predictions are observed to be better than those of Reynolds-averaged Navier-Stokes (RANS) in the regions where turbulence is significant. However, for the regions dominated by strong laminarization, RANS results are seen to approach those of LES and experiments.

scholarly journals Influence of Dimple Height on Turbulent Heat Transfer of Fin Array with Alternate Convex/Concave Dimples

Inventions ◽  
2020 ◽  
Vol 5 (3) ◽  
pp. 33
Author(s):  
Horng-Wen Wu ◽  
Tang-Hong Chen ◽  
Nugroho-Putra Kelana ◽  
De-An Huang
Keyword(s):  
Flow Field ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Heat Transfer ◽  
Navier Stokes ◽  
Bottom Surface ◽  
Turbulent Heat ◽  
Algebraic Equations ◽  
Eddy Simulation ◽  
Turbulent Modeling

This study analyzes transient turbulent modeling of three-dimensional multiple dimpled fin array using large eddy simulation (LES). The Navier–Stokes equations as well as the energy equation were constructed by the finite volume method and then discretized to form algebraic equations, which were solved by semi-implicit method for pressure-linked equation (SIMPLE). The solutions of temperature and velocity were obtained by iterating computation until it converged within each step. This simulation places nine fins on the bottom surface of a channel and changes the height of the dimple (0.4, 0.8, and 1.2 mm) with three different levels of Reynolds number (Re) (3500, 5000, and 6500) to investigate the temperature and flow field without gravity in forced convection. The results indicate that the dimpled fin array can generate vortices between the convex/concave dimples and the fin base and increase the influences of the height of the dimple on the flow field around the fin array. The averaged time-mean of the Nusselt number (Nu) for the dimple height of 0.8 mm is higher than that of the no-dimple case up to 14.4%, while the averaged time-mean Nu for the dimple height of 1.2 mm is lower than that of the no-dimple case up to 11.6%.

Do Arm Postures Vary With the Speed of Reaching?

1999 ◽  
Vol 81 (5) ◽  
pp. 2582-2586 ◽  
Author(s):  
Kiisa C. Nishikawa ◽  
Sara T. Murray ◽  
Martha Flanders
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Optimal Solution ◽  
Reaching Movements ◽  
Total Force ◽  
Joint Torques ◽  
Dynamic Factors ◽  
Human Arm ◽  
Wide Range ◽  
Dynamic Forces

Do arm postures vary with the speed of reaching? For reaching movements in one plane, the hand has been observed to follow a similar path regardless of speed. Recent work on the control of more complex reaching movements raises the question of whether a similar “speed invariance” also holds for the additional degrees of freedom. Therefore we examined human arm movements involving initial and final hand locations distributed throughout the three-dimensional (3D) workspace of the arm. Despite this added complexity, arm kinematics (summarized by the spatial orientation of the “plane of the arm” and the 3D curvature of the hand path) changed very little for movements performed over a wide range of speeds. If the total force (dynamic + quasistatic) had been optimized by the control system (e.g., as in a minimization of the change in joint torques or the change in muscular forces), the optimal solution would change with speed; slow movements would reflect the minimal antigravity torques, whereas fast movements would be more strongly influenced by dynamic factors. The speed-invariant postures observed in this study are instead consistent with a hypothesized optimization of only the dynamic forces.

Performance Analysis of Nek5000 for Single-Assembly Calculations

2018 ◽  
Author(s):  
Elia Merzari ◽  
Ronald Rahaman ◽  
Misun Min ◽  
Paul Fischer
Keyword(s):  
Degrees Of Freedom ◽  
Hybrid Approach ◽  
Reactor Core ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Application Development ◽  
Pressurized Water ◽  
Eddy Simulation ◽  
Common Framework ◽  
Full Core

The ExasSMR project focuses on the exascale application of single and coupled Monte Carlo (MC) and computational fluid dynamics (CFD) physics. Work is based on the Shift MC depletion, OpenMC temperature-dependent MC, and Nek5000 CFD codes. The application development objective is to optimize these applications for exascale execution of full-core simulations and to modularize and integrate them into a common framework for coupled and individual execution. Given the sheer scale of nuclear systems, the main algorithmic driver on the CFD side is weak scaling. The focus for the first four years of the project is on demonstrating scaling up to a full reactor core for high-fidelity simulations of turbulence. Full-core fluid calculations aimed at better predicting the steady-state performance will be conducted with a hybrid approach in which large eddy simulation is used to simulate a portion of a core and unsteady Reynolds-averaged Navier-Stokes handles the rest. This zonal hybrid approach provides an additional scaling dimension besides the number of assemblies. The present manuscript focuses on performance assessment using assembly-level simulations with Nek5000. We discuss the development of two benchmark problems: a subchannel (single-rod) problem to assess internode performance and a larger full-assembly problem representative of a small modular reactor (SMR). We note that current SMR assemblies are considerably simpler than pressurized water reactor assemblies since they contain no mixing vanes. This feature allows for considerable reduction in the degrees of freedom required to simulate the full core. We discuss profiling and scaling results with Nek5000, describe current bottlenecks and potential limitations of the approach, and suggest optimizations for future investigation.

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