Momentum Flux in Plane, Parallel Jets

2004 ◽  
Vol 126 (4) ◽  
pp. 665-670 ◽  
Author(s):  
Robert E. Spall ◽  
Elgin A. Anderson ◽  
Jeffrey Allen
Keyword(s):  
Kinetic Energy ◽  
Dissipation Rate ◽  
Momentum Flux ◽  
Stokes Equations ◽  
Turbulence Kinetic Energy ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Integral Constant ◽  
Plane Parallel ◽  
Merge Point

The evolution of the streamwise momentum flux for two turbulent, plane, parallel jets discharging through slots in a direction normal to a wall was studied both numerically and experimentally. The numerical results, obtained by solving the Reynolds-averaged Navier-Stokes equations employing a standard k−ε turbulence model, predicted to within experimental error measured integrals of the momentum flux downstream of the merge point for jet spacing S/d=5. Integration of the streamwise component of the Reynolds-averaged Navier-Stokes equations over a control volume results in an integral constant that was evaluated numerically for jet spacings S/d=3, 5, 7, 9, and 11, and for different levels of turbulence kinetic energy and dissipation rate at the jet inlet boundaries. Results revealed that the integral constant is decreased as the jet spacing increases, and is also decreased as jet entrainment rates are increased due to higher levels of inlet turbulence kinetic energy, or alternatively, decreased levels of dissipation rate. Streamwise distance to the merge point was also found to decrease for increased levels of turbulence kinetic energy or decreased levels of dissipation rate at the jet inlet.

scholarly journals AUTOMATIC INSERTION OF A TURBULENCE MODEL IN THE FINITE ELEMENT DISCRETIZATION OF THE NAVIER–STOKES EQUATIONS

2009 ◽  
Vol 19 (07) ◽  
pp. 1139-1183 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
TOMÁS CHACÓN REBOLLO ◽  
FRÉDÉRIC HECHT ◽  
ROGER LEWANDOWSKI
Keyword(s):  
Finite Element ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
A Posteriori Error Estimates ◽  
Navier Stokes ◽  
Mesh Adaptivity ◽  
Finite Element Discretization ◽  
Navier Stokes Equations ◽  
Element Discretization

We consider the finite element discretization of the Navier–Stokes equations locally coupled with the equation for the turbulent kinetic energy through an eddy viscosity. We prove a posteriori error estimates which allow to automatically determine the zone where the turbulent kinetic energy must be inserted in the Navier–Stokes equations and also to perform mesh adaptivity in order to optimize the discretization of these equations. Numerical results confirm the interest of such an approach.

Effect of the turbulence models on Rushton turbine generated flow in a stirred vessel

2011 ◽  
Vol 1 (4) ◽  
Author(s):  
Wajdi Chtourou ◽  
Meriem Ammar ◽  
Zied Driss ◽  
Mohamed Abid
Keyword(s):  
Dissipation Rate ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stirred Vessel ◽  
Rushton Turbine ◽  
Numerical Predictions ◽  
Volume Method

AbstractIn this paper, we performed a comparison of four turbulence models using for numerical simulation of the hydrodynamic structure generated by a Rushton turbine in a cylindrical tank. The finite volume method was employed to solve the Navier-Stokes equations governing the transport of momentum. In this study four closure models tested were: k-ɛ standard, k-ɛ RNG, k-ɛ Realizable and RSM (Reynolds Stress Model). MRF (Multi Reference Frame) technique was used with FLUENT software package. The present work aimed to provide improved predictions of turbulent flow in a stirred vessel and in particular to assess the ability to predict the dissipation rate of turbulent kinetic energy (e) that constitutes a most stringent test of prediction capability due to the small scales at which dissipation takes place. The amplitude of local and overall dissipation rate is shown to be strongly dependent on the choice of turbulence model. The numerical predictions were compared with literature results for comparable configurations and with experimental data obtained using Particle Image Velocimetry (PIV). A very good agreement was found with regards to turbulence.

scholarly journals A Modified Gas-Kinetic Scheme for Turbulent Flow

2014 ◽  
Vol 16 (1) ◽  
pp. 239-263 ◽  
Author(s):  
Marcello Righi
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Turbulent Stress ◽  
Navier Stokes Equations

AbstractThe implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

scholarly journals Simulations of Moving Effect of Coastal Vegetation on Tsunami Damping

2016 ◽  
Author(s):  
Ching-Piao Tsai ◽  
Ying-Chi Chen ◽  
Tri Octaviani Sihombing ◽  
Chang Lin
Keyword(s):  
Energy Dissipation ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Wave Height ◽  
Stokes Equations ◽  
Coastal Vegetation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Closure ◽  
Gmo Model

Abstract. A coupled wave-vegetation simulation is presented for the moving effect of the coastal vegetation on tsunami wave height damping. The problem is idealized by solitary wave propagating on a group of emergent cylinders. The numerical model is based on general Reynolds-averaged Navier-Stokes equations associated with renormalization group turbulent closure model by using volume of fluid technique. The general moving object (GMO) model developed in CFD code Flow-3D is applied to simulate the coupled motion of vegetation with wave dynamically. The damping of wave height and the turbulent kinetic energy dissipation as waves passed over both moving and stationary cylinders are discussed. As comparing with the stationary cylinders, it obtains markedly less wave height damping and turbulent kinetic energy dissipation by the moving cylinders. The result implies that the wave decay by the coastal vegetation might be overestimated if the mangrove vegetation was represented as stationary state.

LES of Compressible Turbulent Annular Pipe Flow With a Rotating Wall

2003 ◽  
Author(s):  
Joon Sang Lee ◽  
Xiaofeng Xu ◽  
R. H. Pletcher
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Stokes Equations ◽  
Outer Wall ◽  
Navier Stokes ◽  
Subgrid Scale ◽  
Turbulent Structures ◽  
Navier Stokes Equations ◽  
Rotating Wall ◽  
Annular Pipe

Flow in an annular pipe with and without a wall rotating about its axis was investigated at moderate Reynolds numbers. The compressible filtered Navier-Stokes equations were solved using a second order accurate finite volume method. Low Mach number preconditioning was used to enable the compressible code to work efficiently at low Mach numbers. A dynamic subgrid-scale stress model accounted for the subgrid-scale turbulence. When the outer wall rotated, a significant reduction of turbulent kinetic energy was realized near the rotating wall and the intensity of bursting effects appeared to decrease. This modification of the turbulent structures was related to the vortical structure changes near the rotating wall. It has been observed that the wall vortices were pushed in the direction of rotation and their intensity increased near the non-rotating wall. The consequent effect was to enhance the turbulent kinetic energy and increased the intensity of the heat transfer rate there.

Transient inertial hydrodynamic interaction between two identical spheres settling at small Reynolds number

2008 ◽  
Vol 605 ◽  
pp. 263-279 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Relative Motion ◽  
Hydrodynamic Interaction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Reynolds Number ◽  
Navier Stokes Equations ◽  
Small Constant ◽  
Distance Vector

The flow pattern generated by a sphere accelerated from rest by a small constant applied forceshows scaling behaviour at long times, as can be shown from the solution of the linearized Navier–Stokes equations. In the scaling regime the kinetic energy of the flow grows with thesquare root of time. For two distant settling spheres starting from rest the kinetic energy ofthe flow depends on the distance vector between centres; owing to interference of the flowpatterns. It is argued that this leads to relative motion of the two spheres. Thecorresponding interaction energy is calculated explicitly in the scaling regime.

scholarly journals Simulations of moving effect of coastal vegetation on tsunami damping

2017 ◽  
Vol 17 (5) ◽  
pp. 693-702 ◽  
Author(s):  
Ching-Piao Tsai ◽  
Ying-Chi Chen ◽  
Tri Octaviani Sihombing ◽  
Chang Lin
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Wave Height ◽  
Stokes Equations ◽  
Coastal Vegetation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Turbulent Closure ◽  
Computational Fluid Dynamics Cfd ◽  
Gmo Model

Abstract. A coupled wave–vegetation simulation is presented for the moving effect of the coastal vegetation on tsunami wave height damping. The problem is idealized by solitary wave propagation on a group of emergent cylinders. The numerical model is based on general Reynolds-averaged Navier–Stokes equations with renormalization group turbulent closure model by using volume of fluid technique. The general moving object (GMO) model developed in computational fluid dynamics (CFD) code Flow-3D is applied to simulate the coupled motion of vegetation with wave dynamically. The damping of wave height and the turbulent kinetic energy along moving and stationary cylinders are discussed. The simulated results show that the damping of wave height and the turbulent kinetic energy by the moving cylinders are clearly less than by the stationary cylinders. The result implies that the wave decay by the coastal vegetation may be overestimated if the vegetation was represented as stationary state.

scholarly journals Weak Solutions and Their Kinetic Energy Regarding Time-Periodic Navier–Stokes Equations in Three Dimensional Whole-Space

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1528
Author(s):  
Mads Kyed
Keyword(s):  
Kinetic Energy ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Periodic Forcing ◽  
Navier Stokes Equations ◽  
Whole Space ◽  
Time Periodic Solutions ◽  
Time Periodic

The existence of weak time-periodic solutions to Navier–Stokes equations in three dimensional whole-space with time-periodic forcing terms are established. The solutions are constructed in such a way that the structural properties of their kinetic energy are obtained. No restrictions on either the size or structure of the external force are required.

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