The Reynolds Stress in Channel Flows From a Lagrangian Treatment of the Turbulence Momentum

2019 ◽  
Author(s):  
T.-W. Lee
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Current Approach ◽  
Navier Stokes ◽  
Current Transport ◽  
Lagrangian Analysis ◽  
Navier Stokes Equation ◽  
Mechanistic Approach ◽  
Turbulent Momentum

Abstract We have developed a mechanistic approach for determination of the Reynolds stress, using a Lagrangian analysis of turbulent momentum. Analysis and comparison with DNS and experimental data point toward the soundness of this approach (Lee, 2018). von Karman constant, the inner layer thickness and the Reynolds stress itself are all recovered through this approach, in agreement with DNS data. In addition, the turbulent flow profiles can be calculated iteratively using the basic Reynolds-averaged Navier-Stokes equation, in conjunction with the current transport equation for the Reynolds stress. In this work, we explore these and further uses of the current approach in solving turbulent flow dynamics.

Computational simulation of turbulent flows around a marine propeller by solving the partially averaged Navier–Stokes equation

2019 ◽  
Vol 233 (18) ◽  
pp. 6357-6366
Author(s):  
Woochan Seok ◽  
Sang Bong Lee ◽  
Shin Hyung Rhee
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Stokes Equation ◽  
Leading Edge ◽  
Reynolds Stress Model ◽  
Navier Stokes ◽  
Stress Model ◽  
Navier Stokes Equation ◽  
Local Flow ◽  
Reynolds Averaged Navier Stokes

This study concerns the characteristics of the partially averaged Navier–Stokes method for local flow analysis around a rotating propeller. Partially averaged Navier–Stokes, resolving crucial large-scale structures of turbulent flow at a given computational grid resolution, is a bridging turbulence closure model between the Reynolds-averaged Navier–Stokes equation and the direct numerical simulation. A detailed comparison between partially averaged Navier–Stokes and Reynolds-averaged Navier–Stokes models is made to achieve a better understanding of partially averaged Navier–Stokes characteristics for predicting the coherent structures in turbulent flow. The two-equation k-ω shear stress transport model and the seven-equation Reynolds stress model are selected for Reynolds-averaged Navier–Stokes computations. The problem of interest is the flow around a rotating KP505 propeller in open water conditions at an advance ratio of 0.7. Near the leading edge, the partially averaged Navier–Stokes results are similar to those of Reynolds stress model in terms of the vortical structures. Vorticity predicted by different turbulence models, however, shows significant differences. For a more detailed analysis, the velocity gradient constituting the vorticity is identified at the leading edge. It is proven that partially averaged Navier–Stokes is able to capture the anisotropic characteristics of the flow at the leading edge, where both the geometric and flow characteristics change abruptly.

Analytical Solution of Hydrostatic Pocket Tilting

2016 ◽  
Vol 821 ◽  
pp. 113-119 ◽  
Author(s):  
Eduard Stach ◽  
Jiří Falta ◽  
Matěj Sulitka
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Detailed Model ◽  
Limit Values ◽  
Inertia Effects ◽  
Proposed Model ◽  
Machine Tool Structure

Tilting (parallelism error) of guiding surfaces may cause reduction of load capacity of hydrostatic (HS) guideways and bearings in machine tools (MT). Using coupled finite element (FE) computational models of MT structures, it is nowadays possible to determine the extent of guiding surfaces deformation caused by thermal effects, gravitational force, cutting forces and inertia effects. Assessment of maximum allowable tilt has so far been based merely on experience. The paper presents a detailed model developed for description of the effect of HS bearing tilt on the load capacity characteristics of HS guideways. The model allows an evaluation of the tilt influence on the change of the characteristics as well as determination of the limit values of allowable tilt in interaction with compliant machine tool structure. The proposed model is based on the model of flow over the land of the HS pocket under extended Navier-Stokes equation. The model is verified using an experimental test rig.

scholarly journals An Intrinsic Formulation of Incompressible Navier-Stokes Turbulent Flow

2019 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Navier Stokes ◽  
Natural Consequence ◽  
Mean Velocity ◽  
Turbulence Transition ◽  
The Mean

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

A Priori Analysis of Explicit Algebraic Stress Models for a Turbulent Flow Through a Straight Square Duct

2004 ◽  
Author(s):  
H. Naji ◽  
O. El Yahyaoui ◽  
G. Mompean
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Stokes Equations ◽  
A Priori ◽  
Proximity Effects ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Duct ◽  
Anisotropy Tensor ◽  
Stress Models

The ability of two explicit algebraic Reynolds stress models (EARSMs) to accurately predict the problem of fully turbulent flow in a straight square duct is studied. The first model is devised by Gatski and Rumsey (2001) and the second is the one derived by Wallin and Johansson (2000). These models are studied using a priori procedure based on data resulting from direct numerical simulation (DNS) of the Navier-Stokes equations, which is available for this problem. For this case, we show that the equilibrium assumption for the anisotropy tensor is found to be correct. The analysis leans on the maps of the second and third invariants of the Reynolds stress tensor. In order to handle wall-proximity effects in the near-wall region, damping functions are implemented in the two models. The predictions and DNS obtained for a Reynolds number of 4800 both agree well and show that these models are able to predict such flows.

Validation of the INS3D-UP Code in the Prediction of Turbulent Flow of Liquid Propellants in a Sharp Bend

1995 ◽  
Author(s):  
M. A. R. Sharif ◽  
J. T. Haskew
Keyword(s):  
Turbulent Flow ◽  
Space Shuttle ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Sharp Bend ◽  
Flow Problems ◽  
Fortran Code ◽  
Main Engine ◽  
Liquid Propellants

Abstract The capability of the INS3D-UP code in the prediction of turbulent flow in a sharp bend of circular cross-section has been investigated. The code, developed by the NASA Ames Research Center, is being used by the NASA Marshal Space Flight Center to analyze turbulent flow of liquid propellant in vaned pipe bends designed for use in the Space Shuttle Main Engine. The FORTRAN code is based on finite difference method and uses the concept of pseudocompressibility to solve incompressible Navier-Stokes equation. The Baldwin-Barth turbulence model is embedded in the code for turbulence computation. The flow field, at a Reynolds number of 43,000, in a sharp 90° bend has been predicted and compared with measurement. It is found that the agreement between the predicted and measured velocities is very well. The predicted pressures at the bend wall also compares reasonably well with the measurement. It is concluded that the INS3D-UP code is a good computational tool to analyze similar flow problems.

Preliminary Imaging of Red Blood Cells in Turbulent Flow

2012 ◽  
Author(s):  
Mostafa Shakeri ◽  
Iman Khodarahmi ◽  
M. Keith Sharp
Keyword(s):  
Turbulent Flow ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Imaging System ◽  
Navier Stokes ◽  
Viscous Stress ◽  
Damage Potential ◽  
Navier Stokes Equation ◽  
Considerable Uncertainty ◽  
Mathematical Construct

Considerable uncertainty exists about how momentum and energy are transferred to cells in turbulent flow, which has been shown to cause six times more damage to red blood cells (RBC’s) than laminar flow with the same mean wall shear stress [Kameneva, et al. 2004]. Though it is a purely mathematical construct to yield closure of the time-averaged Navier-Stokes equation for a continuum fluid, which is not valid at the scale of the cell, Reynolds stress has been used as an empirical indicator for damage potential [Sallam & Hwang 1984]. Other scales, including local viscous stress [Jones 1995], flow of plasma around inertia cells [Quinlan & Dooley 2007], shear within eddies [Quinlan & Dooley 2007] and shear between rigid cells within an eddy [Antiga & Steinman 2009], have been forwarded. To provide data to validate these models, an imaging system was assembled to directly observe RBC’s in turbulent flow under a microscope.

scholarly journals An Intrinsic Formulation of Incompressible Navier-Stokes Turbulent Flow

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Velocity Field ◽  
Turbulent Flow ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Velocity Fluctuation ◽  
Navier Stokes ◽  
Natural Consequence ◽  
Mean Velocity ◽  
Turbulence Transition ◽  
The Mean

This paper proposed an explicit and simple representation of velocity fluctuation and the Reynolds stress tensor in terms of the mean velocity field. The proposed turbulence equations are closed. The proposed formulations reveal that the mean vorticity is the key source of producing turbulence. It is found that there are no velocity fluctuation and turbulence if there were no vorticity. As a natural consequence, the laminar- turbulence transition condition was obtained in a rational way.

CFD Simulation of Coaxial Jet Mixer Using RANS Turbulent Models

2012 ◽  
Vol 326-328 ◽  
pp. 416-421 ◽  
Author(s):  
Ku Zilati Ku Shaari ◽  
Afiq Mohd Laziz ◽  
Kerstin Heinen ◽  
Mokhtar Awang ◽  
Suriati Sufian ◽  
...  
Keyword(s):  
Turbulent Flow ◽  
Cfd Simulation ◽  
Navier Stokes ◽  
Suitable Model ◽  
Navier Stokes Equation ◽  
Rans Model ◽  
Turbulent Models ◽  
Simulation Time ◽  
Selection Of ◽  
Good Agreement

The Reynolds Averaged Navier Stokes Equation (RANS) model was used to describe the turbulent flow in a coaxial jet mixer. The effects of turbulent models on the turbulent flow is investigated to help the engineers and researchers in deciding the selection of turbulent model need to be used in order to save the simulation time and to predict the best suitable model to be used. Good agreement of the CFD prediction with the experimental data in certain locations was obtained with species transport and velocity profiled, where dependence of turbulent models and grid sizes were discussed in detail. The results show that, the need of grid study is crucial to obtain reliable results with optimum consumption of computer power. SST and Launder Gibson RSTM models give results superior to the other models, each of which has its own area of capability. Launder Gibson RSTM is good in predicting the flow with recirculation and vortices, while SST is good for the flow with less recirculation and high velocity. The overall results show that RANS model is capable in predicting the area of mixing and the velocity profile correctly in certain locations but not in reproducing the vortices structure in the pipe and nozzle.

Vortex Transport in Separating Flows and Role of Vortical Structures in Reynolds Stress Production and Distribution

2005 ◽  
Author(s):  
Miad Yazdani ◽  
Yasmin Khakpour
Keyword(s):  
Reynolds Stress ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Vortical Structures ◽  
Open Questions ◽  
Production And Distribution ◽  
History Of ◽  
Separating Flows

In this paper we will present some approaches on Reynolds stress production by vortex transport phenomena and nonlinear vorticity generation in momentum equation. First of all we represent a history of recent works to describe how fluid particle motions can be associated with Reynolds stress through either displacement or acceleration terms. In the next section we will describe how vortex stretching causes the Reynolds stress production and what is the dominant effect near and far from the boundary where viscous effects have to be considered. On the other hand, some vortex considered methodologies such as those synthesize boundary layer, as a collection of vortical objects seem to be inappropriate in general flow configuration. Therefore, there must be a moderate consideration in which both vortex and momentum transports come into account as it is done in LES. Furthermore since there exist open questions on Reynolds stress distribution in complex flows such as those with separation, our particular attention is paid to such effects due to vortical structures in separating flows. Further discussions include turbulence development caused by either vortex stretching or gradient terms that is determined by predominant conditions. However, it is seen that at the beginning, vorticity generators in Navier-Stokes equation contribute to dissipation effect. In addition, since such contribution corresponds to vorticity alignment, we investigate maximum vortex aligning and the effects of which causes the deviation of such alignment. The paper provides theoretical and numerical comparisons, where in the former, the vortical structure role is taken into account.

scholarly journals The concept of turbulent «vortex backfill» - models and methods. Power engineering: research, equipment, technology

2019 ◽  
Vol 21 (5) ◽  
pp. 97-109
Author(s):  
L. E. Melamed ◽  
G. A. Filippov
Keyword(s):  
Turbulent Flow ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Internal Resistance ◽  
Navier Stokes ◽  
Flow Profile ◽  
Navier Stokes Equation ◽  
Engineering Research ◽  
Turbulent Vortex ◽  
Fluctuation Method

Models and methods for studying turbulence based on the concept of turbulent "vortex backfill" are presented. The essence of this concept is that the turbulent flow is considered as laminar, flowing through a "vortex backfill ", which creates internal resistance. This resistance can be considered either as distributed, or as locally concentrated. Based on the first representation, a modified Navier-Stokes equation, its approximate analytical and numerical solutions are obtained. Based on the second concept and the local fluctuation method developed for these purposes, a computer model of the turbulent flow in the pipes is obtained. Using simulation, it is shown that, when a certain system of local viscosity fluctuations is specified, the calculated flow profile corresponds to the profile of the turbulent flow velocity. The magnitude and profile of the turbulent viscosity of the flow are completely determined by the structure and properties of the "vortex backfill ". The results of the work confirm the possibility and efficiency of considering turbulence based on this concept.

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