Numerical Simulations of Turbulent Flow Through a 90° Elbow

2019 ◽  
Author(s):  
Ravon Venters ◽  
Brian Helenbrook ◽  
Goodarz Ahmadi
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Navier Stokes ◽  
Mean Square ◽  
Reynolds Stresses ◽  
Streamline Curvature ◽  
Secondary Motion ◽  
Flow Through ◽  
The Mean ◽  
Flow Transitions

Abstract Turbulent flow in an elbow has been numerically investigated. The flow was modeled using two approaches; Reynolds Averaged Navier-Stokes (RANS) and Direct Numerical Simulation (DNS) methods. The DNS allows for all the scales of turbulence to be evaluated, providing a detailed depiction of the flow. The RANS simulation, which is typically used in industry, evaluates time-averaged components of the flow. The numerical results are accompanied by experimental data, which was used to validate the two methods. Profiles of the mean and root-mean-square (RMS) fluctuating components were compared at various points along the midplane of the elbow. Upstream of the elbow, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing slightly near the walls. However, downstream of the elbow, the RANS deviated from the experiment and DNS, showing a longer region of flow re-circulation. This caused the mean and RMS velocities to significantly differ. Examining the cross-section flow field, secondary motion was clearly present. Upstream secondary motion of the first kind was observed which is caused by anisotropy of the reynolds stresses in the turbulent flow. Downstream of the bend, the flow transitions to secondary motion of the second kind which is caused by streamline curvature. Qualitatively, the RANS and DNS showed similar results upstream of the bend, however downstream, the magnitude of the secondary motion differed significantly.

scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

Numerical Modeling of Pulsatile Turbulent Flow in Stenotic Vessels

2003 ◽  
Vol 125 (4) ◽  
pp. 445-460 ◽  
Author(s):  
Sonu S. Varghese ◽  
Steven H. Frankel
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Mean Flow ◽  
Navier Stokes Equation ◽  
Flow Through ◽  
The Mean ◽  
High Reynolds

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-ω turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-ε turbulence model and the standard k-ε model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.

Steady Laminar Flow through Twisted Pipes: Fluid Flow in Square Tubes

1981 ◽  
Vol 103 (4) ◽  
pp. 785-790 ◽  
Author(s):  
J. H. Masliyah ◽  
K. Nandakumar
Keyword(s):  
Laminar Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dissipation Term ◽  
Axial Velocity Profile ◽  
Secondary Motion ◽  
Qualitative Nature ◽  
Flow Through ◽  
Steady Laminar

The Navier-Stokes equation in a rotating frame of reference is solved numerically to obtain the flow field for a steady, fully developed laminar flow of a Newtonian fluid in a twisted tube having a square cross-section. The macroscopic force and energy balance equations and the viscous dissipation term are presented in terms of variables in a rotating reference frame. The computed values of friction factor are presented for dimensionless twist ratios, (i.e., length of tube over a rotation of π radians normalized with respect to half the width of tube) of 20, 10, 5 and 2.5 and for Reynolds numbers up to 2000. The qualitative nature of the axial velocity profile was observed to be unaffected by the swirling motion. The secondary motion was found to be most important near the wall.

The dispersion of matter in turbulent flow through a pipe

1954 ◽  
Vol 223 (1155) ◽  
pp. 446-468 ◽  
Keyword(s):  
Turbulent Flow ◽  
Capillary Tube ◽  
Resistance Coefficient ◽  
Mean Flow ◽  
Combined Action ◽  
Flow Through ◽  
The Mean ◽  
Coefficient Of Diffusion ◽  
Good Agreement ◽  
Made In

The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953 a ) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusion K is found to be 10∙1 av * or K = 7∙14 aU √ γ . Here a is the radius of the pipe, U is the mean flow velocity, γ is the resistance coefficient and v * ‘friction velocity’. Experiments are described in which brine was injected into a straight 3/8 in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a length S as it passes down the pipe. When the interface has moved through a distance X , theory leads to the formula S 2 = 437 aX ( v * / U ). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.

Improved κ-ɛ Modelling of Impeller Flow Performance of a Mixed-Flow Pump under off-Design Operating States

1993 ◽  
Vol 207 (4) ◽  
pp. 219-229 ◽  
Author(s):  
S M Fraser ◽  
Y Zhang
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Navier Stokes ◽  
Mean Flow ◽  
Mixed Flow ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
The Mean ◽  
Flow Pump

Three-dimensional turbulent flow through the impeller passage of a model mixed-flow pump has been simulated by solving the Navier-Stokes equations with an improved κ-ɛ model. The standard κ-ɛ model was found to be unsatisfactory for solving the off-design impeller flow and a converged solution could not be obtained at 49 per cent design flowrate. After careful analysis, it was decided to modify the standard κ-ɛ model by including the extra rates of strain due to the acceleration of impeller rotation and geometrical curvature and removing the mathematical ill-posedness between the mean flow turbulence modelling and the logarithmic wall function.

Direct simulations of low-Reynolds-number turbulent flow in a rotating channel

1993 ◽  
Vol 256 ◽  
pp. 163-197 ◽  
Author(s):  
Reidar Kristoffersen ◽  
Helge I. Andersson
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Complete Suppression ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Computational Mesh ◽  
Developed Pressure ◽  
Rotating Channel

Direct numerical simulations of fully developed pressure-driven turbulent flow in a rotating channel have been performed. The unsteady Navier–Stokes equations were written for flow in a constantly rotating frame of reference and solved numerically by means of a finite-difference technique on a 128 × 128 × 128 computational mesh. The Reynolds number, based on the bulk mean velocity Um and the channel half-width h, was about 2900, while the rotation number Ro = 2|Ω|h/Um varied from 0 to 0.5. Without system rotation, results of the simulation were in good agreement with the accurate reference simulation of Kim, Moin & Moser (1987) and available experimental data. The simulated flow fields subject to rotation revealed fascinating effects exerted by the Coriolis force on channel flow turbulence. With weak rotation (Ro = 0.01) the turbulence statistics across the channel varied only slightly compared with the nonrotating case, and opposite effects were observed near the pressure and suction sides of the channel. With increasing rotation the augmentation and damping of the turbulence along the pressure and suction sides, respectively, became more significant, resulting in highly asymmetric profiles of mean velocity and turbulent Reynolds stresses. In accordance with the experimental observations of Johnston, Halleen & Lezius (1972), the mean velocity profile exhibited an appreciable region with slope 2Ω. At Ro = 0.50 the Reynolds stresses vanished in the vicinity of the stabilized side, and the nearly complete suppression of the turbulent agitation was confirmed by marker particle trackings and two-point velocity correlations. Rotational-induced Taylor-Görtler-like counter-rotating streamwise vortices have been identified, and the simulations suggest that the vortices are shifted slightly towards the pressure side with increasing rotation rates, and the number of vortex pairs therefore tend to increase with Ro.

scholarly journals Numerical simulation of turbulent flow through Schiller’s wavy pipe

2014 ◽  
Vol 761 ◽  
pp. 241-260 ◽  
Author(s):  
G. Daschiel ◽  
V. Krieger ◽  
J. Jovanović ◽  
A. Delgado
Keyword(s):  
Turbulent Flow ◽  
Structural Changes ◽  
Stokes Equations ◽  
Resistance Coefficient ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Pressure Resistance ◽  
Almost All

AbstractThe development of incompressible turbulent flow through a pipe of wavy cross-section was studied numerically by direct integration of the Navier–Stokes equations. Simulations were performed at Reynolds numbers of $4.5\times 10^{3}$ and $10^{4}$ based on the hydraulic diameter and the bulk velocity. Results for the pressure resistance coefficient ${\it\lambda}$ were found to be in excellent agreement with experimental data of Schiller (Z. Angew. Math. Mech., vol. 3, 1922, pp. 2–13). Of particular interest is the decrease in ${\it\lambda}$ below the level predicted from the Blasius correlation, which fits almost all experimental results for pipes and ducts of complex cross-sectional geometries. Simulation databases were used to evaluate turbulence anisotropy and provide insights into structural changes of turbulence leading to flow relaminarization. Anisotropy-invariant mapping of turbulence confirmed that suppression of turbulence is due to statistical axisymmetry in the turbulent stresses.

scholarly journals Accessing the Influence of Hess-Murray Law on Suspension Flow through Ramified Structures

2013 ◽  
Vol 334-335 ◽  
pp. 322-328 ◽  
Author(s):  
Ana Serrenho ◽  
Antonio F. Miguel
Keyword(s):  
Fluid Flow ◽  
Turbulent Flow ◽  
Cross Section ◽  
Particle Transport ◽  
Flow Resistance ◽  
Suspension Flow ◽  
Similar Performance ◽  
Particle Penetration ◽  
Laminar And Turbulent Flow ◽  
Flow Through

The present study focuses on fluid flow and particle transport in symmetric T-shaped structures formed by tubes with circular and square cross-section. The performances of optimized structures (i.e., structures designed based on constructal allometric laws for minimum flow resistance) and not optimized structures were studied. Flow resistance and particle penetration efficiency were studied both for laminar and turbulent flow regimes, and for micrometer and submicrometer particles. Optimized structures have been proven to perform better for fluid flow but they have a similar performance for particle transport.

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.

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