Curved Ducts With Strong Secondary Motion: Velocity Measurements of Developing Laminar and Turbulent Flow

1982 ◽  
Vol 104 (3) ◽  
pp. 350-359 ◽  
Author(s):  
A. M. K. P. Taylor ◽  
J. H. Whitelaw ◽  
M. Yianneskis
Keyword(s):  
Turbulent Flow ◽  
Turbulence Models ◽  
Hydraulic Diameter ◽  
Radius Ratio ◽  
Reynolds Stresses ◽  
Flow Development ◽  
Secondary Motion ◽  
Laminar And Turbulent Flow ◽  
Orthogonal Components ◽  
Secondary Velocity

Two orthogonal components of velocity and associated Reynolds stresses have been measured in a square-sectioned, 90 degree bend of 2.3 radius ratio using laser-Doppler velocimetry for Reynolds numbers of 790 and 40,000. The boundary layers at the bend inlet were 0.25 and 0.15 of the hydraulic diameter and resulted in secondary velocity maxima of 0.6 and 0.4 of the bulk flow velocity respectively. Comparison with fully-developed inlet flow shows that the boundary layer thickness is important to the flow development (mainly in the first half of the bend), particularly so when it is reduced to 0.15 of the hydraulic diameter. Turbulent flow in an identical duct with a radius ratio of 7.0 gives rise to smaller secondary velocities than in the strongly curved bend, although their effect is more important to the streamwise flow development because of the smaller pressure gradients. The detail and accuracy of the measurements make them suitable for evaluation of numerical techniques and turbulence models. Partially-parabolic techniques are applicable to the flows studied and their reduced storage requirements seem essential if satisfactory numerical accuracy is to be achieved.

On the skin friction due to turbulence in ducts of various shapes

2018 ◽  
Vol 838 ◽  
pp. 369-378 ◽  
Author(s):  
P. R. Spalart ◽  
A. Garbaruk ◽  
A. Stabnikov
Keyword(s):  
Reynolds Number ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Mathematical Reasoning ◽  
Turbulence Models ◽  
Turbulence Theory ◽  
Reynolds Stresses ◽  
Cross Sectional ◽  
Law Of The Wall ◽  
Secondary Motion

We consider fully developed turbulence in straight ducts of non-circular cross-sectional shape, for instance a square. A global friction velocity $\overline{u}_{\unicode[STIX]{x1D70F}}$ is defined from the streamwise pressure gradient $|\text{d}p/\text{d}x|$ and a single characteristic length $h$, half the hydraulic diameter (shapes with disparate length scales, due to high aspect ratio, are excluded). We reason that as the Reynolds number $Re$ reaches high values, outside the viscous region the streamwise velocity differences and the secondary motion scale with $\overline{u}_{\unicode[STIX]{x1D70F}}$ and the Reynolds stresses with $\overline{u}_{\unicode[STIX]{x1D70F}}^{2}$. This extends the classical defect-law argument, associated with Townsend and many others, and is successful in channel and pipe flows. We then posit matched asymptotic expansions with overlap of the law of the wall and the behaviour we assumed in the core region. The wall may be smooth, or have a Nikuradse roughness $k_{S}$ (such that it is fully rough, with $k_{S}^{+}\gg 1$). The consequences include the familiar logarithmic behaviour of the velocity profile, but also the surprising prediction that the skin friction tends to uniformity all around the duct, except near possible corners, asymptotically as $Re\rightarrow \infty$ or $k_{S}/h\rightarrow 0$. This is confirmed by numerical solutions for a square and two ellipses, using a conventional turbulence model, albeit the trend with Reynolds number is slow. The magnitude of the secondary motion also scales as expected, and the skin-friction coefficient follows the logarithm of the appropriate Reynolds number. This is a validation of the mathematical reasoning, but is by no means independent physical evidence, because the turbulence models embody the same assumptions as the theory. The uniformity of the skin friction appears to be a new and falsifiable deduction from turbulence theory, and a candidate for high-Reynolds-number experiments.

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.

Partially filled pipes: experiments in laminar and turbulent flow

2018 ◽  
Vol 848 ◽  
pp. 467-507 ◽  
Author(s):  
Henry C.-H. Ng ◽  
Hope L. F. Cregan ◽  
Jonathan M. Dodds ◽  
Robert J. Poole ◽  
David J. C. Dennis
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Turbulent Flow ◽  
Pipe Flow ◽  
Large Scale ◽  
Open Channel ◽  
Streamwise Velocity ◽  
Flow Depth ◽  
Secondary Motion ◽  
Laminar And Turbulent Flow

Pressure-driven laminar and turbulent flow in a horizontal partially filled pipe was investigated using stereoscopic particle imaging velocimetry (S-PIV) in the cross-stream plane. Laminar flow velocity measurements are in excellent agreement with a recent theoretical solution in the literature. For turbulent flow, the flow depth was varied independently of a nominally constant Reynolds number (based on hydraulic diameter, $D_{H}$; bulk velocity, $U_{b}$ and kinematic viscosity $\unicode[STIX]{x1D708}$) of $Re_{H}=U_{b}D_{H}/\unicode[STIX]{x1D708}\approx 30\,000\pm 5\,\%$. When running partially full, the inferred friction factor is no longer a simple function of Reynolds number, but also depends on the Froude number $Fr=U_{b}/\sqrt{gD_{m}}$ where $g$ is gravitational acceleration and $D_{m}$ is hydraulic mean depth. S-PIV measurements in turbulent flow reveal the presence of secondary currents which causes the maximum streamwise velocity to occur below the free surface consistent with results reported in the literature for rectangular cross-section open channel flows. Unlike square duct and rectangular open channel flow the mean secondary motion observed here manifests only as a single pair of vortices mirrored about the vertical bisector and these rollers, which fill the half-width of the pipe, remain at a constant distance from the free surface even with decreasing flow depth for the range of depths tested. Spatial distributions of streamwise Reynolds normal stress and turbulent kinetic energy exhibit preferential arrangement rather than having the same profile around the azimuth of the pipe as in a full pipe flow. Instantaneous fields reveal the signatures of elements of canonical wall-bounded turbulent flows near the pipe wall such as large-scale and very-large-scale motions and associated hairpin packets whilst near the free surface, the signatures of free surface turbulence in the absence of imposed mean shear such as ‘upwellings’, ‘downdrafts’ and ‘whirlpools’ are present. Two-point spatio-temporal correlations of streamwise velocity fluctuation suggest that the large-scale coherent motions present in full pipe flow persist in partially filled pipes but are compressed and distorted by the presence of the free surface and mean secondary motion.

Numerical investigation of friction laws for laminar and turbulent flow in undulated channels

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ali Cemal Benim ◽  
Sai Bhagavan Maddala
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Numerical Investigation ◽  
Focal Point ◽  
Hydraulic Diameter ◽  
Maximum Deviation ◽  
Content Type ◽  
Friction Laws ◽  
Numerical Predictions ◽  
Laminar And Turbulent Flow

Purpose The purpose of this paper is the numerical investigation of the friction laws for incompressible flow in undulated channels, with emphasis on the applicability of the hydraulic diameter concept. A focal point of the study is the derivation of correlations to increase the accuracy of the hydraulic diameter approach. Design/methodology/approach Calculations are performed for laminar and turbulent flow, for Reynolds number ranges between 10–2,000 and 5,000–100,000. For turbulent flow, the shear stress transport (SST) model is used. A simple, sawtooth-like undulation shape is considered, where the channel geometry can be described by means of three length parameters. Letting each to take three values, totally 27 geometries are analyzed. Findings It is observed that the hydraulic diameter concept applied via analytical or empirical expressions to obtain friction coefficients does not lead to accurate results. For laminar flow, the maximum deviations of analytical values from predicted are about 70%, while 20% deviation is observed on average. For turbulent flow, deviations of Blasius correlation from predicted ones are smaller, but still remarkable with about 20% for maximum deviation and about 10% on average. Originality/value Applicability of the hydraulic diameter concept to undulated channels was not computationally explored. A further original ingredient of the work is the derivation of correlations that lead to improved accuracy in calculating the friction coefficient using hydraulic diameter. For laminar flow, the maximum and average deviations of present correlations from numerical predictions are below 5% and 2%, respectively. For turbulent flow, these numbers turn out to be approximately 12% for the maximum deviation and about 2% for the average.

Evaluation of Several Turbulence Models for Turbulent Flow in Concentric and Eccentric Annuli

1998 ◽  
Vol 120 (4) ◽  
pp. 268-275 ◽  
Author(s):  
I. Azouz ◽  
S. A. Shirazi
Keyword(s):  
Turbulent Flow ◽  
Turbulence Models ◽  
Momentum Equation ◽  
Equation Model ◽  
Numerical Code ◽  
Mixing Length ◽  
Reynolds Stresses ◽  
Curvilinear Boundary ◽  
Numerical Predictions ◽  
Eccentric Annuli

Turbulent flow in concentric and eccentric annuli is numerically simulated as part of an investigation aimed at modeling drilled cuttings transport in wellbores. A numerical code is developed to solve the time-averaged momentum equation wherein the Reynolds stresses are modeled using the eddy viscosity approach. A nonorthogonal curvilinear, boundary-fitted coordinate system is used to facilitate the implementation of boundary conditions. Several turbulence models, including a one-layer mixing length model developed as part of this study, a two-layer mixing-length model, and a low Reynolds number, two-equation (k-τ) model are used to simulate turbulent flow in several concentric and eccentric annuli. Performance of these turbulence models is evaluated by comparing numerical predictions to experimental data obtained from several sources. Results show that the proposed one-layer mixing length model performs as well as the two-layer mixing length model and the two-equation model while avoiding some of the difficulties associated with the implementation of these models.

Prediction of Developing Turbulent Flow in a 90° Curved Duct Using Linear and Nonlinear Low-Re k-ε Models

Volume 1 ◽  
2004 ◽  
Author(s):  
M. Raisee ◽  
H. Alemi ◽  
H. Iacovides
Keyword(s):  
Turbulent Flow ◽  
Pressure Coefficient ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Main Stream ◽  
Local Pressure ◽  
Flow Measurements ◽  
Numerical Predictions ◽  
Flow Development ◽  
Curved Section

This paper reports the outcome of applying two different low-Re number eddy-viscosity models to resolve the complex three-dimensional motion that arises in turbulent flow in a square cross-section duct passing around a 90° bend. Flow computations have been obtained using a three-dimensional, non-orthogonal flow solver. For modeling of turbulence, the Launder and Sharma low-Re k–ε model and a recently modified version of nonlinear low-Re k–ε model that have been shown to be suitable for flow and thermal predictions in re-circulating and impinging jet flows, have been employed. A bounded version of the QUICK scheme was used for the approximation of convection in all transport equations. The numerical predictions are validated through comparisons with the reported flow measurements and are used to explain how the curvature influences the flow development. The results of the present investigation indicate that the curvature induces a strong secondary flow in the curved section of the duct. The secondary motion also persists downstream of the bend, although it slowly disappears with the main stream development. At the entrance of the curved section, the curvature alters the flow development by displacing the fluid towards the convex (inner) wall. Comparisons of the predicted stream-wise and cross-stream velocity components with the measured data indicate that both turbulence models employed in the present study can produce reasonable predictions, although the non-linear model predictions are generally closer to the measurements. Both turbulence models successfully reproduce the distribution as well as the levels of the local pressure coefficient in the curved section of the duct.

Turbulent flow in a rectangular duct

1976 ◽  
Vol 78 (2) ◽  
pp. 289-315 ◽  
Author(s):  
A. Melling ◽  
J. H. Whitelaw
Keyword(s):  
Turbulent Flow ◽  
Turbulence Models ◽  
Laser Doppler Anemometer ◽  
Laser Doppler ◽  
Rectangular Duct ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Fully Developed Flow ◽  
Developing Flow ◽  
Better Than

A detailed experimental study of developing turbulent flow in a rectangular duct was made using a laser-Doppler anemometer. The purposes of the work were to obtain data of value to fluid mechanicists, particularly those interested in the development and testing of mathematical turbulence models, and to evaluate the performance of the anemometer. For the first purpose, contours of axial mean velocity and turbulence intensity were measured in the developing flow, and all three mean velocity components and five of the six Reynolds stresses were obtained in the nearly fully developed flow.The symmetry of the present flow appears to be better than that of previous measurements and the range of measurements is more extensive. In addition, the laser-Doppler anemometer has the potential advantage, particularly in the measurement of secondary velocities, of avoiding probe interference.

scholarly journals Optimization of Conical Hydrostatic Bearing for Minimum Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 136-142 ◽  
Author(s):  
L. J. Nypan ◽  
B. J. Hamrock ◽  
H. W. Scibbe ◽  
W. J. Anderson
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Flow Rate ◽  
Load Capacity ◽  
Friction Torque ◽  
Radius Ratio ◽  
Hydrostatic Bearing ◽  
Laminar And Turbulent Flow

Equations for the flow rate, load capacity, and friction torque for a conical hydrostatic bearing were developed. These equations were solved by a digital computer program to determine bearing configurations for minimum friction torque. Design curves are presented that show optimal bearing dimensions for minimum friction torque as a function of dimensionless flow rate for a range of dimensionless load capacity. Results are shown for both laminar and turbulent flow conditions. The results indicate the hydrostatic pocket friction is a significant portion of the total friction torque. However, the bearing dimensions for a minimum friction design are affected very little by inclusion of pocket friction in the analysis. For laminar flow the values of the outerland radius ratio X3 and outer bearing radius ratio X4 did not change significantly with increasing friction factor. For turbulent flow, the outer bearing radius ratio X4 did not change with increasing friction factor; therefore, the value determined for X4 in the laminar flow case is valid for all turbulent flows.

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