Estimating the value of von Kármán’s constant in turbulent pipe flow

2014 ◽  
Vol 749 ◽  
pp. 79-98 ◽  
Author(s):  
S. C. C. Bailey ◽  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits
Keyword(s):  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Data Sets ◽  
Mean Velocity ◽  
Princeton University ◽  
Best Estimate ◽  
Data Points ◽  
Smooth Pipe ◽  
The Mean ◽  
Hot Wires

AbstractFive separate data sets on the mean velocity distributions in the Princeton University/ONR Superpipe are used to establish the best estimate for the value of von Kármán’s constant for the flow in a fully developed, hydraulically smooth pipe. The profiles were taken using Pitot tubes, conventional hot wires and nanoscale thermal anemometry probes. The value of the constant was found to vary significantly due to measurement uncertainties in the mean velocity, friction velocity and the wall distance, and the number of data points included in the analysis. The best estimate for the von Kármán constant in turbulent pipe flow is found to be $0.40 \pm 0.02$. A more precise estimate will require improved instrumentation.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

scholarly journals Experimental study on the mean velocity profile in the high Reynolds number turbulent pipe flow

2015 ◽  
Vol 81 (826) ◽  
pp. 15-00091-15-00091 ◽  
Author(s):  
Yuki WADA ◽  
Noriyuki FURUICHII ◽  
Yoshiya TERAO ◽  
Yoshiyuki TSUJI
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
Mean Velocity ◽  
The Mean ◽  
High Reynolds

Experiments on swirling turbulent flows. Part 1. Similarity in swirling flows

1973 ◽  
Vol 60 (4) ◽  
pp. 665-687 ◽  
Author(s):  
K. S. Yajnik ◽  
M. V. Subbaiah
Keyword(s):  
Turbulent Flows ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Swirling Flows ◽  
Turbulent Pipe Flow ◽  
Extended Form ◽  
Mean Velocity ◽  
Swirl Angle ◽  
The Mean ◽  
Similarity Laws

The effects of swirl on internal turbulent flows are studied by conducting experiments on turbulent pipe flow with variable initial swirl. This first part of the study is primarily concerned with similarity laws. The mean velocity profiles, both away from and close to the wall, are found to admit similarity representations at sufficiently large Reynolds numbers, provided that flow reversal does not take place near the entrance. While the wall law is not sensibly dependent on swirl, the velocity defect law in its extended form is sensitive to swirl. Further, a logarithmic skin-friction law is obtained in which only the additive coefficient depends on swirl. This coefficient is found to vary linearly with the swirl angle in the range of the present experiments.

Scaling of the Mean Velocity Profile for Turbulent Pipe Flow

1997 ◽  
Vol 78 (2) ◽  
pp. 239-242 ◽  
Author(s):  
M. V. Zagarola ◽  
A. J. Smits
Keyword(s):  
Velocity Profile ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Mean Velocity ◽  
The Mean

On an analytical explanation of the phenomena observed in accelerated turbulent pipe flow

2019 ◽  
Vol 881 ◽  
pp. 420-461
Author(s):  
F. Javier García García ◽  
Pablo Fariñas Alvariño
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Pipe Flow ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Pipe Flow ◽  
Intensity Parameter ◽  
Mean Velocity ◽  
The Mean ◽  
Do So

This research presents a new theory that explains analytically the behaviour of any fully developed incompressible turbulent pipe flow, steady or unsteady. We propose the name of theory of underlying laminar flow (TULF), because its main consequence is the description of any turbulent pipe flow as the sum of two components: the underlying laminar flow (ULF) and the purely turbulent component (PTC). We use the framework of the TULF to explain analytically most of the important and interesting phenomena reported in He & Jackson (J. Fluid Mech., vol. 408, 2000, pp. 1–38). To do so, we develop a simple model for the pressure gradient and Reynolds shear stress that could be applied to the linearly accelerated pipe flow described by He & Jackson (2000). The following features of the unsteady flow are explained: the deformation undergone by the mean velocity profiles during the transient, the velocity overshoot observed in the more rapid excursions, the dual deformation of mean velocity profiles when overshoots are present, the laminarisation effects described during acceleration, the rapid decrease of the Reynolds shear stress upon approaching the wall that brings forth the laminar sublayer, and some other minor effects. A new field is defined to characterise the degree of turbulence within the flow, directly calculable from the theory itself. Arguably, this new field would describe the degree of turbulence in a pipe flow more accurately than the familiar turbulence intensity parameter. Finally, a paradox is found in the deformation of the unsteady mean velocity profiles with respect to equal-Reynolds-number steady profiles, which is duly explained. The research also predicts the occurrence of mean velocity undershoots if the flow is decreased rapidly enough.

A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow

2008 ◽  
Vol 608 ◽  
pp. 81-112 ◽  
Author(s):  
XIAOHUA WU ◽  
PARVIZ MOIN
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Large Scale ◽  
Turbulent Pipe Flow ◽  
Bulk Velocity ◽  
Mean Velocity ◽  
Large Scale Structures ◽  
Narrow Region ◽  
The Mean ◽  
Scale Structures

Fully developed incompressible turbulent pipe flow at bulk-velocity- and pipe-diameter-based Reynolds number ReD=44000 was simulated with second-order finite-difference methods on 630 million grid points. The corresponding Kármán number R+, based on pipe radius R, is 1142, and the computational domain length is 15R. The computed mean flow statistics agree well with Princeton Superpipe data at ReD=41727 and at ReD=74000. Second-order turbulence statistics show good agreement with experimental data at ReD=38000. Near the wall the gradient of $\mbox{ln}\overline{u}_{z}^{+}$ with respect to ln(1−r)+ varies with radius except for a narrow region, 70 < (1−r)+ < 120, within which the gradient is approximately 0.149. The gradient of $\overline{u}_{z}^{+}$ with respect to ln{(1−r)++a+} at the present relatively low Reynolds number of ReD=44000 is not consistent with the proposition that the mean axial velocity $\overline{u}_{z}^{+}$ is logarithmic with respect to the sum of the wall distance (1−r)+ and an additive constant a+ within a mesolayer below 300 wall units. For the standard case of a+=0 within the narrow region from (1−r)+=50 to 90, the gradient of $\overline{u}_{z}^{+}$ with respect to ln{(1−r)++a+} is approximately 2.35. Computational results at the lower Reynolds number ReD=5300 also agree well with existing data. The gradient of $\overline{u}_{z}$ with respect to 1−r at ReD=44000 is approximately equal to that at ReD=5300 for the region of 1−r > 0.4. For 5300 < ReD < 44000, bulk-velocity-normalized mean velocity defect profiles from the present DNS and from previous experiments collapse within the same radial range of 1−r > 0.4. A rationale based on the curvature of mean velocity gradient profile is proposed to understand the perplexing existence of logarithmic mean velocity profile in very-low-Reynolds-number pipe flows. Beyond ReD=44000, axial turbulence intensity varies linearly with radius within the range of 0.15 < 1−r < 0.7. Flow visualizations and two-point correlations reveal large-scale structures with comparable near-wall azimuthal dimensions at ReD=44000 and 5300 when measured in wall units. When normalized in outer units, streamwise coherence and azimuthal dimension of the large-scale structures in the pipe core away from the wall are also comparable at these two Reynolds numbers.

Comparison of a Nonlinear k-ε Turbulence Closure Model With Stress Transport Models

1993 ◽  
Author(s):  
Muhammad A. R. Sharif ◽  
Yat-Kit E. Wong
Keyword(s):  
Pipe Flow ◽  
Flow Problem ◽  
Swirling Flow ◽  
Transport Model ◽  
Turbulent Pipe Flow ◽  
Turbulence Closure ◽  
Closure Model ◽  
Transport Models ◽  
Mean Velocity ◽  
Turbulence Closure Model

Abstract The performance of a nonlinear k-ϵ turbulence closure model (NKEM), in the prediction of isothermal incompressible turbulent flows, is compared with that of the stress transport models such as the differential Reynolds stress transport model (RSTM) and the algebraic stress transport model (ASTM). Fully developed turbulent pipe flow and confined turbulent swirling flow with a central non-swirling jet are numerically predicted using the Marker and Cell (MAC) finite difference method. Comparison of the prediction with the experiment show that all three models perform reasonably well for the pipe flow problem. For the swirling flow problem, the RSTM and ASTM is superior than the NKEM. RSTM and ASTM provide good agreement with measured mean velocity profiles. However, the turbulent stresses are over- or under-predicted. NKEM performs badly in prediction of mean velocity as well as the turbulent stresses.

Asymptotic scaling in turbulent pipe flow

2007 ◽  
Vol 365 (1852) ◽  
pp. 771-787 ◽  
Author(s):  
B.J McKeon ◽  
J.F Morrison
Keyword(s):  
Asymptotic Behaviour ◽  
Pipe Flow ◽  
Physical Space ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Turbulent Pipe Flow ◽  
Inertial Subrange ◽  
Velocity Spectrum ◽  
Mean Velocity ◽  
High Reynolds

The streamwise velocity component in turbulent pipe flow is assessed to determine whether it exhibits asymptotic behaviour that is indicative of high Reynolds numbers. The asymptotic behaviour of both the mean velocity (in the form of the log law) and that of the second moment of the streamwise component of velocity in the outer and overlap regions is consistent with the development of spectral regions which indicate inertial scaling. It is shown that an ‘inertial sublayer’ in physical space may be considered as a spatial analogue of the inertial subrange in the velocity spectrum and such behaviour only appears for Reynolds numbers R + >5×10 3 , approximately, much higher than was generally thought.

Large Eddy Simulation of Fully Developed Turbulent Pipe Flow

2004 ◽  
Author(s):  
Sowjanya Vijiapurapu ◽  
Jie Cui
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Grid Resolution ◽  
Turbulent Pipe Flow ◽  
Scale Model ◽  
Subgrid Scale ◽  
Mean Velocity ◽  
Fine Mesh ◽  
Large Eddy

Fully developed turbulent pipe flow is investigated by large eddy simulations (LES). The three-dimensional, unsteady, incompressible, filtered continuity and Navier-Stokes equations in cylindrical coordinates are discretized by a finite difference method. The spatial derivatives are approximated by second order conservative schemes. This scheme eliminates the numerical generation or dissipation of energy. The pressure Poisson equation is solved by FFT method and time is advanced through a third order Runge-Kutta method. The commonly used subgrid scale (SGS) models — the Smagorinsky model and the dynamic model are implemented and simulations are performed for fully developed turbulent pipe flow at two different Reynolds numbers. The flow features in terms of mean velocity as well as higher order turbulence intensities and correlations are presented and compared to experimental and DNS data available in literature. Extensive comparisons are made for cases using different grid resolution, different streamwise domain dimension, different sub-grid scale model, and, at two different Reynolds number. For two Reynolds numbers (5,000 and 30,000) tested in this study, the fine mesh (64 × 96 × 64, circumferential × radial × longitudinal) produces better results than the coarse mesh (32 × 48 × 32), indicating the significance of the grid resolution, especially near the pipe surface. On the fine mesh for the two Reynolds numbers, the results exhibit a slight Reynolds number effect, indicating the mesh needs to be further refined at higher Reynolds number. Simulations were performed for two domain sizes, namely 6D and 12D, where D is the pipe diameter. When the streamwise grid resolution remains unchanged, the two simulations show negligible difference. This ensures that a 6D domain is adequate to include the largest eddies in a fully developed turbulent pipe flow at the current Reynolds number. When the fine mesh is used, the subgrid scale models (Smagorinsky and Dynamic) provide limited contribution to the total turbulent kinetic energy. Although the current results agree quite well with other published LES simulations, when compared with the Law of the wall, benchmark experiments and DNS results, the simulated mean velocity in the log region is higher than the experimental and DNS data. Overall, it was observed that the numerical methods work satisfactorily well for turbulent pipe flows at low and high Reynolds numbers, and, the method has capability to be used in the simulation of flows with practical interest.

Sign in / Sign up

Export Citation Format

Share Document