Measurements of the Turbulence Structure Downstream of a Tube Bundle at High Reynolds Numbers

1994 ◽  
Vol 116 (4) ◽  
pp. 848-855 ◽  
Author(s):  
U. Karnik
Keyword(s):  
Natural Gas ◽  
Static Pressure ◽  
Tube Bundle ◽  
Reynolds Numbers ◽  
Turbulence Structure ◽  
Mean Velocity ◽  
Diameter Pipe ◽  
The Mean ◽  
High Reynolds ◽  
Hot Film

Mean and turbulent velocity profiles are measured in natural gas at a static pressure of approximately 5200 kPa and a Reynolds number of around 7 × 106. These measurements are obtained by conventional hot film anemometry suitably modified for use in a natural gas environment. Measurements are taken in a 102.26 mm nominal diameter pipe following a development length of around 76D. The mean velocity profile and the turbulence intensities at this location are typical for a fully developed pipe flow. Further, measurements downstream of a 19 tube bundle flow conditioner are also presented. The tube bundle is traversed downstream of a 90 degree, long radius (r = 1.5D) elbow and the measurements are taken at 19D downstream of the elbow exit. Measurements include those of the axial mean and turbulent velocities and the integral length scales. It is found that the decay of turbulence is slower and the magnitude of the length scale is smaller in comparison to measurements at lower Reynolds numbers. Orifice meter comparisons, performed in a 19D test section (meter run), confirm earlier findings that turbulence is one of the factors that affects orifice meter accuracy.

scholarly journals Natural logarithms

2013 ◽  
Vol 718 ◽  
pp. 1-4 ◽  
Author(s):  
B. J. McKeon
Keyword(s):  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Significant Advance ◽  
Mean Velocity ◽  
Velocity Fluctuations ◽  
Logarithmic Scaling ◽  
The Mean ◽  
High Reynolds

AbstractMarusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at high Reynolds number, but perhaps the most exciting implication of the experimental results lies in the agreement with the predictions of such scaling from a model introduced by Townsend (J. Fluid Mech., vol. 11, 1961, pp. 97–120), commonly termed the attached eddy hypothesis. The elegantly simple, yet powerful, study by Marusic et al. should spark further investigation of the behaviour of all fluctuating velocity components at high Reynolds numbers and the outstanding predictions of the attached eddy hypothesis.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

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 Fluid motion between parallel planes. Dynamical stability

1946 ◽  
Vol 186 (1006) ◽  
pp. 391-409 ◽  
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Small Disturbance ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
The Mean ◽  
Parabolic Flow ◽  
High Reynolds

If U is the velocity of the mean motion the following main results are obtained: 1. The region where U = c , c being the wave velocity, is the source where vibrations are generated; i.e. the slowly varying vibrations give rise to large rapidly varying vibrations in passing through the critical point. 2. Curved profiles admit a periodic motion at sufficiently high Reynolds numbers. 3. Parabolic flow is unstable at high Reynolds numbers; i.e. an infinitely small disturbance is sufficient to break up such flow. The critical Reynolds number is equal to R = U 0 h/v =6700, and the corresponding wavelength is about three times the width of the channel ( U 0 is the mean velocity at the axis, and h is the half-width of the channel).

The intermediate wake of a body of revolution at high Reynolds numbers

2010 ◽  
Vol 659 ◽  
pp. 516-539 ◽  
Author(s):  
JUAN M. JIMÉNEZ ◽  
M. HULTMARK ◽  
A. J. SMITS
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Stress Distributions ◽  
Body Of Revolution ◽  
Self Similarity ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
Order Of Magnitude ◽  
The Mean ◽  
High Reynolds

Results are presented on the flow field downstream of a body of revolution for Reynolds numbers based on a model length ranging from 1.1 × 106 to 67 × 106. The maximum Reynolds number is more than an order of magnitude larger than that obtained in previous laboratory wake studies. Measurements are taken in the intermediate wake at locations 3, 6, 9, 12 and 15 diameters downstream from the stern in the midline plane. The model is based on an idealized submarine shape (DARPA SUBOFF), and it is mounted in a wind tunnel on a support shaped like a semi-infinite sail. The mean velocity distributions on the side opposite the support demonstrate self-similarity at all locations and Reynolds numbers, whereas the mean velocity distribution on the side of the support displays significant effects of the support wake. None of the Reynolds stress distributions of the flow attain self-similarity, and for all except the lowest Reynolds number, the support introduces a significant asymmetry into the wake which results in a decrease in the radial and streamwise turbulence intensities on the support side. The distributions continue to evolve with downstream position and Reynolds number, although a slow approach to the expected asymptotic behaviour is observed with increasing distance downstream.

scholarly journals Comparison of 2D Grid Simulations for Flow Past Cylinder at High Reynolds Numbers

2019 ◽  
Vol 15 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Lenka Lausová ◽  
Ivan Kološ ◽  
Vladimíra Michalcová
Keyword(s):  
Reynolds Numbers ◽  
Wake Region ◽  
Mean Velocity ◽  
Ansys Fluent ◽  
Flow Past ◽  
Different Types ◽  
Fluent Software ◽  
The Mean ◽  
High Reynolds ◽  
Volume Method

Abstract The paper focuses on the verification of the suitability of the SST k - ω model on the flow past a circular cylinder in 2D for a high Reynolds number. The study compares the results of drag and lifts coefficients with respect to different types of meshes and time steps. The mean velocity field in the wake region behind the cylinder is evaluated and compared to experimental data available from literature. The numerical simulations are solved using CFD codes in the ANSYS Fluent software and use the finite volume method.

Mean-flow scaling of turbulent pipe flow

1998 ◽  
Vol 373 ◽  
pp. 33-79 ◽  
Author(s):  
MARK V. ZAGAROLA ◽  
ALEXANDER J. SMITS
Keyword(s):  
Friction Factor ◽  
Friction Velocity ◽  
Outer Region ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Mean Velocity ◽  
Velocity Scale ◽  
The Mean ◽  
Log Law ◽  
High Reynolds

Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60<y+<500 or y+<0.15R+, the outer limit depending on whether the Kármán number R+ is greater or less than 9×103; and a log law for 600<y+<0.07R+. The log law is only evident if the Reynolds number is greater than approximately 400×103 (R+>9×103). Von Kármán's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600<y+<0.07R+, and the additive constant was shown to be 6.15 when the log law is expressed in inner scaling variables.A new theory is developed to explain the scaling in both overlap regions. This theory requires a velocity scale for the outer region such that the ratio of the outer velocity scale to the inner velocity scale (the friction velocity) is a function of Reynolds number at low Reynolds numbers, and approaches a constant value at high Reynolds numbers. A reasonable candidate for the outer velocity scale is the velocity deficit in the pipe, UCL−Ū, which is a true outer velocity scale, in contrast to the friction velocity which is a velocity scale associated with the near-wall region which is ‘impressed’ on the outer region. The proposed velocity scale was used to normalize the velocity profiles in the outer region and was found to give significantly better agreement between different Reynolds numbers than the friction velocity.The friction factor data at high Reynolds numbers were found to be significantly larger (>5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

Axisymmetric internal waves generated by a travelling oscillating body

1969 ◽  
Vol 35 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T. N. Stevenson
Keyword(s):  
Internal Waves ◽  
Salt Solution ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Dispersive Waves ◽  
The Mean ◽  
Oscillating Sphere

Experiments are presented in which axisymmetric internal waves are generated by an oscillating sphere moving vertically in a stably stratified salt solution. The Reynolds numbers for the sphere based on the diameter and the mean velocity are between 10 and 200. Lighthill's theory for dispersive waves is used to calculate the phase configuration of the internal waves. The agreement between experiment and theory is reasonably good.

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