Front Dynamics in Miscible Displacement Flow in a Curved Pipe

2018 ◽  
Author(s):  
Mohammadreza Yavari ◽  
Elaheh Bagherizadeh ◽  
Majid Bazargan
Keyword(s):  
Digital Camera ◽  
Reynolds Numbers ◽  
Miscible Displacement ◽  
Displacement Efficiency ◽  
Mean Velocity ◽  
Curved Pipe ◽  
Two Fluids ◽  
The Mean ◽  
Atwood Number ◽  
Front Dynamics

Miscible displacement flow in a curved pipe with two fluids of equal viscosity and in the regime of low Atwood number is studied experimentally at different Reynolds and Atwood numbers. By using a curved pipe the effect of curvature on miscible displacement flow is studied. Curvature may be present in many displacement flow processes in nature or industry which underlines the necessity of studying its effect on displacement flow. As the flow is controlled by gravity as the main driving force, only low to moderate Reynolds numbers are considered and Atwood number is varied by adding NaCl salt to fresh water. This makes it possible to create different values of Atwood numbers which can be varied continuously. The position of the leading front is carefully recorded using a digital camera and is used as a measure of displacement efficiency. It is observed that the ratio of the front velocity to the mean velocity approaches a certain value as Reynolds number increases. The effect of Atwood number on flow dynamics is also studied based on experimental results and is interpreted following the conventions employed in some of the previous researches.

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.

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.

LDV and PIV Velocity Results in a Thermosiphon

2003 ◽  
Author(s):  
J. Kulman ◽  
D. Gray ◽  
S. Sivanagere ◽  
S. Guffey
Keyword(s):  
Large Scale ◽  
Single Phase ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Patterns ◽  
Laser Doppler Velocimeter ◽  
Mean Velocity ◽  
Developed Turbulence ◽  
The Mean ◽  
Good Agreement

Heat transfer and flow characteristics have been determined for a single-phase rectangular loop thermosiphon. The plane of the loop was vertical, and tests were performed with in-plane tilt angles ranging from 3.6° CW to 4.2° CCW. Velocity profiles were measured in one vertical leg of the loop using both a single-component Laser Doppler Velocimeter (LDV), and a commercial Particle Image Velocimeter (PIV) system. The LDV data and PIV data were found to be in good agreement. The measured average velocities were approximately 2–2.5 cm/s at an average heating rate of 70 W, and were independent of tilt angle. Significant RMS fluctuations of 10–20% of the mean velocity were observed in the test section, in spite of the laminar or transitional Reynolds numbers (order of 700, based on the hydraulic diameter). These fluctuations have been attributed to vortex shedding from the upstream temperature probes and mitre bends, rather than to fully developed turbulence. Animations of the PIV data clearly show these large scale unsteady flow patterns. Multiple steady state flow patterns were not observed.

Free Span Vibrations of Submarine Pipelines in Steady Flows—Effect of Free-Stream Turbulence on Mean Drag Coefficients

1985 ◽  
Vol 107 (4) ◽  
pp. 415-420 ◽  
Author(s):  
A. To̸rum ◽  
N. M. Anand
Keyword(s):  
Free Stream ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Steady Flows ◽  
Mean Velocity ◽  
Free Stream Turbulence ◽  
The Mean ◽  
Elastically Supported ◽  
Wave Induced ◽  
Rigid Smooth

In this paper part of the results of a laboratory study related to free span vibrations of submarine pipelines in steady and wave-induced fluid flows are summarized. Tests have been carried out using an elastically supported rigid smooth circular cylinder close to a plane smooth boundary in steady flows with turbulence intensities of 3.4, 5.5, and 9.5 percent for four cylinder gap to diameter ratios, G/D equal to 0.5, 0.75, 1.0, and 3.0. The range of Reynolds numbers based on mean velocity of flow and cylinder diameter was 0.65·104 to 0.35·105. Effect of turbulence intensity on the mean drag force and vibration amplitudes are discussed.

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.

Effect of Upstream Flow Processes on Hydrodynamic Development in a Duct

1977 ◽  
Vol 99 (3) ◽  
pp. 556-560 ◽  
Author(s):  
E. M. Sparrow ◽  
C. E. Anderson
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Viscous Effects ◽  
Mean Velocity ◽  
Inertia Effects ◽  
Reynolds Number Flow ◽  
Compact Size ◽  
Number Flow ◽  
The Mean

Consideration is given to the developing laminar flow in a parallel plate channel, with the fluid being drawn from a large upstream space. The flow fields upstream and downstream of the channel inlet were solved simultaneously. A finite-difference technique was employed which was facilitated by a coordinate transformation that telescoped the broadly extended flow domain into a more compact size. For the solutions, the Reynolds number was assigned values from 1 to 1000, covering the range from viscous-dominated flows to those where both viscous and inertia effects are relevant. Streamline maps indicate that whereas a low Reynolds number flow glides smoothly into the channel, a high Reynolds number flow has to turn sharply to enter the channel, with the result that the sharply turning fluid tends to overshoot at first and then readjust. A significant amount of upstream predevelopment occurs at low and intermediate Reynolds numbers. Thus, for example, at Re = 1 and 100, the center-line velocities at inlet are, respectively, 1.37 and 1.13 times the mean velocity (the fully developed center-line velocity is 1.5 times the mean). The upstream pressure drop, measured in terms of the velocity head, is substantially increased by viscous effects at low and intermediate Reynolds numbers.

Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers

2016 ◽  
Vol 795 ◽  
pp. 210-240 ◽  
Author(s):  
D. T. Squire ◽  
C. Morrill-Winter ◽  
N. Hutchins ◽  
M. P. Schultz ◽  
J. C. Klewicki ◽  
...  
Keyword(s):  
Outer Region ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Rough Wall ◽  
Turbulent Shear ◽  
Smooth Wall ◽  
Mean Velocity ◽  
Wide Range ◽  
Velocity Variance ◽  
The Mean

Turbulent boundary layer measurements above a smooth wall and sandpaper roughness are presented across a wide range of friction Reynolds numbers, ${\it\delta}_{99}^{+}$, and equivalent sand grain roughness Reynolds numbers, $k_{s}^{+}$ (smooth wall: $2020\leqslant {\it\delta}_{99}^{+}\leqslant 21\,430$, rough wall: $2890\leqslant {\it\delta}_{99}^{+}\leqslant 29\,900$; $22\leqslant k_{s}^{+}\leqslant 155$; and $28\leqslant {\it\delta}_{99}^{+}/k_{s}^{+}\leqslant 199$). For the rough-wall measurements, the mean wall shear stress is determined using a floating element drag balance. All smooth- and rough-wall data exhibit, over an inertial sublayer, regions of logarithmic dependence in the mean velocity and streamwise velocity variance. These logarithmic slopes are apparently the same between smooth and rough walls, indicating similar dynamics are present in this region. The streamwise mean velocity defect and skewness profiles each show convincing collapse in the outer region of the flow, suggesting that Townsend’s (The Structure of Turbulent Shear Flow, vol. 1, 1956, Cambridge University Press.) wall-similarity hypothesis is a good approximation for these statistics even at these finite friction Reynolds numbers. Outer-layer collapse is also observed in the rough-wall streamwise velocity variance, but only for flows with ${\it\delta}_{99}^{+}\gtrsim 14\,000$. At Reynolds numbers lower than this, profile invariance is only apparent when the flow is fully rough. In transitionally rough flows at low ${\it\delta}_{99}^{+}$, the outer region of the inner-normalised streamwise velocity variance indicates a dependence on $k_{s}^{+}$ for the present rough surface.

Investigations of Tripping Effect on the Friction Factor in Turbulent Pipe Flows

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
A. Al-Salaymeh ◽  
O. A. Bayoumi
Keyword(s):  
Friction Factor ◽  
Reynolds Numbers ◽  
Original Data ◽  
Turbulent Pipe Flow ◽  
Wall Friction ◽  
Mean Flow ◽  
Mean Velocity ◽  
Fully Developed Turbulent Flow ◽  
The Mean ◽  
The Difference

Tripping devices are usually installed at the entrance of laboratory-scale pipe test sections to obtain a fully developed turbulent flow sooner. The tripping of laminar flow to induce turbulence can be carried out in different ways, such as using cylindrical wires, sand papers, well-organized tape elements, fences, etc. Claims of tripping effects have been made since the classical experiments of Nikuradse (1932, Gesetzmässigkeit der turbulenten Strömung in glatten Rohren, Forschungsheft 356, Ausgabe B, Vol. 3, VDI-Verlag, Berlin), which covered a significant range of Reynolds numbers. Nikuradse’s data have become the metric by which theories are established and have also been the subject of intense scrutiny. Several subsequent experiments reported friction factors as much as 5% lower than those measured by Nikuradse, and the authors of those reports attributed the difference to tripping effects, e.g., work of Durst et al. (2003, “Investigation of the Mean-Flow Scaling and Tripping Effect on Fully Developed Turbulent Pipe Flow,” J. Hydrodynam., 15(1), pp. 14–22). In the present study, measurements with and without ring tripping devices of different blocking areas of 10%, 20%, 30%, and 40% have been carried out to determine the effect of entrance condition on the developing flow field in pipes. Along with pressure drop measurements to compute the skin friction, both the Pitot tube and hot-wire anemometry measurements have been used to accurately determine the mean velocity profile over the working test section at different Reynolds numbers based on the mean velocity and pipe diameter in the range of 1.0×105–4.5×105. The results we obtained suggest that the tripping technique has an insignificant effect on the wall friction factor, in agreement with Nikuradse’s original data.

Structure of Turbulent Flows Over Forward Facing Steps With Adverse Pressure Gradient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Hassan Iftekhar ◽  
Martin Agelin-Chaab
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Turbulent Flows ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Step Height ◽  
Reattachment Length ◽  
Mean Velocity ◽  
The Mean

This paper reports an experimental study on the effects of adverse pressure gradient (APG) and Reynolds number on turbulent flows over a forward facing step (FFS) by employing three APGs and three Reynolds numbers. A particle image velocimetry (PIV) technique was used to conduct velocity measurements at several locations downstream, and the flow statistics up to 68 step heights are reported. The step height was maintained at 6 mm, and the Reynolds numbers based on the step height and freestream mean velocity were 1600, 3200, and 4800. The mean reattachment length increases with the increase in Reynolds number without the APG whereas the mean reattachment length remains constant for increasing APG. The proper orthogonal decomposition (POD) results confirmed that higher Reynolds numbers caused the large-scale structures to be more defined and organized close to the step surface.

scholarly journals Turbulent boundary layers and channels at moderate Reynolds numbers

2010 ◽  
Vol 657 ◽  
pp. 335-360 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
SERGIO HOYAS ◽  
MARK P. SIMENS ◽  
YOSHINORI MIZUNO
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Pressure Fluctuations ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Rotational Flow ◽  
Mean Velocity ◽  
The Mean ◽  
External Flows

The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/δ = 0.3–0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reθ ≈ 2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

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