The Kinematics and Dynamics of Ciliary Fluid Systems

1968 ◽  
Vol 49 (3) ◽  
pp. 617-629
Author(s):  
C. E. MILLER
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Energy Loss ◽  
Reynolds Numbers ◽  
Kinematics And Dynamics ◽  
Newtonian Mechanics ◽  
Mucociliary System ◽  
Fluid Systems ◽  
Two Systems ◽  
Sophisticated Model

1. The difficulties of directly applying the methods of Newtonian mechanics to solve the problem of mucus flow in the mammalian trachea are discussed. 2. In order to circumvent these difficulties, a sophisticated model of the mucociliary system, called the circular rheociliometer, was constructed. A brief account is given of the model and the homomorphic relation it has to the mucociliary system of mammal. 3. Kinematic experiments are described in which observations on the model are compared with observations on the mucociliary system of the cat's trachea. 4. A coefficient of energy, which is the ratio of energy loss in the fluid to the kinetic energy supplied by the cilia, is developed. The coefficient of energy is plotted against the Reynolds number for the model and for the cat's trachea. It is shown that both sets of data fall within the same range of Reynolds numbers. 5. Based on other kinematic and dynamic similarities, which are shown to exist between the two systems, a hypothetical mechanical exemplar of the mucociliary system is derived.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

Fluid Flow Analysis in a Pebble Bed Modular Reactor Using RANS Turbulence Models

2008 ◽  
Author(s):  
Margaret Mkhosi ◽  
Richard Denning ◽  
Audeen Fentiman
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Intensity ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Pebble Bed ◽  
Rans Turbulence Models ◽  
Flow Domain

The computational fluid dynamics code FLUENT has been used to analyze turbulent fluid flow over pebbles in a pebble bed modular reactor. The objective of the analysis is to evaluate the capability of the various RANS turbulence models to predict mean velocities, turbulent kinetic energy, and turbulence intensity inside the bed. The code was run using three RANS turbulence models: standard k-ε, standard k-ω and the Reynolds stress turbulence models at turbulent Reynolds numbers, corresponding to normal operation of the reactor. For the k-ε turbulence model, the analyses were performed at a range of Reynolds numbers between 1300 and 22 000 based on the approach velocity and the sphere diameter of 6 cm. Predictions of the mean velocities, turbulent kinetic energy, and turbulence intensity for the three models are compared at the Reynolds number of 5500 for all the RANS models analyzed. A unit-cell approach is used and the fluid flow domain consists of three unit cells. The packing of the pebbles is an orthorhombic arrangement consisting of seven layers of pebbles with the mean flow parallel to the z-axis. For each Reynolds number analyzed, the velocity is observed to accelerate to twice the inlet velocity within the pebble bed. From the velocity contours, it can be seen that the flow appears to have reached an asymptotic behavior by the end of the first unit cell. The velocity vectors for the standard k-ε and the Reynolds stress model show similar patterns for the Reynolds number analyzed. For the standard k-ω, the vectors are different from the other two. Secondary flow structures are observed for the standard k-ω after the flow passes through the gap between spheres. This feature is not observable in the case of both the standard k-ε and the RSM. Analysis of the turbulent kinetic energy contours shows that there is higher turbulence kinetic energy near the inlet than inside the bed. As the Reynolds number increases, kinetic energy inside the bed increases. The turbulent kinetic energy values obtained for the standard k-ε and the RSM are similar, showing maximum turbulence kinetic energy of 7.5 m2·s−2, whereas the standard k-ω shows a maximum of about 20 m2·s−2. Another observation is that the turbulence intensity is spread throughout the flow domain for the k-ε and RSM whereas for the k-ω, the intensity is concentrated at the front of the second sphere. Preliminary analysis performed for the pressure drop using the standard k-ε model for various velocities show that the dependence of pressure on velocity varies as V1.76.

The Drag on Spheres and Cylinders in a Stream of Dust-Laden Air

1959 ◽  
Vol 26 (4) ◽  
pp. 584-586
Author(s):  
Thomas Gillespie ◽  
A. W. Gunter
Keyword(s):  
Particle Size ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Drag Coefficient ◽  
Flow Pattern ◽  
Reynolds Numbers ◽  
Dust Concentration ◽  
Phase System ◽  
Two Phase ◽  
Coefficient Versus

Abstract A system has been developed for measuring the drag on small spheres and cylinders in a stream of dust-laden air. The drag was found to be proportional to the kinetic energy of the air plus the kinetic energy of the dust, and to be independent of particle size for particles having diameters in the range of 50 to 400μ. The well-known drag-coefficient versus Reynolds-number plots are the same for dust-free and dust-laden air provided the drag coefficient is calculated using the density of the two-phase system and the Reynolds numbers are calculated using the density of air alone. This suggests that the dust has little effect on the flow pattern. The results indicate that an instrument utilizing the drag principle to measure dust concentration could be developed.

Experimental Measurements of the Wake of a Sphere at Subcritical Reynolds Numbers

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Robert Muyshondt ◽  
Thien Nguyen ◽  
Y. A. Hassan ◽  
N. K. Anand
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Kinetic Energy ◽  
Cross Correlation ◽  
Reynolds Numbers ◽  
Velocity Fields ◽  
Stereoscopic Particle Image Velocimetry ◽  
Recirculation Region ◽  
Flow Structures ◽  
Vortex Identification

Abstract This work experimentally investigated the flow phenomena and vortex structures in the wake of a sphere located in a water loop at Reynolds numbers of Re = 850, 1,250, and 1,700. Velocity fields in the wake region were obtained by applying the time-resolved stereoscopic particle image velocimetry (TR-SPIV) technique. From the acquired TR-SPIV velocity vector fields, the statistical values of mean and fluctuating velocities were computed. Spectral analysis, two-point velocity–velocity cross-correlation, proper orthogonal decomposition (POD) and vortex identification analyses were also performed. The velocity fields show a recirculation region that decreases in length with an increase of Reynolds numbers. The power spectra from the spectral analysis had peaks corresponding to a Strouhal number of St = 0.2, which is a value commonly found in the literature studies of flow over a sphere. The two-point cross-correlation analysis revealed elliptical structures in the wake, with estimated integral length scales ranging between 12% and 63% of the sphere diameter. The POD analysis revealed the statistically dominant flow structures that captured the most flow kinetic energy. It is seen that the flow kinetic energy captured in the smaller scale flow structures increased as Reynolds number increased. The POD modes contained smaller structure as the Reynolds number increased and as mode order increased. In addition, spectral analysis performed on the POD temporal coefficients revealed peaks corresponding to St = 0.2, similar to the spectral analysis on the fluctuating velocity. The ability of POD to produce low-order reconstructions of the flow was also utilized to facilitate vortex identification analysis, which identified average vortex sizes of 0.41D for Re1, 0.33D for Re2, and 0.32D for Re3.

Sensitivity of stratified turbulence to the buoyancy Reynolds number

2013 ◽  
Vol 725 ◽  
pp. 1-22 ◽  
Author(s):  
P. Bartello ◽  
S. M. Tobias
Keyword(s):  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Froude Number ◽  
Relative Size ◽  
Stratified Flow ◽  
Reynolds Numbers ◽  
Stratified Turbulence ◽  
Integral Scale

AbstractIn this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$, to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $, of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $, decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$, indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.

Poiseuille flow in jet viscometer orifices

1968 ◽  
Vol 303 (1475) ◽  
pp. 429-451 ◽  
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Velocity Profile ◽  
Reynolds Numbers ◽  
Correction Coefficient ◽  
Geometrical Shape ◽  
Energy Correction ◽  
Constant Diameter ◽  
Rate Of Increase ◽  
Parabolic Velocity Profile

A photomicrographic technique is described for determining the geometrical shape of glass jet viscometer orifices. These orifices are composed of a radiused entrance, a short constant diameter section, and a ‘diffuser type’ exit in which pressure recovery takes place. The length/diameter ratio of the constant diameter section of these orifices governs the highest Reynolds number for attaining 95% parabolic velocity profile, as calculated on the basis of Sparrow, Lin & Lundgren’s (1964) theoretical analysis of the development of parabolic velocity profile in the entrance region of tubes. Thirteen orifices were examined, and for these the highest admissible diameter Reynolds numbers were between 12 and 81. Thus, rates of shear, which can be calculated from the Poiseuille equation with an error of less than 1.5%, can amount to 6 x 10 5 s -1 without the liquid passing through the orifice suffering a temperature rise by viscous heating of more than 0.05°C. No kinetic energy correction is required for Reynolds numbers less than 10. For larger Reynolds numbers a correction should be made. The kinetic energy correction coefficient increases steeply with the Reynolds number, but the rate of increase depends upon the shape of the orifice profile. The largest kinetic energy correction coefficients of the thirteen orifices have values between 0.55 and 0.84. Within the range of Reynolds numbers admissible for 95% development of parabolic velocity profile, substantial temporary viscosity reductions were found. Neither surface tension nor elastic properties of the liquid affect the flow behaviour under the described experimental conditions.

Direct Numerical Simulation of Homogeneous Turbulent Shear Flow Containing Bubbles

2006 ◽  
Author(s):  
T. Kawamura ◽  
T. Nakatani
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Production Rate ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Hypothetical Model ◽  
Turbulent Reynolds Number

Direct numerical simulations of homogeneous shear turbulent flows containing deformable bubbles were carried out for clarifying the mechanism of drag reduction by microbubbles. The results show that presence of bubbles can suppress or enhance the development of turbulence depending on condition. The dissipation rate of turbulent kinetic energy is always increased by bubbles, while the production rate can be either increased or decreased depending on the turbulent and shear Reynolds numbers. As a result, the growth rate of turbulent kinetic energy can be either increased or decreased by bubbles depending on conditions. It was shown that the production rate tends to decrease at smaller shear Reynolds number, at larger turbulent Reynolds number, and at larger Weber number. Based on the results, a hypothetical model to explain the dependency on the Reynolds numbers has been proposed.

scholarly journals The decay of isotropic magnetohydrodynamics turbulence and the effects of cross-helicity

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Antoine Briard ◽  
Thomas Gomez
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Total Energy ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Inertial Range ◽  
Mhd Turbulence ◽  
Previous Prediction

Decaying homogeneous and isotropic magnetohydrodynamics (MHD) turbulence is investigated numerically at large Reynolds numbers thanks to the eddy-damped quasi-normal Markovian (EDQNM) approximation. Without any background mean magnetic field, the total energy spectrum $E$ scales as $k^{-3/2}$ in the inertial range as a consequence of the modelling. Moreover, the total energy is shown, both analytically and numerically, to decay at the same rate as kinetic energy in hydrodynamic isotropic turbulence: this differs from a previous prediction, and thus physical arguments are proposed to reconcile both results. Afterwards, the MHD turbulence is made imbalanced by an initial non-zero cross-helicity. A spectral modelling is developed for the velocity–magnetic correlation in a general homogeneous framework, which reveals that cross-helicity can contain subtle anisotropic effects. In the inertial range, as the Reynolds number increases, the slope of the cross-helical spectrum becomes closer to $k^{-5/3}$ than $k^{-2}$. Furthermore, the Elsässer spectra deviate from $k^{-3/2}$ with cross-helicity at large Reynolds numbers. Regarding the pressure spectrum $E_{P}$, its kinetic and magnetic parts are found to scale with $k^{-2}$ in the inertial range, whereas the part due to cross-helicity rather scales in $k^{-7/3}$. Finally, the two $4/3$rd laws for the total energy and cross-helicity are assessed numerically at large Reynolds numbers.

Effect of Reynolds Number on the Unsteady Flow and Acoustic Fields of Supersonic Cavity

2003 ◽  
Author(s):  
A. Hamed ◽  
D. Basu ◽  
K. Das
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Unsteady Flow ◽  
Sound Pressure ◽  
Pressure Fluctuations ◽  
Reynolds Numbers ◽  
Acoustic Fields ◽  
Sound Pressure Levels ◽  
Scale Structures ◽  
Supersonic Cavity

Numerical simulations are conducted to study the flow and acoustic fields for unsteady supersonic turbulent flow over an open cavity using Detached Eddy Simulations for two different Reynolds numbers. Results are presented for pressure fluctuations history, vorticity iso-surfaces and turbulent kinetic energy and sound pressure levels spectra. The results reveal higher sound pressure levels (SPL), and finer scale structures within the cavity at the higher Reynolds number.

Chaotic Lid-Driven Square Cavity Flows at Extreme Reynolds Numbers

2014 ◽  
Vol 15 (3) ◽  
pp. 596-617 ◽  
Author(s):  
Salvador Garcia
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Energy Range ◽  
Reynolds Numbers ◽  
The Other ◽  
Total Kinetic Energy ◽  
Cavity Flows ◽  
Lower Side ◽  
Square Cavity ◽  
Lower Fragment

AbstractThis paper investigates the chaotic lid-driven square cavity flows at extreme Reynolds numbers. Several observations have been made from this study. Firstly, at extreme Reynolds numbers two principles add at the genesis of tiny, loose counterclockwise- or clockwise-rotating eddies. One concerns the arousing of them owing to the influence of the clockwise- or counterclockwise currents nearby; the other, the arousing of counterclockwise-rotating eddies near attached to the moving (lid) top wall which moves from left to right. Secondly, unexpectedly, the kinetic energy soon reaches the qualitative temporal limit’s pace, fluctuating briskly, randomly inside the total kinetic energy range, fluctuations which concentrate on two distinct fragments: one on its upper side, the upper fragment, the other on its lower side, the lower fragment, switching briskly, randomly from each other; and further on many small fragments arousing randomly within both, switching briskly, randomly from one another. As the Reynolds number Re → ∞, both distance and then close, and the kinetic energy fluctuates shorter and shorter at the upper fragment and longer and longer at the lower fragment, displaying tall high spikes which enlarge and then disappear. As the time t → ∞ (at the Reynolds number Re fixed) they recur from time to time with roughly the same amplitude. For the most part, at the upper fragment the leading eddy rotates clockwise, and at the lower fragment, in stark contrast, it rotates counterclockwise. At Re=109 the leading eddy — at its qualitative temporal limit’s pace — appears to rotate solely counterclockwise.

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