Showing papers on "Reynolds number published in 2009"
TL;DR: In this paper, the authors review studies of the statistics of isotropic turbulence in an incompressible fluid at high Reynolds numbers using direct numerical simulation (DNS) from the viewpoint of fundamental physics.
Abstract: We review studies of the statistics of isotropic turbulence in an incompressible fluid at high Reynolds numbers using direct numerical simulation (DNS) from the viewpoint of fundamental physics. The Reynolds number achieved by the largest DNS, with 4096 3 grid points, is comparable with the largest Reynolds number in laboratory experiments. The high-quality DNS data in the inertial subrange and the dissipative range enable the examination of detailed statistics at small scales, such as the normalized energy-dissipation rate, energy and energy-flux spectra, the intermittency of the velocity gradients and increments, scaling exponents, and flow-field structure. We emphasize basic questions of turbulence, universality in the sense of Kolmogorov’s theory, and the dependence of the statistics on the Reynolds number and scale.
630 citations
TL;DR: In this paper, the authors demonstrate that periodic, micropatterned superhydrophobic surfaces, previously noted for their ability to provide laminar flowdrag reduction, are capable of reducing drag in the turbulent flow regime.
Abstract: In this paper, we demonstrate that periodic, micropatterned superhydrophobic surfaces, previously noted for their ability to provide laminar flowdrag reduction, are capable of reducing drag in the turbulent flow regime. Superhydrophobic surfaces contain micro- or nanoscale hydrophobic features which can support a shear-free air-water interface between peaks in the surface topology. Particle image velocimetry and pressure drop measurements were used to observe significant slip velocities, shear stress, and pressure drop reductions corresponding to drag reductions approaching 50%. At a given Reynolds number,drag reduction is found to increase with increasing feature size and spacing, as in laminar flows. No observable drag reduction was noted in the laminar regime, consistent with previous experimental results for the channel geometry considered. The onset of drag reduction occurs at a critical Reynolds number where the viscous sublayer thickness approaches the scale of the superhydrophobic microfeatures and performance is seen to increase with further reduction in viscous sublayer height. These results indicate superhydrophobic surfaces may provide a significant drag reducing mechanism for marine vessels.
550 citations
TL;DR: In this article, a nominally zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940.
Abstract: A nominally-zero-pressure-gradient incompressible boundary layer over a smooth flat plate was simulated for a continuous momentum thickness Reynolds number range of 80 ≤ Reθ ≤ 940. Transition which is completed at approximately Reθ = 750 was triggered by intermittent localized disturbances arising from patches of isotropic turbulence introduced periodically from the free stream at Reθ = 80. Streamwise pressure gradient is quantified with several measures and is demonstrated to be weak. Blasius boundary layer is maintained in the early transitional region of 80 < Reθ < 180 within which the maximum deviation of skin friction from the theoretical solution is less than 1%. Mean and second-order turbulence statistics are compared with classic experimental data, and they constitute a rare DNS dataset for the spatially developing zero-pressure-gradient turbulent flat-plate boundary layer. Our calculations indicate that in the present spatially developing low-Reynolds-number turbulent flat-plate boundary layer, total shear stress mildly overshoots the wall shear stress in the near-wall region of 2–20 wall units with vanishing normal gradient at the wall. Overshoots as high as 10% across a wider percentage of the boundary layer thickness exist in the late transitional region. The former is a residual effect of the latter. The instantaneous flow fields are vividly populated by hairpin vortices. This is the first time that direct evidence (in the form of a solution of the Navier–Stokes equations, obeying the statistical measurements, as opposed to synthetic superposition of the structures) shows such dominance of these structures. Hairpin packets arising from upstream fragmented Λ structures are found to be instrumental in the breakdown of the present boundary layer bypass transition.
521 citations
TL;DR: The analysis and experiments suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100
Abstract: The aerodynamic performance of hovering insects is largely explained by the presence of a stably attached leading edge vortex (LEV) on top of their wings. Although LEVs have been visualized on real, physically modeled, and simulated insects, the physical mechanisms responsible for their stability are poorly understood. To gain fundamental insight into LEV stability on flapping fly wings we expressed the Navier–Stokes equations in a rotating frame of reference attached to the wing's surface. Using these equations we show that LEV dynamics on flapping wings are governed by three terms: angular, centripetal and Coriolis acceleration. Our analysis for hovering conditions shows that angular acceleration is proportional to the inverse of dimensionless stroke amplitude, whereas Coriolis and centripetal acceleration are proportional to the inverse of the Rossby number. Using a dynamically scaled robot model of a flapping fruit fly wing to systematically vary these dimensionless numbers, we determined which of the three accelerations mediate LEV stability. Our force measurements and flow visualizations indicate that the LEV is stabilized by the `quasi-steady' centripetal and Coriolis accelerations that are present at low Rossby number and result from the propeller-like sweep of the wing. In contrast, the unsteady angular acceleration that results from the back and forth motion of a flapping wing does not appear to play a role in the stable attachment of the LEV. Angular acceleration is, however, critical for LEV integrity as we found it can mediate LEV spiral bursting, a high Reynolds number effect. Our analysis and experiments further suggest that the mechanism responsible for LEV stability is not dependent on Reynolds number, at least over the range most relevant for insect flight (100
499 citations
TL;DR: In this article, it was shown that the appearance of the outer peak in the broadband streamwise intensity is consistent with the attenuation of small scales due to large wire length l. The authors also established the basis for a maximum flow frequency, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated.
Abstract: Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the outer peak is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ= 18830). Beyond these Reynolds numbers and for internal geometries the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a maximum flow frequency, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx 1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra. © 2009 Copyright Cambridge University Press.
479 citations
TL;DR: In this article, the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to 10 scale heights was studied and it was shown that increasing the box size has little or no effect on the statistical properties of the turbulence.
Abstract: We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to 10 scale heights. Maxwell and Reynolds stresses are found to increase by more than a factor of 2 when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This, in turn, generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short timescales creates zonal flow structures with lifetimes of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.
400 citations
TL;DR: In this paper, the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate was investigated for three-dimensional flows over impulsively translated low-aspect-ratio flat plates.
Abstract: Three-dimensional flows over impulsively translated low-aspect-ratio flat plates are investigated for Reynolds numbers of 300 and 500, with a focus on the unsteady vortex dynamics at post-stall angles of attack. Numerical simulations, validated by an oil tow-tank experiment, are performed to study the influence of aspect ratio, angle of attack and planform geometry on the wake vortices and the resulting forces on the plate. Immediately following the impulsive start, the separated flows create wake vortices that share the same topology for all aspect ratios. At large time, the tip vortices significantly influence the vortex dynamics and the corresponding forces on the wings. Depending on the aspect ratio, angle of attack and Reynolds number, the flow at large time reaches a stable steady state, a periodic cycle or aperiodic shedding. For cases of high angles of attack, an asymmetric wake develops in the spanwise direction at large time. The present results are compared to higher Reynolds number flows. Some non-rectangular planforms are also considered to examine the difference in the wakes and forces. After the impulsive start, the time at which maximum lift occurs is fairly constant for a wide range of flow conditions during the initial transient. Due to the influence of the tip vortices, the three-dimensional dynamics of the wake vortices are found to be quite different from the two-dimensional von Karman vortex street in terms of stability and shedding frequency.
354 citations
TL;DR: In this paper, the authors investigated the extent or existence of similarities between fully developed turbulent pipes and channels, and in zero-pressure-gradient turbulent boundary layers, through streamwise velocity measurements in these three flows.
Abstract: The extent or existence of similarities between fully developed turbulent pipes and channels, and in zero-pressure-gradient turbulent boundary layers has come into question in recent years. This is in contrast to the traditionally accepted view that, upon appropriate normalization, all three flows can be regarded as the same in the near-wall region. In this paper, the authors aim to provide clarification of this issue through streamwise velocity measurements in these three flows with carefully matched Reynolds number and measurement resolution. Results show that mean statistics in the near-wall region collapse well. However, the premultiplied energy spectra of streamwise velocity fluctuations show marked structural differences that cannot be explained by scaling arguments. It is concluded that, while similarities exist at these Reynolds numbers, one should exercise caution when drawing comparisons between the three shear flows, even near the wall.
350 citations
TL;DR: In this paper, a new method is introduced for estimating the convection velocity of individual modes in turbulent shear flows that only requires spectral information in the temporal or spatial direction over which a modal decomposition is desired, while only using local derivatives in other directions.
Abstract: A new method is introduced for estimating the convection velocity of individual modes in turbulent shear flows that, in contrast to most previous ones, only requires spectral information in the temporal or spatial direction over which a modal decomposition is desired, while only using local derivatives in other directions. If no spectral information is desired, the method provides a natural definition for the average convection velocity, as well as a way to estimate the accuracy of the frozen-turbulence approximation. Existing data from numerical turbulent channels at friction Reynolds numbers Reτ 1900 are used to validate the new method against classical ones, and to characterize the dependence of the convection velocity on the eddy wavelength and wall distance. The results indicate that the small scales in turbulent channels travel at the local mean velocity, while large ‘global’ modes travel at a more uniform speed proportional to the bulk velocity. To estimate the systematic deviations introduced in experimental spectra by the use of Taylor’s approximation with a wavelengthindependent convection velocity, a semi-empirical fit to the computed convection velocities is provided. It represents well the data throughout the Reynolds number range of the simulations. It is shown that Taylor’s approximation not only displaces the large scales near the wall to shorter apparent wavelengths but also modifies the shape of the spectrum, giving rise to spurious peaks similar to those observed in some experiments. To a lesser extent the opposite is true above the logarithmic layer. The effect increases with the Reynolds number, suggesting that some of the recent challenges to the k −1 x energy spectrum may have to be reconsidered.
348 citations
TL;DR: In this paper, an analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier-Stokes equations, and an expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter.
Abstract: This study is devoted to a theoretical description of an unsteady laminar viscous flow in a spreading film of a Newtonian fluid. Such flow is generated by normal drop impact onto a dry substrate with high Weber and Reynolds numbers. An analytical self-similar solution for the viscous flow in the spreading drop is obtained which satisfies the full Navier–Stokes equations. The characteristic thickness of a boundary layer developed near the wall uniformly increases as a square root of time. An expression for the thickness of the boundary layer is used for the estimation of the residual film thickness formed by normal drop impact and the maximum spreading diameter. The theoretical predictions agree well with the existing experimental data. A possible explanation of the mechanism of formation of an uprising liquid sheet leading to splash is also proposed.
323 citations
TL;DR: In this paper, the thermal conductivity of nanofluid has been determined by model proposed by Patel et al. and the fluid was considered as Newtonian as well as non-Newtonian for a wide range of Reynolds number (Re = 5 to 1500) and solid volume fraction (0.00 ⩽ ϕ⩽ 0.050 ).
TL;DR: A robust, implicit, low-dissipation method suitable for LES/DNS of compressible turbulent flows is discussed, which is stable without the addition of any explicit dissipation terms at very high Reynolds numbers for flows without shocks.
TL;DR: In this article, a detailed analysis of the flow over smoothly contoured constrictions in a plane channel is presented, which is a generic case of a flow separating from a curved surface with well-defined flow conditions.
TL;DR: In this paper, the aerodynamic behavior of a vertical axis wind turbine is analyzed by means of 2D particle image velocimetry (PIV), focusing on the development of dynamic stall at different tip speed ratios.
Abstract: The aerodynamic behavior of a vertical axis wind turbine (VAWT) is analyzed by means of 2D particle image velocimetry (PIV), focusing on the development of dynamic stall at different tip speed ratios. The VAWT has an unsteady aerodynamic behavior due to the variation with the azimuth angle θ of the blade’s sections’ angle of attack, perceived velocity and Reynolds number. The phenomenon of dynamic stall is then an inherent effect of the operation of a VAWT at low tip speed ratios, impacting both loads and power. The present work is driven by the need to understand this phenomenon, by visualizing and quantifying it, and to create a database for model validation. The experimental method uses PIV to visualize the development of the flow over the suction side of the airfoil for two different reference Reynolds numbers and three tip speed ratios in the operational regime of a small urban wind turbine. The field-of-view of the experiment covers the entire rotation of the blade and almost the entire rotor area. The analysis describes the evolution of the flow around the airfoil and in the rotor area, with special focus on the leading edge separation vortex and trailing edge shed vorticity development. The method also allows the quantification of the flow, both the velocity field and the vorticity/circulation (only the results of the vorticity/circulation distribution are presented), in terms of the phase locked average and the random component.
TL;DR: In this paper, the authors investigated the effect of separation bubble formation and boundary layer separation on coherent structures in low Reynolds number flows and showed that roll-up vortices formed in the separated shear layer due to the amplification of natural disturbances, and these structures played a key role in flow transition to turbulence.
Abstract: Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 10 3 ≤ Re c ≤ 210 × 10 3 , and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.
TL;DR: In this paper, an extensive set of experimental data, for zero pressure gradient boundary layers, over a wide range of Reynolds number is re-evaluated with the help of a composite profile fitted to the mean-velocity data.
TL;DR: In this paper, direct numerical simulations (DNSs) and experiments of a spatially developing zero-pressure gradient turbulent boundary layer are presented up to Reynolds number Re-theta=2500, based on momentum of the boundary layer.
Abstract: Direct numerical simulations (DNSs) and experiments of a spatially developing zero-pressure-gradient turbulent boundary layer are presented up to Reynolds number Re-theta=2500, based on momentum th ...
TL;DR: In this paper, two formulas for explicitly evaluating drag coefficient and settling velocity of spherical particles, respectively, in the entire subcritical region were proposed for Reynolds numbers up to 2 × 105.
TL;DR: In this paper, the effects of bubble length, liquid slug length, and gravity on the liquid film thickness were investigated, and experimental correlation for the initial liquid-film thickness based on capillary number, Reynolds number, and Weber number was proposed.
TL;DR: An improved version of the authors's published correlation (Shah 1979), extended to a wider range of parameters, is presented in this article, which is shown to be in good agreement with data ranging from highly turbulent flows to the laminar flow conditions of Nusselt's analytical solutions.
Abstract: An improved version of the authors's published correlation (Shah 1979), extended to a wider range of parameters, is presented. The new correlation has been shown to be in good agreement with data ranging from highly turbulent flows to the laminar flow conditions of Nusselt's analytical solutions. The data used for the correlation's validation includes 22 fluids (water, halocarbon refrigerants, hydrocarbon refrigerants, and organics) condensing in horizontal, vertical, and downward-inclined tubes. The range of parameters includes tube diameters from 2 to 49 mm, reduced pressure from 0.0008 to 0.9, flow rates from 4 to 820 kg/m2·s, all liquid Reynolds numbers from 68 to 85,000, and liquid Prandtl numbers from 1 to 18. A total of 1189 data points from 39 sources are predicted with a mean deviation of 14.4%. Comparisons are also made with some other well-known correlations.
TL;DR: In this article, a numerical study has been performed by using both single phase method and combined Euler and Lagrange method on the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions.
TL;DR: In this article, the authors present an experimental study on the mean Nusselt number, friction factor and enhancement efficiency characteristics in a round tube with short-length twisted tape insert under uniform wall heat flux boundary conditions.
TL;DR: In this article, an experimental investigation of the near wake of a finite-length square cylinder, with one end mounted on a flat plate and the other free, was carried out mainly in a closed-loop low-speed wind tunnel at a Reynolds number Red, based on d and the free-stream velocity of 9300 using hot-wire anemometry, laser Doppler anEMometry and particle image velocimetry (PIV).
Abstract: This paper reports an experimental investigation of the near wake of a finite-length square cylinder, with one end mounted on a flat plate and the other free. The cylinder aspect ratio or height-to-width ratio H/d ranges from 3 to 7. Measurements were carried out mainly in a closed-loop low-speed wind tunnel at a Reynolds number Red, based on d and the free-stream velocity of 9300 using hot-wire anemometry, laser Doppler anemometry and particle image velocimetry (PIV). The planar PIV measurements were performed in the three orthogonal planes of the three-dimensional cylinder wake, along with flow visualization conducted simultaneously in two orthogonal planes (Red = 221). Three types of vortices, i.e. the tip, base and spanwise vortices were observed and the near wake is characterized by the interactions of these vortices. Both flow visualization and two-point correlation point to an inherent connection between the three types of vortices. A model is proposed for the three-dimensional flow structure based on the present measurements, which is distinct from previously proposed models. The instantaneous flow structure around the cylinder is arch-type, regardless of H/d, consisting of two spanwise vortical ‘legs’, one on each side of the cylinder, and their connection or ‘bridge’ near the free end. Both tip and base vortices are the streamwise projections of the arch-type structure in the (y, z) plane, associated with the free-end downwash flow and upwash flow from the wall, respectively. Other issues such as the topological characteristics, spatial arrangement and interactions among the vortical structures are also addressed.
TL;DR: It was found that flexibility can enhance aerodynamic performance and that the best performance is realized when the wing is excited by a non-linear resonance at 1/3 of the natural frequency, which points to the importance of considering non- linear resonances for enhancing aerodynamics performance.
Abstract: In the present study, a computational investigation was carried out to understand the influence of flexibility on the aerodynamic performance of a hovering wing. A flexible, two-dimensional, two-link model moving within a viscous fluid was considered. The Navier-Stokes equations governing the fluid dynamics were solved together with the equations governing the structural dynamics by using a strongly coupled fluid-structure interaction scheme. Harmonic kinematics was used to prescribe the motions of one of the links, thus effectively reducing the wing to a single degree-of-freedom oscillator. The wing's flexibility was characterized by the ratio of the flapping frequency to the natural frequency of the structure. Apart from the rigid case, different values of this frequency ratio (only in the range of 1/2 to 1/6) were considered at the Reynolds numbers of 75, 250 and 1000. It was found that flexibility can enhance aerodynamic performance and that the best performance is realized when the wing is excited by a non-linear resonance at 1/3 of the natural frequency. Specifically, at Reynolds numbers of 75, 250 and 1000, the aerodynamic performance that is characterized by the ratio of lift coefficient to drag coefficient is respectively increased by 28%, 23% and 21% when compared with the corresponding ratios of a rigid wing driven with the same kinematics. For all Reynolds numbers, the lift generated per unit driving power is also enhanced in a similar manner. The wake capture mechanism is enhanced, due to a stronger flow around the wing at stroke reversal, resulting from a stronger end of stroke vortex at the trailing edge. The present study provides some clues about how flexibility affects the aerodynamic performance in low Reynolds number flapping flight. In addition, it points to the importance of considering non-linear resonances for enhancing aerodynamic performance.
TL;DR: The results indicate that channel curvature can lead to microfluidic designs with reduced fluidic resistance, useful for lower power inertial focusing or separation and will enable design of practical particle/cell separation, filtration, and focusing systems for critical applications in biomedicine and environmental cleanup.
Abstract: Particles in finite-inertia confined channel flows are known to segregate and focus to equilibrium positions whose number corresponds with the fold of symmetry of the channel's cross section. The addition of curvature into channels presumably modifies these equilibrium inertial focusing positions, because of the secondary flow induced in curved channels. Here, we identify the critical interaction of the secondary flow field with inertial lift forces to create complex sets of particle focusing positions that vary with the channel Reynolds number (Re(C)) and the inertial force ratio, which is a new dimensionless parameter that is based on the ratio of inertial lift to drag forces from the secondary flow. We use these results to identify microfluidic channel geometries to focus particles at rates an order of magnitude higher than previously shown (channel Reynolds number, Re(C) = 270) and develop design criteria for the focusing of potentially arbitrary-sized particles. In addition, our results indicate that channel curvature can lead to microfluidic designs with reduced fluidic resistance, useful for lower power inertial focusing or separation. These results will enable design of practical particle/cell separation, filtration, and focusing systems for critical applications in biomedicine and environmental cleanup.
Book•
15 Sep 2009
TL;DR: In this article, the authors present an approach to control volume of particle flows in a 3D model of a particle stream, based on low Reynolds number and Stokes' Law.
Abstract: Preface. Acknowledgments. List of Symbols. 1 Conservation Laws and Continua. 1.1. Introduction. 1.2. Conservation Laws: Systems Approach. 1.3. Conservation Laws: Control Volume Approach. 1.4. Conservation Laws: Differential Element Approach. 1.5. Continua. 1.6. Sources, Sinks, Reactions, and Box Models. 1.7. Summary. Exercises. References. Bibliography. 2 Low-Concentration Particle Suspensions and Flows. 2.1. Introduction. 2.2. Drag on a Sphere. 2.3. Drag Force on Nonspherical Particles. 2.4. Low Reynolds Number Particle Dynamics and Stokes' Law. 2.5. Particle Motions in Electric Fields. 2.6. Quiescent and Perfect-Mix Batch Sedimentation. 2.7. Continuous Sedimentation Processes. 2.8. Inertial Forces on Particles and Stopping Distance. 2.9. Inertial Forces in Particle Flows. 2.10. Rotating Flows. 2.11. Centrifugation. 2.12. Summary. Exercises. References. Bibliography. 3 Interactions of Small Charged Particles. 3.1. Introduction. 3.2. Importance of Surface. 3.3. Acquisition of Surface Charge. 3.4. Particle Size, Shape, and Polydispersity. 3.5. The Double Layer and Colloidal Stability. 3.6. The Schulze-Hardy Rule. 3.7. Electrophoresis and Zeta Potential. 3.8. Particle Collision and Fast Coagulation. 3.9. Slow Coagulation. 3.10. Summary. Exercises. References. Bibliography. 4 Adsorption, Partitioning, and Interfaces. 4.1. Introduction. 4.2. Accumulation of Solutes at Interfaces. 4.3. Adsorption at Solid-Liquid and Solid-Gas Interfaces. 4.4. Adsorption Isotherms. 4.5. Linear Equilibrium Partitioning Between Two Phases. 4.6. Partitioning and Separation in Flow Systems. 4.7. Summary. Exercises. References. Bibliography. 5 Basic Fluid Mechanics of Environmental Transport. 5.1. Introduction. 5.2. The Joy of Fluid Mechanics. 5.3. The Navier-Stokes Equations. 5.4. Fluid Statics and the Buoyancy Force. 5.5. Capillarity and Interfacial Tension. 5.6. The Modified Pressure and Free-Surface Flows. 5.7. Steady Unidirectional Circular Streamline Flows. 5.8. Fluid Shear Stresses and the Viscosity of Newtonian Fluids. 5.9. Slip Flow. 5.10. Field-Flow Fractionation. 5.11. Nonsteady Unidirectional Flows: Stokes' First Problem. 5.12. Low Reynolds Number Flows. 5.13. Ideal Fluids, Potential Flows, and Stream Functions. 5.14. The Bernoulli Equation. 5.15. Steady Viscous Momentum Boundary Layers. 5.16. Turbulent Flows. 5.17. Summary. Exercises. References. Bibliography. 6 Diffusive Mass Transport. 6.1. Introduction. 6.2. Thermodynamics of Diffusion. 6.3. Fick's First Law and General Diffusive Transport. 6.4. The Diffusion Coefficient. 6.5. Steady-State Diffusion Problems with No Overall Diffusive Mass Transfer. 6.6. Steady-State Mass Balances Over Differential Elements. 6.7. Fick's Second Law and Nonsteady-State Diffusion. 6.8. Effective Diffusion Coefficients in Porous Media. 6.9. Hindered Diffusion. 6.10. When Chemicals Diffuse Against a Concentration Gradient. 6.11. Summary. Exercises. References. Bibliography. 7 Convective Diffusion, Dispersion, and Mass Transfer. 7.1. Introduction and Simple Example of Convective Diffusion. 7.2. The Convective-Diffusion Equation. 7.3. Mass Transport in Steady Laminar Flow in a Cylindrical Tube. 7.4. Taylor-Aris Dispersion. 7.5. Turbulent Dispersion: The Lagrangian Approach. 7.6. Turbulent Dispersion: The Eulerian Approach. 7.7. Mass Transfer in Laminar Flow Along Reacting or Dissolving Solid Surfaces. 7.8. Mass-Transfer Coefficients, Models, and Correlations for Laminar and Turbulent Flows. 7.9. Interphase Mass Transport and Resistance Models. 7.10. Summary. Exercises. References. 8 Filtration and Mass Transport in Porous Media. 8.1. Introduction. 8.2. Porosity, Velocity, and Porous Media Continua. 8.3. Coefficients of Mechanical, Molecular, and Hydrodynamic Dispersion. 8.4. Porous Media Dispersion Equation in a Homogeneous Isotropic Medium. 8.5. Solution of the Dispersion Equation in an Infinite One-Dimensional Medium. 8.6. Analytical Chromatography. 8.7. Filtration. 8.8. Osmotic Pressure and Reverse Osmosis. 8.9. Summary. Exercises. References. Bibliography. 9 Reaction Kinetics. 9.1. Introduction. 9.2. First-Order Reactions. 9.3. Second-Order Reactions. 9.4. Pseudo-First-Order Reactions. 9.5. Zero-Order Reactions. 9.6. Elementary and Nonelementary Reactions. 9.7. Simple Series and Parallel Reactions. 9.8. Reversible Reactions. 9.9. Characteristic Reaction Times. 9.10. Arrhenius' Law and the Effect of Temperature on Reaction Rate. 9.11. The Fastest Reactions: Diffusion-Controlled Reactions. 9.12. Summary. Exercises. References. Bibliography. 10 Mixing and Reactor Modeling. 10.1. Introduction. 10.2. Simple Closed-Reactor and Residence-Time Distributions. 10.3. Measurement of Residence-Time Distributions. 10.4. Residence-Time Distributions from Discrete Data. 10.5. Perfect Mixing and Ideal Plug Flow. 10.6. F, W, and Disinfection. 10.7. Moments of Residence-Time Distributions. 10.8. Other Residence-Time Models. 10.9. Axial-Dispersion Model. 10.10. Fitting Residence-Time Distributions to Data. 10.11. Mixing and Reactions. 10.12. Summary. Exercises. References. Bibliography. Appendix I. S I Units and Physical Constants. Bibliography. Appendix II. Review of Vectors. Bibliography. Appendix III. Equations of Fluid Mechanics and Convective Diffusion in Rectangular, Cylindrical, and Spherical Coordinates. Bibliography. Appendix IV. Physical Properties of Water and Air. Bibliography. Index.
TL;DR: It is shown that even though the wake transitions to a weakly three-dimensional state when the gap flow is active, the three- dimensional modes are too weak to affect the dynamic response of the system, which is found to be identical to that obtained from the two-dimensional computations.
Abstract: We investigate numerically vortex-induced vibrations (VIV) of two identical two-dimensional elastically mounted cylinders in tandem in the proximity–wake interference regime at Reynolds number Re = 200 for systems having both one (transverse vibrations) and two (transverse and in-line) degrees of freedom (1-DOF and 2-DOF, respectively). For the 1-DOF system the computed results are in good qualitative agreement with available experiments at higher Reynolds numbers. Similar to these experiments our simulations reveal: (1) larger amplitudes of motion and a wider lock-in region for the tandem arrangement when compared with an isolated cylinder; (2) that at low reduced velocities the vibration amplitude of the front cylinder exceeds that of the rear cylinder; and (3) that above a threshold reduced velocity, large-amplitude VIV are excited for the rear cylinder with amplitudes significantly larger than those of the front cylinder. By analysing the simulated flow patterns we identify the VIV excitation mechanisms that lead to such complex responses and elucidate the near-wake vorticity dynamics and vortex-shedding modes excited in each case. We show that at low reduced velocities vortex shedding provides the initial excitation mechanism, which gives rise to a vertical separation between the two cylinders. When this vertical separation exceeds one cylinder diameter, however, a significant portion of the incoming flow is able to pass through the gap between the two cylinders and the gap-flow mechanism starts to dominate the VIV dynamics. The gap flow is able to periodically force either the top or the bottom shear layer of the front cylinder into the gap region, setting off a series of very complex vortex-to-vortex and vortex-to-cylinder interactions, which induces pressure gradients that result in a large oscillatory force in phase with the vortex shedding and lead to the experimentally observed larger vibration amplitudes. When the vortex shedding is the dominant mechanism the front cylinder vibration amplitude is larger than that of the rear cylinder. The reversing of this trend above a threshold reduced velocity is associated with the onset of the gap flow. The important role of the gap flow is further illustrated via a series of simulations for the 2-DOF system. We show that when the gap-flow mechanism is triggered, the 2-DOF system can develop and sustain large VIV amplitudes comparable to those observed in the corresponding (same reduced velocity) 1-DOF system. For sufficiently high reduced velocities, however, the two cylinders in the 2-DOF system approach each other, thus significantly reducing the size of the gap region. In such cases the gap flow is entirely eliminated, and the two cylinders vibrate together as a single body with vibration amplitudes up to 50% lower than the amplitudes of the corresponding 1-DOF in which the gap flow is active. Three-dimensional simulations are also carried out to examine the adequacy of two-dimensional simulations for describing the dynamic response of the tandem system at Re = 200. It is shown that even though the wake transitions to a weakly three-dimensional state when the gap flow is active, the three-dimensional modes are too weak to affect the dynamic response of the system, which is found to be identical to that obtained from the two-dimensional computations.
TL;DR: In this paper, an analysis of fully developed channel flow at Reynolds number of Re = u τ δ / ν = 4000 based on the friction velocity, u τ, and half the channel height, δ.
TL;DR: In this article, the axial evolution of temperature, convective heat transfer coefficient and the friction coefficient at the inner and outer walls' region are shown and discussed, and it is shown that the dimensionless axial velocity profile does not significantly change with the nanoparticle volume fraction.
TL;DR: In this paper, the laminar separation bubble on an SD7003 aerofoil at a Reynolds number Re = 66000 was investigated to determine the dominant frequencies of the transition process and the flapping of the bubble.
Abstract: The laminar separation bubble on an SD7003 aerofoil at a Reynolds number Re = 66000 was investigated to determine the dominant frequencies of the transition process and the flapping of the bubble. The measurements were performed with a high-resolution time-resolved particle image velocimetry (TR-PIV) system. Contrary to typical measurements performed through conventional PIV, the different modes can be identified by applying TR-PIV. The interaction between the shed vortices is analysed, and their significance for the production of turbulence is presented. In the shear layer above the bubble the generation and amplification of vortices due to Kelvin–Helmholtz instabilities is observed. It is found that these instabilities have a weak coherence in the spanwise direction. In a later stage of transition these vortices lead to a three-dimensional breakdown to turbulence.