Showing papers on "Drag coefficient published in 2004"

On the limiting aerodynamic roughness of the ocean in very strong winds

Abstract: The aerodynamic friction between air and sea is an important part of the momentum balance in the development of tropical cyclones. Measurements of the drag coefficient, relating the tangential stress ( frictional drag) between wind and water to the wind speed and air density, have yielded reliable information in wind speeds less than 20 m/s ( about 39 knots). In these moderate conditions it is generally accepted that the drag coefficient ( or equivalently, the aerodynamic roughness'') increases with the wind speed. Can one merely extrapolate this wind speed tendency to describe the aerodynamic roughness of the ocean in the extreme wind speeds that occur in hurricanes ( wind speeds greater than 30 m/s)? This paper attempts to answer this question, guided by laboratory extreme wind experiments, and concludes that the aerodynamic roughness approaches a limiting value in high winds. A fluid mechanical explanation of this phenomenon is given.

A Simple Universal Equation for Grain Settling Velocity

Abstract: A new equation is presented for sediment fall velocity as a function of grain diameter for given values of fluid viscosity and fluid and solid density. Sediment fall velocity is a fundamental parameter in the modeling and interpretation of fluviatile and coastal deposition. The equation applies to the entire range of viscous to turbulent conditions, and its simple explicit form makes it easy to use in computer models and other applications in sedimentology, geomorphology, and engineering. The equation is derived from dimensional analysis and converges on Stokes' law for small grains and a constant drag coefficient for large grains. Its two physically interpretable parameters are easily adjusted for shape effects or for the use of sieve diameter rather than nominal grain diameter. It gives a close fit to published and new experimental data for both quartz sand and low-density materials, with no more error than previous equations of more complicated form.

Effects of hydrophobic surface on skin-friction drag

Abstract: Effects of hydrophobic surface on skin-friction drag are investigated through direct numerical simulations of a turbulent channel flow. Hydrophobic surface is represented by a slip-boundary condition on the surface. When a slip-boundary condition is used in the streamwise direction, the skin-friction drag decreases and turbulence intensities and turbulence structures, near-wall streamwise vortices in particular, are significantly weakened. When a slip-boundary condition is used in the spanwise direction, on the other hand, the drag is increased. It is found that near-wall turbulence structures are modified differently, resulting in drag increase. It is also found that the slip length must be greater than a certain value in order to have a noticeable effect on turbulence. An important implication of the present finding is that drag reduction in turbulent boundary layers is unlikely with hydrophobic surface with its slip length on the order of a submicron scale.

The limited growth of vegetated shear layers

Abstract: [1] In contrast to free shear layers, which grow continuously downstream, shear layers generated by submerged vegetation grow only to a finite thickness. Because these shear layers are characterized by coherent vortex structures and rapid vertical mixing, their thickness controls exchange between the vegetation and the overlying water. Experiments conducted in a laboratory flume show that the growth of these obstructed shear layers is arrested once the production of shear-layer-scale turbulent kinetic energy (SKE) is balanced by dissipation of SKE within the canopy. This equilibrium condition, along with a mixing length closure scheme, was used in a one-dimensional numerical model to predict the mean velocity profiles of the experimental shear layers. The agreement between model and experiment is very good, but field application of the model is limited by a lack of description of the drag coefficient in a submerged canopy.

A canopy model of mean winds through urban areas

Abstract: SUMMARY An urban canopy model is developed for spatially averaged mean winds within and above urban areas. The urban roughness elements are represented as a canopy-element drag carefully formulated in terms of morphological parameters of the building arrays and a mean sectional drag coefficient for a single building. Turbulent stresses are represented using a mixing-length model, with a mixing length that depends upon the density of the canopy and distance from the ground, which captures processes known to occur in canopies. The urban canopy model is sufficiently simple that it can be implemented in numerical weather-prediction models. The urban canopy model compares well with wind tunnel measurements of the mean wind profile through a homogeneous canopy of cubical roughness elements and with measurements of the effective roughness length of cubical roughness elements. These comparisons give confidence that the basic approach of a canopy model can be extended from fine-scale vegetation canopies to the canopies of large-scale roughness elements that characterize urban areas. The urban canopy model is also used to investigate the adjustment to inhomogeneous canopies. The canonical case of adjustment of a rural boundary layer to a uniform urban canopy shows that the winds within the urban canopy adjust after a distance x0 = 3Lc ln K ,w hereLc is the canopy drag length-scale, which characterizes the canopy-element drag, and ln K depends weakly on canopy parameters and varies between about 0.5 and 2. Thus the density and shape of buildings within a radius x0 only determine the local canopy winds. In this sense x0 gives a dynamical definition of the size of a neighbourhood. The urban canopy model compares well with observations of the deceleration of the wind associated with adjustment of a rural boundary layer to a canopy of cubical roughness elements, but only when the sectional drag coefficient is taken to be somewhat larger than expected. We attribute this discrepancy to displacement of streamlines around the large-scale urban roughness elements, which yields a stress that decelerates the wind. A challenge for future research is to incorporate this additional ‘dispersive stress’ into the urban canopy model.

Critical assessment of turbulent drag reduction through spanwise wall oscillations

Abstract: Direct numerical simulations of the incompressible Navier–Stokes equations are employed to study the turbulent wall-shear stress in a turbulent channel flow forced by lateral sinusoidal oscillations of the walls. The objective is to produce a documented database of numerically computed friction reductions. To this aim, the particular numerical requirements for such simulations, owing for example to the time-varying direction of the skin-friction vector, are considered and appropriately accounted for. A detailed analysis of the dependence of drag reduction on the oscillatory parameters allows us to address conflicting results hitherto reported in the literature. At the Reynolds number of the present simulations, we compute a maximum drag reduction of 44.7%, and we assess the possibility for the power saved to be higher than the power spent for the movement of the walls (when mechanical losses are neglected). A maximum net energy saving of 7.3% is computed. Furthermore, the scaling of the amount of drag reduction is addressed. A parameter, which depends on both the maximum wall velocity and the period of the oscillation, is found to be linearly related to drag reduction, as long as the half-period of the oscillation is shorter than a typical lifetime of the turbulent near-wall structures. For longer periods of oscillation, the scaling parameter predicts that drag reduction will decrease to zero more slowly than the numerical data. The same parameter also describes well the optimum period of oscillation for fixed maximum wall displacement, which is smaller than the optimum period for fixed maximum wall velocity, and depends on the maximum displacement itself.

On the Aerodynamic Drag Force Acting on Interplanetary Coronal Mass Ejections

Abstract: It is well known that the interaction of an interplanetary coronal mass ejection (ICME) with the solar wind leads to an equalisation of the ICME and solar wind velocities at 1 AU. This can be understood in terms of an aerodynamic drag force per unit mass of the form FD/M=−(ρeACD/M)(Vi−Ve)∣Vi−Ve∣, where A and M are the ICME cross-section and sum of the mass and virtual mass, Vi and Ve the speed of the ICME and solar wind, ρe the solar wind density, CD a dimensionless drag coefficient, and the inverse deceleration length γ=ρeA/M. The optimal radial parameterisation of γ and CD beyond approximately 15 solar radii is calculated. Magnetohydrodynamic simulations show that for dense ICMEs, CD varies slowly between the Sun and 1 AU, and is of order unity. When the ICME and solar wind densities are similar, CD is larger (between 3 and 10), but remains approximately constant with radial distance. For tenuous ICMEs, the ICME and solar wind velocities equalise rapidly due to the very effective drag force. For ICMEs denser that the ambient solar wind, both approaches show that γ is approximately independent of radius, while for tenuous ICMEs, γ falls off linearly with distance. When the ICME density is similar to or less than that in the solar wind, inclusion of virtual mass effects is essential.

Simulation of Heterogeneous Structure in a Circulating Fluidized-Bed Riser by Combining the Two-Fluid Model with the EMMS Approach

Abstract: To consider the critical effect of mesoscale structure on the drag coefficient, this paper presents a drag model based on the energy-minimization multiscale (EMMS) approach. The proposed structure parameters are obtained from the EMMS model, and then the average drag coefficient can be calculated from the structure parameters and further incorporated into the two-fluid model to simulate the gas-solid flow in a circulating fluidized-bed riser. Simulation results indicate that the simulated flow structures are different for the EMMS-based drag model and the hybrid model using the Wen and Yu correlation and the Ergun equation. The former shows its improvement in predicting the solids entrainment rate, the mesoscale heterogeneous structure involving clusters or strands, and the radial and axial voidage distributions. The simulation results support the idea that the average drag coefficient is an important factor for the two-fluid model and suggest that the EMMS approach could be used as a kind of multiscale closure law for drag coefficient.

Wave Breaking and Ocean Surface Layer Thermal Response

Abstract: The effect of breaking waves on ocean surface temperatures and surface boundary layer deepening is investigated. The modification of the Mellor‐Yamada turbulence closure model by Craig and Banner and others to include surface wave breaking energetics reduces summertime surface temperatures when the surface layer is relatively shallow. The effect of the Charnock constant in the relevant drag coefficient relation is also studied.

Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder

Abstract: We present a numerical study of a two-dimensional time-dependent flow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coefficient at the cylinder and for the pressure difference between the front and the back of the cylinder at the final time. In addition, the accuracy of these values obtained with different time stepping schemes and different finite element methods is studied

The role of drag in insect hovering.

Abstract: SUMMARY Studies of insect flight have focused on aerodynamic lift, both in quasi-steady and unsteady regimes. This is partly influenced by the choice of hovering motions along a horizontal stroke plane, where aerodynamic drag makes no contribution to the vertical force. In contrast, some of the best hoverers– dragonflies and hoverflies – employ inclined stroke planes, where the drag in the down- and upstrokes does not cancel each other. Here, computation of an idealized dragonfly wing motion shows that a dragonfly uses drag to support about three quarters of its weight. This can explain an anomalous factor of four in previous estimates of dragonfly lift coefficients, where drag was assumed to be small. To investigate force generation and energy cost of hovering flight using different combination of lift and drag, I study a family of wing motion parameterized by the inclined angle of the stroke plane. The lift-to-drag ratio is no longer a measure of efficiency, except in the case of horizontal stroke plane. In addition, because the flow is highly stalled, lift and drag are of comparable magnitude, and the aerodynamic efficiency is roughly the same up to an inclined angle about 60°, which curiously agrees with the angle observed in dragonfly flight. Finally, the lessons from this special family of wing motion suggests a strategy for improving efficiency of normal hovering, and a unifying view of different wing motions employed by insects.

Stokes drag on a sphere in a nematic liquid crystal.

Abstract: The Stokes-Einstein relation relates the diffusion coefficient of a spherical Brownian particle in a viscous fluid to its friction coefficient. For a particle suspended in anisotropic liquid, theory predicts that the drag coefficient should also be anisotropic. Using video microscopy coupled with particle tracking routines, the Brownian fluctuations of micrometer-sized particles were analyzed to yield a quantitative measurement of the diffusion coefficients parallel and perpendicular to the nematic director. The experimental values agree quite well with recent numerical calculations that take into account the distortions of the director field in the vicinity of the particles.

The effects of hydraulic resistance on dam-break and other shallow inertial flows

Abstract: The effects of resistive forces on unsteady shallow flows over rigid horizontal boundaries are investigated theoretically. The dynamics of this type of motion are driven by the streamwise gradient of the hydrostatic pressure, which balances the inertia of the fluid and the basal resistance. Drag forces are often negligible provided the fluid is sufficiently deep. However, close to the front of some flows where the depth of the moving layer becomes small, it is possible for drag to substantially influence the motion. Here we consider three aspects of unsteady shallow flows. First we consider a regime in which the drag, inertia and buoyancy (pressure gradient) are formally of the same magnitude throughout the entire current and we construct a new class of similarity solutions for the motion. This reveals the range of solution types possible, which includes those with continuous profiles, those with discontinuous profiles and weak shocks and those which are continuous but have critical points of transition at which the gradients may be discontinuous. Next we analyse one-dimensional dam-break flow and calculate how drag slows the motion. There is always a region close to the front in which drag forces are not negligible. We employ matched asymptotic expansions to combine the flow at the front with the flow in the bulk of the domain and derive theoretical predictions that are compared to laboratory measurements of dam-break flows. Finally we investigate a modified form of dam-break flow in which the vertical profile of the horizontal velocity field is no longer assumed to be uniform. It is found that in the absence of drag it is no longer possible to find a kinematically consistent front of the fluid motion. However the inclusion of drag forces within the region close to the front resolves this difficulty. We calculate velocity and depth profiles within the drag-affected region, and obtain the leading-order expression for the rate at which the fluid propagates when the magnitude of the drag force is modelled using Chae#169;zy, Newtonian and power-law fluid closures; this compares well with experimental data and provide new insights into dam-break flows.

Turbulent drag reduction in dam-break flows

Abstract: The role of turbulence is investigated in dam-break flows, where a finite volume of fluid is released from a compartment into a long, rectangular channel. After a sudden removal of the lock gate, a gravity current, undular bore, or solitary wave develops, depending on the ambient fluid height in the channel. The temporal evolution of the moving front has been measured and evaluated. It was observed that the dilution using a very small amount (a few weight ppm) of a long chain polymer (polyethylene-oxide) in the fluid strongly affected flow properties. Pronounced drag reduction has been found in dry bed flows (whereas the polymer increased the viscosity of the fluid). The presence of a few mm-thick ambient fluid layer in the channel effectively destroyed drag reduction, in spite of the fact that strong turbulence was obvious and the propagation velocity of the front was almost unchanged.

Flow resistance of emergent vegetation

Abstract: Conventional resistance equations (such as those of Manning, Chezy and Darcy–Weisbach) are inappropriate for flow through emergent vegetation, where resistance is exerted primarily by stem drag throughout the flow depth rather than by shear stress at the bed. An alternative equation form is suggested, in which the resistance coefficient is related to measurable vegetation characteristics and can incorporate bed roughness when this is significant. Equation performance is confirmed by comparison of predicted and measured stage–discharge relationships for flow through artificial cylindrical stems, and by comparison of calibrated and measured drag coefficient values for natural vegetation.

Effect of Surface Waves on Air–Sea Momentum Exchange. Part II: Behavior of Drag Coefficient under Tropical Cyclones

Abstract: Present parameterizations of air–sea momentum flux at high wind speed, including hurricane wind forcing, are based on extrapolation from field measurements in much weaker wind regimes. They predict monotonic increase of drag coefficient (Cd) with wind speed. Under hurricane wind forcing, the present numerical experiments using a coupled ocean wave and wave boundary layer model show that Cd at extreme wind speeds strongly depends on the wave field. Higher, longer, and more developed waves in the right-front quadrant of the storm produce higher sea drag; lower, shorter, and younger waves in the rear-left quadrant produce lower sea drag. Hurricane intensity, translation speed, as well as the asymmetry of wind forcing are major factors that determine the spatial distribution of Cd. At high winds above 30 m s−1, the present model predicts a significant reduction of Cd and an overall tendency to level off and even decrease with wind speed. This tendency is consistent with recent observational, experime...

Large eddy simulations on the effects of surface geometry of building arrays on turbulent organized structures

Abstract: Turbulent organized structures (TOS) above building arrays were investigated using a large-eddy simulation (LES) model for a city (LES-CITY). Square and staggered building arrays produced contrasting behaviour in terms of turbulence that roughly corresponded to the conventional classification of ‘D-type’ and ‘K-type’ roughness, respectively: (1) The drag coefficients (referred to the building height) for staggered arrays were sensitive to building area density, but those for square arrays were not. (2) The relative contributions of ejections to sweeps (S2/S4) at the building height for square arrays were sensitive to building area density and nearly equalled or exceeded 1.0 (ejection dominant), but those for staggered arrays were insensitive to building area density and were mostly below 1.0 (sweep dominant). (3) Streaky patterns of longitudinal low speed regions (i.e., low speed streaks) existed in all flows regardless of array type. Height variations of the buildings in the square array drastically increased the drag coefficient and modified the turbulent flow structures. The mechanism of D-type and K-type urban-like roughness flows and the difference from vegetation flows are discussed. Although urban-like roughness flows exhibited mixed properties of mixing layers and flat-wall boundary layers as far as S2/S4 was concerned, the turbulent organized structures of urban-like roughness flows resembled those of flat-wall boundary layers.

Momentum Transfer and Turbulent Kinetic Energy Budgets within a Dense Model Canopy

Abstract: Second-order closure models for the canopy sublayer (CSL) employ aset of closure schemes developed for `free-air' flow equations andthen add extra terms to account for canopy related processes. Muchof the current research thrust in CSL closure has focused on thesecanopy modifications. Instead of offering new closure formulationshere, we propose a new mixing length model that accounts for basicenergetic modes within the CSL. Detailed flume experiments withcylindrical rods in dense arrays to represent a rigid canopy areconducted to test the closure model. We show that when this lengthscale model is combined with standard second-order closureschemes, first and second moments, triple velocity correlations,the mean turbulent kinetic energy dissipation rate, and the wakeproduction are all well reproduced within the CSL provided thedrag coefficient (CD) is well parameterized. The maintheoretical novelty here is the analytical linkage betweengradient-diffusion closure schemes for the triple velocitycorrelation and non-local momentum transfer via cumulant expansionmethods. We showed that second-order closure models reproducereasonably well the relative importance of ejections and sweeps onmomentum transfer despite their local closure approximations.Hence, it is demonstrated that for simple canopy morphology (e.g.,cylindrical rods) with well-defined length scales, standard closureschemes can reproduce key flow statistics without much revision.When all these results are taken together, it appears that thepredictive skills of second-order closure models are not limitedby closure formulations; rather, they are limited by our abilityto independently connect the drag coefficient and the effectivemixing length to the canopy roughness density. With rapidadvancements in laser altimetry, the canopy roughness densitydistribution will become available for many terrestrialecosystems. Quantifying the sheltering effect, the homogeneity andisotropy of the drag coefficient, and more importantly, thecanonical mixing length, for such variable roughness density isstill lacking.

Wall effects in flow past a circular cylinder in a plane channel: a numerical study

Abstract: This paper describes a numerical study on the steady flow of an incompressible Newtonian fluid past a circular cylinder confined in a plane rectangular channel. Using FLUENT (version 6), two-dimensional steady state computations were carried out for an uniform inlet velocity and for different values of the Reynolds numbers in the range between 0.1 and 200 and blockage ratios (ratio of the channel width to the cylinder diameter) in the range between 1.54 and 20. The flow parameters such as drag coefficient, length of the recirculation zone, and the angle of separation are presented as functions of the Reynolds number and blockage ratio. The total drag coefficient (CD) was found to decrease with an increase in the blockage ratio (λ) for a fixed value of the Reynolds number (Re) and to decrease with increasing Reynolds number for a fixed value of λ. Similarly, for a fixed value of λ, both the angle of separation and the length of the recirculation zone increase with the increasing Reynolds number.

How flexibility induces streamlining in a two-dimensional flow

Abstract: Recent work in bio-fluid dynamics has studied the relation of fluid drag to flow speed for flexible organic structures, such as tree leaves, seaweed, and coral beds, and found a reduction in drag growth due to body reconfiguration with increasing flow speed. Our theoretical and experimental work isolates the role of elastic bending in this process. Using a flexible glass fiber wetted into a vertical soap-film flow, we identify a transition in flow speed beyond which fluid forces dominate the elastic response, and yield large deformations of the fiber that greatly reduce drag. We construct free-streamline models that couple fluid and elastic forces and solve them in an efficient numerical scheme. Shape self-similarity emerges, with a scaling set by the balance of forces in a small “tip region” about the flow’s stagnation point. The result is a transition from the classical U2 drag scaling of rigid bodies to a new U4/3 drag law. We derive an asymptotic expansion for the fiber shape and flow, based on the le...

Form Drag and Mixing Due to Tidal Flow past a Sharp Point

Abstract: Barotropic tidal currents flowing over rough topography may be slowed by two bottom boundary‐related processes: tangential stress of the bottom boundary layer, which is generally well represented by a quadratic drag law, and normal stress from bottom pressure, known as form drag. Form drag is rarely estimated from oceanic observations because it is difficult to measure the bottom pressure over a large spatial domain. The ‘‘external’’ and ‘‘internal’’ components of the form drag are associated, respectively, with sea surface and isopycnals deformations. This study presents model and observational estimates of the components of drag for Three Tree Point, a sloping ridge projecting 1 km into Puget Sound, Washington. Internal form drag was integrated from repeat microstructure sections and exceeded the net drag due to bottom friction by a factor of 10‐50 during maximum flood. In observations and numerical simulations, form drag was produced by a lee wave, as well as by horizontal flow separation in the model. The external form drag was not measured, but in numerical simulations was found to be comparable to the internal form drag. Form drag appears to be the primary mechanism for extracting energy from the barotropic tide. Turbulent buoyancy flux is strongest near the ridge in both observations and model results.

Drag Reduction by Polymers in Wall Bounded Turbulence

Abstract: We elucidate the mechanism of drag reduction by polymers in turbulent wall-bounded flows: while momentum is produced at a fixed rate by the forcing, polymer stretching results in the suppression of momentum flux to the wall. On the basis of the equations of fluid mechanics we develop the phenomenology of the ``maximum drag reduction asymptote'' which is the maximum drag reduction attained by polymers. Based on Newtonian information only we demonstrate the existence of drag reduction, and with one experimental parameter we reach agreement with the experimental measurements.