Showing papers on "Drag coefficient published in 2011"

Drag reduction by riblets

Abstract: The interaction of the overlying turbulent flow with riblets, and its impact on their drag reduction properties are analysed. In the so-called viscous regime of vanishing riblet spacing, the drag reduction is proportional to the riblet size, but for larger riblets the proportionality breaks down, and the drag reduction eventually becomes an increase. It is found that the groove cross section A + is a better characterization of this breakdown than the riblet spacing, with an optimum A + 1/2 ≈ 11. It is also found that the breakdown is not associated with the lodging of quasi-streamwise vortices inside the riblet grooves, or with the inapplicability of the Stokes hypothesis to the flow along the grooves, but with the appearance of quasi-two-dimensional spanwise vortices below y + ≈ 30, with typical streamwise wavelengths l + ≈ 150. They are connected with a Kelvin–Helmholtzlike instability of the mean velocity profile, also found in flows over plant canopies and other surfaces with transpiration. A simplified stability model for the ribbed surface approximately accounts for the scaling of the viscous breakdown with A + .

Drag Reduction by Leidenfrost Vapor Layers

Abstract: We demonstrate and quantify a highly effective drag reduction technique that exploits the Leidenfrost effect to create a continuous and robust lubricating vapor layer on the surface of a heated solid sphere moving in a liquid. Using high-speed video, we show that such vapor layers can reduce the hydrodynamic drag by over 85%. These results appear to approach the ultimate limit of drag reduction possible by different methods based on gas-layer lubrication and can stimulate the development of related energy saving technologies.

Aerobreakup of Newtonian and Viscoelastic Liquids

Abstract: In this review, we consider and unify all aspects of the dynamics of Newtonian and viscoelastic liquid drops in high-speed gas flows, including shock waves. The path to understanding is opened by novel, laser-induced fluorescence visualizations at spatial resolutions of up to 200 pixels for millimeter and exposure times as low as 5 ns. The central role of the competition between Rayleigh-Taylor and Kelvin-Helmholtz instabilities is assessed in the frame of rich aerodynamics, from low subsonic to supersonic, and the multitude of characteristic length scales and timescales at play with varying liquid properties. Acceleration and liquid redistribution (drop deformation) early in the evolution set the stage for this competition, and we insist on an interpretation of the drag coefficient that is physically meaningful. Two principal breakup regimes (patterns of bodily loss of coherence) are identified depending on whether the gas finds its way through the liquid mass, causing gross disintegration, or goes aroun...

Constitutive Models for Filtered Two-Fluid Models of Fluidized Gas–Particle Flows

Abstract: Our prior study [Igci et al., AIChE J., 2008, 54, 1431–1448] presented a methodology where computational results obtained through highly resolved simulations of a given microscopic two-fluid model (TFM) for gas-particle flows are filtered to deduce models for the residual correlations appearing in the corresponding filtered TFM equations that are appropriate for coarse-grid simulations of gas-particle flows. In the present study, we have performed a large number of highly resolved simulations of a kinetic theory based TFM in two- and three-dimensional periodic domains using this methodology and filtered the results to generate computational data on the filtered drag coefficient, the filtered particle phase pressure, and the filtered particle phase viscosity. These results have been captured in the form of correlations that can readily be employed in coarse-grid simulations of gas-particle flows.

Numerical study of flow through and around a circular array of cylinders

Abstract: This paper describes a study of the local and global effect of an isolated group of cylinders on an incident uniform flow. Using high resolution two-dimensional computations, we analysed the flow through and around a localised circular array of cylinders, where the ratio of array diameter (D-G) to cylinder diameter (D) is 21. The number of cylinders varied from N-C = 7 to 133, and they were arranged in a series of concentric rings to allow even distribution within the array with an average void fraction phi = N-C(D/DG)(2), which varied from 0.016 to 0.30. The characteristic Reynolds number of the array was Re-G = 2100. A range of diagnostic tools were applied, including the lift/drag forces on each cylinder (and the whole array), Eulerian and Lagrangian average velocity within the array, and the decay of maximum vorticity with distance downstream. To interpret the flow field, we used vorticity and the dimensionless form of the second invariant of the velocity gradient tensor. A mathematical model, based on representing the bodies as point forces, sources and dipoles, was applied to interpret the results. Three distinct flow regimes were identified. For low void fractions (phi 0.15), the array generates a wake in a similar way to a solid body of the same scale. For low void fraction arrays, the mathematical model provides a reasonable assessment of the forces on individual bodies within the array, the Eulerian mean velocity and the upstream velocity field. While it broadly captures the change in the rate of decay of the maximum vorticity magnitude Omega(max) downstream, the magnitude is underpredicted.

Flow past a square cylinder at low Reynolds numbers

Abstract: Results are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, Re ⩽ 150. A stabilized finite-element formulation is employed to discretize the equations of incompressible fluid flow in two-dimensions. For the first time, values of the laminar separation Reynolds number, Res, and separation angle, θs, at Res are predicted. Also, the variation of θs with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. θs=180∘ at Re = Res. For Re > 5, θs approaches the limit of 135 ∘. The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as Re−0.66. Flow characteristics at Re ⩽ 40 are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free-stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag. Copyright © 2010 John Wiley & Sons, Ltd.

Hydraulic Radius for Evaluating Resistance Induced by Simulated Emergent Vegetation in Open-Channel Flows

Abstract: The resistance induced by simulated emergent vegetation in open-channel flows has been interpreted differently in the literature, largely attributable to inconsistent uses of velocity and length scales in the definition of friction factor or drag coefficient and Reynolds number. By drawing analogies between pipe flows and vegetated channel flows, this study proposes a new friction function with the Reynolds number that is redefined by using a vegetation-related hydraulic radius. The new relationship is useful for consolidating various experimental data across a wide range of vegetation density. The results clearly show a monotonic decrease of the drag coefficient with the new Reynolds number, which is qualitatively comparable to other drag coefficient relationships for nonvegetated flows. This study also proposes a procedure for correcting sidewall and bed effects in the evaluation of vegetation drag.

Direct numerical simulation of the flow over a sphere at Re = 3700

Abstract: The direct numerical simulation of the flow over a sphere is performed. The computations are carried out in the sub-critical regime at Re = 3700 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation is used for simulating the flow. At this Reynolds number, flow separates laminarly near the equator of the sphere and transition to turbulence occurs in the separated shear layer. The vortices formed are shed at a large-scale frequency, St = 0.215, and at random azimuthal locations in the shear layer, giving a helical-like appearance to the wake. The main features of the flow including the power spectra of a set of selected monitoring probes at different positions in the wake of the sphere are described and discussed in detail. In addition, a large number of turbulence statistics are computed and compared with previous experimental and numerical data at comparable Reynolds numbers. Particular attention is devoted to assessing the prediction of the mean flow parameters, such as wall-pressure distribution, skin friction, drag coefficient, among others, in order to provide reliable data for testing and developing statistical turbulence models. In addition to the presented results, the capability of the methodology used on unstructured grids for accurately solving flows in complex geometries is also pointed out.

Drag reduction: enticing turbulence, and then an industry

Abstract: We examine drag-reduction proposals, as presented in this volume and in general, first with concrete examples of how to bridge the distance from pure science through engineering to what makes inventions go into service; namely, the value to the public. We point out that the true drag reduction can be markedly different from an estimate based simply on the difference between turbulent and laminar skin friction over the laminarized region, or between the respective skin frictions of the baseline and the riblettreated flow. In some situations, this difference is favourable, and is due to secondary differences in pressure drag. We reiterate that the benefit of riblets, if it is expressed as a percentage in skin-friction reduction, is unfortunately lower at full-size Reynolds numbers than in a small-scale experiment or simulation. The Reynolds number-independent measure of such benefits is a shift of the logarithmic law, or ‘DU + ’. Anticipating the design of a flight test and then a product, we note the relative ease in representing riblets or laminarization in computational fluid dynamics, in contrast with the huge numerical and turbulence-modelling challenge of resolving active flow control systems in a calculation of the full flow field. We discuss in general terms the practical factors that have limited applications of concepts that would appear more than ready after all these years, particularly riblets and laminar-flow control.

Physics and control of wall turbulence for drag reduction

Abstract: Turbulence physics responsible for high skin-friction drag in turbulent boundary layers is first reviewed. A self-sustaining process of near-wall turbulence structures is then discussed from the perspective of controlling this process for the purpose of skin-friction drag reduction. After recognizing that key parts of this self-sustaining process are linear, a linear systems approach to boundary-layer control is discussed. It is shown that singular-value decomposition analysis of the linear system allows us to examine different approaches to boundary-layer control without carrying out the expensive nonlinear simulations. Results from the linear analysis are consistent with those observed in full nonlinear simulations, thus demonstrating the validity of the linear analysis. Finally, fundamental performance limit expected of optimal control input is discussed.

Verification of filtered two-fluid models for gas-particle flows in risers

Abstract: The effect of solid boundaries on the closure relationships for filtered two-fluid models for riser flows was probed by filtering the results obtained through highly resolved kinetic theory-based two-fluid model simulations. The closures for the filtered drag coefficient and particle phase stress depended not only on particle volume fraction and the filter length but also on the distance from the wall. The wall corrections to the filtered closures are nearly independent of the filter length and particle volume fraction. Simulations of filtered model equations yielded grid length independent solutions when the grid length is � half the filter length or smaller. Coarse statistical results obtained by solving the filtered models with different filter lengths were the same and corresponded to those from highly resolved simulations of the kinetic theory model, which was used to construct the filtered models, thus verifying the fidelity of the filtered modeling approach. V V C 2010 American Institute of Chemical Engineers AIChE J, 57: 2691–2707, 2011

A parameterization of the ice‐ocean drag coefficient

Abstract: [1] A parameterization of the ice-ocean drag coefficient (Cw) was developed through partitioning the oceanic drag force into three components: (1) form drag on the floe edge, (2) form drag on the ridge keel, and (3) skin friction on the ice bottom. Through these quantities, Cw was expressed as a function of observable sea ice geometric parameters. Sensitivity studies were carried out to investigate the influence of varying sea ice conditions on Cw. The results revealed that Cw increases first and then decreases with increasing ice concentration (A), similar to the observations of the air-ice drag coefficient, and which is mainly attributed to the nonmonotonic variation of the form drag on the floe edge with ice concentration. Moreover, the form drag on the floe edge is always the dominant component, having a proportion of more than 60% in sea ice with a large aspect ratio (draft/length ≥ 1/100), indicating the necessity of including this term in sea ice dynamic models, particularly for the marginal ice zone (MIZ). The form drag on the ridge keel becomes dominant only when the ridging intensity is extremely high (depth/spacing ≥ 1/20). Additionally, a large value of Cw cannot be caused only by the inclusion of form drag terms but also by large skin friction over rough ice bottoms. Finally, for typical situations in the MIZ with moderate ridging intensity, the parameterization will underestimate Cw by approximately 30% for a rough ice bottom and by over 80% for a smooth ice bottom if no form drags are considered.

Aerodynamic drag in cycling: methods of assessment

Abstract: When cycling on level ground at a speed greater than 14 m/s, aerodynamic drag is the most important resistive force. About 90% of the total mechanical power output is necessary to overcome it. Aerodynamic drag is mainly affected by the effective frontal area which is the product of the projected frontal area and the coefficient of drag. The effective frontal area represents the position of the cyclist on the bicycle and the aerodynamics of the cyclist-bicycle system in this position. In order to optimise performance, estimation of these parameters is necessary. The aim of this study is to describe and comment on the methods used during the last 30 years for the evaluation of the effective frontal area and the projected frontal area in cycling, in both laboratory and actual conditions. Most of the field methods are not expensive and can be realised with few materials, providing valid results in comparison with the reference method in aerodynamics, the wind tunnel. Finally, knowledge of these parameters can be useful in practice or to create theoretical models of cycling performance.

A framework for understanding drag parameterizations for coral reefs

Abstract: [1] In a hydrodynamic sense, a coral reef is a complex array of obstacles that exerts a net drag force on water moving over the reef. This drag is typically parameterized in ocean circulation models using drag coefficients (CD) or roughness length scales (z0); however, published CD for coral reefs span two orders of magnitude, posing a challenge to predictive modeling. Here we examine the reasons for the large range in reported CD and assess the limitations of using CD and z0 to parameterize drag on reefs. Using a formal framework based on the 3-D spatially averaged momentum equations, we show that CD and z0 are functions of canopy geometry and velocity profile shape. Using an idealized two-layer model, we illustrate that CD can vary by more than an order of magnitude for the same geometry and flow depending on the reference velocity selected and that differences in definition account for much of the range in reported CD values. Roughness length scales z0 are typically used in 3-D circulation models to adjust CD for reference height, but this relies on spatially averaged near-bottom velocity profiles being logarithmic. Measurements from a shallow backreef indicate that z0 determined from fits to point measurements of velocity profiles can be very different from z0 required to parameterize spatially averaged drag. More sophisticated parameterizations for drag and shear stresses are required to simulate 3-D velocity fields over shallow reefs; in the meantime, we urge caution when using published CD and z0 values for coral reefs.

Drag coefficients of variously shaped solid particles, drops, and bubbles

Abstract: This article, which is largely a review, deals with the drag force and drag coefficient for rigid spherical and deformable particles in ordinary and non-Newtonian fluids. The most important theoretical formulas for small Reynolds numbers of Re ≪ 1 and semiempirical formulas for the drag coefficient in a wide Re range up to 106 are presented. The deformation of drops and bubbles and its effect on the drag coefficient are considered.

Bluff-body drag reduction using a deflector

Abstract: A passive flow control on a generic car model was experimentally studied. This control consists of a deflector placed on the upper edge of the model rear window. The study was carried out in a wind tunnel at Reynolds numbers based on the model height of 3.1 × 105 and 7.7 × 105. The flow was investigated via standard and stereoscopic particle image velocimetry, Kiel pressure probes and surface flow visualization. The aerodynamic drag was measured using an external balance and calculated using a wake survey method. Drag reductions up to 9% were obtained depending on the deflector angle. The deflector increases the separated region on the rear window. The results show that when this separated region is wide enough, it disrupts the development of the counter-rotating longitudinal vortices appearing on the lateral edges of the rear window. The current study suggests that flow control on such geometries should consider all the flow structures that contribute to the model wake flow.

Wave attenuation due to Posidonia oceanica meadows

Abstract: An experimental study carried out in a flume to a scale of 1/20 is presented to assess the wave height attenuation induced by submerged meadows of Posidonia oceanica. After examination of the appropriate scaling laws and selection of the model material, an extensive test programme included both regular and random waves. A semi-empirical formulation for estimating the wave height transformation along the meadow is obtained, based on energy conservation and considering that dissipation is only due to drag forces. The latter were linearized to obtain an exponential decay law. The formulation proposed depends on the drag coefficient and includes also an empirical parameter accounting for wave steepness. The model improves previous results and extends its applicability to random waves. The drag coefficient associated to the meadows is found to be better related to the Keulegan–Carpenter parameter than to the Reynolds number. Its value is given also for models proposed by others.

Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating flow

Abstract: A single bubble is placed in a solid-body rotating flow of silicon oil. From the measurement of its equilibrium position, lift and drag forces are determined. Five different silicon oils have been used, providing five different viscosities and Morton numbers. Experiments have been performed over a wide range of bubble Reynolds numbers (0.7 ≤ Re ≤ 380), Rossby numbers (0.58 ≤ Ro ≤ 26) and bubble aspect ratios (1 ≤ χ ≤ 3). For spherical bubbles, the drag coefficient at the first order is the same as that of clean spherical bubbles in a uniform flow. It noticeably increases with the local shear S = Ro−1, following a Ro−5/2 power law. The lift coefficient tends to 0.5 for large Re numbers and rapidly decreases as Re tends to zero, in agreement with existing simulations. It becomes hardly measurable for Re approaching unity. When bubbles start to shrink with Re numbers decreasing slowly, drag and lift coefficients instantaneously follow their stationary curves versus Re. In the standard Eotvos–Reynolds diagram, the transitions from spherical to deformed shapes slightly differ from the uniform flow case, with asymmetric shapes appearing. The aspect ratio χ for deformed bubbles increases with the Weber number following a law which lies in between the two expressions derived from the potential flow theory by Moore (J. Fluid Mech., vol. 6, 1959, pp. 113–130) and Moore (J. Fluid Mech., vol. 23, 1965, pp. 749–766) at low- and moderate We, and the bubble orients with an angle between its minor axis and the direction of the flow that increases for low Ro. The drag coefficient increases with χ, to an extent which is well predicted by the Moore (1965) drag law at high Re and Ro. The lift coefficient is a function of both χ and Re. It increases linearly with (χ − 1) at high Re, in line with the inviscid theory, while in the intermediate range of Reynolds numbers, a decrease of lift with aspect ratio is observed. However, the deformation is not sufficient for a reversal of lift to occur.

Depth-Averaged Drag Coefficient for Modeling Flow through Suspended Canopies

Abstract: Aquatic suspended canopies are porous obstacles that extend down from the free-surface but have a gap between the canopy and bed. Examples of suspended canopies include those formed by aquaculture structures or floating vegetation. The major difference between suspended canopies and the more common submerged canopies, which are located on the bottom boundary, is the influence of the bottom boundary layer beneath the suspended canopy. Data from laboratory experiments are presented which explore aspects of the flow through and beneath suspended canopies constructed from rigid cylinders. The experiments, using both acoustic Doppler and two-dimensional (2D) particle tracking velocimetry, give details of the flow structure that may be divided vertically into a bottom boundary layer, a canopy shear layer, and an internal canopy layer. The experimental data show that the penetration of the shear layer into the canopy is limited by the distance between the canopy and bottom boundary layer. Peaks in velocity spectra indicate an interaction between the bottom boundary and canopy shear layer. An analytical model is also developed that can be used to calculate a drag coefficient that includes the effect of both canopy drag and bed friction. This drag coefficient is suitable for use in 2D (depth-averaged) hydrodynamic modeling. The model also allows the average velocity within and beneath the canopy to be calculated, and is used to investigate the effect of canopy density and thickness on both total drag and bottom friction.

Separation flow control on a generic ground vehicle using steady microjet arrays

Abstract: A model of a generic vehicle shape, the Ahmed body with a 25° slant, is equipped with an array of blowing steady microjets 6 mm downstream of the separation line between the roof and the slanted rear window. The goal of the present study is to evaluate the effectiveness of this actuation method in reducing the aerodynamic drag, by reducing or suppressing the 3D closed separation bubble located on the slanted surface. The efficiency of this control approach is quantified with the help of aerodynamic load measurements. The changes in the flow field when control is applied are examined using PIV and wall pressure measurements and skin friction visualisations. By activating the steady microjet array, the drag coefficient was reduced by 9–14% and the lift coefficient up to 42%, depending on the Reynolds number. The strong modification of the flow topology under progressive flow control is particularly studied.