Showing papers on "Drag coefficient published in 2008"

Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders

Abstract: This paper investigates the drag exerted by randomly distributed, rigid, emergent circular cylinders of uniform diameter d . Laboratory measurements are presented for solid volume fraction ϕ=0.091 , 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Rep ≡ Up d∕ν=25 to 685, where Up =temporally and cross-sectionally averaged pore velocity and ν =kinematic viscosity. These ranges coincide with conditions in aquatic plant canopies. The temporally and cross-sectionally averaged drag coefficient, CD , decreased with increasing Rep and increased with increasing ϕ under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length ⟨ fD ¯ ⟩H to the product of the viscosity, μ , and Up exhibits a linear Rep dependence of the form ⟨ fD ¯ ⟩H ∕(μ Up )= α0 + α1 Rep , consistent with Ergun’s formulation for packed columns. In the range of experimental conditions, α1 increases monotonically with ϕ . In contrast, α0 is constant within uncertainty for 0.15⩽ϕ⩽0.35 , which suggests...

Feedback shear layer control for bluff body drag reduction

Abstract: Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Survey of Aerodynamic Drag Reduction at High Speed by Energy Deposition

Abstract: A selected survey of aerodynamic drag reduction at high speed is presented. The dimensionless governing parameters are described for energy deposition in an ideal gas. The types of energy deposition are divided into two categories. First, energy deposition in a uniform supersonic flow is discussed. Second, energy deposition upstream of a simple aerodynamic body is examined. Both steady and unsteady (pulsed) energy deposition are examined for both categories, as well as the conditions for the formation of shock waves and recirculation regions. The capability of energy deposition to reduce drag is demonstrated experimentally. Areas for future research are briefly discussed.

Lateral dispersion in random cylinder arrays at high Reynolds number

Abstract: Laser-induced fluorescence was used to measure the lateral dispersion of passive solute in random arrays of rigid, emergent cylinders of solid volume fraction φ=0.010–0.35. Such densities correspond to those observed in aquatic plant canopies and complement those in packed beds of spheres, where φ≥0.5. This paper focuses on pore Reynolds numbers greater than Res=250, for which our laboratory experiments demonstrate that the spatially averaged turbulence intensity and Kyy/(Upd), the lateral dispersion coefficient normalized by the mean velocity in the fluid volume, Up, and the cylinder diameter, d, are independent of Res. First, Kyy/(Upd) increases rapidly with φ from φ =0 to φ=0.031. Then, Kyy/(Upd) decreases from φ=0.031 to φ=0.20. Finally, Kyy/(Upd) increases again, more gradually, from φ=0.20 to φ=0.35. These observations are accurately described by the linear superposition of the proposed model of turbulent diffusion and existing models of dispersion due to the spatially heterogeneous velocity field that arises from the presence of the cylinders. The contribution from turbulent diffusion scales with the mean turbulence intensity, the characteristic length scale of turbulent mixing and the effective porosity. From a balance between the production of turbulent kinetic energy by the cylinder wakes and its viscous dissipation, the mean turbulence intensity for a given cylinder diameter and cylinder density is predicted to be a function of the form drag coefficient and the integral length scale lt. We propose and experimentally verify that lt=min{d, 〈sn〉A}, where 〈sn〉A is the average surface-to-surface distance between a cylinder in the array and its nearest neighbour. We farther propose that only turbulent eddies with mixing length scale greater than d contribute significantly to net lateral dispersion, and that neighbouring cylinder centres must be farther than r* from each other for the pore space between them to contain such eddies. If the integral length scale and the length scale for mixing are equal, then r*=2d. Our laboratory data agree well with predictions based on this definition of r*.

Compressibility and Rarefaction Effects on Drag of a Spherical Particle

Abstract: A review of compressibility and rarefaction effects on spherical particle drag was conducted based on existing experimental data, theoretical limits, and direct simulation Monte Carlo method results. The data indicated a nexus point with respect to effects of Mach number and Knudsen number. In particular, it was found that a single drag coefficient (of about 1.63) is obtained for all particle conditions when the particle Reynolds number is about 45, and is independent of compressibility or rarefaction effects. At lower Reynolds numbers, the drag is dominated by rarefaction, and at higher Reynolds numbers, it is dominated by compressibility. The nexus, therefore, allows construction of two separate models for these two regimes. The compression-dominated regime is obtained using a modification of the Clift-Gauvin model to specifically incorporate Mach number effects. The resulting model was based on a wide range of experimental data and showed superior prediction robustness compared with previous models. For the rarefaction-dominated regime, the present model was constructed to directly integrate the theoretical creeping flow limits, including the incompressible continuum flow limit (Stokes drag), the incompressible weak rarefaction limit (Basset-Knudsen correction), and the incompressible free-molecular flow limit (Epstein theory). Empirical correlations are used to extend this model to finite particle Reynolds numbers within the rarefaction-dominated regime.

Anomalous hydrodynamic drafting of interacting flapping flags.

Abstract: In aggregates of objects moving through a fluid, bodies downstream of a leader generally experience reduced drag force. This conventional drafting holds for objects of fixed shape, but interactions of deformable bodies in a flow are poorly understood, as in schools of fish. In our experiments on "schooling" flapping flags, we find that it is the leader of a group who enjoys a significant drag reduction (of up to 50%), while the downstream flag suffers a drag increase. This counterintuitive inverted drag relationship is rationalized by dissecting the mutual influence of shape and flow in determining drag. Inverted drafting has never been observed with rigid bodies, apparently due to the inability to deform in response to the altered flow field of neighbors.

Colloquium : Theory of drag reduction by polymers in wall-bounded turbulence

Abstract: The flow of fluids in channels, pipes, or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases manyfold when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a ``skin'' or a ``bulk'' effect. In this Colloquium the phenomenology of drag reduction by polymers is summarized, stressing both its universal and nonuniversal aspects, and a recent theory is reviewed that provides a quantitative explanation of all the known phenomenology. Both flexible and rodlike polymers are treated, explaining the existence of universal properties like the maximum drag reduction asymptote, as well as nonuniversal crossover phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally other agents for drag reduction are discussed with a stress on the important example of bubbles.

Steady Flow of Power Law Fluids across a Circular Cylinder

Abstract: The momentum equations describing the steady cross-flow of power law fluids past an unconfined circular cylinder have been solved numerically using a semi-implicit finite volume method The numerical results highlighting the roles of Reynolds number and power law index on the global and detailed flow characteristics have been presented over wide ranges of conditions as 5 ≤ Re ≤ 40 and 06 ≤ n ≤ 2 The shear-thinning behaviour (n 1) show the opposite behaviour Furthermore, while the wake size shows non-monotonous variation with the power law index, but it does not seem to influence the values of drag coefficient The stagnation pressure coefficient and drag coefficient also show a complex dependence on the power law index and Reynolds number In addition, the pressure coefficient, vorticity and viscosity distributions on the surface of the cylinder have also been presented to gain further physical insights into the detailed flow kinematics

A simple formula for predicting settling velocity of sediment particles

Abstract: Based on the general relationship described by Cheng between the drag coefficient and the Reynolds number of a particle, a new relationship between the Reynolds number and a dimensionless particle parameter is proposed. Using a trial-and-error procedure to minimize errors, the coefficients were determined and a formula was developed for predicting the settling velocity of natural sediment particles. This formula has higher prediction accuracy than other published formulas and it is applicable to all Reynolds numbers less than 2×105.

Inclusion of a Drag Approach in the Town Energy Balance (TEB) Scheme: Offline 1D Evaluation in a Street Canyon

Abstract: The Town Energy Balance module bridges the micro- and mesoscale and simulates local-scale urban surface energy balance for use in mesoscale meteorological models. Previous offline evaluations show that this urban module is able to simulate in good behavior road, wall, and roof temperatures and to correctly partition radiation forcing into turbulent and storage heat fluxes. However, to improve prediction of the meteorological fields inside the street canyon, a new version has been developed, following the methodology described in a companion paper by Masson and Seity. It resolves the surface boundary layer inside and above urban canopy by introducing a drag force approach to account for the vertical effects of buildings. This new version is tested offline, with one-dimensional simulation, in a street canyon using atmospheric and radiation data recorded at the top of a 30-m-high tower as the upper boundary conditions. Results are compared with simulations using the original single-layer version of the Town Energy Balance module on one hand and with measurements within and above a street canyon on the other hand. Measurements were obtained during the intensive observation period of the Basel Urban Boundary Layer Experiment. Results show that this new version produces profiles of wind speed, friction velocity, turbulent kinetic energy, turbulent heat flux, and potential temperature that are more consistent with observations than with the single-layer version. Furthermore, this new version can still be easily coupled to mesoscale meteorological models.

Momentum Transfer within Canopies

Abstract: To understand the basic characteristics of the observed S-shaped wind profile and the exponential flux profile within forest canopies, three hypotheses are postulated. The relationship between these fundamental profiles is well established by combining the postulated hypotheses with momentum equations. Robust agreements between theoretical predictions and observations indicate that the nature of momentum transfer within canopies can be well understood by combining the postulated hypotheses and momentum equations. The exponential Reynolds stress profiles were successfully predicted by the leaf area index (LAI) profile alone. The characteristics of the S-shaped wind profile were theoretically explained by the plant morphology and local drag coefficient distribution. Predictions of maximum drag coefficient were located around the maximum leaf area level for most forest canopies but lower than the maximum leaf area level for a corn canopy. A universal relationship of the Reynolds stress between the t...

Simulation of flow around a row of square cylinders

Abstract: In this paper, the low-Reynolds number (Re = 80) flow around a row of nine square cylinders placed normal to the oncoming flow is investigated using the latticeBoltzmann method. The effects of the cylinder spacing on the flow are studied for spacing to diameter ratios of 0.3 to 12. No significant interaction between the wakes is observed with spacings greater than six times the diameter. At smaller spacings, the flow regimes as revealed by vorticity field and drag coefficient signal are: synchronized, quasi-periodic and chaotic. These regimes are shown to result from the interaction between primary (vortex shedding) and secondary (cylinder interaction) frequencies; the strength of the latter frequency in turn depends on the cylinder spacing. The secondary frequency is also related to transition between narrow and wide wakes behind a cylinder. The mean drag coefficient and Strouhal number are found to increase rapidly with a decrease in spacing; correlations of these parameters with spacing are proposed. The Strouhal number based on gap velocity becomes approximately constant for a large range of spacings, highlighting the significance of gap velocity for this class of flows. It is also possible to analyse the vortex pattern in the synchronized and quasi-periodic regimes with the help of vorticity dynamics. These results, most of which have been obtained for the first time, are of fundamental significance.

Variable Order Modeling of Diffusive-convective Effects on the Oscillatory Flow Past a Sphere:

Abstract: This work advances our understanding of the drag force acting on a particle due to the oscillatory flow of a viscous fluid with finite Reynolds and Strouhal numbers. The drag force is is determined using the novel concept of variable order (VO) calculus, where the order of derivative can vary with the parameters and variables, according to the dynamics of the flow. Using the VO formulation we determine: (i) The region of validity of Tchen's equation for oscillatory flow, (ii) the region where the order of the derivative is fractional but constant, and (iii) the region where the strong non-linearity of the flow requires a variable order derivative to account for the increased complexity of the flow.

Reliable determination of vortex parameters from measurements of the microwave complex resistivity

Abstract: We discuss and propose a complete data treatment, in close contact to typical microwave experimental data, in order to derive vortex parameters, such as pinning constant and viscous drag coefficient (also referred to as ``vortex viscosity''), in a way as model independent as possible. We show that many of the accepted models for the complex resistivity can be described by a single, very general analytical expression. Using typical measurements of real and imaginary resistivity as a function of the applied field, we show that, even for single-frequency measurements, it is always possible to obtain (a) estimates of viscous drag coefficient and pinning constant with well-defined upper and lower bounds and (b) quantitative information about thermal creep. It turns out that neglecting thermal creep, in particular and counterintuitively at low temperatures, might result in a severe overestimation of the viscous drag coefficient. We also discuss the impact of thermal creep on the determination of the pinning constant. The present results might lead to a reconsideration of several estimates of the vortex parameters.

Permeability calculations in three-dimensional isotropic and oriented fiber networks

Abstract: Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today’s high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%–15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure.

CFD simulation of the flow field in a bubble column reactor: Importance of the drag force formulation to describe regime transitions

Abstract: This paper deals with the simulation of a quasi two-dimensional bubble column. In particular, the aim is to predict regime transitions occuring in bubble column reactors, which is very important for their design. It is shown that taking into account bubble–bubble interactions through a drag coefficient depending on the local void fraction [M. Simonnet, C. Gentric, E. Olmos, N. Midoux, Experimental determination of the drag coefficient in a swarm of bubbles, Chem. Eng. Sci. 62 (2007) 858–866] allows to predict the onset of the regime transitions. This has been verified both with the Eulerian and Lagrangian approaches. It is also shown that the use of this drag correlation allows to reproduce some typical characteristics of the different regimes (velocity profiles becoming parabolic in the transition regime, typical transient phenomena, accumulation of large bubbles in the column centre in the transition and heterogeneous regimes).

Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams

Abstract: The shear flow of two-dimensional foams is probed as a function of shear rate and disorder. Disordered, bidisperse foams exhibit strongly shear rate dependent velocity profiles. This behavior is captured quantitatively in a simple model based on the balance of the time-averaged drag forces in the system, which are found to exhibit power-law scaling with the foam velocity and strain rate. Disorder makes the scaling of the bulk drag forces different from that of the local interbubble drag forces, which we evidence by rheometrical measurements. In monodisperse, ordered foams, rate independent velocity profiles are found, which lends further credibility to this picture.

Transition Issues for Atmospheric Entry

Abstract: *Much has been learned about the physics underlying the transition process at supersonic and hypersonic speeds through years of analysis, experiment and computation. The application has been principally to simple shapes like plates, cones and spherical nosetips. But the shapes of the new entry vehicles are not simple. They will invariably be at angle of attack so three dimensional effects will be very important, as will roughness effects due to ablation. This paper will review the physics basis of our present understanding of the transition process. Further, because of the complex geometries, it will address the need for careful experimental work as per the guidelines enunciated years ago by the U.S. Transition Study Group. Following these guidelines is essential to obtaining reliable, usable data for use in refining transition estimation techniques . I. Introduction Entry vehicles descend rapidly through the atmosphere and decelerate as the drag forces increase with the increasing atmospheric density. The vehicle starts out fully laminar. Since Reynolds numbers increase rapidly through the des cent, transition tends to move very rapidly over the whole vehicle over a narrow range of altitudes. O ne tries to minimize the aerodynamic heating loads in entry so as to minimize the thermal protection needs of the vehicle. This means delaying transition to as low an altitude as possible . The history of high -performance entry vehicles begins with the development of the ICBM in the 1950’s. These v ehicles were essentially cone -cylinders with large nose bluntness to minimize stagnation point heating. The nose materials were often subliming ablators to take advantage of the further reduction in stagnation region heating due to the surface blowing from the subliming surface. Transition would move forward from the cylinder to the cone as the vehicle descende d through the atmosphere. If transition occurred asymmetrically on the cylinder or cone (leading to drag asymmetry), it was essential that the asymmetric effects be small enough to be corrected by the control system of the missile so as to minimize the cir cle of error about the target. In some cases, the transition unexpectedly moved forward onto the spherical nose , a phenomenon named the “blunt -body -paradox.” A study in that time period by Allen and Eggers 1 showed that for orbital and sub -orbital entry ( < 8 km/sec) , the convective aerodynamic heating rate was directly related to the vehicle’s ballistic coefficient, (W/C DA). The lower the ballistic coefficient, the lower the heating rates in entry. Hence the tendency to low weight and high drag coefficient. The highly blunted capsul e shapes of the Mercury, Gemini, Apollo and Soyuz vehicles with a blat ing heat shields are a consequence of this argument . At entry speeds above about 10 km/sec , the shock layers ahead of the entering blunt shapes become lumino us and radiate. These radiative heat transfer rates are highly density dependent. Thus the blunt body may not be the best entry shape for supercircular entry speeds. Studies by Allen et al 2,3 show that to minimize total heat transfer or total ablated mass , the optimum shape gets progressively slenderer as the entry speed is increased. Not enough was done with these vehicles to identify the major transition issues.