Showing papers on "Drag coefficient published in 1997"

Application of neural networks to turbulence control for drag reduction

Abstract: A new adaptive controller based on a neural network was constructed and applied to turbulent channel flow for drag reduction. A simple control network, which employs blowing and suction at the wall based only on the wall-shear stresses in the spanwise direction, was shown to reduce the skin friction by as much as 20% in direct numerical simulations of a low-Reynolds number turbulent channel flow. Also, a stable pattern was observed in the distribution of weights associated with the neural network. This allowed us to derive a simple control scheme that produced the same amount of drag reduction. This simple control scheme generates optimum wall blowing and suction proportional to a local sum of the wall-shear stress in the spanwise direction. The distribution of corresponding weights is simple and localized, thus making real implementation relatively easy. Turbulence characteristics and relevant practical issues are also discussed.

Drag force due to vegetation in mangrove swamps

Abstract: Field studies of tidal flows in largely pristine mangrove swamps suggestthat the momentum equation simplifies to a balance between the water surfaceslope and the drag force. The controlling parameter is the vegetation lengthscale LE, which is a function of the projected area ofmangrove vegetation and the volume of the vegetation. The value ofLE varies greatly with mangrove species and water depth. It isfound that the drag coefficient is related to the Reynolds number Re definedusing LE. The drag coefficient decreases with increasingvalues of Re from a maximum value of 10 at low value of Re (<104), and converges towards 0.4 for Re < 5 ×104.

Drag reduction by polymer additives in a turbulent pipe flow : numerical and laboratory experiments

Abstract: In order to study the roles of stress anisotropy and of elasticity in the mechanism of drag reduction by polymer additives we investigate a turbulent pipe flow of a dilute polymer solution. The investigation is carried out by means of direct numerical simulation (DNS) and laser Doppler velocimetry (LDV). In our DNS two different models are used to describe the effects of polymers on the flow. The first is a constitutive equation based on Batchelor's theory of elongated particles suspended in a Newtonian solvent which models the viscous anisotropic effects caused by the polymer orientation. The second is an extension of the first model with an elastic component, and can be interpreted as an anisotropic Maxwell model. The LDV experiments have been carried out in a recirculating pipe flow facility in which we have used a solution of water and 20 w.p.p.m. Superfloc A110. Turbulence statistics up to the fourth moment, as well as power spectra of various velocity components, have been measured. The results of the drag-reduced flow are first compared with those of a standard turbulent pipe flow of water at the same friction velocity at a Reynolds number of Reτ≈1035. Next the results of the numerical simulation and of the measurements are compared in order to elucidate the role of polymers in the phenomenon of drag reduction. For the case of the viscous anisotropic polymer model, almost all turbulence statistics and power spectra calculated agree in a qualitative sense with the measurements. The addition of elastic effects, on the other hand, has an adverse effect on the drag reduction, i.e. the viscoelastic polymer model shows less drag reduction than the anisotropic model without elasticity. Moreover, for the case of the viscoelastic model not all turbulence statistics show the right behaviour. On the basis of these results, we propose that the viscous anisotropic stresses introduced by extended polymers play a key role in the mechanism of drag reduction by polymer additives.

Moderate Reynolds number flows through periodic and random arrays of aligned cylinders

Abstract: The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

The effects of slightly soluble surfactants on the flow around a spherical bubble

Abstract: This paper reports the results of a numerical investigation of the transient evolution of the flow around a spherical bubble rising in a liquid contaminated by a weakly soluble surfactant. For that purpose the full Navier–Stokes equations are solved together with the bulk and interfacial surfactant concentration equations, using values of the physical-chemical constants of a typical surfactant characterized by a simple surface kinetics. The whole system is strongly coupled by nonlinear boundary conditions linking the diffusion flux and the interfacial shear stress to the interfacial surfactant concentration and its gradient. The influence of surfactant characteristics is studied by varying arbitrarily some physical-chemical parameters. In all cases, starting from the flow around a clean bubble, the results describe the temporal evolution of the relevant scalar and dynamic interfacial quantities as well as the changes in the flow structure and the increase of the drag coefficient. Since surface diffusion is extremely weak compared to advection, part of the bubble (and in certain cases all the interface) tends to become stagnant. This results in a dramatic increase of the drag which in several cases reaches the value corresponding to a rigid sphere. The present results confirm the validity of the well-known stagnant-cap model for describing the flow around a bubble contaminated by slightly soluble surfactants. They also show that a simple relation between the cap angle and the bulk concentration cannot generally be obtained because diffusion from the bulk plays a significant role.

Nonrigid, Nonsubmerged, Vegetative Roughness on Floodplains

Abstract: Individual pine and cedar tree saplings and branches were used to model the resistance to flow in a water flume for nonsubmerged and nonrigid vegetation to determine the amount that streamlining decreases the drag coefficient and reduces the momentum absorbing area. Currently, vegetation on floodplains is commonly assumed to behave as rigid roughness that can lead to large errors in the relationships between velocity and drag force. This presents a basic fluid mechanics problem. An extreme variation of roughness with depth of flow can result due to a large increase in the momentum absorbing area in nonsubmerged vegetation as depth is increased. This deems all the available roughness equations (which generally are based on relative roughness approach) useless for this application. In this paper a dimensional analysis, supported by experimental results, is developed to obtain a relationship between roughness conditions (i.e., density and flexural rigidity) and flow conditions (i.e., velocity and depth) for floodplains and vegetative zones of natural waterways.

Dragonfly flight. I. Gliding flight and steady-state aerodynamic forces.

Abstract: The free gliding flight of the dragonfly Sympetrum sanguineum was filmed in a large flight enclosure. Reconstruction of the glide paths showed the flights to involve accelerations. Where the acceleration could be considered constant, the lift and drag forces acting on the dragonfly were calculated. The maximum lift coefficient (CL) recorded from these glides was 0.93; however, this is not necessarily the maximum possible from the wings. Lift and drag forces were additionally measured from isolated wings and bodies of S. sanguineum and the damselfly Calopteryx splendens in a steady air flow at Reynolds numbers of 700-2400 for the wings and 2500-15 000 for the bodies. The maximum lift coefficients (CL,max) were 1.07 for S. sanguineum and 1.15 for C. splendens, which are greater than those recorded for all other insects except the locust. The drag coefficient at zero angle of attack ranged between 0.07 and 0.14, being little more than the Blassius value predicted for flat plates. Dragonfly wings thus show exceptional steady-state aerodynamic properties in comparison with the wings of other insects. A resolved-flow model was tested on the body drag data. The parasite drag is significantly affected by viscous forces normal to the longitudinal body axis. The linear dependence of drag on velocity must thus be included in models to predict the parasite drag on dragonflies at non-zero body angles.

Turbulent drag reduction using compliant surfaces

Abstract: Over the past forty years intensive investigations into the use of compliant surfaces have been undertaken, both theoretically and experimentally, in order to obtain turbulent drag reduction in boundary–layer flows. Although positive results were found in some of the studies, none of these had been successfully validated by independent researchers. In this paper the results are reported of a recent investigation carried out by the authors to verify the experimental results of Semenov in 1991 and Kulik and co–workers in 1991, who successfully demonstrated the ability of compliant surfaces to reduce the skin–friction drag and surface–flow noise in a turbulent boundary layer. A strain–gauge force balance was used in the present study to directly measure the turbulent skin–friction drag of a slender body of revolution in a water tunnel. Changes in the structure of turbulent boundary layer over a compliant surface in comparison with that over a rigid surface were also examined. The results clearly demonstrate that the turbulent skin friction is reduced for one of the two compliant coatings tested, indicating a drag reduction of up to 7 per cent within the entire speed range of the tests. The intensities of skin–friction and wall–pressure fluctuations measured immediately downstream from the compliant coating show reductions in the intensities of up to 7 and 19 per cent, respectively. The results also indicate reductions in turbulence intensity by up to 5 per cent across almost the entire boundary layer. Furthermore, an upwards shift of the logarithmic velocity profile is also evident indicating that the thickness of the viscous sublayer is increased as a result of turbulent drag reduction due to the compliant coating. It is considered that the results of the present experimental investigation convincingly demonstrate for the first time since the earlier work in Russia (by Semenov and Kulik) that a compliant surface can indeed produce turbulent drag reduction in boundary–layer flows.

Hydrodynamics of a DNA molecule in a flow field

Abstract: The behavior of dilute flexible polymer molecules in flowing liquids remains controversial, despite a long history of experimental and theoretical study. The simplest theory, introduced by Kuhn [1] some 60 years ago, treats the polymer as an elastic “dumbbell” in which an elastic spring connects two “beads” onto which are lumped the viscous drag forces that in reality act along the entire chain. In the simplest version of the dumbbell model, the drag force F d on each bead is given by Stokes law, F d = ςk B TV, where V is the velocity of the solvent relative to that of the bead, and the drag coefficient ςk B T is independent of the deformation of the molecule.

Creeping motion of a sphere in tubes filled with a Bingham plastic material

Abstract: Numerical simulations have been undertaken for the creeping flow of a Bingham plastic past a sphere contained in a cylindrical tube. Different diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both yielded and practically unyielded regions. The emphasis is on determining the extent and shape of unyielded/yielded regions along with the drag coefficient for the whole range of Bingham numbers. The present results extend previous simulations for creeping flow of a sphere in an infinite medium and provide calculations of the Stokes drag coefficient in the case of wall effects.

Turbulent drag reduction by passive mechanisms

Abstract: In many situations involving flows of high Reynolds number (where inertial forces dominate over viscous forces), such as aircraft flight and the pipeline transportation of fuels, turbulent drag is an important factor limiting performance. This has led to an extensive search for both active and passive methods for drag reduction1. Here we report the results of a series of wind-tunnel experiments that demonstrate a passive means of effectively controlling turbulence in channel flow. Our approach involves the introduction of specified patterns of protrusions on the confining walls, which interact with the coherent, energy-bearing eddy structures in the wall region, and so influence the rate at which energy is dissipated in the turbulent flow. We show that relatively small changes in the arrangement of these protrusions can alter the response of the system from one of drag decrease to increased mixing (drag enhancement).

An analytical one-dimensional model of momentum transfer by vegetation of arbitrary structure

Abstract: An analyticalone-dimensional model of momentum transferby vegetation with variable foliage distribution,sheltering and drag coefficientis developed. The model relies on a simpleparameterization of the ratio of theabove-canopy friction velocity, u*, to thewind speed at the top of the canopy,u(h), to predict vegetation roughness length(z0) and displacement height(d) as functions of canopy height (h) and dragarea index. Model predictionsof d/h and z/h compare very favorably withobserved values.A model sensitivity analysis suggests that shelteringeffects for momentum transfertend to make canopies with non-uniform foliagedistribution resemble canopies withmore uniform foliage distribution and that anyinfluence wind speed has on d/hand z0/h is more likely to be related to theinfluence that wind speed may haveon u*/u(h) rather than the influence windspeed may have on the foliage dragcoefficient. Model results indicate that z0/hand d/h are sensitive to uncertaintiesin the numerical values of the model parameters,foliage density and distribution,sheltering effects and variations in drag coefficientwithin the canopy. In additionz0/h is also shown to be sensitive to thepresence or absence of the roughnesssublayer. Given the simplicity of the model it issuggested that it may be of usefor land surface parameterizations in large scalemodels.

Electro‐osmotic Drag of Water in Ionomeric Membranes New Measurements Employing a Direct Methanol Fuel Cell

Abstract: A direct methanol fuel cell (DMFC) employing a proton conducting membrane was used to determine the electro-osmotic drag coefficient of water in the ionomeric membrane. Water flux across the membrane in such a cell (operated with 1.0 M aqueous methanol at the anode and dry O{sub 2} at the cathode) is driven by protonic drag exclusively at sufficiently high current densities. This is evidenced experimentally by a linear relationship between cell current and flux of water measured crossing the membrane. Application of the DMFC for such water-drag measurements is significantly simpler experimentally than the approach described by the authors before, particularly so for measurements above room temperature. In measurements the authors performed in the DMFC configuration on Nafion 117 membranes, the water drag coefficient was found to increase with temperature, from 2.0 H{sub 2}O/H{sup +} at 15 C to 5.1 H{sub 2}O/H{sup +} at 130 C. Implications of these new results on water management in DMFCs are briefly discussed.

Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids

Abstract: Previous numerical simulations for the flow of Bingham plastics past a sphere contained in cylindrical tubes of different diameter ratios are extended to Herschel–Bulkley fluids with the purpose of comparing them with experiments. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient as a function of the pertinent dimensionless groups. Good overall agreement is obtained between the numerical results and the experimental studies.

An Evaluation of the Bounce-Back Boundary Condition for Lattice Boltzmann Simulations

Abstract: The bounce-back boundary condition for lattice Boltzmann simulations is evaluated for flow about an infinite periodic array of cylinders. The solution is compared with results from a more accurate boundary condition formulation for the lattice Boltzmann method and with finite difference solutions. The bounce-back boundary condition is used to simulate boundaries of cylinders with both circular and octagonal cross-sections. The convergences of the velocity and total drag associated with this method are slightly sublinear with grid spacing. Error is also a function of relaxation time, increasing exponentially for large relaxation times. However, the accuracy does not exhibit a trend with Reynolds number between 0.1 and 100. The square lattice Boltzmann grid conforms to the octagonal cylinder but only approximates the circular cylinder, and the resulting error associated with the octagonal cylinder is half the error of the circular cylinder.

The Effect of Rotation and Surface Friction on Orographic Drag

Abstract: A numerical, hydrostatic model is used to investigate the form and magnitude of the pressure drag created by 3D elliptical mountains of various heights (h) and aspect ratios (R) in flows characterized by uniform upstream velocity (U) and stability (N). Three series of simulations, corresponding to increasing degrees of realism, are performed: (i) without rotation and surface friction; (ii) with rotation, but no surface friction; (iii) with rotation and surface friction. For the simulations with rotation, the Coriolis parameter has a typical midlatitude value and the upstream flow is geostrophically balanced. The surface friction is introduced by the use of a typical roughness length. For low values of the nondimensional height (Nh/U), the pressure drag is reduced by the effect of rotation, in agreement with well-known results of linear theory. This seems to be valid until Nh/U ∼ 1.4, that is, in the high drag regime. On the other hand, for large values of Nh/U, that is, in the blocked flow regime...

Edge, cavity and aperture tones at very low Mach numbers

Abstract: This paper discusses self-sustaining oscillations of high-Reynolds-number shear layers and jets incident on edges and corners at infinitesimal Mach number. These oscillations are frequently sources of narrow-band sound, and are usually attributed to the formation of discrete vortices whose interactions with the edge or corner produce impulsive pressures that lead to the formation of new vorticity and complete a feedback cycle of operation. Linearized analyses of these interactions are presented in which free shear layers are modelled by vortex sheets. Detailed results are given for shear flows over rectangular wall apertures and shallow cavities, and for the classical jet-edge interaction. The operating stages of self-sustained oscillations are identified with poles in the upper half of the complex frequency plane of a certain impulse response function. It is argued that the real parts of these poles determine the Strouhal numbers of the operating stages observed experimentally for the real, nonlinear system. The response function coincides with the Rayleigh conductivity of the 'window' spanned by the shear flow for wall apertures and jet-edge interactions, and to a frequency dependent drag coefficient for shallow wall cavities. When the interaction occurs in the neighbourhood of an acoustic resonator, exemplified by the flue organ pipe, the poles are augmented by a sequence of poles whose real parts are close to the resonance frequencies of the resonator, and the resonator can 'speak' at one of these frequencies (by extracting energy from the mean flow) provided the corresponding pole has positive imaginary part. The Strouhal numbers predicted by this theory for a shallow wall cavity agree well with data extrapolated to zero Mach number from measurements in air, and predictions for the jet-edge interaction are in excellent accord with data from various sources in the literature. In the latter case, the linear theory also agrees for all operating stages with an empirical, nonlinear model that takes account of the formation of discrete vortices in the jet.

Actual and 'optimum' flight speeds: field data reassessed

Abstract: Previously published field observations of the air speeds of 36 species of birds, all observed by the same method (ornithodolite), were compared with estimates of the corresponding minimum power speeds, calculated with a default body drag coefficient of 0.1. This value, which was derived from recent wind tunnel studies, represents a downward revision from default values previously used and leads, in turn, to an upward revision of estimated minimum power speeds. The mean observed air speeds are now distributed around the minimum power speed, rather than in between the speeds for minimum power and maximum range, as they were before. Although the field data do not represent migration, examination of the marginal effects of small changes of speed, on power and lift:drag ratio, indicates that flying at the maximum range speed on migration may not represent an 'optimal' or even a practical strategy and that cruising speeds may be limited by the muscle power available or by aerobic capacity. Caution in constructing 'optimisation' theories is indicated.

The force balance of sea ice in a numerical model of the Arctic Ocean

Abstract: The balance of forces in the sea ice model of Hibler [1979] is examined. The model predicts that internal stress gradients are an important force in much of the Arctic Ocean except in summer, when they are significant only off the northern coasts of Greenland and the Canadian Archipelago. A partition of the internal stress gradient between the pressure gradient and the viscous terms reveals that both are significant, although they operate on very different timescales. The acceleration term is generally negligible, while the sum of Coriolis plus sea surface tilt is small. Thus the seasonal average force balance in fall, winter, and spring is mostly between three terms of roughly equal magnitudes: air drag, water drag, and internal stress gradients. This is also true for the monthly average force balance. However, we find that there is a transition around the weekly timescale and that on a daily basis the force balance at a particular location and time is often between only two terms: either between air drag and water drag or between air drag and internal stress gradients. The model is in agreement with the observations of Thorndike and Colony [1982] in that the correlation between geostrophic wind forcing and the model's ice velocity field is high. This result is discussed in the context of the force balance; we show that the presence of significant internal stress gradients does not preclude high wind-ice correlation. A breakdown of the internal stress gradient into component parts reveals that the shear viscous force is far from negligible, which casts strong doubt on the theoretical validity of the cavitating fluid approximation (in which this component is neglected). Finally, the role of ice pressure is examined by varying the parameter P*. We find a strong sensitivity in terms of the force balance, as well as ice thickness and velocity.

Drag Prediction and Transition in Hypersonic Flow

Abstract: This paper discusses progress on issues such as instability studies, nose-bluntness and angle-of-attack effects, and leading-edge-contamination problems from theoretical, computational, and experimental points of view. Also included is a review of wind-tunnel and flight data, including high-Re flight transition data, the levels of noise in flight and in wind tunnels, and how noise levels can affect parametric trends. A review of work done on drag accounting and the role of viscous drag for hypersonic vehicles is also provided.

Fetch limited drag coefficients

Abstract: Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Riso Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.

Effect of Concentration on Settling Velocity of Sediment Particles

Abstract: The drag coefficient for dispersed particles settling in a fluid is related to the particle Reynolds number with the same function as that used for a single particle falling in a clear fluid, after taking into account the effects of concentration both on the effective density of particles and on the viscosity of fluid-sediment mixture. A new method is developed for evaluating the settling velocity of natural sediment particles dispersed in a fluid; it agrees well with the available experimental data. The differences among various empirical expressions are illustrated using the present relationship.