Showing papers on "Drag coefficient published in 2003"

Sphere Drag and Settling Velocity Revisited

Abstract: Sphere drag data from throughout the twentieth century are available in tabular form. However, much of the data arose from experiments in small diameter cylindrical vessels, where the results might have been influenced by the wall effect. Wall effect corrections developed by others were applied to 178 of the 480 data points collected. This corrected data set is believed to be free of the influence of wall effects. Existing drag and settling velocity correlations were compared to this data set. In addition, new correlations of the same forms were developed using the corrected data. Two new correlations of sphere terminal velocity are proposed, one applicable for all Reynolds numbers less than 2310 5 , and the other designed to predict settling velocities with exceptional accuracy for terminal Reynolds numbers less than 4,000, a region that contains almost all applications of interest in environmental engineering. The trial and error solution for settling velocity using the Fair and Geyer equation for drag should be retired in favor of the direct calculation available from these new correlations.

Adjustment of a turbulent boundary layer to a canopy of roughness elements

Abstract: Am odel is developed for the adjustment of the spatially averaged time-mean flow of ad eep turbulent boundary layer over small roughness elements to a canopy of larger three-dimensional roughness elements. Scaling arguments identify three stages of the adjustment. First, the drag and the finite volumes of the canopy elements decelerate air parcels; the associated pressure gradient decelerates the flow within an impact region upwind of the canopy. Secondly, within an adjustment region of length of order Lc downwind of the leading edge of the canopy, the flow within the canopy decelerates substantially until it comes into a local balance between downward transport of momentum by turbulent stresses and removal of momentum by the drag of the canopy elements. The adjustment length, Lc ,i s proportional to(i) the reciprocal of the roughness density (defined to be the frontal area of canopy elements per unit floor area) and (ii) the drag coefficient of individual canopy elements. Further downstream, within a roughness-change region ,t hecanopy is shown to affect the flow above as if it were a change in roughness length, leading to the development of an internal boundary layer. A quantitative model for the adjustment of the flow is developed by calculating analytically small perturbations to a logarithmic turbulent velocity profile induced by the drag due to a sparse canopy with L/Lc � 1, where L is the length of the canopy. These linearized solutions are then evaluated numerically with a nonlinear correction to account for the drag varying with the velocity. A further correction is derived to account for the finite volume of the canopy elements. The calculations are shown to agree with experimental measurements in a fine-scale vegetation canopy, when the drag is more important than the finite volume effects, and a canopy of coarse-scale cuboids, when the finite volume effects are of comparable importance to the drag in the impact region. An expression is derived showing how the effective roughness length of the canopy, z eff 0 ,i s related to the drag in the canopy. The value of z eff varies smoothly with fetch through the adjustment region from the roughness length of the upstream surface to the equilibrium roughness length of the canopy. Hence, the analysis shows how to resolve the unphysical flow singularities obtained with previous models of flow over sudden changes in surface roughness.

Direct numerical simulations of turbulent channel flow with transverse square bars on one wall

Abstract: Direct numerical simulations have been carried out for a fully developed turbulent channel flow with a smooth upper wall and a lower wall consisting of square bars separated by a rectangular cavity. A wide range of of the Clauser roughness function reflects that of the form drag.

Turbulent channel flow near maximum drag reduction: simulations, experiments and mechanisms

Abstract: It is well known that the drag in a turbulent flow of a polymer solution is significantly reduced compared to Newtonian flow. Here we consider this phenomenon by means of a direct numerical simulation of a turbulent channel flow. The polymers are modelled as elastic dumbbells using the FENE-P model. In the computations the polymer model is solved simultaneously with the flow equations, i.e. the polymers are deformed by the flow and in their turn influence the flow structures by exerting a polymer stress. We have studied the results of varying the polymer parameters, such as the maximum extension, the elasticity and the concentration. For the case of highly extensible polymers the results of our simulations are very close to the maximum drag reduction or Virk (1975) asymptote. Our simulation results show that at approximately maximum drag reduction the slope of the mean velocity profile is increased compared to the standard logarithmic profile in turbulent wall flows. For the r.m.s. of the streamwise velocity fluctuations we find initially an increase in magnitude which near maximum drag reduction changes to a decrease. For the velocity fluctuations in the spanwise and wall-normal directions we find a continuous decrease as a function of drag reduction. The Reynolds shear stress is strongly reduced, especially near the wall, and this is compensated by a polymer stress, which at maximum drag reduction amounts to about 40% of the total stress. These results have been compared with LDV experiments of Ptasinski et al. (2001) and the agreement, both qualitatively and quantitatively, is in most cases very good. In addition we have performed an analysis of the turbulent kinetic energy budgets. The main result is a reduction of energy transfer from the streamwise direction, where the production of turbulent kinetic energy takes place, to the other directions. A substantial part of the energy production by the mean flow is transferred directly into elastic energy of the polymers. The turbulent velocity fluctuations also contribute energy to the polymers. The elastic energy of the polymers is subsequently dissipated by polymer relaxation. We have also computed the various contributions to the pressure fluctuations and identified how these change as a function of drag reduction. Finally, we discuss some cross-correlations and various length scales. These simulation results are explained here by two mechanisms. First, as suggested by Lumley (1969) the polymers damp the cross-stream or wall-normal velocity fluctuations and suppress the bursting in the buffer layer. Secondly, the ‘shear sheltering’ mechanism acts to amplify the streamwise fluctuations in the thickened buffer layer, while reducing and decoupling the motions within and above this layer. The expression for the substantial reduction in the wall drag derived by considering the long time scales of the nonlinear fluctuations of this damped shear layer, is shown to be consistent with the experimental data of Virk et al. (1967) and Virk (1975).

Drag reduction by polymer additives in a turbulent channel flow

Abstract: Turbulent drag reduction by polymer additives in a channel is investigated using direct numerical simulation. The dilute polymer solution is expressed with an Oldroyd-B model that shows a linear elastic behaviour. Simulations are carried out by changing the Weissenberg number at the Reynolds numbers of 4000 and 20 000 based on the bulk velocity and channel height. The onset criterion for drag reduction predicted in the present study shows a good agreement with previous theoretical and experimental studies. In addition, the flow statistics such as the r.m.s. velocity fluctuations are also in good agreement with previous experimental observations. The onset mechanism of drag reduction is interpreted based on elastic theory, which is one of the most plausible hypotheses suggested in the past. The transport equations for the kinetic and elastic energy are derived for the first time. It is observed that the polymer stores the elastic energy from the flow very near the wall and then releases it there when the relaxation time is short, showing no drag reduction. However, when the relaxation time is long enough, the elastic energy stored in the very near-wall region is transported to and released in the buffer and log layers, showing a significant amount of drag reduction.

Effect of turbulence on the drag and lift of a particle

Abstract: A direct numerical simulation (DNS) is used to study the effect of a freestream isotropic turbulent flow on the drag and lift forces on a spherical particle. The particle diameter is about 1.5–10 times the Kolmogorov scale, the particle Reynolds number is about 60–600, and the freestream turbulence intensity is about 10%–25%. The isotropic turbulent field considered here is stationary, i.e., frozen in time. It is shown that the freestream turbulence does not have a substantial and systematic effect on the time-averaged mean drag. The standard drag correlation based on the instantaneous or mean relative velocity results in a reasonably accurate prediction of the mean drag obtained from the DNS. However, the accuracy of prediction of the instantaneous drag decreases with increasing particle size. For the smaller particles, the low frequency oscillations in the DNS drag are well captured by the standard drag, but for the larger particles significant differences exist even for the low frequency components. In...

Drag and reconfiguration of freshwater macrophytes

Abstract: SUMMARY 1. Submerged freshwater macrophytes face large hydrodynamic forces in flowing waters in streams and on wave-swept lake shores and require morphological adaptations to reduce the drag and the physical damage. This experiment studied five species of freshwater macrophytes and strap-formed plastic leaves to test the predictions that: (i) increasing flexibility leads to greater reconfiguration and lower drag coefficients, (ii) flexible plants experience a steeper decline of drag coefficients with increasing water velocity than unflexible plants and (iii) plants mounted vertically on a horizontal substratum bend over in fast flow attaining a shielded position of low drag. 2. The results confirmed all three predictions. In fast flow, plants mounted upright on a horizontal platform gradually approached a position aligned with the flow, depending on their flexibility. In the range 8–50 cm s−1 the deflection followed an interspecific negative linear relationship between log (tangent Φ) and velocity, where Φ represents the shoot angle normal to the horizontal level. Above 50 cm s−1, further deflection was reduced perhaps by a combination of the elasticity and packing of shoots and the increasing lift generated by fast flow. 3. Drag coefficients of plants ranged between 0.01 and 0.1, typical of moderately to very streamlined objects. Drag coefficients declined log-log linearly at increasing velocity, following negative slopes between −0.67 and −1.24 (median: −1.0) because of reconfiguration and formation of a shielding canopy. Drag coefficients declined much less (median: −0.55) for plants floating freely in the streaming water and which were capable of changing their shape but unable to form a shielding canopy. Drag coefficients declined even less for relatively unflexible plastic leaves (−0.30 to −0.40), and they remained constant for stiff, bluff objects. 4. The experiments suggest that flow resistance of flexible, submerged macrophytes in natural streams may increase in direct proportion to water velocity because they form a shielding submerged canopy, and high water stages at peak flow may result in greater proportions of the water passing unimpeded above the canopy. In contrast, stiff amphibious and emergent reed plants should experience an increase of flow resistance with at least the square of velocity as reconfiguration is small and former aerial plant surfaces come into contact with the streaming water at higher water stages. Field experiments to test these predictions are urgently needed.

Dense granular flow around an immersed cylinder

Abstract: The flow around a fixed cylinder immersed in a uniform granular flow is studied experimentally. Experiments are performed in a tall vertical chute producing a quasi two-dimensional granular flow. A storage bin at the top of the chute feeds glass particles into the channel while the mean velocity of the flow is controlled by varying the exit width of a hopper located at the channel bottom. Measurements of the drag force acting on a fixed cylinder are made using a strain gauge force measurement system. The flow velocity field is measured through a transparent wall using a particle image velocimetry analysis of high speed video recordings of the flow. Experiments are performed for a range of upstream particle velocities, cylinder diameters, and two sizes of glass particles. For the range of velocities studied, the mean drag force acting on the cylinder is independent of the mean flow velocity, contrary to what is expected from any ordinary fluid. The drag force increases with cylinder diameter and decreases with particle diameter. The drag force scales with the asymptotic static stress state in a tall granular bed. The drag coefficient, defined in terms of a dynamic pressure and an effective cylinder diameter, scales with the flow Froude number based on the hydraulic diameter of the channel. This analysis indicates that the drag acting on the cylinder is strongly affected by the surrounding channel geometry. Although the drag force on the cylinder does not change with the upstream flow velocity, the flow streamlines do change with velocity. A large stagnation zone forms at the leading edge of the cylinder while at the trailing edge an empty wake is observed. The wake size increases with flow velocity. Measurements of the flow vorticity and granular temperature are also presented and discussed.

Drag force, diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime.

Abstract: The transport of small particles in the free-molecule regime is investigated on the basis of gas kinetic theory. Drag force formulations were derived in two limiting collision models-namely, specular and diffuse scattering-by considering the potential force of interactions between the particle and fluid molecules. A parametrized drag coefficient equation is proposed and accounts for the transition from specular to diffuse scattering as particle size exceeds a critical value. The resulting formulations are shown to be consistent with the Chapman-Enskog theory of molecular diffusion. In the limit of rigid-body interactions, these formulations can be simplified also to Epstein's solutions [P. S. Epstein, Phys. Rev. 23, 710 (1924)].

Computational Fluid Dynamics-Based Drag Prediction and Decomposition

Abstract: A method for the computation and breakdown of the aerodynamic drag into viscous and wave components is proposed. Given a numerical solution of the Reynolds averaged Navier-Stokes equations, the method, based on a Taylor's series expansion of the far-field drag expression, allows for the determination of the drag related to entropy variations in the flow. The identification of a spurious contribution, due to the numerical dissipation and discretization error of the flow solver algorithm, allows for drag computations weakly dependent on mesh size. Therefore, accurate drag evaluations are possible even on moderately sized grids. Results are presented for transonic flows around an airfoil and a wing-body configuration

Maximum drag reduction in a turbulent channel flow by polymer additives

Abstract: Maximum drag reduction (MDR) in a turbulent channel flow by polymer additives is studied using direct numerical simulation. An Oldroyd-B model is adopted to express the polymer stress because MDR is closely related to the elasticity of the polymer solution. The Reynolds number considered is 4000, based on the bulk velocity and the channel height, and the amount of MDR from the present study is 44%, which is in good agreement with Virk's asymptote at this Reynolds number. For ‘large drag reduction’, the variations of turbulence statistics such as the mean streamwise velocity and r.m.s. velocity fluctuations are quite different from those of ‘small drag reduction’. For example, for small drag reduction, the r.m.s. streamwise velocity fluctuations decrease in the sublayer but increase in the buffer and log layers with increasing Weissenberg number, but they decrease in the whole channel for large drag reduction. As the flow approaches the MDR limit, the significant decrease in the production of turbulent kinetic energy is compensated by the increase in energy transfer from the polymer elastic energy to the turbulent kinetic energy. This is why turbulence inside the channel does not disappear but survives in the MDR state.

The effect of microbubbles on developed turbulence

Abstract: The motion and the action of microbubbles in homogeneous and isotropic turbulence are investigated through (three-dimensional) direct numerical simulations of the Navier–Stokes equations and applying the Lagrangian approach to track the bubble trajectories. The forces acting on the bubbles are added mass, drag, lift, and gravity. The bubbles are found to accumulate in vortices, preferably on the side with downward velocity. This effect, mainly caused by the lift force, leads to a reduced average bubble rise velocity. Once the reaction of the bubbles on the carrier flow is embodied using a point-force approximation, an attenuation of the turbulence on large scales and an extra forcing on small scales is found.

Polymer-induced drag reduction: Effects of the variations in elasticity and inertia in turbulent viscoelastic channel flow

Abstract: In this work we systematically investigate the effects of the flow elasticity and inertia in polymer-induced drag reduction through (pseudo)spectral simulations of a turbulent channel flow of a dilute polymer solution. Viscoelastic effects are modeled by the finite-extensibility nonlinear elastic dumbbell model with the Peterlin approximation. The present work updates the low Weissenberg results (Weτ0⩽50) reported in earlier works by Sureshkumar et al. [Phys. Fluids 9, 743 (1997)] and Dimitropoulos et al. [J. Non-Newtonian Fluid Mech. 79, 433 (1998)] for a zero shear rate friction Reynolds number, Reτ0=125, by allowing for a lower value for the numerical diffusivity. In addition, we examine two effects on drag reduction: (A) high elasticity, by varying Weτ0 from 62.5 to 125 for a constant Reτ0=125, (B) friction Reynolds number, Reτ0=180, 395, and 590, for a constant Weτ0=50. In the high elasticity region, the mean Reynolds, Remean, continues to increase with increasing Weτ0, albeit at a smaller rate. Thus...

The discrete adjoint approach to aerodynamic shape optimization

Abstract: A viscous discrete adjoint approach to automatic aerodynamic shape optimization is developed, and the merits of the viscous discrete and continuous adjoint approaches are discussed. The viscous discrete and continuous adjoint gradients for inverse design and drag minimization cost functions are compared with finite-difference and complex-step gradients. The optimization of airfoils in two-dimensional flow for inverse design and drag minimization is illustrated. Both the discrete and continuous adjoint methods are used to formulate two new design problems. First, the timedependent optimal design problem is established, and both the time accurate discrete and continuous adjoint equations are derived. An application to the reduction of the time-averaged drag coefficient while maintaining time-averaged lift and thickness distribution of a pitching airfoil in transonic flow is demonstrated. Second, the remote inverse design problem is formulated. The optimization of a three-dimensional biconvex wing in supersonic flow verifies the feasibility to reduce the near field pressure peak. Coupled drag minimization and remote inverse design cases produce wings with a lower drag and a reduced near field peak pressure signature.

Aircraft Drag Reduction-A Review

Abstract: The paper summarizes the state of the art in aeronautical drag reduction across the speed range for the conventional drag components of viscous drag, drag due to lift and wave drag. It also describes several emerging drag-reduction approaches that are either active or reactive/interactive and the drag reduction potentially available from synergistic combinations of advanced configuration aerodynamics, viscous drag-reduction approaches, revolutionary structural concepts and propulsion integration.

Investigation of an Oscillating Surface Plasma for Turbulent Drag Reduction

Abstract: An oscillating, weakly ionized surface plasma has been investigated for use in turbulent boundary layer viscous drag reduction. The study was based on reports showing that mechanical spanwise oscillations of a wall can reduce viscous drag due to a turbulent boundary layer by up to 40%. It was hypothesized that the plasma induced body force in high electric field gradients of a surface plasma along strip electrodes could also be configured to oscillate the flow. Thin dielectric panels with millimeter-scale, flush- mounted, triad electrode arrays with one and two-phase high voltage excitation were tested. Results showed that while a small oscillation could be obtained, the effect was lost at a low frequency (less than 100Hz). Furthermore, a mean flow was generated during the oscillation that complicates the effect. Hot-wire and pitot probe diagnostics are presented along with phase-averaged images revealing plasma structure.

Modelling the flight of a soccer ball in a direct free kick.

Abstract: This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m·s−1, the ball's initial elevation must be constr...

Canopy Architecture and Turbulence Structure in a Coniferous Forest

Abstract: Synchronous sonic anemometric measurements at five heightswithin a mixed coniferous forest were used to test two different parameterisations ofcanopy architecture in the application of a second-order turbulence closure model. Inthe computation of the leaf drag area, the aerodynamic sheltering was replaced with anarchitectural sheltering, assumed to be analogous to the clumping index defined in radiativetransfer theory. Consequently, the ratio of leaf area density and sheltering factor was approximatedby the effective leaf area or the mean contact number, both obtained from the inversion of non-destructive optical measurements. The first parameter represents the equivalentrandomly dispersed leaf area in terms of shading, the second is the average number of leavesthat a straight line intercepts penetrating the canopy with a certain zenith angle. Theselection of this direction was determined by the analysis of the mean angle of the wind vectorduring sweep events. The drag coefficient values obtained from the inversion of themomentum flux equation, using the two proposed parameterisations, are in good agreement withvalues found in the literature. The predicted profiles of turbulence statistics reasonablymatch actual measurements, especially in the case of the mean contact numberparameterisation. The vertical profile of leaf drag area, obtained by forcing the turbulence modelto match the observed standard deviation of vertical velocity (σw), is intermediatebetween the two empirical ones. Finally, the proposed canopy parameterisations were appliedto a Lagrangian transport model to predict vertical profiles of air temperature, H2O andCO2 concentration.

Interaction of a shock with a sphere suspended in a vertical shock tube

Abstract: Shock wave interaction with a sphere is one of the benchmark tests in shock dynamics. However, unlike wind tunnel experiments, unsteady drag force on a sphere installed in a shock tube have not been measured quantitatively. This paper presents an experimental and numerical study of the unsteady drag force acting on a 80 mm diameter sphere which was vertically suspended in a 300 mm x 300 mm vertical shock tube and loaded with a planar shock wave of M s = 1.22 in air. The drag force history on the sphere was measured by an accelerometer installed in it. Accelerometer output signals were subjected to deconvolution data processing, producing a drag history comparable to that obtained by solving numerically the Navier-Stokes equations. A good agreement was obtained between the measured and computed drag force histories. In order to interpret the interaction of shock wave over the sphere, high speed video recordings and double exposure holographic interferometric observations were also conducted. It was found that the maximum drag force appeared not at the time instant when the shock arrived at the equator of the sphere, but at some earlier time before the transition of the reflected shock wave from regular to Mach reflection took place. A negative value of the drag force was observed, even though for a very short duration of time, when the Mach stem of the transmitted shock wave relfected and focused at the rear stagnation point of the sphere.

Drag Partition for Regularly-Arrayed Rough Surfaces

Abstract: Vegetation and other roughness elements distributed across a surface can providesignificant protection against wind erosion by extracting momentum from the flowand thereby reducing the shear stress acting at the surface. A theoretical model haspreviously been presented to specify the partition of drag forces for rough surfacesand to predict required vegetation density to suppress wind erosion. However, themodel parameters have not yet been constrained and the predictive capacity of themodel has remained uncertain. A wind-tunnel study was conducted to measure thedrag partition for a range of roughness densities and to parameterise the model inorder to improve its range of potential applicability. The drag forces acting on bothan array of roughness elements and the intervening surface were measured independentlyand simultaneously using new drag balance instrumentation. A detailed measure of thespatial heterogeneity of surface shear stresses was also made using Irwin sensors. Thedata agreed well with previous results and confirmed the general form of the model.Analysis of the drag partition confirmed the parameter definition β = CR/CS(where CR and CS are roughness element and surface drag coefficients,respectively) and a constant proportional difference between the mean and maximumsurface shear stress was found. The results of this experiment suggest that the definitionfor m, the surface shear stress inhomogeneity parameter, should be revised, although thetheoretical and physical reasons for including this parameter in the model appear to bevalid. Best-fit values for m ranged from 0.53 to 0.58.

Feedback control of a circular cylinder wake in experiment and simulation (invited)

Abstract: The effect of feedback flow control on the wake of a circular cylinder at a Reynolds number of 100 is investigated in both water tunnel experiment and direct numerical simulation. Our control approach uses a low dimensional model based on proper orthogonal decomposition (POD). The controller applies linear proportional and differential feedback to the estimate of the first POD mode. The range of validity of the POD model is explored in detail. Actuation is implemented as displacement of the cylinder normal to the flow. We demonstrate that the threshold peak amplitude below which the control actuation ceases to be effective is in the order of 5% of the cylinder diameter. The closed loop feedback simulations explore the effect of both fixed phase and variable phase feedback on the wake. While fixed phase feedback is effective in reducing drag and unsteady lift, it fails to stabilize this state once the low drag state has been reached. Variable phase feedback, however, achieves the same drag and unsteady lift reductions while being able to stabilize the flow in the low drag state. In the low drag state, the near wake is entirely steady, while the far wake exhibits vortex shedding at a reduced intensity. We achieved a drag reduction of close to 90% of the vortex-induced drag, and lowered the unsteady lift force by the same amount.

Simple and Low-Cost Aerodynamic Drag Reduction Devices for Tractor-Trailer Trucks

Abstract: Three simple, low cost aerodynamic drag reduction devices have been developed for application to the trailer of a tractor-trailer truck. The three devices have undergone extensive operational testing where they have amassed over 85,000 miles of use. These technologies have shown a combined fuel savings of 10% at an average speed of 47.5 mph. This improvement in fuel economy correlates to an equivalent drag reduction of approximately 30% with a corresponding drag coefficient of 0.45. Observations and anecdotal evidence from the test activity have shown that the addition of these devices to the trailers has not had a negative impact on either the operational utility of the trailers or the maintenance procedures and requirements.

Impact of flow distortion corrections on turbulent fluxes estimated by the inertial dissipation method during the FETCH experiment on R/V L'Atalante

Abstract: [1] The FETCH campaign was for a large part devoted to the measurement and analysis of turbulent fluxes in fetch-limited conditions. Turbulent measurements were performed on board the R/V L'Atalante, on an ASIS spar buoy and on aircraft. On the R/V L'Atalante, turbulent data were obtained from a sonic anemometer and from a microwave refractometer. The main focus of this paper is to present results of momentum and heat fluxes obtained from the R/V L'Atalante, using the inertial-dissipation method and taking into account flow distortion effects. Numerical simulations of airflow distortion caused by the ship structure have been performed to correct the wind measurements on the R/V L'Atalante during the FETCH experiment. These simulations include different configurations of inlet velocities and six relative wind directions. The impact of airflow distortion on turbulent flux parameterizations is presented in detail. The results show a very large dependence on azimuth angle. When the ship is heading into the wind (relative wind direction within ±38° of the bow), the airflow distortion leads to an overestimation of the drag coefficient, associated with a wind speed reduction at the sensor location. For relative wind directions of more than ±38° from the bow, flow distortion causes the wind to accelerate at the sensor location, which leads to an underestimate of the drag coefficient. The vertical displacement of the flow streamlines could not be fully established by numerical simulation, but the results are in qualitative agreement with those inferred from the data by prescribing the consistency of momentum flux as a function of azimuth angle. Both show that the vertical elevation of the flow can be considered as constant (1.21 m from numerical simulations) only within about ±20° from bow axis. Values of vertical displacements up to 5 m are found from the data for high wind speeds and beam-on flows. Our study also shows that the relative contributions of the streamline vertical displacement and the mean wind speed underestimate or overestimate vary significantly with relative wind direction. The relative contribution due to vertical streamline displacement is higher for heat flux than for momentum flux. The consistency of our correction for airflow distortion is assessed by the fact that the correction reduces the standard deviation of the drag coefficient: only if this correction is taken into account, do the curves of the drag coefficient versus wind speed become similar for data corresponding to wind in the bow direction and from the side. When the complete numerical airflow correction is applied to the data set limited to relative wind directions at ±30° from the bow axis, the drag coefficient formula is CD10N × 1000 = 0.56 + 0.063 U10N, for U10N > 6 m s−1. This formula provides CD10N values comparable to the ones found from the ASIS buoy data for wind speeds of about 13 m s−1. They are however smaller by 9% at higher winds (>15 m s−1). This formula is also similar, within a few percent, to the parameterizations of Smith [1980], Anderson [1993], and Yelland et al. [1998]. The exchange coefficient for evaporation is found to be 1.00 × 10−3 on average with a small standard deviation of 0.31 × 10−3. A slight increase of CE10N value with wind speed is, however, observed with a variation of about 20% (0.2 × 10−3) for wind speeds between 6 and 17 m s−1, following CE10N × 1000 = 0.82 + 0.02 U10n, for U10n > 6 m s−1.