Estimation Of Drag Coefficient Research Articles

Turbulent Fluxes in the Hurricane Boundary Layer. Part I: Momentum Flux

Abstract An important outcome from the ONR-sponsored Coupled Boundary Layer Air–Sea Transfer (CBLAST) Hurricane Program is the first-ever direct measurements of momentum flux from within hurricane boundary layers. In 2003, a specially instrumented NOAA P3 aircraft obtained measurements suitable for computing surface wind stress and ultimately estimating drag coefficients in regions with surface wind between 18 and 30 m s−1. Analyses of data are presented from 48 flux legs flown within 400 m of the surface in two storms. Results suggest a roll-off in the drag coefficient at higher wind speeds, in qualitative agreement with laboratory and modeling studies and inferences of drag coefficients using a log-profile method. However, the amount of roll-off and the wind speed at which the roll-off occurs remains uncertain, underscoring the need for additional measurements.

Estimation of drag coefficient in James River Estuary using tidal velocity data from a vessel‐towed ADCP

A phase‐matching method is introduced to calculate the bottom drag coefficient in tidal channels with significant lateral variation of depth. The method is based on the fact that the bottom friction in a tidal channel causes tidal velocity to have a phase difference across the channel. The calculation involves a few steps. First, the observed horizontal velocity components are analyzed to obtain the amplitude and phase of the velocity at the major tidal frequency. The phase of the longitudinal velocity is then fitted to a relationship derived from the linearized momentum balance. The drag coefficient is then calculated. This method is applicable to narrow (approximately a few kilometers wide) tidal channels without strong stratification and where the cross‐channel variation of surface elevation is negligible compared to tidal amplitude. This analytic approach is easy to implement when appropriate observational data are available. It allows a spatial variation of the drag coefficient, and the resolution is only limited by that of the observations. The method is validated by identical twin experiments and applied to tidal velocity data, obtained in the James River Estuary, using an acoustic Doppler current profiler during spring tides and neap tides in October–November 1996. The obtained bottom drag coefficient ranged from 1.2 × 10−3 to 6.9 × 10−3 at different positions along two cross‐channel transects each 4 km long and 2 to 14 m deep. The maximum drag coefficient is found in the shallowest water near the banks of the estuary, while the minimum values occur between 9 and 12 m in the center of the channel. The friction of the lateral boundary may have contributed to the apparent increase of the bottom friction on the banks. The transverse mean values of the drag coefficient ranges between 2.2 and 2.3 × 10−3 for the spring and neap tides, respectively.

Bottom friction and bed forms on the southern flank of Georges Bank

We present observational estimates of bottom stress, bottom roughness, and quadratic drag coefficient for the southern flank of Georges Bank, a shallow region dominated by strong semidiurnal tides. Our estimates are based on near‐bottom velocity measurements from two Benthic Acoustic Stress Sensor (BASS) tripod deployments at a depth of 76 m taken during winter (February–April 1995) and summer (July–August 1995). The dominant tidal constituent is the M2, which provides 76–89% of the total kinetic energy. Typical bottom friction velocities are 1.1–1.2 cm s−1 in the time mean, with standard deviations of 0.4–0.5 cm s−1. A representative drag coefficient is cD = 3.0 ± 0.1 × 10−3 at 1.2 m above the bottom. Our drag coefficient estimates at this and other elevations correspond to the apparent bottom roughness range z0 = 0.05–0.09 cm. Bottom photographs (taken February–June) show that from February until April the sea floor was covered by sand ripples 1–2 cm in height. These ripples were approximately aligned with the local isobath; their flanks were perpendicular to the major axis of the tidal ellipse. Ripples exhibited stationary behavior; that is, they did not migrate with the flow. Intermittent modification of the ripple pattern happened during times of strong wave‐current interaction, but along‐isobath ripples formed again after each wave event. Observations of bed forms affected by surface waves coincided with periods of wave‐enhanced bottom stress predicted by the Grant and Madsen [1979] combined wave‐current interaction model. Model results and bottom photographs indicate that sediments were kept in suspension only under extreme conditions, here the February 1995 storm. Sand ripples gradually eroded during late March and April until the sea floor was almost flat. Coinciding with slow ripple erosion, bioturbation levels increased. Our estimates of bottom stress do not exhibit seasonal changes, so that seasonal variation of bottom shear stress cannot explain the transition from a rippled to a nearly flat bottom. We conclude that biogenic modification of bottom sediment enhanced the critical shear stress for initiation of sediment movement, thereby prohibiting ripple formation in spring and summer.

INSTRUMENTATION TO MEASURE DRAG ON IDEALIZED VEGETAL ELEMENTS IN OVERLAND FLOW

Information on shear stress acting on soil particles is necessary to quantify potential soil erosion. Movement ofwater across a rough surface generates a resistive force, part of which acts on the largescale roughness elements while theremainder acts on the intervening soil surface. An important largescale roughness element is vegetation, which acts toreduce shear stresses on the soil and thereby reduces potential erosion. Insight into the drag force acting on individualvegetative elements is necessary for understanding this dynamic. An instrumentation system was developed to measure thedrag force on individual elements representative of vegetation. Vegetative elements were modeled in a hydraulic flume usingrigid circular cylinders and idealized shapes to account for differences in the rate of change in upstream frontal area withflow depth. Data were gathered for a horizontal flume and for a 1% flume slope. Flow rates ranged from 0.004 to 0.028 m3s1with average flow depths ranging from 1.9 to 9.8 cm and average flow velocities ranging from 0.41 to 1.02 m s1. Sixteenelement shapes were considered, resulting in a total of 80 test scenarios. The test conditions resulted in both partial andcomplete submergence of the elements. Results are presented as actual drag force and dimensionless drag coefficient. Therelationship between drag force divided by velocity squared and upstream projected area is well represented by a straight linefor cylinders and all other elements. Drag coefficient is a function of element shape and is represented by an average valueover the range of flow depths investigated. The overall error in the estimated drag coefficient is 7.3%.

DRAG COEFFICIENTS OF AGRICULTURAL GRAINS IN VERTICAL PNEUMATIC CONVEYING

A study was made of drag coefficients in vertical pneumatic conveying of agricultural grains. From experimentsconducted on rough rice and milled rice, it was found that the values of drag coefficient computed using the basic relationshipfor slip velocity of a single particle in an air stream were closely related to the solid flow rate per unit crosssectional areaof the conveying pipe and solidtoair ratio. Generalized equations were developed for estimation of drag coefficient in termsof particle equivalent diameter, solid flow rate per unit crosssectional area of pipe, and solidtoair ratio. The equationswere also verified for another agricultural grain, namely corn. The closeness between experimental and predicted valuesvalidated the equations for general use for grain particles ranging in size approximately from 3 to 7mm mean diameter.

Reynolds Stress and Turbulent Energy Production in a Tidal Channel

Abstract A high-frequency (1.2 MHz) acoustic Doppler current profiler (ADCP) moored on the seabed has been used to observe the mean and turbulent flow components in a narrow tidally energetic channel over six tidal cycles at neap and spring tides. The Reynolds stress has been estimated from the difference in variance between the along-beam velocities of opposing acoustic beams with a correction for the sampling scheme and bin size. Shear stress was found to vary regularly with the predominantly semidiurnal tidal flow with the stresses on the spring ebb flow (up to 4.5 Pa) being generally greater than on the flood flow (<2 Pa) when the currents are weaker. The vertical structure approximated to linear stress profiles decreasing from maximum values near the bed to almost zero stresses just below the surface. The variation in the bed stress was well represented by a quadratic drag law, based on the depth-mean current, with an estimated drag coefficient of 2.6 ± 0.2 × 10−3. The production of turbulent kinetic...

Power law fluid flow over a bundle of cylinders at intermediate Reynolds numbers

Extensive theoretical estimates of pressure, friction and total drag coefficients for the cross flow of power law fluids normal to an array of long circular cylinders are reported in this paper. The equations of continuity and of momentum have been solved numerically for the unknown velocities and pressure which, in turn, have been processed further to infer the values of drag coefficients. The inter-cylinder interactions have been approximated by the two commonly employed “concentric cylinders” cell models. The results reported herein embrace the following ranges of physical and kinematic conditions: power law flow behaviour index: 0.5, 0.6, 0.8 and 1; Reynolds number, 1–500 and the voidage of 0.4 and 0.5, albeit limited results are also presented for voidage values of 0.6 and 0.9. The accuracy of the numerical solution procedure has been established by carrying out extensive comparisons with the previously available analytical and/or numerical results for the flow of Newtonian and power law fluids. Similarly, the applicability of this simple approach of the cell model has been demonstrated by presenting detailed comparisons between the present predictions and the limited experimental results available in the literature for the flow of shear-thinning polymer solutions over banks of cylinders.

Field estimates of body drag coefficient on the basis of dives in passerine birds.

During forward flight, a bird's body generates drag that tends to decelerate its speed. By flapping its wings, or by converting potential energy into work if gliding, the bird produces both lift and thrust to balance the pull of gravity and drag. In flight mechanics, a dimensionless number, the body drag coefficient (C(D,par)), describes the magnitude of the drag caused by the body. The drag coefficient depends on the shape (or streamlining), the surface texture of the body and the Reynolds number. It is an important variable when using flight mechanical models to estimate the potential migratory flight range and characteristic flight speeds of birds. Previous wind tunnel measurements on dead, frozen bird bodies indicated that C(D,par) is 0.4 for small birds, while large birds should have lower values of approximately 0.2. More recent studies of a few birds flying in a wind tunnel suggested that previous values probably overestimated C(D,par). We measured maximum dive speeds of passerine birds during the spring migration across the western Mediterranean. When the birds reach their top speed, the pull of gravity should balance the drag of the body (and wings), giving us an opportunity to estimate C(D,par). Our results indicate that C(D,par) decreases with increasing Reynolds number within the range 0.17-0.77, with a mean C(D,par) of 0.37 for small passerines. A somewhat lower mean value could not be excluded because diving birds may control their speed below the theoretical maximum. Our measurements therefore support the notion that 0.4 (the 'old' default value) is a realistic value of C(D,par) for small passerines.

Identification of Release Conditions and Aerodynamic Forces in Pitched-Baseball Trajectories

Pitched-baseball trajectories were measured in three dimensions during competitions at the 1996 Summer Olympic games using two high-speed video cameras and standard DLT techniques. A dynamic model of baseball flight including aerodynamic drag and Magnus lift forces was used to simulate trajectories. This simulation together with the measured trajectory position data constituted the components of an estimation scheme to determine 8 of the 9 release conditions (3 components each of velocity, position, and angular velocity) as well as the mean drag coefficient CD and terminal conditions at home plate. The average pitch loses 5% of its initial velocity during flight. The dependence of estimated drag coefficient on Reynolds number hints at the possibility of the drag crisis occurring in pitched baseballs. Such data may be used to quantify a pitcher’s performance (including fastball speed and amount of curve-ball break) and its improvement or degradation over time. It may also be used to understand the effects of release parameters on baseball trajectories.

Horizontal flight of a swallow (Hirundo rustica) observed in a wind tunnel, with a new method for directly measuring mechanical power.

A swallow flying in the Lund wind tunnel was observed from the side and from behind, by two synchronised high-speed video cameras. The side-view camera provided a record of the vertical position of a white mark, applied to the feathers behind and below the eye, from which the vertical acceleration was obtained. The rear-view camera provided measurements of the mean angle of the left and right humeri above horizontal. From these data, the force acting on the body, the moment applied by each pectoralis muscle to the humerus and the rotation of the humerus were estimated and used to analyse the time course of a number of variables, including the work done by the muscles in each wing beat. The average mechanical power turned out to be more than that predicted on the basis of current estimates of body drag coefficient and profile power ratio, possibly because the bird was not flying steadily in a minimum-drag configuration. We hope to develop the method further by correlating the mechanical measurements with observations of the vortex wake and to apply it to birds that have been conditioned to hold a constant position in the test section.

Modeling and identification of open-frame variable configuration unmanned underwater vehicles

A lumped parameter model of open-frame unmanned underwater vehicles (UUV's) including the effects of propeller-hull and propeller-propeller interactions is presented. The identification of the model parameters consists of a least squares method using only on-board sensor data without requiring any towing tank tests. The identification scheme is based on separate tests for the estimation of drag and thruster installation coefficients, taking into account propeller-hull and propeller-propeller effects first and inertia parameters subsequently. The scheme has been experimentally implemented on ROMEO, the latest UUV developed by CNR-IAN. Experimental results show both the effectiveness of the proposed method and the relevance of the propeller-hull and propeller-propeller interactions that are usually neglected in standard UUV models.

2820 水中を上昇する気泡の界面状態に関する研究

The surface condition of a spherical gas bubble rising in water was investigated numerically. We numerically estimated drag coefficients and Sherwood number of the "Stagnant Cap Model" by directly solving the Navier-Stokes equation and the convection-diffusion equation. We compared the numerical results with the experimental results that we precisely estimated the drag coefficients and the Sherwood number for the dissolution of gas bubbles in the transient regime where the bubble changes from behaving as a fluid sphere to behaving as a solid particle by using the experimental system that use a CCD camera coupled with a microscope to track the rising bubble. The experimental and numerical results are in good agreement and clarified the mechanism of the transient process where the bubble behavior changes from that of a fluid sphere to that of a solid particle.

Gas Dissolution Process with Chemical Reaction of a Spherical Rising Gas Bubble. 2nd Report. Numerical Analysis for Dissolution Process of a CO2 Bubbles in Strong Alkaline Solution.

Gas dissolution process with chemical reaction of a spherical rising gas bubble was investigated numerically. We numerically estimated drag coefficients and Sherwood number of the Stagnant Cap Model by directly solving the Navier-Stokes equation and the convection-diffusion equation when a carbon dioxide bubble dissolves in strong alkaeine solution with chemical reactions. In this analysis, we assume that the chemical equilibrium does not attain near the bubble is and include the chemical reaction term in the convection-diffusion equation. We compared the results with the measured rising speed and dissolution rate. The results reveal that the experimental and numerical results are in good agreement and the dissolution rate with the chemical reactions can be estimated even when the chemical equilibrium does not attain near the bubble. We also observed that the behavior of the bubble returns to that of a fluid sphere after it is closed to that of a solid particle when the concentration of sodium hydroxide is as high as 1 mol/1.

Effects of Contamination on Gas Dissolution Process of a Spherical Rising Gas Bubble in Water.

The effects of contamination on gas dissolution process of a spherical rising gas bubble in water was investigated experimentally and numerically. We developed an experimental system that use a CCD camera coupled with a microscope to track rising bubble. By measuring bubble size and rising speed from bubble motion data captured by a personal computer, we could precisely estimate drag coefficients and Sherwood number for dissolution of gas bubbles in transient regime where bubble changes from behaving as a fluid sphere to behaving as a solid particle. We also numerically estimated drag coefficients and Sherwood number of the Stagnant Cap Model by directly solving Navier-Stokes equation and convection diffusion equation. The experimental and numerical results are in good agreement and clarified mechanism of transient process where bubble behavior changes from that of a fluid sphere to that of a solid particle.

Wind Stress Measurements from the Open Ocean Corrected for Airflow Distortion by the Ship

A large dataset of wind stress estimates, covering a wide range of wind speed and stability conditions, was obtained during three cruises of the RRS Discovery in the Southern Ocean. These data were used by Yelland and Taylor to determine the relationship between 10-m height, neutral stability values for the drag coefficient, and the wind speed, and to devise a new formulation for the nondimensional dissipation function under diabatic conditions. These results have been reevaluated allowing for the airflow distortion caused by the ship. The acceleration and vertical displacement of the flow have been modeled in three dimensions using computational fluid dynamics (CFD). The CFD modeling was tested, first by comparison with wind tunnel measurements on models of two Canadian research ships and second, by analysis of data from four anemometers on the foremast of the RRS Charles Darwin. Originally, the four anemometers gave drag coefficient values that differed by up to 20% from one to another and were all unexpectedly high. The CFD results showed that the airflow had been decelerated by 4%‐14% and displaced vertically by about 1 m. These effects caused the original drag coefficient results to be overestimated by up to 60%. After correcting for flow distortion effects, the results from the different anemometers became consistent, which gave confidence in the quantitative CFD-derived corrections. The CFD modeling showed that the anemometer position on the RRS Discovery was much less affected by airflow distortion. For a given wind speed the CFD corrections reduced the drag coefficient by about 6%. The resulting mean drag coefficient to wind speed relationship confirmed that suggested by Smith from a more limited set of open ocean data. The effects of flow distortion are sensitive to changes in the relative wind direction. It is shown that much of the scatter in drag coefficient estimates may be due to variations in airflow distortion rather than to the effect of changing sea states. The Discovery wind stress data is examined for evidence of a sea-state dependence: none is found. It is concluded that a wave-age-dependent wind stress formulation is not applicable to open ocean conditions.

DESIGN OF A ROUGHENED APRON TO DISSIPATE ENERGY.

The 600 MW Pergau hydroelectric project in Northern Peninsular Malaysia draws water from a reservoir of the Sungai Pergau impounded by the Kuala Yong Dam. Additional water for the Kuala Yong reservoir is drawn from local streams by way of a 24 km long aqueduct tunnel. Some 60% of this additional flow is pumped into the upstream end of the aqueduct from a pool created by a 8 m high concrete-faced rockfill weir on the Sungai Terang. Flood flows of over 1000 m 3 /s pass over this weir and there is insufficient depth downstream to create a hydraulic jump. This paper describes the development of roughened apron in a series of physical model studies. A staggered arrangement of blocks in double rows on the apron provided a satisfactory deceleration of the stream and acceptable flow patterns. A simple analytical technique using an estimated drag coefficient has been put forward as a rational approach to the design of roughness patterns.

Tidally forced under-ice Ekman layers observed by an acoustic Doppler current profiler

A simple, tidally forced Ekman model is fit to acoustic Doppler current profiler observations of the horizontal velocity field sampled during the Resolute portion of the SARES project. An assimilation inversion technique is demonstrated that does not require the use of Lagrange multipliers or an adjoint equation. The gradient of the cost function is obtained through direct differentiation of the equations of motion and associated boundary conditions. Both the standard depth-independent pressure gradient and a new depth-dependent pressure gradient are assimilated into the model. The depth-dependent pressure gradient reduced the residual error over the depth-independent case and produced estimates of eddy viscosities and drag coefficients that were consistent with a marked change in the stratification observed during the course of the experiment. The results suggest that a depth-dependent pressure gradient may be more important than a depth-dependent eddy viscosity in describing under-ice tidally forced Ekman layers. A maximum value of 4.75 × 10 −3 m 2 s −1 is obtained for the vertical eddy viscosity, which implies a nutrient transport 50 times less than that required to meet ice-algal demand. This result suggests that turbulence associated with the passage of high frequency internal waves, rather than the background tide, is likely responsible for bringing nutrients to the ice-water interface.

Terminal Velocity of Spherical Gas Bubbles below Reynolds Numbers of 100.

Drag coefficients of a spherical rising gas bubble were estimated experimentally and numerically. We developed an experimental apparatus in which a CCD camera with a microscope follows the rising bubble and used it to precisely estimate the drag coefficients of the bubble below Reynolds number of 100 by measurement of the bubble size and the terminal velocity. We also estimated numerically drag coefficients of a gas bubble in an infinite liquid by directly solving a Navier-Stokes equation. The experimental results agree well with the numerical results. Moreover, we compared the experimental results with several proposed equations for estimating drag coefficients and determined the region of applicability of each equation. Finally, we proposed an equation for estimation of drag coefficient by correlating with experimental results.

Estimation of drag coefficient at low wind speeds over the monsoon trough land region during MONTBLEX‐90

Using observational data acquired during the Monsoon Trough Boundary Layer Experiment (MONTBLEX‐90), the drag coefficient CD is estimated over two land stations, Jodhpur (arid region) and Kharagpur (moist region), by eddy correlation of velocity data from sonic anemometers. At low winds CD varies with wind speed according to a power law, which at Jodhpur takes the form CD=0.04 Ū10−1.06 (Ū10 being the mean wind speed at 10 m). The large values of the drag coefficient at low winds are associated with both near‐neutral and strongly unstable situations. On the other hand, the CD values at Kharagpur are less than at Jodhpur by nearly 50% for wind speeds &gt; 3ms−1, and cannot be explained by the different roughness lengths at the two sites.

Aerodynamic Drag on Trains in Tunnels Part 1: Synthesis and Definitions

Aerodynamic drag on trains in tunnels includes friction drag and pressure drag, which are respectively the algebraic sums of the longitudinal components of all shear and normal forces on the train surfaces. The first of these is broadly similar to its counterpart in the open. The second is shown to include two effects that are usually negligible in the open. It is shown that the overall drag force must be regarded as the sum of individual components, each of which behaves differently from the others. The components can be represented by non-dimensional coefficients whose numerical values are nearly constant for a wide range of train journeys. In contrast, the overall drag coefficient is shown to vary significantly, even during any particular journey. The principal causes of aerodynamic drag in tunnels are also the principal causes of pressure waves that give rise to potential aural discomfort for passengers. It is argued that a common method of analysis is appropriate for the prediction of both of these effects. Ill-defined train areas are shown to be a potentially serious source of confusion in the estimation and interpretation of drag coefficients. The relevant train area is shown to be its aerodynamic area, the definition of which is explained.