Showing papers on "Drag coefficient published in 1981"

Open Ocean Momentum Flux Measurements in Moderate to Strong Winds

Abstract: Measurements of the momentum flux were made by the Reynolds flux and dissipation methods on a deep water stable tower operated by the Bedford Institute of Oceanography, A modified Gill propeller-vane anemometer was used to measure the velocity. Drag coefficients from 196 Reynolds flux measurements agree well with those reported in Smith (1980) based on independent observations at the same site. Based on 192 runs, a comparison of the dissipation and Reynolds flux results shows excellent agreement on average, for wind speeds from 4 to 20 m s−1. The much more extensive dissipation data set (1086 h from the tower and 505 h from the weathership PAPA, CCGS Quadra) was used to investigate the dependence of the drag coefficient on wind speed, fetch and stability. The drag coefficient reduced to 10 m height and neutral conditions (CDN), is independent of stability and fetch (for fetch/height ≳800) but increases with wind speed above 10 m s−1. Some time series of the momentum flux and drag coefficient are ...

Bubbles in viscous liquids: shapes, wakes and velocities

Abstract: The shapes and terminal velocities of bubbles rising in viscous liquids have been determined. For Morton numbers (M) greater than 4 × 10−3 the drag coefficient and dimensionless bubble shape are functions only of Reynolds number (R). Shape regimes and terminal rise velocities have been correlated. The flow field around a rising bubble was visualized through the hydrogen bubble tracer technique. For M > 4 × 10−3 and R 110 the wake was open and unsteady. Streamlines for the flow were obtained by raising a cine camera at the same speed as the bubble and filming the H2 tracer bubbles. Results are presented for R < 150 and 7·4 × 10−4 < M < 850.

The translational and rotational drag on a cylinder moving in a membrane

Abstract: The translational and rotational drag coefficients for a cylinder undergoing uniform translational and rotational motion in a model lipid bilayer membrane is calculated from the appropriate linearized Navier–Stokes equations. The calculation serves as a model for the lateral and rotational diffusion of membrane-bound particles and can be used to infer the ‘microviscosity’ of the membrane from the measured diffusion coefficients. The drag coefficients are obtained exactly using dual integral equation techniques. The region of validity of an earlier asymptotic solution obtained by Saffman (1976) is elucidated.

A kinetic theory for polymer melts. I. The equation for the single‐link orientational distribution function

Abstract: In this series of papers we show how a kinetic theory of undiluted polymers can be developed using the Curtiss–Bird–Hassager phase‐space formulation. The polymer molecule is modeled as a Kramers freely jointed bead–rod chain. The objective is to obtain a molecular‐theory expression for the stress tensor from which the rheological properties of polymer melts can be obtained. This development is put forth as an alternative to the Doi–Edwards theory; using a very different approach, we have rederived some of their results and generalized or extended others. In this first paper we develop the partial differential equation for the chain configurational distribution function, and then proceed to get the equation for the orientational distribution function for a single link in the chain. A modification of Stokes’ law is introduced that includes a tensor drag coefficient, characterized by two scalar parameters ζ (the friction coefficient) and e (the link tension coefficient). In addition, to describe the increase of the drag force on a bead with chain length, at constant bead density, a ’’chain constraint exponent’’ β is used, which can vary from zero (the Doi–Edwards limit) to about 0.5. Solutions to the partial differential equation for the single‐link distribution function are given in several forms, including an explicit series solution to terms of third order in the velocity gradients.

A linear stratified ocean model of the coastal undercurrent

Abstract: The linear, stratified ocean model of McCreary (1981) is used to study the wind-driven response of the ocean near an eastern coast. The model can be regarded as an extension of the inviscid models of Lighthill (1969) and of Gill & Clarke (1974) that allows the vertical diffusion of heat and momentum into the deep ocean. Solutions are still found as expansions of vertical normal modes. Vertical mixing affects each mode as a linear drag with a drag coefficient that increases rapidly with mode-number, n. A zonally uniform band of steady equatorward winds forces the ocean, and the resulting flow field has many features in common with observations at eastern boundaries. There is a surface equatorward jet and a poleward Coastal Undercurrent confined within 10-20 km of the coast. Both currents extend well poleward of the wind band. Upwelling does not reach great depths, but occurs only above the core of the Undercurrent. Weak downwelling occurs at greater depths. There is offshore Ekman drift in the surface mixed layer and return flow at a depth slightly above the core of the Undercurrent. The baroclinic alongshore pressure gradient field and the vertical mixing of heat and momentum are essential elements of the model dynamics, but the $\beta $ and horizontal mixing are not. Low-order vertical modes (n 6) tend toward a two-dimensional balance. They generate the transverse circulation pattern associated with coastal Ekman pumping.

Design and experimental results for a flapped natural-laminar-flow airfoil for general aviation applications

Abstract: A natural-laminar-flow airfoil for general aviation applications, the NLF(1)-0416, was designed and analyzed theoretically and verified experimentally in the Langley Low-Turbulence Pressure Tunnel. The basic objective of combining the high maximum lift of the NASA low-speed airfoils with the low cruise drag of the NACA 6-series airfoils was achieved. The safety requirement that the maximum lift coefficient not be significantly affected with transition fixed near the leading edge was also met. Comparisons of the theoretical and experimental results show excellent agreement. Comparisons with other airfoils, both laminar flow and turbulent flow, confirm the achievement of the basic objective.

An Aerodynamic Analysis of Bird Wings as Fixed Aerofoils

Abstract: The aerodynamic properties of bird wings were examined at Reynolds numbers of 1-5 × 10 4 and were correlated with morphological parameters such as apsect ratio, camber, nose radius and position of maximum thickness. The many qualitative differences between the aerodynamic properties of bird, insect and aeroplane wings are attributable mainly to their differing Reynolds numbers. Bird wings, which operate at lower Reynolds numbers than aerofoils, have high minimum drag coefficients (0·03-0·13), low maximum lift coefficients (0·8-1·2) and low maximum lift/drag ratios (3–17). Bird and insect wings have low aerofoil efficiency factors (0·2-0·8) compared to conventional aerofoils (0·9-0·95) because of their low Reynolds numbers and high profile drag, rather than because of a reduced mechanical efficiency of animal wings. For bird wings there is clearly a trade-off between lift and drag performance. Bird wings with low drag generally had low maximum lift coefficients whereas wings with high maximum lift coefficients had high drag coefficients. The pattern of air flow over bird wings, as indicated by pressure-distribution data, is consistent with aerodynamic theory for aeroplane wings at low Reynolds numbers, and with the observed lift and drag coefficients.

Oscillating flow over steep sand ripples

Abstract: Although the form and dimensions of steep vortex ripples are well studied in relation to the oscillating flow which generates them, nevertheless the accompanying fluid motion is not yet understood quantitatively. In this paper we present a method of calculation based on the assumption that the sand-water interface is fixed and that the effect of sand in suspension is, to a first approximation, negligible. The method employs a simple conformal transformation of the fluid flow onto the exterior of a polygon, and thence onto the interior of a unit circle. The initial, irrotational flow is represented by a logarithmic vortex at the centre of the circle. Other vortices within the fluid are each represented by a symmetric system of P vortices and their images in the unit circle, P being the number of sides of the original polygon. Typically P is equal to 5. However, P is not limited to integer values but may be any rational number greater than 2 (see § 15). To proceed with the calculation it is assumed that separation of the boundary layer takes place at the sharp crests of the ripples, and that the shed vorticity can be represented by discrete vortices, with strengths given by Prandtl's rule. (For a typical time sequence see figures 7 and 8.) After a complete cycle, a vortex pair is formed, which can escape upwards from the neighbourhood of the boundary. The total momentum per ripple wavelength and the horizontal force on the bottom are expressible very simply in terms of the shed vortices at any instant. The force consists of two parts: an added-mass term which dissipates no energy, and a ‘vortex drag’, which extracts energy from the oscillating flow. The calculation is at first carried out with point vortices, in a virtually inviscid theory. However, it is found appropriate to assume that each vortex has a solid core whose radius expands with time like [e( t − t n )] ½ , where t n denotes the time of birth, and e is a small parameter analogous to a viscosity. The expansion of the vortex tends to reduce the total energy (which otherwise would increase without limit) at a rate independent of e. If the cores of two neighbouring vortices overlap they are assumed to merge, by certain simple rules. Calculation of the effective vortex drag in an oscillating flow yields drag coefficients $\overline{C}_D$ of the order of 10 −1 , in good agreement with the measurements of Bagnold (1946) and of Carstens, Nielson & Altinbilek (1969). The tendency for the highest drag coefficients to occur when the ratio 2 a / L of the total horizontal excursion of the particles to the ripple length is about 1·5 is confirmed. When 2 a / L = 4, the drag falls to about half its value at ‘resonance’.

An experimental investigation of the initial force of impact on a sphere striking a liquid surface

Abstract: Detailed experimental results are presented for the initial impact force on a sphere striking a horizontal liquid surface vertically at speeds in the range 1-3 m s−1. Results are discussed in terms of an impact drag coefficient. Liquids having viscosities in the range 10−3−102 Pa s have been studied. For low viscosities the results have been compared with the theoretical calculations of Shiffman & Spencer. Good agreement has been found in most respects; in particular the impact force varies as the square root of the depth for depths less than a tenth of the radius. The impact drag coefficient has also been studied through the transition from inertia to viscosity-dominated conditions. The variation of the impact drag coefficient is presented as a function of Reynolds number, and its variation in the range 5 × 10−2 < Re < 5 × 103 is shown to resemble that of a fully immersed sphere moving steadily in a homogeneous fluid.

Aluminum Oxide Particle Size for Solid Rocket Motor Performance Prediction

Abstract: A new method for predicting aluminum oxide particle size was developed for use in the Air Force Improved Solid Performance Program (SPP). Theoretical models of particle growth and breakup in rocket nozzles were compared with available particle size data. It was found that no adequate theoretical model existed to relate particle size to propellant composition and motor parameters; therefore, an empirical approach was adopted using linear and nonlinear least-squares methods. Correlations were attempted with parameters, groupings, and functional forms suggested by the theoretical models. A relatively simple model employing only three free parameters was recommended for use in SPP. Nomenclature a = speed of sound CD = drag coefficient Dc = critical diameter for breakup £>, = diameter of particles in ith class D0 = diameter before breakup Dt = nozzle throat diameter D43 = mass-weighted average diameter dp = particle diameter Isp = specific impulse ni = number of particles in /th class n, m = generalized exponents m = motor mass flow rate P = pressure Rec = particle Reynolds number based on ac Ret = Reynolds number at nozzle throat Rc = nozzle throat radius of curvature R t = nozzle throat radius S = pcDt /ppdp = dimensionless scale parameter for two-phase flow s = estimate of standard deviation T = temperature Aw = magnitude of particle-gas velocity difference Vc = chamber volume a, j8 = generalized coefficients £ = aluminum oxide concentration, g-mole/lOOg fjig = gas viscosity pg = gas density PL = liquid density a = standard deviation of \ogloD\ surface tension T =pcyc/m = chamber residence time Subscripts

Universal Similarity in the Wakes of Stationary and Vibrating Bluff Structures

Abstract: A universal wake Strouhal number, St * = f s d′/U b , has been proposed and is based upon the Strouhal frequency f s of the incident flow, the measured wake width d' at the end of the vortex formation region, and the mean velocity U b at the edge of the separated boundary layer. This universal parameter collapses the characteristic wake scales for bluff bodies onto a single curve over the entire range of subcritical and transcritical wake Reynolds numbers Re * . The pressure drag, vortex shedding frequency and base pressure are related through a dependence between St C D , the product of the Strouhal number and drag coefficient, and the base pressure parameter K. There is a general collapse of the data up to K = 2, which is the upper limit thus far for bluff body flows.

Newtonian fluid sphere with rigid or mobile interface in a shear-thinning liquid: drag and mass transfer

Abstract: The drag force and the mass transfer rate of a Newtonian fluid sphere, having mobile or rigid interface, moving in a power law fluid, are obtained by an approximate solution of equations of motion in the creeping flow regime. It is shown that both the drag and mass transfer increase as the flow index of the external fluid decreases. The increase of drag due to the pseudoplastic anomaly is more significant at large viscosity ratio parameter. The results obtained are in good agreement with available experimental data and with those analyses based on variational principle when the non-Newtonian flow behavior is not very pronounced. Also, the predicted mass transfer rates are in good agreement with the trends presented in the literature. Unlike in the case of drag force, the effect of the pseudoplastic anomaly on mass transfer rate is more pronounced for low values of the viscosity ratio parameter. The analysis was extended to include the case when the surface of the sphere was immobilized by surface...

Measurements of the rate of dissipation of turbulent kinetic energy, ∊, over the ocean

Abstract: In a series of cruises during the last three years, the Naval Postgraduate School Environmental Physics Group has made more than 1000 shipboard measurements of the rate of dissipation of turbulent kinetic energy, ɛ, using inertial subrange (high frequency) techniques. Utilizing the bulk-aerodynamic method to obtain the relevant Monin-Obukhov surface layer scaling parameters, the overwater dimensionless dissipation function 321-01, has been examined with unprecedented statistical certainty. The results agree well with those of Wyngaard and Cote (1971) for the stable case but they agree more closely with the parameterization of McBean and Elliott (1975) for unstable conditions. Drag coefficients computed from the ɛ data are in good agreement with the curve given by Garratt (1977).

Aircraft Excrescence Drag

Abstract: : A review has been undertaken of the available data on the subject of the drag of excrescences on aircraft surfaces. Information from this review has been summarized and presented in a way that is readily usable for prediction and design purposes. The basic characteristics of boundary layers are discussed and, where possible, the drag of excrescences is related to those characteristics. In particular, because the size of many types of surface imperfection is small in comparison with boundary layer thicknesses, the drag of such imperfections can be correlated in terms of the properties of inner regions of the boundary layer. Several previously published analyses of this type are highlighted and, where possible, extensions to other data sources or other types of excrescence are presented. The practical problems of applying these data in the varying velocity gradients existing on aircraft surfaces are treated and one section is devoted to the drag of auxiliary air inlet and exit openings. Gaps in existing data which offer opportunities for research effort are pointed out.

Modeling the geostrophic drag coefficient for AIDJEX

Abstract: A model of the planetary boundary layer flow over the Arctic pack ice was found to relate geostrophic flow determined from a large-scale pressure field to the surface stress vector. A summary of the model and some data comparison is presented.

Analytical Prediction of Vortex Lift

Abstract: General integral expressions are derived for the nonlinear lift and pitching moment of arbitrary wing planforms in subsonic flow The analysis uses the suction analogy and an assumed pressure distribution based on classical linear theory results The potential flow lift constant and certain wing geometric parameters are the only unknowns in the integral expressions Results of the analysis are compared with experimental data and other numerical methods for several representative wings, including ogee and double-delta planforms The present method is shown to be as accurate as other numerical schemes for predicting total lift, induced drag, and pitching moment b c c CL CD Cm CT Cs cc, ccd E2 Nomenclature = aspect ratio = wing span =chord = reference length = lift coefficient = drag coefficient = pitching moment coefficient = thrust coefficient = suction coefficient = section lift coefficient = section induced drag coefficient = section suction coefficient = pressure loading coefficient = drag = proportionality constant, Eq (32) = proportionality constant, Eq (53) = chordwise function, Eq (44) ff(rj) = span wise f unction, Eq (28) K = potential constant L =lift loading constant, Eq (5) S = suction force SR = reference area s = suction force per unit length T = leading edge thrust, Eq (7) T' = leading edge thrust per unit length V = freestream speed Wj = downwash velocity component, Eq (11) a = angle of attack F = vorticity p = freestream density £ = nondimensional chordwise coordinate 77 = nondimensional spanwise coordinate A = leading edge sweep angle Subscripts P = potential flow E =edge / = induced VLE = leading edge vortex VSE = side edge vortex

Motion of and mass transfer from an assemblage of solid spheres moving in a non-newtonian fluid at high reynolds numbers

Abstract: An approximate solution for the motion of an assemblage of solid spheres moving in a power-law fluid in the high Reynolds number region is obtained using a combination of Happel's free-surface cell model and the boundary layer theory. It is theoretically predicted that the drag coefficient will decrease with the increase of the shear-thinning anomaly. The results of the present analysis are in reasonably good agreement with the available experimental data for fixed and fluidized beds. The influence of the non-Newtonian behavior on the mass transfer rate from an assemblage of solid spheres is also discussed.

A study of the turbulent structure in a tidal flow

Abstract: Field measurements have shown that the unsteady phases of a tidal flow has a strong effect on the turbulent mechanism. Laboratory measurements were therefore undertaken to study this effect. The drag coefficient, roughness length, turbulent spectra of the horizontal and vertical velocity fluctuations together with their product were determined from the measured data. Frequency distribution of the bursting events and the contribution of these events to the Reynolds shear stress together with the duration of the events were evaluated by taking measurements at various heights above the bed during the accelerating and decelerating phases of the flow. The results were compared with those obtained from measurements carried out on the Great Ouse estuary and with those obtained by other workers.

Wind-Tunnel Measurements of Wing-Canard Interference and a Comparison with Various Theories

Abstract: Wind-tunnel tests and analyses of the aerodynamics of wing-canard combinations for low speed applications are presented. Systematic tests are conducted in a 7 x 10 wind tunnel to explore various combinations of wing-canard vertical and horizontal positioning. The goals of the tests are (1) to investigate potential improved stalling characteristics over conventional tail-aft configurations, (2) to investigate the existence of a lift coefficient advantage, and (3) to determine induced drag levels. The measurements obtained are compared with calculations made using the Prandtl-Munk theory, and with a vortex-lattice panel code. Results indicate that the panel code gives excellent results for lift and induced drag at moderate lift coefficient, whereas Prandtl-Munk theory gives conservative results for induced drag. The application is a light transport aircraft used for short-haul operations.

Design of low-drag axisymmetric shapes by the inverse method

Abstract: The inverse method ir applied to the design of a low-drag aerodynamics shape. The problem treated is an axisymmetric bardy generated by means of an axial distributiun of line sources and sinks. Recommended lowdrag shapes are examined to determine if modlCication uf Lhc external velocity will lead lo v reduced drag by body reshaping. It is found that the delay of transition un a particular known body shape can bc achieved. This results in an improved body shape with lower drag coefficient and better transition charactfristlcs at s volume Reynolds number of 5 x 10'. This study demonstrates the importance of the inverse rnelhud in determining luwdrag shapes.

The applicability of the Gibbs equation for grain settling velocities to conditions other than quartz grains in water

Abstract: Gibbs et al. (1971) have derived empirical equations that yield settling velocities in water for spherical grains of approximately quartz density. The present investigation examines the applicability of their relationships to other grain densities, fluids, and to gravity fields other than Earth's. The comparison is with "data" generated from a standard drag coefficient versus Reynolds number curve that is applicable to the settling of spheres in any Newtonian fluid. This comparison shows that the Gibbs et al. relationships cannot be used for gravity fields other than Earth's or for fluids other than water, in each case the errors being extreme. Their relationships do yield good results over the range of grain densities represented by the common heavy minerals settling in water. As the density progressively departs from that of quartz, the amount of error increases, reaching 8.5 percent for densities as high as magnetite. A correction factor is introduced which is a function of grain density, the use of which greatly improves the estimated settling velocities of the common heavy minerals and of low-density materials such as foraminifera shells.

Characteristics of Circular Cylinders in Turbulent Flows

Abstract: The effect of a free-stream turbulence of high intensity on the flow past a rigid circular cylinder was experimentally studied in a Reynolds-number range 7.9×103∼5.4×l04. Square-meshed grids were used to produce homogeneous turbulent-flow fields. The intensity and scale of a turbulent flow in which the cylinder was immersed were varied by positioning the cylinder at various locations downstream of the grid. Measurements were made of the time-averaged drag coefficient, Strouhal number of the vortex shedding, spanwise correlation length and length of the vortex formation region in the wake of the cylinder. These properties of flow around the cylinder were found to be considerably different from those measured in a smooth flow.

MC DRAG - A Computer Program for Estimating the Drag Coefficients of Projectiles

Abstract: : This report presents a FORTRAN program 'MC DRAG' for estimating a projectile's zero-yaw drag coefficient from the given values of certain size and shape parameters. The results are valid over a Mach number range of 0.5 to 5 and a projectile diameter range of 4 to 400 millimetres. A user's guide and a FORTRAN listing of MC DRAG is provided. The program is applied to three illustrative examples: (1) an experimental low-drag small arms bullet, the 5. 56mm BRL-1 design; (2) a 55mm scale model of the Minuteman re-entry stage vehicle; (3) the 155mm long-range artillery shell M549. The MC DRAG program estimates drag coefficient to within 3% error at supersonic speeds, 11% error at transonic speeds, and 6% error at subsonic speeds.

Theory of the Motion of an Artificial Earth Satellite

Abstract: An improved analytical solution is obtained for the motion of an artificial Earth satellite under the combined influences of gravity and atmospheric drag. The gravitational model includes zonal harmonics throughJ 4, and the atmospheric model assumes a nonrotating spherical power density function. The differential equations are developed through second order under the assumption that the second zonal harmonic and the drag coefficient are both first-order terms, while the remaining zonal harmonics are of second order. Canonical transformations and the method of averaging are used to obtain transformations of variables which significantly simplify the transformed differential equations. A solution for these transformed equations is found; and this solution, in conjunction with the transformations cited above, gives equations for computing the six osculating orbital elements which describe the orbital motion of the satellite. The solution is valid for all eccentricities greater than 0 and less than 0.1 and all inclinations not near 0o or the critical inclination. Approximately ninety percent of the satellites currently in orbit satisfy all these restrictions.

Wave slam on a sphere penetrating a free surface

Abstract: The problem of vertical motion of a sphere across an oscillating free surface is analysed by assuming the fluid to be inviscid and the free surface to be an equipotential surface. New analytical solutions for the added-mass coefficients of a double spherical bowl are derived. These are used in the derivation of the drag coefficient of a sphere during vertical entry and of the slamming coefficient of a fixed sphere which is exposed to wave action. An additional important parameter in hydroballistics is the wetting factor of a sphere penetrating a free surface for which a new analytic solution is also derived in this paper. A comparison between some experimental data and the analytic expressions for the slamming coefficient and the wetting factor, shows good agreement between theory and measurements.

On critical roughness Reynolds numbers of the atmospheric surface layer

Abstract: Detailed features of drag coefficient (C10) varying with wind velocity (U10) are used to determine critical values of roughness Reynolds number (Re). Boundary-layer regimes of the atmospheric surface layer are identified as aerodynamically smooth, Re 2 (U10>7 m s−1). Features of C10 varying with Re and determination of critical values of Re are also substantiated.

Optimum tail shapes for bodies of revolution

Abstract: This paper has n dual purpose: to describe a method of designifig short tails for bodies 01 revolution that sutisfy Stratford's criterion for zero shear at the wall, and to show n few shapes that have been calculated. Stratford's original two-dimensional solution, extended to axisymmetric flow, has been used to implement the prucedure. The method involves simultrmneous solution of the extended Stcatford equation together with the necessary boundary conditions by means of an inverse potential flow program. Tails designed by this procedure are entirely at incipient separmtion (no skin friction); therefore the pressure recovery Is the most rapid possible, making the resultant tail the shortest possible, subject to no separation. The Final result Is a geometry uniquely determined for freestream conditions, the transition point, and of course the basic forebody. The computer program can operate in one of two modes: 1) the forebody geometry can be malntained (except for a small region near the tall juncture) with only the tail shape determined by the method or 2) the forebudy ve1ocity distribution can he malntalned up to the paint of pressure recovery. The forebody geometry wlll then be altered for some distance upstream of the tail juncture. A number of solutions are presented for both of the above modes. Nomenclature A = reference area CIIYOj =drag coefficient based on (vol~me)~ C,,* =drag coefficient based on frontal area C, =pressure coefficient, C, = I - u2 /u&C, = Stratford type pressure coefficient C, = 1 - u2 /ud, I = reference length L = length representative of the length of the body r =radius of body at any point t?, = Reynolds number, U,S/U s =distance along body surface, see Fig. I u =velocity along body outside the boundary layer u, =freestreamvelocity SIA bscripts