Showing papers on "Drag coefficient published in 1976"

Drag Coefficients of Spheres in Continuum and Rarefied Flows

Abstract: A CCURATE representations of the drag coefficients of -^Vspheres over a wide range of flow conditions are a necessary prerequisite to the calculation of gas-particle flows. For greatest utility these representations should be in a form suitable for computer calculations. Two such correlations, both still used in computer programs, were published prior to the collection of a considerable body of experimental data, and, consequently are outdated. A third representation, published subsequently, requires the use of tabular data, and is inaccurate in some flow regimes of interest. This paper presents a new correlation, suitable for utilization in computer calculations, which simplifies in the limit to certain equations derived from theory, and which offers significantly improved agreement with the experimental data. The flow regimes of interest include continuum, slip, transition, and molecular flow at Mach numbers up to 6, and at Reynolds numbers up to the laminar-turbulent transition. The effect on drag of a temperature difference between the sphere and the gas is incorporated.

On Drag of Evaporating Liquid Droplets

Abstract: —Drag data of water, methanol, heptane and benzene droplets are reported here. This data together with the data of Eisenklam et al. cover the entire range of Reynolds numbers from 1 to 2000 and mass transfer numbers from 0 to 3. The present study shows that the drag coefficients as a function of Reynolds numbers correlate well with the “standard drag” curve provided the characteristic density is the free stream density and the characteristic viscosity coefficient is μ r (Tr ). The basis for the choice of these two characteristic properties is discussed. The present correlation is insensitive to the mass transfer number. This suggests that mass efflux has little effect on drag of evaporating droplets. Present study indicates that for the determination of the drag coefficient of any evaporative droplet at quasisteady state, one needs only to know the wet bulb temperature as a function of free stream temperature. This information is sufficient to calculate μ r (Tr ). The “standard drag” curve can th...

Golf Ball Aerodynamics

Abstract: A wind tunnel technique has been developed to measure the aerodynamic forces acting on golf balls over a wide range of Reynolds number and spin rate. Balls with round dimples and hexagonal dimples have been investigated. The dimples are found to induce a critical Reynolds number behaviour at a lower value of Reynolds number than that experienced by a smooth sphere and beyond this point, unlike the behaviour of a sand-roughened sphere, there is little dependence of the forces on further increases in Reynolds number. A hexagonally-dimpled ball has a higher lift coefficient and a slightly lower drag coefficient than a conventional round-dimpled ball. Trajectories are calculated using the aerodynamic data and the ranges are compared with data obtained from a driving machine on a golf course.

Aerodynamics, kinematics, and energetics of horizontal flapping flight in the long-eared bat Plecotus auritus

Abstract: The kinematics, aerodynamics, and energetics of Plecotus auritus in slow horizontal flight, 2–35 m s-1, are analysed. At this speed the inclination of the stroke path is ca. 58 degrees to the horizontal, the stroke angle ca. 91 degrees, and the stroke frequency ca. 11-9 Hz. A method, based on steady-state aerodynamic and momenthum theories, is derived to calculate the lift and drag coefficients as averaged over the whole wing the whole wing-stroke for horizontal flapping flight. This is a further development of Pennycuick's (1968) and Weis-Fogh's (1972) expressions for calculating the lift coefficient. The lift coefficient obtained varies between 1-4 and 1-6, the drag coefficient between 0-4 and 1-2, and the lift:drag ratio between 1-2 and 4-0. The corresponding, calculated, total specific mechanical power output of the wing muscles varies between 27-0 and 40-4 W kg-1 body mass. A maximum estimate of mechanical efficiency is 0–26. The aerodynamic efficiency varies between 0–07 and 0–10. The force coefficient, total mechanical power output, and mechanical and aerodynamic efficiencies are all plausible, demonstrating that the slow flapping flight of Plecotus is thus explicable by steady-state aerodynamics. The downstroke is the power stroke for the vertical upward forces and the upstroke for the horizontal forward forces.

Flow of inelastic and viscoelastic fluids past a sphere

Abstract: This is essentially an engineering study undertaken with a view to providing drag coefficient correlations for the motion of a solid sphere in inelastic and viscoelastic fluids over a wide range of Reynolds numbers. An approximate closed form analytical solution has been obtained for the motion of a solid sphere in powerlaw fluids and this solution has been verified experimentally. The high Reynolds number flow was analysed theoretically using boundary layer theory; the results were used to separate form and skin friction. Viscoelastic fluids showed “drag reduction” at high Reynolds number. About 300 experimental data points were used to obtain drag coefficient correlations over a wide range of material and flow parameters.

A theoretical study of body drag in subcritical axisymmetric flow.

Abstract: A method of predicting body drag in subcritical axisymmetric flow is outlined which requires only detailed body shape, free-stream conditions and transition point to be prescribed. Results of calculations for a range of body shapes are shown essentially to confirm information in Royal Aeronautical Society Data Sheets but clearly demonstrate that fineness ratio alone is not sufficient to characterise body shape. For example, at a fixed fineness ratio of 0.18, detailed changes in body contour are shown to produce 10 per cent changes in drag coefficient.

Intraplate stress as an indicator of plate tectonic driving forces

Abstract: To test driving force models for plate tectonics, the global intraplate stress fields predicted by various force systems are compared with the long-wavelength features of the observed stress field as determined by midplate earthquake mechanisms, in situ measurements, and stress-induced geologic structures. The calculated stresses are obtained by a finite difference solution to the equilibrium equations for thin elastic spherical shells in the membrane state of stress. Buoyancy forces at spreading centers and convergent plate boundaries and viscous drag at the base of the lithosphere are modeled as surface tractions applied to the shell. Drag is modeled as both a resistive and a driving force, and both symmetric and nonsymmetric forces at subduction zones are considered. The net driving push at spreading centers is found to be at least comparable in magnitude to other forces acting on the lithosphere and in particular is 0.7 to 1.5 times the net driving pull at convergence zones. Subducting lithosphere, which from seismic and thermal evidence has more potential energy available to drive plates than does a spreading center, thus converts relatively little of this energy to a net force acting on the surface plates. The drag coefficient at the base of the lithosphere may be greater by a factor of 3 to almost 10 beneath continents than beneath oceans without substantially affecting the fit between calculated and observed stress fields. Intraplate stresses calculated for models in which viscous drag at the base of the lithosphere acts in the direction of absolute plate velocity to drive plate motion are in much poorer agreement with observed stresses than are those calculated for models in which drag resists plate motions.

Drag on an axially symmetric body in the Stokes’ flow of micropolar fluid

Abstract: The Stokes’ flow problem is considered for micropolar fluids in which the obstacle has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. A general expression for the drag is derived by using the arguments involving an axisymmetric point force and application is illustrated for the flow past a sphere.

Aerodynamics of hovering flight in the long-eared bat Plecotus auritus

Abstract: Steady-state aerodynamic and momentum theories were used for calculations of the lift and drag coefficients of Plecotus auritus in hovering flight. The lift coefficient obtained varies between 3-1 and 6-4, and the drag coefficient between --5-0 and 10-5, for the possible assumptions regarding the effective angles of attack during the upstroke. This demonstrates that hovering flight in Plecotus auritus can not be explained by quasi-steady-state aerodynamics. Thus, non-steady-state aerodynamics must prevail.

Heat Transfer in Flows with Drag Reduction

Abstract: Publisher Summary The chapter reviews the models proposed to describe both momentum and heat transfer in flows with drag reduction and examine their limitations. A phenomenological model for calculating heat transfer in flows with drag reduction is presented. The model is based on a mean velocity closure that uses Van Driest's mixing length expression with a variable damping parameter and the classical Reynolds–Prandtl analogy between momentum and heat transfer. The model has been used to analyze the heat transfer in pipe flows both in the thermally established region and in the entrance region. The effect of the temperature-dependent fluid properties is also analyzed. Algorithms providing implicit relations between the heat transfer, the friction, the properties of the fluid and the flow, which do not include any empirical coefficients, are derived for each case.Drag reduction is due to the reduction of the turbulent exchange of momentum near the wall. This reduction is accompanied by a comparable reduction in the turbulent transfer of heat and mass. When the relative transfer by the vertical turbulent fluctuations in the wall region is reduced, features that characterize heat transfer in laminar flows are observed. It is well known that in laminar flows it is necessary to distinguish between the two modes of heat transfer, that the effect of the temperature dependent fluid properties is larger than in turbulent flows, and that the entrance region is longer, and that its length is Reynolds number dependent. Although the proposed model does not explain the physical mechanisms of the phenomenon of drag reduction, it provides a better understanding of the observed features, and a valuable tool for analyzing and predicting transport processes in flows with drag reduction.

Theoretical determination of the minimum drag of airfoils at supersonic speeds

Abstract: A method is reported for determining mathematically the combined disturbance field, and in certain cases the minimum drag, of wings at supersonic speeds. The simplest analytic example is provided by the wing of elliptic planform, which achieves its minimum drag when the lift is distributed uniformly over the surface. With a symmetrical distribution of thickness, the requirement of minimum drag for a given total volume is found to lead to profiles of constant curvature.

Relationships between velocity profiles and drag reduction in turbulent fiber suspension flow

Abstract: Analytical relationships between velocity profiles and flow resistance data are developed for suspensions of papermaking fibers in turbulent shear. The relationships apply to suspensions of synthetic fibers. The wall layer appears to be unaffected by the presence of fibers, and the cause of drag reduction can be attributed to the turbulent core region.

Measurements of Turbulence in the Irish Sea Benthic Boundary Layer

Abstract: A description is given of the instruments and techniques that have been developed to observe the turbulent structure and related hydrodynamic parameters (e.g., drag coefficient,roughness length, friction velocity) of the benthic boundary layer in the sea. This work has involved the use of vertically separated electromagnetic current meters mounted on a probe which was lowered to the sea bed from a vessel at the surface. The horizontal and vertical turbulent velocity fluctuations u and w, have been recorded simultaneously at two heights in the lower 2 m of the boundary layer together with velocity profile measurements be tween the surface and the sea bed. These observations are an extension of those of other workers in estuarine and coastal waters and have been made under more or less open sea conditions. Measurements have been made over a large area of the Irish Sea and in the Menai Strait, at depths of 10-60 m and maximum surface currents of the order of 1 ms-1.These have corresponded to a range of sediment types, which, in addition to their known distributions, have been observed from grab samples and with an underwater camera mounted on the probe. Time series of the turbulent velocity fluctuations have been ana lyzed using standard digital methods and for each record the spectra, cross-spectra, phase, and coherency of u and w have been computed. These data are being used to determine those scales of motion contributing to the Reynolds stress (-puw, wherep is the fluid density). The distributions of u, w, and uw have been examined in order to determine those mechanisms involved in the generation and transfer of turbulent energy and, in particular, the intermittent nature of the Reynolds stress.

Numerical Methods for Separated Flow Solutions around a Circular Cylinder

Abstract: Numerical solutions of the Navier-Stokes equations were obtained for separated flows around a circular cylinder at Reynolds numbers 40, 80, and 200. The flowfields were obtained by using three finite-difference techniques. The implicit scheme solved by matrix factorizations gave the best accuracy and used the least computer time. The flow pattern in the recirculating region of a circular cylinder begins to oscillate as the Reynolds number exceeds 40. The calculated drag coefficients, separation angles, and Strouhal numbers were compared with available experimental data. Computational inaccuracy resulting from numerical approximations needs to be identified before a complicated flow phenomenon can be realistically analyzed.

Numerical method to calculate the induced drag or optimum loading for arbitrary non-planar aircraft

Abstract: A simple unified numerical method applicable to non-planar subsonic aircraft has been developed for calculating either the induced drag for an arbitrary loading or the optimum aircraft loading which results in minimum induced drag. The method utilizes a vortex lattice representation of the aircraft lifting surfaces coupled with the classic equations and theorems for computing and minimizing induced drag. Correlation of results from the numerical method with non-planar solutions obtained from other more complex theories indicates very good agreement. Comparison of the induced-drag computations using the numerical method with experimental data for planar and non-planar configurations was also very good.

Recent Measurements of Wind Stress on Arctic Sea Ice

Abstract: Eddy flux measurements of wind stress on the arctic pack ice have been made in summer and winter in terrain ranging from fiat to hummocked. Parameterization by a drag coefficient dependent on a surface parameter is suggested. Reduced values of the drag coefficient were observed in highly stable stratification. The coefficient for sensible heat flux is lower than the drag coefficient. Wind drag on ice ridges has been measured by a pressure differential method.

Influence of particle drag coefficient on particle motion in high-speed flow with typical laser velocimeter applications

Abstract: The effect of using different particle drag coefficient C sub D equations for computing the velocity of seeded particles in high-speed gas flows was investigated. The C sub D equations investigated included the Stokes equation, a second incompressible equation valid for higher relative Reynolds numbers, and six equations that account for the effects of compressibility together with the effects of relative Reynolds numbers greater than one. The flows investigated were center-line nozzle flows, normal shocks, and oblique shocks for free-stream Mach numbers of 1.6 to 6 and stagnation pressures of 1 and 3.4 atmospheres. The net result was empirical C sub D equation based on the latest sphere C sub D data for the low relative Mach number and Reynolds number conditions that are encountered in supersonic flows.

Wind-Driven Flow of Water Influenced by a Canopy

Abstract: A time-dependent numerical model, which treats fully evolved wind-driven canopy flow as a coupled two-layer system, is developed. The interfacial stress is formulated in terms of a coupling coefficient and the flow differential. The resistance afforded by a vegetative canopy is parameterized in terms of a drag coefficient and dimensional properties of the canopy elements. With flow confined strictly to the canopy, the calming effect of the canopy is introduced through a sheltering coefficient. The canopy is modeled as a set of rigid uniform structures orientated normal to the flow and evenly distributed with specified density over the bottom. The algorithm is tested by simulating the steady-state water-surface profiles observed in a laboratory channel containing wire screen obstructions. The model is applied next to a wind-driven rectangular basin with simulated vegetation specified over half the bottom.

Analysis of the drag reducing regime of pulp suspension flow

Abstract: Under certain conditions of turbulent flow, values of friction loss for wood pulp fiber suspensions are lower than those for water at the same flow rate This phenomenon of drag reduction is discussed with reference to pipe flow, and results from an investigation of flow resistance and velocity profiles of turbulent fiber suspensions are reviewed Analytical expressions relating velocity profiles and flow resistance are derived and supported with experimental data These relationships can be used to predict flow resistance in piping systems Drag reduction also occurs when a rotating disk is immersed in a suspension of wood pulp fibers, and a method is proposed for predicting pipe friction loss and velocity profiles for fully developed turbulent flow in pipes from torque measurements obtained from a rotating disk The method has been applied successfully over a limited range of conditions

Airfoil Section Drag Reduction at Transonic Speeds by Numerical Optimization

Abstract: A practical procedure for the design of low drag, transonic airfoils is demonstrated. The procedure uses an optimization program, based on a gradient algorithm coupled with an aerodynamic analysis program, that solves the full, non-linear potential equation for transonic flow. The procedure is useful for the design of retrofit modifications for drag reduction of existing aircraft as well as for the design of low drag profiles for new aircraft. Results are presented for the modification of four different airfoils to decrease the drag at a given transonic Mach number.

Drag reduction in laminar flow

Abstract: WHEN certain long-chain polymers are added to water, the drag exerted by the solution on fixed boundaries is reduced1. Although this applies to both internal and external flows, evidence indicates that the effect occurs only in the turbulent regime, at least for steady flow. The work reported here deals with the forced oscillation of a liquid column contained within a semicircular manometer tube, and shows that the addition of a polymer produces a reduction in drag when the flow is laminar.

Sphere drag at transonic speeds and high Reynolds numbers

Abstract: M of sphere drag have been made in the AEDC aeroballistics range "G" over the Maeh number range 0.9 A/o, <1.4 at a Reynolds number of approximately 10. These values of sphere drag were found to be larger than the values derived from the experimental summary curves presented in Ref. 1. The change in sphere drag with Mach number near Mach 1, as well as with Reynolds number in excess of 10, is significant and care is required in establishing summary curves. On the basis of these more recent measurements and those contained in Refs. 2 and .3, the summary curves presented in Ref. 1 have been reevaluated. A plot of the revised values of sphere drag f or 5 x 10

Turbulent Boundary Layers on Rough Walls.

Abstract: : The influence of wall roughness on the alteration of the characteristics of the turbulent boundary layer to produce increased heat transfer and skin friction during re-entry is examined. Attention is restricted to roughness heights which are small compared with the boundary layer thickness. It is shown that rough wall transfer rates can be calculated almost as reliably as for smooth walls provided that the geometry of the roughness is known. In this regard it is pointed out that models of roughness effects for use in finite-difference boundary layer calculation procedures should be in the form of drag coefficients and sub-layer Stanton numbers to be applied as 'slip' values at a characteristic roughness height; use of mixing length models of turbulent transport with nonzero wall values is shown to have serious shortcomings. The effect of heat conduction through roughness elements is demonstrated and the implications with respect to the validity of existing sub-layer Stanton number correlations are discussed. A thorough review of the pertinent literature is included with the view towards making this report a self contained treatment of the subject.

Supercritical Flow Over Sills

Abstract: Experimental investigations have been carried out to study the supercritical flow over a square section sill for all flow situations, except the jump condition. The supercritical flow has been categorized into two distinct types depending upon the ratio of the sill height to upstream depth and the Froude number. This classification also corresponds to the splashing and nonsplashing conditions. The stagnation, wake, and reattachment pressures have been investigated. The flow conditions have been explored when the downstream face pressures and the bed pressures become negative. An almost constant drag coefficient value, obtained from the present experiments, substantiated the drag characteristics of bluff bodies in open channels.

Production and Dissipation of Energy in the Turbulent Flow of a Particle-Fluid Mixture, With Some Results on Drag Reduction

Abstract: The production and dissipation of energy in a two-phase model for particle-fluid turbulent flow is considered. For plane parallel mean flow use of several scaling arguments yields a balance between production and drag dissipation for the particles, and between production and viscous dissipation for the fluid. A simple particle motion model is used to obtain estimates of the drag dissipation. Energy balance considerations are made for situations where drag reduction by the addition of particles is observed. Significant drag reduction is found to occur for sufficiently large Reynolds number. Discussion of the extra effectiveness of polymers for drag reduction is given within the framework of energy balance.

Drag reducer for lift surface of aircraft

Abstract: One or more aerodynamic bodies of preselected shape and placement are employed on the lower surface of an aircraft wing or other aerodynamic lifting surface for the purpose of reducing its drag. These anti-drag bodies singly or collectively provide a reduction in the lower speed profile drag of the associated lifting surface, an increase in its lift at a given angle of attack, and an increase in its critical Mach number.