Showing papers on "Drag coefficient published in 1973"

Drag reduction in turbulent flow by polymer additives

Abstract: A brief survey is given of the drag reduction phenomenon, emphasizing the aspects which must be explained by any theory: onset, the existence of intrinsic drag reduction, the Newtonian plug, saturation with increasing concentration, and the maximum drag reduction asymptote. In addition, the polymer properties observed to be favorable are noted. Experimental and theoretical arguments are cited, indicating that sublayer stability arguments are not relevant. Recent evidence is given, linking the onset phenom-enon to a molecular time scale. The behavior of isolated molecules in flow fields is briefly surveyed, indicating the possibility of large increases in viscosity in relatively rotation free strain rate fields; indirect experimental evidence for such behavior is cited, and it is shown how, by reducing the intensity of the smallest eddies, this can explain the various aspects noted. The maximum drag reduction asymptote is discussed, in connection with recent measurements of turbulent fluctuations in drag reducing flows, and it is shown how both of these may be related to changes in the large eddy structure caused by the polymer induced changes in the small eddies.

Drag due to regular arrays of roughness elements of varying geometry

Abstract: Comparisons are made of experimental studies on the drag, at high Reynolds number, due to regular arrays of roughness elements of various shapes immersed in a turbulent boundary layer. Using a variant of Millikan's dimensional analysis, the form of the velocity profile is deduced in terms of the dimensions and concentration of the roughness elements. A drag formula results which is shown to be in good agreement with data. Available measurements of the partition of drag between the elements and the intervening surface indicates that equipartition occurs at quite low concentrations. The interaction between elements is then small, so that the drag coefficient of a typical roughness element is nearly constant. A re-examination of some of O'Loughlin's velocity-profile data, obtained below the tops of the roughness elements, suggests the existence of a nearly constant-stress layer scaled to the shear stress of the intervening surface. Above the roughness elements, the mean-velocity profile undergoes a transition to the form appropriate to the total shear stress exerted by the roughened surface. A formula is given which describes the one-dimensional velocity profile over the entire range, excluding the viscous sublayer on the intervening surface. The viscous sublayer appears to correspond quite closely to that on a smooth plate.

Drag reduction of a submersible hull by electrolysis

Abstract: Viscous drag reduction of a fully-submerged body of revolution is obtained by creating hydrogen gas on the hull by electrolysis. The bubbles alter both the laminar and turbulent boundary-layer characteristics resulting in a significant reduction in the viscous drag on the 3-foot model up to a speed of 8.5 feet per second, the maximum test velocity. Results show that the amount of drag reduction depends on the ratio of the mass flow of water in the wake to the time-rate of hydrogen mass produced beneath the boundary-layer. The results presented herein are model results and should NOT be considered directly applicable to any existing prototype.

Motion of particles entrained in a plasma jet

Abstract: The motion of small particles (glass microspheres, 30 to 140 microns in diameter) entrained in a free argon plasma jet was studied by means of high-speed cine streak photography. Radial temperature and velocity profiles as well as axial profiles of temperature, velocity, and argon concentration in the jet were experimentally determined by means of a plasma calorimetric probe. The system was found to be characterized by low relative Reynolds numbers (0.2 to 20) and extremely high deceleration rates (about –2,000 g). Under these conditions, an increase of drag coefficient over that predicted by the standard curve was experimentally observed. This increase was attributed to the nonsteady flow field around the particle (the so-called “history term” in the equation of motion). A general computer program has been proposed which predicts the particle velocity, acceleration and temperature along its trajectory.

Contribution of form drag on pressure ridges to the air stress on Arctic ice

Abstract: Various methods of measuring air stress on the arctic ice surface are discussed; however, none of them could possibly take into account the form drag due to pressure ridges. An expression is derived for the form drag per unit area in terms of certain key parameters of ridge statistics and a suitable drag coefficient. By using the available field and laboratory measurements of these parameters an estimate is made of the ratio of the form drag to the frictional stress. It depends on the geographical location in the Arctic, the season of the year, and the meteorological conditions in the atmospheric surface layer. It is found, contrary to the common assumption, that the form drag on pressure ridges may be much larger than the frictional stress on the ice surface, especially under stably stratified conditions.

On bubbles with small immobile adsorbed films rising in liquids at low Reynolds numbers

Abstract: Surface-active impurities may collect as a stationary film on the lowest part of a bubble rising in liquid while the remainder of the surface moves freely. Numerical approximations for the motion are available if the Reynolds number is low, but they fail for small films. We give the steady-state asymptotic solution for that case, and obtain the perturbation of the drag coefficient from its value for a completely free surface. It depends on the amount by which the surface tension is reduced at the rear stagnation point. This reduction has usually been taken to be the maximum possible for the particular impurity; we consider also the case where dilution is so great that that maximum cannot be reached because the impurity would then be diffusing off the surface at the rear faster than onto it elsewhere.

Wind stress on Arctic sea ice

Abstract: Wind velocity fluctuations have been recorded with a sonic anemometer over sea ice at a number of locations in the Arctic Ocean and in Robeson Channel and used to compute surface stresses and drag coefficients. The wind drag coefficient is found to correlate well with the rms elevation of the ice and snow surface at wavelengths shorter than 13 meters. A formula for the estimation of drag coefficients from surface profiles is given. The form drag of ridges can be of similar magnitude to the measured surface drag and should be allowed for. Gust factors are examined. Spectra and other turbulence parameters are found to be in agreement with other boundary layer turbulence measurements over ice, water, and land.

Low-Reynolds-number fall of slender cylinders near boundaries

Abstract: The motion of bodies through fluid at low Reynolds number is appreciably affected by the container walls. Consequently the Stokes-flow theory due to Batchelor (1970) and others for a slender body falling in an unbounded fluid is difficult to test experimentally unless it is extended to take account of nearby boundaries. Theoretical expressions are given here for certain drag coefficients of a circular cylindrical slender rod of finite length falling close to a single plane wall or falling midway between two parallel plane walls. Experiments with a very viscous liquid are described in which cylinders of small thickness-to-length ratios (ranging from 1:10 to 1:100 approximately) are made to fall in suitable orientations. From their times of fall over a measured distance experimental drag coefficients are determined and compared with the corresponding theoretical value from the extension of Batchelor's theory. For rods falling in a horizontal orientation the theoretical and experimental results are consistent within the order of accuracy of the experiments. However, when results are compared for rods falling in a vertical orientation there is a significant difference for which possible explanations are presented.

Bubble‐free expansion of gas‐fluidized beds of fine particles

Abstract: Five different fine powders with average particle size of about 100 microns or smaller were fluidized with air over their respective bubblefree ranges of fluidization. Photographs taken through the front transparent wall of the column showed that the beds contained cavities and microchannels whose sizes were of the same order of magnitude as the particle size. It is shown that interparticle van der Waals adn capillary forces play an important role in the bubble-free expansion of small particles. Measurements of bed expansion and average particle drag coefficients are consistent with the proposed role of interparticle forces.

Geostrophic drag coefficients

Abstract: Data on the relationship of the surface wind to the geostrophic wind at Porton Down, Salisbury Plain, are presented for various stability conditions and analysed in the light of the Rossbynumber similarity theory. For near-neutral conditions, the geostrophic drag coefficients for geostrophic wind speeds 5 to 15 m s-1 are close to those found by other workers but at higher speeds the values are low. Comparisons of geostrophic and radar wind speeds for ⋍900-m height, suggest that undetectably small mean cyclonic curvatures of the trajectories of the air are responsible for this departure.

Wall Drag on Free-Moving Ciliated Micro-Organisms

Abstract: It is generally assumed that wall drag on free-moving, self-propelled or passively moving micro-organisms is not significant under normal observation conditions. Yet the point at which such drag becomes significant has not been determined quantitatively. By comparing the relative velocities of sinking as well as swimming ciliates in tubes of various bore widths it has been determined that wall drag on sinking cells is about 8% significant at 108-132 body radii (or minor semi-axes) from the cell surface while the corresponding range for swimming cells is less than 1-4·2 body radii. These results are compared with the mathematical approximations for Stokes radius R_8 and depth of penetration of diffusing vorticity δ which characterize steady and quasi-steady Stokes flow respectively around a solid body. It is found that the asymptotic nature of the velocity profile of steady flow is reflected in the lack of agreement between R_8 and the measured distance for 8% drag. Conversely, the sharp gradient (or propulsive envelope) of the quasi-steady velocity profile is reflected in the substantial agreement between δ and the measured distance for > 0% drag. It is suggested that the given formula for δ which includes allowance for a propagated wave is a valid measure of the thickness of the quasi-steady region and that observations on motile ciliates be restricted to organisms at least 4 cell radii from the nearest wall if measurements free of wall-drag effects are to be obtained.

Measurements of the Drag of Some Characteristic Aircraft Excrescences Immersed in Turbulent Boundary Layers

Abstract: : Measurements are described of the drag of various forms of excrescence mounted on balances installed in the walls of the working section of the RAE 8 ft x 8 ft wind tunnel. The tests cover a range of Mach numbers between 0.2 and 2.8 (but not transonic) and a range of Reynolds number. The excrescences tested include two-dimensional steps and ridges, circular cylinders and wings mounted normal to the surface, and holes and fairings. It is shown, for excrescences which are of height small compared with the boundary-layer thickness, that the scale effects on drag are well correlated in terms of the wall variables of the turbulent boundary layer, but that there is a dependence of drag on Mach number. For steps and ridges the effect of chamfering or rounding the upper corners was found to be beneficial at subsonic speeds but far less so at supersonic speeds. For circular holes the drag depends strongly upon the depth to diameter ratio. In an Appendix the oil-flow patterns obtained for a range of depth of circular holes are shown. The fairings tested were either half-bodies of revolution with pointed or rounded ends or of square or rectangular section with pointed ends. The effects of different amounts of immersion of the bodies into the boundary layer were found in some cases by testing geometrically similar bodies of different sizes.

Development of the Viking Parachute Configuration by Wind-Tunnel Investigation

Abstract: Several experimental investigations to obtain the drag performance of 10% scale-model disk-gap-band-type parachute assemblies trailing in the Viking forebody wake were conducted over the range of Mach 0.2 to 2.6. The wind-tunnel tests varied both the canopy trailing distance and ratio of suspension line length to canopy diameter. The data obtained permitted optimization of both parameters. Parachute drag performance in the forebody wake is markedly degraded transonically beginning at Mach 0.6, reaching a minimum value at Mach 1.0, then approaches the subsonic value for the selected configuration as Mach number is increased to 1.4. Further increase in Mach number causes the drag coefficient to again decline. A 20% increase in parachute-alone transonic drag coefficient was obtained by increasing suspension-line length ratio from 1.16 to 1.73.

Towing a long cable at slow speeds: a three-dimensional dynamic model

Abstract: The gross (greater than 25 meters) three-dimensional motions of a cable towing a heavy instrument package at depths of 4 kilometers during complex maneuvers of the tow ship have been modeled using a computer program. Actual tracks of the towing vessel have been used as boundary conditions for the model, and the predicted paths for the instrument package have been compared with actual tracks of the instrument package as monitored by transponder navigation. Ship speeds during the maneuvers ranged from 0.5 to 1.5 m/sec while the length of the towing cable ranged from 4 to 6 km. Tangential drag as well as inertial forces were ignored in the model. The drag coefficient, CD, was considered to be unknown and was found by minimizing the root mean square discrepancy between observed and calculated positions of the instrument package. At the minimum rms error of 170 m, CD was 2.7, but because of the approximate nature of the simulation, this value may not reflect the actual drag coefficient for the cable. (Author)

Characterization of drag reduction and degradation effects in the turbulent pipe flow of dilute polymer solutions

Abstract: Turbulent drag reduction data were obtained at Re = 9000 in a 0.62-cm-I.D. pipe for five Polyox compounds covering a wide range of molecular weights. The concentration dependence of drag reduction was shown to obey an improved form of Virk's drag reduction equation, which was previously applied only to flows in capillary tubes. The efficiency of the drag-reducing polymer additives on a unit concentration basis at infinite dilution was determined by using a characteristic parameter, DRm/[c], for each compound. A linear relationship was found to exist between this parameter and polymer molecular weight. The polymer degradation data were analyzed through use of a variable related to the dissipated energy in the wall region. The polymer molecular weight was found to decrease as a hyperbolic function of the dissipated energy function. By examining the change of molecular weight with respect to this function, a degradation index characteristic of the entire Polyox polymer family was established. This index may be of general application and provide a method by which the shear stability of various species of drag-reducing polymers may be meaningfully compared.

Behavior of the mean wind, the drag coefficient, and the wave field in the open ocean

Abstract: Micrometeorological data obtained at ocean station Papa during May and June 1970 are analyzed to determine the variation of the stress, drag coefficient, and wave energy in relation to the synoptic weather system. Two periods associated with the passage of high wind speed disturbances are examined. The drag coefficient C10, determined by the dissipation technique, has an average value of (1.63 ± 0.28) × 10−3 for wind speeds up to 17 m sec−1 and is observed to have a possible dependence on spectral shape of the wave field. The development of the wave field during the two storms is discussed.

Motion of a turbulent buoyant thermal in a calm stably stratified atmosphere

Abstract: A simple model for the motion of a turbulent buoyant thermal in a calm, stably stratified atmosphere is proposed. Using this model, the average motion of the thermal can be described in terms of its initial density difference, velocity and effective radius, and the three nondimensional gross parameters: mass entrainment constant, effective drag coefficient, and turbulence dissipation rate. Relations between the local turbulence field and the three gross parameters are discussed. Also, the maximum height a thermal can reach in a stable atmosphere for various initial conditions and gross parameters can be approximated by a simple power law relation.

Density and composition of the lower thermosphere

Abstract: This paper presents a new median model of the lower thermosphere. It is based on a critical evaluation of all the measurements of density and composition in this region and carries forward the process of re-examination begun by von Zahn in this 1970 paper. Whereas von Zahn emphasized mass spectrometric measurements, the emphasis here is on results derived from observations of the drag force on satellites. In situ measurements of drag coefficient and accommodation coefficient are employed to evaluate the published values of density. In reviewing the compositional data, recent spectroscopic measurements and laboratory results on surface physics and chemistry are utilized. In the resulting model, the O/O2 ratio is 1.6 at 120 km. The O/N2 ratios are 0.69 at 150 km and 1.76 at 200 km, in the midst of recent measurements. The median density at 150 km is 1.83 μg/m³.

Aerodynamic Forces on a Triangular Cylinder

Abstract: Wind tunnel studies have been conducted on flow around an equilateral triangular cylinder mounted with the point upstream. Instantaneous pressure measurements taken around the cross section have enabled a simple picture to be drawn of the pressure perturbations due to the vortex shedding at the rear. Integration of the pressures produces a mean and fluctuating force and moment coefficients. Mean lift and moment coefficients are found to be zero as anticipated from symmetry. Fluctuating lift and moment coefficients occur at the frequency of shedding of a pair of vortices and vary with Reynolds number. The fluctuating drag coefficient is significantly smaller and occurs at double the frequency. Measurements made of the velocity field in the vortex street showed that the velocity and wave length of the street increased downstream and reached a steady state within 10 days.