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Showing papers on "Drag coefficient published in 1979"


Journal ArticleDOI
TL;DR: In this article, the relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model, and satisfactory agreements were obtained at wide ranges of the particle concentration and Reynolds number.
Abstract: Drag coefficient and relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model. The results are compared with a number of experimental data, and satisfactory agreements are obtained at wide ranges of the particle concentration and Reynolds number. Characteristics differences between fluid particle systems and solid particle systems at higher Reynolds numbers or at higher concentration regimes were successfully predicted by the model. Results showed that the drag law in various dispersed two-phase flows could be put on a general and unified base by the present method.

1,685 citations


Journal ArticleDOI
TL;DR: In this paper, it was found that if the drag coefficient and Reynolds number are defined empirically in terms of the arithmetic mean particle diameter, the effects of shape and rotation can be fully accounted for by defining a shape parameter, F, for each particle.

221 citations


01 Dec 1979
TL;DR: In this paper, it was shown that the distribution of lift which causes the least drag is reduced to the solution of the problem for systems of airfoils which are situated in a plane perpendicular to the direction of flight.
Abstract: Equations are derived to demonstrate which distribution of lifting elements result in a minimum amount of aerodynamic drag. The lifting elements were arranged (1) in one line, (2) parallel lying in a transverse plane, and (3) in any direction in a transverse plane. It was shown that the distribution of lift which causes the least drag is reduced to the solution of the problem for systems of airfoils which are situated in a plane perpendicular to the direction of flight.

183 citations


Journal ArticleDOI
TL;DR: In this article, the bottom boundary layer of a tidal current is measured in terms of the Reynolds stress tensor components, and it is shown that the structure of the boundary layer is similar to its atmospheric counterpart, but there is less evidence to suggest that it is structurally similar.
Abstract: Summary. Measurements of turbulence in the neutrally stratified bottom boundary layer of a tidal current are described. It is shown that whereas the bottom boundary layer is similar to its atmospheric counterpart, in terms of appropriately scaled spectra of the turbulent velocity fluctuations and the Reynolds stress, there is less evidence to suggest that it is structurally similar when measured in terms of the Reynolds stress tensor components. These differences appear to be more pronounced in deep flows where there is some evidence to suggest that the indices of structural similarity may vary over the tidal cycle; this behaviour may be due in part to the presence of inactive motions in the boundary layer. The statistical properties of the turbulence are described and in particular the high sampling variability of the Reynolds stress is shown to be associated with intermittently large momentum fluxes occurring in the boundary layer. The use of an intermittency factor in determining the burst period is also discussed. Suspended sediment is shown to have no effect on the turbulent structure of this example of a boundary layer. Estimates of the drag coefficient for a range of sediment types and bed forms have been obtained and finally it is shown that levelling errors are a major source of inaccuracy in boundary layer stress measurements.

162 citations


01 Dec 1979
TL;DR: In this paper, the authors developed constitutive relations for the drag force for bubbly, droplet, and particulate flows by a unified method and introduced simple drag-similarity criteria and a mixture-viscosity model.
Abstract: The ability to predict the interfacial drag between phases is of considerable importance for analyzing a dispersed two-phase system undertransient conditions. The present report develops constitutive relations for the drag force for bubbly, droplet, and particulate flows by a unified method. Simple drag-similarity criteria and a mixture-viscosity model are introduced in the analysis. The present drag correlations cover all concentration ranges and wide Reynolds-number ranges, from the Stokes regime up to the Newton's regime or the churn-turbulent-flow regime.

143 citations


Journal ArticleDOI
TL;DR: Combining boundary layer theory and experimental data for the pressure distribution and boundary layer thickness over the surface of a sphere, the following expression was obtained for the drag coefficient: C D = 1+ 9.06 R e 1 2 2 Using this formula as a basis, an expression was developed for relating the settling velocity of spherical particles to their diameter at any value of the Reynolds Number as mentioned in this paper.

119 citations


Journal ArticleDOI
TL;DR: In this paper, a theoretical study was conducted to investigate the effects of large temperature differences on the rate of pure heat transfer from a very hot gas to stationary spheres using finite difference techniques.
Abstract: A theoretical study has been conducted to investigate the effects of large temperature differences on the rate of pure heat transfer from a very hot gas to stationary spheres. In the numerical analysis, the momentum and energy equations for variable property flow past a sphere were solved simultaneously, using finite difference techniques. Results were obtained for Reynolds numbers up to 50 and surface temperature to gas temperature ratios varying between 0.25 and unity. These ranges cover most of the conditions commonly encountered in heterogeneous plasmas, transferred arc, and other high temperature chemical engineering processes. The flow behavior, drag coefficients, and Nusselt number were calculated for each case. The constant property solutions were in excellent agreement with numerical and experimental results reported in the literature, thus justifying the validity of the model and of the underlying assumptions. In general, the effect of variable properties was to drastically increase the flow velocity, vorticity, and temperature and vorticity gradients near the surface. A generalized heat transfer correlation was derived which, in addition to constant property conditions, included the effect of large variations in the physical properties of the fluid as a result of large temperature differences.

83 citations


Journal ArticleDOI
TL;DR: In this article, the drag and heat-transfer characteristics of longitudinally ribbed surfaces have been examined for the case of a turbulent boundary layer, where the purpose of the longitudinal fins is to confine the turbulent bursts to regions of small transverse extent, thus altering the local turbulence production.
Abstract: THE drag and heat-transfer characteristics of longitudinally ribbed surfaces have been examined for the case of a turbulent boundary layer. The purpose of the longitudinal fins is to confine the turbulent bursts to regions of small transverse extent, thus altering the local turbulence production. Rectangular, triangular, and razor blade rib geometries were examined. There was some indication that small drag reductions (< 4%) were obtained with two of the triangular grooved models, but further testing, consisting of detailed pitot and hot-wire surveys, is required for validation. The heat-transfer results indicated that several of the triangular grooved surfaces had heat-transfer increases 10% greater than the corresponding drag increases. These surfaces are unique in that heat-transfer augmentation results previously reported in the literature for airflows over external surfaces have always shown greater increases in drag than heat transfer.

65 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that by cooling laminar boundary layers in air at subsonic and low supersonic speeds, they are more stable than adiabatic boundary layers and therefore more resistant to transition to turbulent flow.
Abstract: Drag reductions are possible for cryo-fueled aircraft by using fuel to cool selected aerodynamic surfaces on its way to the engines. This is because cooled laminar boundary layers in air at subsonic and low supersonic speeds are more stable than adiabatic boundary layers and therefore more resistant to transition to turbulent flow. Calculations for A/=0.85 hydrogen-fueled transport show that drag reductions in cruise of about 20% are within reason. The weight of the fuel saved is well in excess of the weight of the required cooling system. These results suggest that the hydrogen fueled aircraft employing surface cooling is quite attractive as an energy conservative aircraft and warrants more detailed study.

48 citations



Journal ArticleDOI
TL;DR: In this article, a numerical method for calculating transonic flow past an aerofoil with an allowance for viscous effects, provided that the boundary layer remains fully attached over the aerodynamic surface.
Abstract: An account is given of a numerical method for calculating transonic flow past an aerofoil with an allowance for viscous effects, providing that the boundary layer remains fully attached over the aerofoil surface. The method has been developed by combining, in an iterative manner, calculations of the inviscid flow with calculations of the compressible boundary layer and wake. The solution for the inviscid flow is obtained by an iterative scheme, originally established by Garabedian & Korn, which has been modified to give a more realistic representation of shock waves. The boundary-layer development is treated as laminar initially; at a certain transition position a turbulent boundary layer is assumed to develop, and this is determined by the lag-entrainment method of Green et al. Comparisons of the results from the numerical scheme with some experimental measurements are shown for various examples in which shock waves of moderate strength are present. The method predicts, with reasonable accuracy, both the detailed pressure distribution and the variation of drag coefficient with lift coefficient.

Journal ArticleDOI
TL;DR: In this article, the Goodyear and Wave-Guard floating tire breakwaters from measurements on ⅛-scale and ¼-scale models using regular and irregular waves were generated.
Abstract: Wave-transmission and peak-mooring force design curves were generated for the Goodyear and Wave-Guard floating tire breakwaters from measurements on ⅛-scale and ¼-scale models using regular and irregular waves, and found to be in good agreement with available full-scale data. These curves may be used to determine the breakwater size needed to attenuate a given regular design wave to an acceptable level, and also to determine the maximum mooring load associated with this. A simple semi-empirical energy-dissipation model was developed and found to simulate measured wave-transmission characteristics with sufficient precision to be useful in many engineering applications; e.g., the ratio of transmitted to incident wave height is stated as an exponential function of wave steepness, ratio of wavelength to breakwater-beam-size, breakwater porosity, and a drag coefficient. An empirical relationship for the peak mooring force was obtained.

Journal ArticleDOI
Ronald B. Smith1
TL;DR: In this article, the two-dimensional flow of a stratified rotating fluid over a ridge is considered using the linear theory model of Queney (1947), and a general expression for the wave drag, or alternatively the vertical flux of angular momentum, is derived.
Abstract: The two-dimensional flow of a stratified rotating fluid over a ridge is considered using the linear theory model of Queney (1947). A general expression for the wave drag, or alternatively the vertical flux of angular momentum, is derived. As progressively wider mountains are considered, the wave drag decreases and the flow becomes more nearly geostrophic. With typical wind speeds, many mountain ranges, for example, the Alps, Andes and the Scandinavian mountains, have a drag between 0.1 and 0.9 of their f = 0 drag value and thus fall into the mesoscale category where the Coriolis force is important but not dominant.

Journal ArticleDOI
TL;DR: In this article, three different types of base cavities, one solid walled and two ventilated, each with six different depths ranging from 0.1 to 0.9 body diameters, were evaluated for axisymmetric bodies.
Abstract: Base cavities (hollow extensions mounted behind the rear end of a bluff body) are known to reduce substantially the aerodynamic drag of two-dimensional bodies. For axisymmetric bodies their effect is not well established, and the objective of this work was to assess their drag-reducing potential. Experiments were performed using three different types of base cavities, one solid walled and two ventilated, each with six different depths ranging from 0.1 to 0.9 body diameters. All three types of cavities reduced the body drag for small cavity depths, with a maximum drag coefficient reduction of 0.027 being obtained with a ventilated cavity 0.2 diameters deep. The reductions are an order of magnitude lower than those reported for two-dimensional bodies, but are achieved with a much shorter cavity depth. Although the ventilated cavities had a beneficial effect for small depths, at large depths (greater than 0.5 diameters) they had an opposite effect – a very large drag increase. The cause of this increase is as yet not understood. Hot-wire investigation revealed that base cavities suppress wake periodicity. For cavities of small depth this correlated with a reduction in drag, but for large cavity depths the trends of the intensity of the periodic motion and of drag were not always the same.

Journal ArticleDOI
TL;DR: In this article, a cemlation of the minimum qgglomerate size for bnakup was obtained in terms of the do of AI/AI2O3 surface tension and shear forces.
Abstract: Aluminized propdlrnts often p~uce large AI/AIP03 qglomentes which burn slowly compwd to rocket motor stay times. Two-phase llow velocity lags in the nozzle cause breakup of suffickntly Iargt aggIomentcs and thereby permit msonaMe combustion eftickacks to be achieved. High-spd photogmphs of the agglomerate pmxsses in a windowed rocket motor were used to obtain data on bmkup as a function of agglomerate size and two-phase flow vclocitics. The breakup process produces a cloud of much smaller droplets. A cemlation of the minimum qgglomerate size for bnakup was obtained in terms of the do of AI/AI2O3 surface tension and shear forces. Generally, agglomerotr: breakup occurs when the Weber number exceeds the range of 20 to 30. Nomenclature C,, = drag coefficient d,, = diameter of agglomerate, m F = drag force on agglomerate, N M = Mach number Red = Reynolds number based on diameter of agglomerate u = velocity, m/s We = Weber number p = density, kg/m rr = surface tension, N/m Subscripts performance compared with the theoretical would occur. Studies of the overall combustion efficiency of aluminized propellants burning in rocket motors reveal the performance losses due to incomplete combustion of aluminum and particle lag. It has been hypothesized that the two-phase flow processes in the nozzle produce breakup of sufficiently large agglomerates and thereby permit reasonable combustion efficiencies to be achieved. However, until now, direct observations of agglomerate breakup dnder rocket motor nozzle flow conditions did ,- ot exist.


Journal ArticleDOI
TL;DR: In this paper, the authors found that the turbulent drag reduction produced by injection of polymer at the centerline of a pipe flow was increased with streamwise distance from the injection point, due to radial dispersion of the injected polymer.
Abstract: Turbulent drag reduction produced by injection of polymer at the centerline of a pipe flow was found to increase with streamwise distance from the injection point. This was due to radial dispersion of the injected polymer. A tentative relationship between the two is proposed.

Journal ArticleDOI
TL;DR: In this article, an analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M ∞ ≤ 2·0 and Re∞d up to 107.
Abstract: Our analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M ∞ ≤ 2·0 and Re∞d up to 107. Bashforth’s chronographic measurements (1868) are of a quality comparable to modern measurements. The data of Mayevski (chronograph, 1868), Hutton (ballistic pendulum, 1787-1791), and Didion (ballistic pendulum, 1839-1840) are of lesser accuracy but in agreement with Bashforth’s. These cannon data are combined with modern data to provide the most extensive curves available of CD vs. Re∞d in this region. Interesting features of these curves for M ∞ ≤ 1·0 are briefly described.



Journal ArticleDOI
TL;DR: In this paper, the drag coefficients of smooth solid particles moving singly through still air at Reynolds numbers in the range of 103 to 104 were measured and the effects of non-steady velocity and particle form were determined.
Abstract: Measurements were made of the drag coefficients of smooth solid particles moving singly through still air at Reynolds numbers in the range of 103 to 104. Spheres were observed during acceleration, deceleration and at terminal velocity. Discs were tested during acceleration and at steady velocity. Other particles in the shapes of discs, circular cylinders and rectangular parallelepipeds were tested at steady velocity in their preferred and, in some cases, non-preferred orientations. The effects of non-steady velocity and of particle form were determined. An unexpected influence of particle density was observed for some of the particles.

Book ChapterDOI
01 Jan 1979
TL;DR: In this paper, the parameters relating to the interaction of particles and gas in a dispersed phase flow are presented, and these parameters are essential to the development of numerical and analytic submodels of pulverized coal combustion.
Abstract: The parameters relating to the interaction of particles and gas in a dispersed-phase flow are presented in this chapter. These parameters are essential to the development of numerical and analytic submodels of pulverized-coal combustion.

Journal ArticleDOI
TL;DR: In this article, the spatial and energy distributions of 7000 m/s helium atoms scattered from a 6061-T6 aluminum plate and an anodized 1235-0 aluminum surface were used to predict the atmospheric-helium contribution to the drag of a satellite having a predominantly convex exterior.
Abstract: The primary objectives of this study were to obtain the necessary data and develop a calculation procedure that would facilitate predicting the atmospheric-helium contribution to the drag of a satellite having a predominantly convex exterior Molecular-beam techniques were used to measure, for several incidence angles, the spatial and energy distributions of 7000 m/s helium atoms scattered from a 6061-T6 aluminum plate and an anodized 1235-0 aluminum surface From these measured distributions, tangential and normal momentum accommodation coefficients were calculated as functions of incidence angle Using these calculated accommodation coefficients, one can predict drag coefficients for satellites having predominantly convex exteriors For spherical satellites, drag coefficients of 264 and 262 were predicted for the subject surfaces

Journal ArticleDOI
TL;DR: In this article, a numerical solution of the barotropic vorticity equation in which the effects of Ekman boundary layers have been retained was examined by the flow of barotropic fluid over an isolated hill in a rapidly rotating system.
Abstract: The flow of barotropic fluid over an isolated hill in a rapidly rotating system is examined by the numerical solution of the barotropic vorticity equation in which the effects of Ekman boundary layers have been retained. The force due to pressure variations across the hill, which can be decomposed into components at right angles to the incident flow (the “lift” force) and parallel to the incident flow (the “drag” force), is typically of the order 2ρΩUV (ρ being the density of the fluid, Ω the angular velocity of the system, U the incident flow velocity and V the volume of the hill). In the steady state, the drag force is generally small compared to the lift force, but in the early transient stages of the evolution of the flow, the drag force may be as large as 2ρΩUV. It is shown that when the hill is sufficiently high and the Ekman number sufficiently small, nonlinear effects in the vicinity of the hill can greatly prolong this period of transient behaviour. This effect may be important in a numb...

DOI
01 Aug 1979
TL;DR: In this article, two systems for remote measurements of the air-sea fluxes of momentum, sensible heat and moisture during moderate to strong winds are described, one employs the dissipation method and the other the Reynolds flux or eddy correlation method.
Abstract: : Two systems for remote measurements of the air-sea fluxes of momentum, sensible heat and moisture during moderate to strong winds are described. One employs the dissipation method and the other the Reynolds flux or eddy correlation method. A modified Gill propeller-vane anemometer is the velocity sensor and a method of resolving the vertical velocity component, that accounts for the propeller's non-cosine behavior and avoids its non-linear operating region, is derived. The dynamic responses of the sensors are found from measurements in the actual turbulent conditions of the flux measurements. The results of an experiment on the Bedford tower, a stable platform moored in 59m of water 10 km offshore, are presented. Spectra, cospectra, turbulence statistics and transfer coefficients are calculated from the Reynolds flux velocity and temperature data and found to be comparable to previously reported values. Simultaneous dissipation and Reynolds flux estimates of both the momentum and sensible heat fluxes in up to 20 m/s winds are shown to be in excellent agreement. Also presented are the results of a second experiment where the systems were deployed on the weathership CCGS Quadra. A comparison of ship and tower drag coefficients from the dissipation system, demonstrates that the Bedford tower is essentially an open ocean site.

Journal ArticleDOI
TL;DR: In this article, long hair-like fibres were injected at the boundary and centreline of a turbulent pipe flow of water and polymeric solution, and pressure drop and mean velocity profiles were measured at various Reynolds numbers and injection rates.

Journal ArticleDOI
TL;DR: In this article, the hydrodynamic drag on a molecule moving in a viscous fluid is described by an intermolecular potential energy, rather than by imposing boundary conditions on a sharply defined surface.
Abstract: We present some calculations of the hydrodynamic drag on a molecule moving in a viscous fluid. The interaction of the molecule with the fluid is described by an intermolecular potential energy, rather than by imposing boundary conditions on a sharply defined surface. Our procedure requires solution of the Navier–Stokes equations for slow stationary flow of a viscous compressible fluid past a fixed force field. This is done here for two very simple models for the intermolecular potential: a ramp potential and a step potential. The results show that it is possible to calculate a drag force without imposing boundary conditions on a surface.

Journal ArticleDOI
TL;DR: In this article, an analytical investigation into the nature of particle trajectories in cascades of airfoils has been carried out in order to predict the location, velocity, and angle of particle impact on the turbines of turbines.
Abstract: An analytical investigation into the nature of particle trajectories in cascades of airfoils has been carried out in order to predict the location, velocity, and angle of particle impact on the airfoils of turbines. As a result of this analysis it has been shown that for any given inviscid flow, particle trajectories are uniquely determined by the specification of only two dimensionless parameters, the most important of which is the Stokes number. In addition, computed results have indicated that particle trajectories are virtually invariant with cascade Mach number. Finally, a comparison of analytically and experimentally determined trajectories for the flow around the circular leading edge of a blunt body has shown excellent agreement over a wide range of Stokes number.

Journal ArticleDOI
TL;DR: In this article, a critical comparison has been made between the drag characteristics of a number of the best available axisymmetric body shapes using a numerical drag calculation scheme, assuming a turbulent boundary layer over most of the body surface at Rv = 10.
Abstract: A critical comparison has been made between the drag characteristics of a number of the best available axisymmetric body shapes using a numerical drag calculation scheme. Assuming a turbulent boundary layer over most of the body surface at Rv = 10 , the study shows that all profiles have almost equal drag coefficients when referenced to the two-third power of the body volume. However, based on the projected area, several laminar bodies were found to have substantially lower drag coefficients. Transition studies indicate that a short run of laminar boundary-layer flow, XIL to about 0.2, may be expected by moving the maximum thickness forward and carefully designing the nose shape through the inverse method. At Rv = 5 x 10, all bodies, with the exception of the Shark and F-57, have the same transition and drag characteristics. The study also shows that the F-57 shape has a much higher transition risk than the Shark in the range 0 . 0 8 < X / L < 0 . 1 3 . Otherwise, the F-57 shape has better performance. Increasing the flow acceleration in this range is expected to eliminate the transition possibility and the superiority of the F-57 profile becomes undisputed.

Journal ArticleDOI
TL;DR: The use of the Reynolds number as the only correlating factor for drag force measurements may be inadequate in circumstances involving highly turbulent flows as mentioned in this paper, and the results of previous investigations relating to the effects of turbulence scale and intensity are examined