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Showing papers on "Drag coefficient published in 1977"


Journal ArticleDOI
TL;DR: In this article, the effects of wind stress and wind profiles over the ocean reported in the literature over the past 10 years are consistent with Charnock's (1955) relation between aerodynamic roughness length (z0) and friction velocity (u*), viz, z0= αu*2/g, with α= 0.41±0.0144 and g= 9.81 m s−2.
Abstract: Observations of wind stress and wind profiles over the ocean reported in the literature over the past 10 years are consistent with Charnock's (1955) relation between aerodynamic roughness length (z0) and friction velocity (u*), viz, z0= αu*2/g, with α= 0.0144 and g= 9.81 m s−2. They also imply a von Karman constant = 0.41±0.025. For practical purposes Charnock's relation may he closely approximated in the range 4&

930 citations


Journal ArticleDOI
TL;DR: In this paper, a critical analysis of available compliant wall data which indicated drag reduction under turbulent boundary layers is presented, and detailed structural dynamic calculations suggest that the surfaces responded in a resonant, rather than compliant, manner.
Abstract: A critical analysis of available compliant wall data which indicated drag reduction under turbulent boundary layers is presented. Detailed structural dynamic calculations suggest that the surfaces responded in a resonant, rather than a compliant, manner. Alternate explanations are given for drag reductions observed in two classes of experiments: (1) flexible pipe flows and (2) water−backed membranes in air. Analysis indicates that the wall motion for the remaining data is typified by short wavelengths in agreement with the requirements of a possible compliant wall drag reduction mechanism recently suggested by Langley.

166 citations


Journal ArticleDOI
TL;DR: In this article, the basic dynamics of turbulent boundary layers of several media is described qualitatively: suspensions of several types and polymer solutions, and experimental evidence of this expansion is presented, and compared with calculations.
Abstract: The basic dynamics of turbulent boundary layers of several media is described qualitatively: suspensions of several types and polymer solutions. Despite the considerable differences in these media, it is argued that a number of the flows are affected only in the buffer layer, and drag reduction can result if behavior in the sublayer and buffer layer differ. In polymer solutions, it is argued that molecular expansion is responsible for the difference, and experimental evidence of this expansion is presented, and compared with calculations.

115 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived simple approximate solutions to the equations of motion for both short and long times, and compared these approximate solutions with accurate results obtained by numerical integration from an exact but implicit solution.
Abstract: We consider two‐dimensional motion of a projectile experiencing a constant gravitational force and a fluid drag force which is quadratic in the projectile’s speed. The equations of motions are coupled nonlinear equations. Their solutions have general properties which are easily visualized, although much different from those obtained when a drag force is neglected. Because of these features a study of these equations would provide an interesting counterpoint to the already familiar case of no drag. In this paper we derive simple approximate solutions to the equations of motion for both short and long times. A numerical example is used to compare these approximate solutions with accurate results obtained by numerical integration from an exact but implicit solution. Finally, the origin of the quadratic drag force is discussed.

104 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of flow of a viscous fluid around a spherical drop at intermediate Reynolds numbers up to Re=200 for arbitrary values of the ratio of dynamic viscosities inside and outside the drop was examined.
Abstract: The problem of flow of a viscous fluid around a spherical drop has been examined for the limiting case of small and large Reynolds numbers in several investigations (see [1–3], for instance; there is a detailed review of various approximate solutions in [4]). For the intermediate range of Reynolds numbers (approximately 1≤Re≤100), where numerical integration of the complete Navier-Stokes equations is necessary, there are solutions of special cases of the problem —flow of air around a solid sphere [5–7], a gas bubble [8, 9], and water drops [10]. The present paper deals with flow around a spherical drop at intermediate Reynolds numbers up to Re=200 for arbitrary values of the ratio of dynamic viscosities Μ=Μ1/Μ2 inside and outside the drop. It is shown that a return flow can arise behind the drop in flow without separation. In such conditions the circulatory flow inside the drop breaks up. An approximate formula for the drag coefficient of the drop is given.

102 citations


Journal ArticleDOI
TL;DR: In this paper, the authors provide quantitative information on the drag coefficients for isolated gas bubbles moving in the low and high Reynolds number region and bubble shapes and velocity transition and discontinuity in non-Newtonian media.

75 citations


Journal ArticleDOI
R. King1
TL;DR: In this paper, three aspects of the yawed cylinder-fluid interactions over a range of yaw angles ±45° from the vertical for the Reynolds number range 2,000 < Re < 20,000.
Abstract: Yawed cylinders are cylinders inclined forward or backwards in the plane of the flowing fluid. They are used in many practical situations such as braced frame members and raked marine piles. This paper describes an examination of three aspects of the yawed cylinder-fluid interactions over a range of yaw angles ±45° from the vertical for the Reynolds number range 2,000 < Re < 20,000. viz. 1. Establishment of the stability criteria of vortex-excited oscillations. 2. Measurement of ‘steady’ drag forces and equivalent drag coefficients. 3. Visualization of the local flow over stationary and oscillating cylinder. After a brief review of previous experimental and theoretical work, the results of the three items listed above are presented and discussed. Vortex-excited oscillations were recorded in the in-line and crossflow directions throughout the range of yaw angles and the results of items 2, 3 were used to justify the forms of the stability criteria proposed for these oscillations.

74 citations


Proceedings ArticleDOI
01 Mar 1977
TL;DR: The ability to treat multiple design-point problems by numerical optimization has been enhanced by the development of improved airfoil shape functions, which permit a considerable increase in the range of profiles attainable during the optimization process.
Abstract: Recent applications of numerical optimization to the design of advanced airfoils for transonic aircraft have shown that low-drag sections can be developed for a given design Mach number without an accompanying drag increase at lower Mach numbers. This is achieved by imposing a constraint on the drag coefficient at an off-design Mach number while the drag at the design Mach number is the objective function. Such a procedure doubles the computation time over that for single design-point problems, but the final result is worth the increased cost of computation. The ability to treat such multiple design-point problems by numerical optimization has been enhanced by the development of improved airfoil shape functions. Such functions permit a considerable increase in the range of profiles attainable during the optimization process.

73 citations


Journal ArticleDOI
TL;DR: In this article, the local and average skin shear coefficients in terms of the geometry of the elements and the flow Reynolds number were derived for smooth and sand coated two-dimensional triangular elements simulating ripples and dunes.
Abstract: Measurements of shear and pressure distribution on smooth and sand coated two-dimensional triangular elements, simulating ripples and dunes, have been reported. Relations have been derived for the local and average skin shear coefficients in terms of the geometry of the elements and the flow Reynolds number. The local pressure coefficient and the form drag coefficient have been related to the relative roughness and the geometry of the elements. Analysis of the data has shown that the grain resistance of undulated beds calculated by the existing methods is generally greater than the measured average grain resistance of the bad. A large amount of alluvial channel data show agreement with the relation for form drag of the two-dimensional triangular roughness.

64 citations


Journal ArticleDOI
TL;DR: In this paper, the characteristics of a series of cloud-delineated wake patterns downwind of isolated mountain barriers on the Alaskan Peninsula and eastern Aleutian Islands have been studied using a geometrically corrected NOAA satellite picture in conjunction with available meteorological information.
Abstract: The characteristics of a series of cloud-delineated wake patterns downwind of isolated mountain barriers on the Alaskan Peninsula and eastern Aleutian Islands have been studied using a geometrically corrected NOAA satellite picture in conjunction with available meteorological information. Four of these wakes are shown to be atmospheric analogs of Karman-type vortex streets observed in laboratory experiments. A critical Reynolds number of 92±5 has been estimated for the flow. The drag coefficients associated with the vortex streets varied from 1.1 for an irregular, asymmetrical wake to 2.3 for a regular, symmetrical wake; the turbulent eddy viscosity ranged from 1.2−1.8×103 m2 s−1 for the four vortex streets. The two vortex streets having the lowest Reynolds number flows (R= 97, 112) appear to have developed through a “double vortex street” laminar instability while the vortex street having the largest Reynolds number flow (R = 183) apparently developed through a “single vortex street” instability...

50 citations


Journal ArticleDOI
TL;DR: In this article, the Batchelor equation for suspension rheology is used to predict the major drag reduction phenomena observed experimentally, and it is shown that mixed polymer-fiber systems may be much more effective in their drag reduction capabilities than is either kind of additive when used alone.
Abstract: It is shown that the rheological behavior of dilute polymeric solutions can be described, at least semi‐quantitatively, by means of an equation containing a single viscosity coefficient and a single time constant. This expression and the Batchelor equation for suspension rheology are used to predict the major drag‐reduction phenomena observed experimentally. It is shown that mixed polymer‐fiber systems may be much more effective in their drag reduction capabilities than is either kind of additive when used alone. This latter prediction finds its qualitative verification in drag coefficients which are several‐fold lower than those observed at the asymptote of ’’maximum’’ drag reduction in polymer solutions.

Journal ArticleDOI
01 Apr 1977-Wear
TL;DR: In this article, an analytical solution for the performance characteristics of a double-layered porous slider bearing is presented, where the effect of the double layer is to increase the load capacity and the frictional drag but to decrease the coefficient of friction.

Journal ArticleDOI
TL;DR: In this article, the influence of intermittent convection on surface-layer stress estimates during the GARP Atlantic Tropical Experiment (GATE) is described, and a negative correlation between the drag coefficient (CD) and the wind speed is found when short averaging periods are used.
Abstract: The influence of intermittent convection on surface-layer stress estimates during the GARP Atlantic Tropical Experiment (GATE) is described. A negative correlation between the drag coefficient (CD) and the wind speed (% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaara% aaaa!36DE!\[\bar U\]) is found when short averaging periods are used. Well-defined, discrete events produce this negative correlation, and these events are shown to correspond to the passage of convective plumes. Constraints on averaging times necessary to obtain reasonable stress estimates using the bulk method are discussed.

01 Jun 1977
TL;DR: A current overview of aerodynamic drag reduction concepts which have potential for reducing aircraft fuel consumption is presented in this article, where the discussion shows where the greatest percentages of aircraft fuel is burned and what areas have the greatest potential for fuel conservation.
Abstract: A current overview of aerodynamic drag reduction concepts which have potential for reducing aircraft fuel consumption is presented. The discussion shows where the greatest percentages of aircraft fuel is burned and what areas have the greatest potential for fuel conservation. The paper deals with aerodynamic improvements and touches only briefly on structural and propulsion improvements. Concepts for reducing pressure drag (i.e., roughness, wave, interference, and separation drag), drag due to lift/induced drag, and skin-friction drag at subsonic and supersonic speeds are emphasized.

Journal ArticleDOI
TL;DR: In this article, it is argued from a fluctuation-dissipation relation that direct (hard sphere, electrostatic) interactions between macromolecules also contribute to the Stokes' law drag coefficient.
Abstract: The Stokes’ law drag coefficient for a rigid macromolecule in solution has long been known to depend on the macromolecule concentration. This concentration dependence has generally been interpreted entirely in terms of hydrodynamic interactions between the macromolecules. It is argued here from a fluctuation–dissipation relation that direct (e.g., hard sphere, electrostatic) interactions between macromolecules also contribute to the drag coefficient. An approximate calculation indicates that the contribution of direct intermacromolecular interactions to the drag coefficient can be as important as the contribution of hydrodynamic intermacromolecular interactions.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the plane flow of a second-order fluid past submerged obstacles such as circular and elliptical cylinders in situations where inertia effects cannot be neglected, and analyzed the effect of the short memory of the fluid upon the flow features.
Abstract: Considers the plane flow of a second-order fluid past submerged obstacles such as circular and elliptical cylinders in situations where inertia effects cannot be neglected. The effect of the short memory of the fluid upon the flow features is analyzed in detail. In particular, it is found that the viscoelasticity of the fluid reduces the drag coefficient for very low Reynolds numbers, while the opposite is true for large Reynolds numbers.

Journal ArticleDOI
01 Jan 1977
TL;DR: In this paper, a numerical solution for the spray equation has been developed for thin sprays injected into a type of stratified charge internal combustion chamber, which can treat general three dimensional geometries, using a statistical approach.
Abstract: A numerical solution technique has been developed for the spray equation and has been applied to thin sprays injected into a type of stratified charge internal combustion chamber. The difference equation method can treat general three dimensional geometries, using a statistical approach. The effects of independent variations of a large number of system parameters was studied, including initial spray dispersion, amount and type of gas swirl, gas density, injection timing, chamber geometry, initial droplet size distribution, injection velocity, drag coefficient of injection. It was found that in the particular geometry chosen the gas swirl, the droplet size distribution produced by the injector, and the chamber gas density into which the spray is injected are the most important factors influencing the spray motion and vaporization. Although the calculations reported here applied to internal combustion engine conditions, the general method is applicable to other spray-injected combustors, including stationary combustors and rocket motors. Results from calculations indicate that the technique, used in coordination with selected laboratory measurements, could significantly enhance spray-injected combustor design efforts.

Journal ArticleDOI
TL;DR: In this article, a nonlinear drag force law was proposed to account for the effect of increased drag on the upward return flow of the fluid and the influence of sediment on the hydrostatic pressure.
Abstract: Kinematical effects which hinder settling are due to the upward return flow of the fluid and to the influence of the sediment on the hydrostatic pressure. Dynamical effects of increased drag must be accounted for with a nonlinear drag force law.

Journal ArticleDOI
TL;DR: In this article, complete developed and entry region mass transfer rates in turbulent pipe flow of drag reducing polymer solutions were studied experimentally using electrochemical techniques, and the authors interpreted the data by using the law of the wall, valid for Newtonian fluids at large Schmidt numbers, whereby K+ is related to Sc−0.74.
Abstract: Completely developed and entry region mass transfer rates in turbulent pipe flow of drag reducing polymer solutions were studied experimentally using electrochemical techniques. The percent change in the fully developed mass transfer rate at a given volumetric flow was found to be greater than the percent change in the pressure gradient. The data are interpreted by using the law of the wall, valid for Newtonian fluids at large Schmidt numbers, whereby K+ is related to Sc−0.74. The proportionality constant is correlated with percent drag reduction and is found to decrease with increasing drag reduction. The use of an analogy between momentum and mass transfer predicts a somewhat greater mass transfer reduction than was observed.


Journal ArticleDOI
TL;DR: In this article, the effects of spacing, orientation and Reynolds number on the drag of each cylinder in a group of two and three cylinders were measured by means of strain gages, and the results indicated that the drag is strongly affected by mutual interaction with neighboring cylinders over a range of separation distances and angles of orientation with respect to the free-stream flow.
Abstract: An experimental investigation of the effects of spacing, orientation and Reynolds number on the drag of each cylinder in a group of two and three cylinders was carried out. The drag forces were measured by means of strain gages. The results indicate that the drag is strongly affected by mutual interaction with neighboring cylinders over a range of separation distances and angles of orientation with respect to the free-stream flow. The interaction decreases with increasing orientation angle, becoming very weak at θ = 90 deg when the cylinders are separated by at least two diameters. For spacings of approximately four diameters, the drag coefficients for the three-cylinder geometry reach a value which will remain almost constant for larger spacings. This is true for all three cylinders and for all orientations. The orientation of the cylinders influences only slightly the drag on the upstream cylinder for groups of both two and three cylinders. For downstream cylinders, the drag coefficient decreases with increasing Reynolds number due to the increased amount of unsteadiness contained in the flow behind the upstream cylinder.

Journal ArticleDOI
TL;DR: In this article, the effects of wall interference on the drag and vortex shedding characteristics of cavitating two-dimensional triangular prisms and circular cylinders were investigated and the results indicated that wall interference effects are relatively small at very low cavitation numbers (σ → σch ) which correspond to choking conditions.
Abstract: An experimental program has been carried out to determine the effects of wall interference on the drag and vortex shedding characteristics of cavitating two-dimensional triangular prisms and circular cylinders. The former shapes were chosen to eliminate effects of Reynolds number in interpreting the results. Direct pressure measurements were made to estimate the drag force. The vortex shedding frequency of the cavitating bodies was recorded with the help of a pressure transducer. The gap velocity u1 and the jet contraction velocity uj are shown to be the proper velocity scales to form the drag coefficients and Strouhal numbers for the bluff shapes tested. The drag coefficient was found to increase due to wall interference effects when partial cavitation conditions prevailed. The trend of the drag coefficient data indicated that wall interference effects are relatively small at very low cavitation numbers (σ → σch ) which correspond to choking conditions. As choking conditions are reached, the vortex shedding from the cavitating source becomes intermittent and finally vortex shedding ceases.

Journal ArticleDOI
TL;DR: In this article, the effects of the flow time scales on the onset and magnitude of drag reduction in turbulent pipe flow were studied using comparatively low molecular weight samples of water soluble polymers in glycerine water mixtures and in two different pipe sizes.
Abstract: The effects of the flow time scales on the onset and magnitude of drag reduction in turbulent pipe flow were studied using comparatively low molecular weight samples of water soluble polymers in glycerine‐water mixtures and in two different pipe sizes. The results show that onset depends only on the time scale νuτ2 with no Reynolds number dependence. The magnitude of drag reduction after the molecules are extended was found to increase with pipe diameter. A correlation with the lifetime of large eddies or the mean period of turbulence production is suggested.

Proceedings ArticleDOI
03 Oct 1977
TL;DR: In this paper, an experimental program has been conducted to determine the quantitative relationship between far-field noise and drag coefficient for circular cylinders and the results show a strong dependence of SPL on drag coefficient varying as 50 to 90 times log (CD) depending on directivity angle and bandwidth.
Abstract: An experimental program has been conducted to determine the quantitative relationship between far-field noise and drag coefficient for circular cylinders. The test program included smooth and roughened cylinders with Reynolds numbers between 45,000 and 450,000 and Mach numbers between 0.1 and 0.5. The resulting drag coefficients varied between 0.75 and 1.2. The results show a strong dependence of SPL on drag coefficient varying as 50 to 90 times log (CD) depending on directivity angle and bandwidth. This represents the first controlled laboratory data available to directly verify the quantitative relationship between noise and drag coefficient at constant Mach numbers. aF b

Proceedings ArticleDOI
01 Jun 1977
TL;DR: A series of wind-tunnel tests covering a range of Mach numbers and Reynolds numbers in subsonic and transonic flows was conducted on a circular cylinder placed normal to the flow as mentioned in this paper.
Abstract: A series of wind-tunnel tests covering a range of Mach numbers and Reynolds numbers in subsonic and transonic flows was conducted on a circular cylinder placed normal to the flow. Form drag coefficients were determined from surface-pressure measurements and displayed as a function of Mach number to show the drag rise phenomenon. Buried wire gages arranged on the model surface were used to measure skin-friction distributions and vortex-shedding frequencies at different flow conditions. It was found that detectable periodic shedding ceases above M = 0.9. The measured skin-friction distributions indicate the positions of mean separation points clearly; these values are documented for the different flow conditions.

Journal ArticleDOI
TL;DR: In this paper, a two-degree-of-freedom lumped-mass model was used to gain understanding of the equilibrium and stability of a circularly towed cable, in particular for no drag, viscous drag, and viscous charge with a cross wind.
Abstract: A two-degree-of-freedom lumped-mass model is used to gain understanding of the equilibrium and stability of a circularly towed cable. Particular cases considered are those of no drag, viscous drag, and viscous drag with a crosswind.

Journal ArticleDOI
TL;DR: In this paper, the effect of polymer modification of the mean flow profile in the outer layer of a polymeric polymeric system is investigated and an engineering approximation to the Seyer and Metzner model of turbulent viscoelastic flow is described.
Abstract: Available drag reduction correlations are presented and their utility for engineering scale‐up to a scale‐up from a correlation based on friction velocity and the availability of some turbulent flow data with the process fluid of interest is compared. A further purpose is to investigate the consequences of polymer modification of the mean flow profile in the outer layer. Emphasis is placed on accuracy and ability to portray the drag reducing activity of complex systems. In the case of very dilute polymeric systems in large conduits, very accurate predictions may be needed to assess the performance of a particular additive. Similarly, equations capable of detailed predictions of observed behavior can provide needed insight into the mechanism of drag reduction. Inasmuch as the semi‐logarithmic resistance law, e.g., the Seyer and Metzner model of turbulent viscoelastic flow, provides a scale‐up criterion significantly more complicated to use than a number of other models, an engineering approximation to this model is described. It is shown that for accurate predictions to be made at modest levels of drag reduction activity, the model must be modified to compensate for thickening of the sublayer.

Journal ArticleDOI
TL;DR: In this paper, experimental results for the drag and added mass coefficients for a smooth circular cylinder in oscillatory flow are presented, and the test results are correlated with the Reynolds number with the ratio of the amplitude of the motion to cylinder diameter as a parameter.
Abstract: Experimental results for the drag and added mass coefficients for a smooth circular cylinder in oscillatory flow are presented. The test results are correlated with the Reynolds number with the ratio of the amplitude of the motion to cylinder diameter as a parameter. The low Reynolds number results of Keulegan and Carpenter are replotted in this same format and together with the present high Reynolds number results give a fairly complete picture of the variation of the drag and added mass coefficients with Reynolds number for fixed values of the relative amplitude parameter. The results show that generally both the added mass and drag coefficients are highly dependent on the Reynolds number as well as the relative amplitude parameter. Above a Reynolds number of about 2 x 10 5 the two coefficients become essentially independent of the Reynolds number.

01 May 1977
TL;DR: In this article, the authors used classical drag equations to calculate total and induced drag and ratios of stabilizer lift to wing lift for a variety of conventional and canard configurations, and evaluated the flight efficiencies of such configurations that are trimmed in pitch and have various values of static margin.
Abstract: Classical drag equations were used to calculate total and induced drag and ratios of stabilizer lift to wing lift for a variety of conventional and canard configurations. The Flight efficiencies of such configurations that are trimmed in pitch and have various values of static margin are evaluated. Classical calculation methods are compared with more modern lifting surface theory.

Journal ArticleDOI
TL;DR: In this article, a new energy-dissipation closure was proposed to describe the observed effects of drag reduction on the mean velocity, turbulent energy, and turbulent length-scale distributions.
Abstract: Earlier models for flows with drag reduction are reviewed and compared with a new energy‐dissipation closure which describes the observed effects of drag reduction on the mean velocity, turbulent energy, and turbulent length‐scale distributions, and suggests a new maximum drag reduction law related to the onset of drag reduction.