Showing papers on "Drag coefficient published in 1968"

Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 × 10 6

Abstract: In a large range of Reynolds numbers, 6 × 104 < Re < 5 × 106, the flow around single cylinders with smooth surfaces has been investigated. The high values of the Reynolds numbers were obtained in a test channel which could be pressurized up to 40 bar of static pressure. New experiments were performed to measure the local pressure and skin friction distribution around the cylinder. From these results the total drag, the pressure drag and the friction drag were calculated. By means of the skin friction distribution the position of the separation points, separation bubbles or transition points can be localized. These data allow one to define three states of the flow: the subcritical flow, where the boundary layer separates laminarly; the critical flow, in which a separation bubble, followed by a turbulent reattachment, occurs; and the supercritical flow, where an immediate transition from the laminar to the turbulent boundary layer is observed at a critical distance from the stagnation point. According to the total drag coefficient the values found in this paper connect the subcritical region represented by the measurements of Wieselsberger (1923) and Fage & Warsap (1930) with the supercritical range in which Roshko (1961) carried out his experiments.

Mass, heat and momentum exchange between stands of plants and their atmospheric environment

Abstract: A model of mass and momentum transfer in the air layer occupied by a stand of plants is presented which takes account of the differing mechanisms of mass exchange and momentum dissipation near to the leaf surfaces. An analysis of momentum transfer leads to expressions for the vertical transport coefficient and windspeed in terms of the mean drag coefficient of the leaves, the drag coefficient of the stand as a whole and the area of leaf per unit volume of space. These expressions are used in the solution of the equations describing mass transfer with constant concentration of mass at the leaf surface. The effect of a chemical or physical resistance to transfer at the leaf surface is examined. The resistance to mass exchange between the stand and the atmosphere above is compared with that for momentum exchange. The transfer of water vapour in the stand is considered, the boundary conditions at the leaf surfaces being linked with those for sensible heat transfer. It is shown that, when leaf resistance to transpiration is negligible, the vapour and heat-fluxes are readily obtained from simple mass transfer theory and a knowledge of the distribution of radiation in the stand. The formal relations are extended to allow for finite leaf resistance. Computed profiles of the fluxes, temperature and humidity in a plant stand of assumed characteristics with defined boundary conditions are presented and compared with published observations. The interrelationship between leaf resistance, transpiration and leaf temperature is discussed. An expression for the total evaporation from a stand is derived and contrasted with a relation based on the analysis of Penman and Schofield (1951) and Monteith (1965).

On the Flow Near the Trailing Edge of a Flat Plate

Abstract: It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l, generally valid near the plate when the Reynolds number Re is large, fails within a distance O(lRe$^{-\frac{3}{4}}$) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier-Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake down-stream of the trailing edge. The contribution to the drag coefficient is found to be O(Re$^{-\frac{3}{4}}$) and the multiplicative constant is explicitly worked out for the linearized equations.

On high-frequency oscillatory viscous flows

Abstract: The equations governing high-frequency oscillatory viscous flows are investigated through the separation of the steady and the unsteady parts All Reynolds number ranges are studied and the orders of magnitude of the steady streaming produced by the Reynolds stresses are establishedThe oscillating circular cylinder at low Reynolds numbers is studied through the method of inner and outer expansions Steady recirculating cells exist near the cylinder The results compare very well with experiments Analytic expressions for the streamfunction and the drag coefficient are obtainedThe oscillating flow towards an infinite plate is investigated in detail The steady streaming is caused by the steady component of the Reynolds stress The pressure gradient always causes reverse flow near the solid boundary

An Experimental Study on Aerodynamic Drag of Rectangular Cylinders

Abstract: An experimental study is carried out on the aerodynamic drag of rectangular cylinders, where the REYNOLDS number ranges up to 6×104. It is revealed that the drag coefficient, CD, varies con-siderably with the d/h ratio of rectangles, and that the maximum value of CD is as high as 2.6 for d/h of 2/3 compared with CD of about 2.0 for the cases of flat plate and square cylinder (Fig.1). The STROUHAL number of the shedding vortices, on the contrary, remains approximately constant for d/h up to 1.0, decreases slowly for larger values of d/h, and then increases abruptly at d/h ratio of about 2.8 (Fig.2), where the flow reattaches on the lateral surfaces of the cylinder.

The form drag of two-dimensional bluff-plates immersed in turbulent boundary layers

Abstract: Measurements of the distributions of pressure on a bluff flat plate (fence) have been correlated with the characteristics of the smooth-wall boundary layer in which it is immersed. For zero pressure-gradient flows, correlations are obtained for the variation of form drag with plate height h which are analogous in form to the ‘law of the wall’ and the ‘velocity-defect law’ for the boundary-layer velocity profile. The data for adverse pressure-gradient flows is suggestive of a ‘law of the wake’ type correlation. Pressures on the upstream face of the bluff-plate are determined by a wall-similarity law, even for h/δ > 1, and are independent of the pressure-gradient history of the flow; the separation induced upstream is apparently of the Stratford-Townsend type. The effects of the history of the boundary layer are manifested only in the flow in the rear separation bubble, and then only for h/δ > ½. The base pressure is also sensitive to free-stream pressure gradients downstream of the bluff-plate. The relative extent of upstream influence of the bluff-plate on the boundary layer is found to increase rapidly as h/δ decreases. One set of measurements of the mean flow field is also presented.

The motion of a spherical liquid drop at high Reynolds number

Abstract: The steady motion of a liquid drop in another liquid of comparable density and viscosity is studied theoretically. Both inside and outside the drop, the Reynolds number is taken to be large enough for boundary-layer theory to hold, but small enough for surface tension to keep the drop nearly spherical. Surface-active impurities are assumed absent. We investigate the boundary layers associated with the inviscid first approximation to the flow, which is shown to be Hill's spherical vortex inside, and potential flow outside. The boundary layers are shown to perturb the velocity field only slightly at high Reynolds numbers, and to obey linear equations which are used to find first and second approximations to the drag coefficient and the rate of internal circulation.Drag coefficients calculated from the theory agree quite well with experimental values for liquids which satisfy the conditions of the theory. There appear to be no experimental results available to test our prediction of the internal circulation.

Flow of a Rarefied Gas past an Axisymmetric Body. II. Case of a Sphere

Abstract: The drag exerted by the flow on a sphere is explicitly calculated by using the relation between the drag and a certain functional. A comparison of the results with the experimental data of Millikan gives excellent agreement.

Drag coefficient of small spherical particles.

Abstract: An experimental study was conducted to determine the drag coefficient of small, inert, spherical particles accelerating in a laminar, nonreacting, incompressible continuum flow. The Reynolds number range covered in the study was from 200 to 1700, and particle sizes ranged from 150 to 450/1. Glass beads, HP 295 ball powder, and sapphire balls were used. The convective flow behind the shock wave in a shock tube was used to accelerate the particles. The diameter and temporal displacement of a single particle were determined by use of a rotating drum camera in conjunction with an oscillating light source. Using the photographic data, the particle density, the shock speed, the initial temperature and pressure, and the normal shock relations, the particle drag coefficient was calculated. Experiments with HP 295 ball powder produced drag results that were as much as 85% higher than the standard drag coefficient curve. This increase was found to be dependent on the relative Mach number of the flow about the particle even though the Mach number was less than 0.3. The glass beads yielded similar results but to a lesser extent. The sapphire balls produced the best results, yielding the lowest drag values, less scatter, and little sensitivity to Mach number. Many possible influences were considered to explain the foregoing anomalous results. Photomicrographs showed that the ball powder was very rough and that the sapphire balls were the most smooth. It is concluded that the particles in solid rocket nozzles are "rough" and hence their drag coefficients are much higher than would normally be the case.

Lee waves in a stratified flow Part 1. Thin barrier

Abstract: The lee-wave amplitudes and wave drag for a thin barrier in a two-dimensional stratified flow in which the upstream dynamic pressure and density gradient are constant (Long's model) are determined as functions of barrier height and Froude number for a channel of finite height and for a half-space. Variational approximations to these quantities are obtained and validated by comparison with the earlier results of Drazin & Moore (1967) for the channel and with the results of an exact solution for the half-space, as obtained through separation of variables. An approximate solution of the integral equation for the channel also is obtained through a reduction to a singular integral equation of potential theory. The wave drag tends to increase with decreasing wind speed, but it seems likely that the flow is unstable in the region of high drag. The maximum attainable drag coefficient consistent with stable lee-wave formation appears to be roughly two and almost certainly less than three.

Electromagnetic Propulsion for Cargo Submarines

Abstract: An application of electromagnetic propulsion to large submarine tankers may lead to increased propulsion efficiency. The general theory of external field d.c. electromagnetic propulsion is discussed and propulsion efficiencies are deduced for 2-, 4-, or 6-pole configurations. Application for submarine tanker hulls of L/d = 8.75 and prismatic coefficient 0.68 is then discussed for cases of 4 or 6 poles and submerged displacements of 25,000, 50,000, and 100,000 metric tons. For the 6-pole arrangement, at 29 knots, the thrust power is estimated to be 86% of the electric power supplied at 100,000 tons, 83% at 50,000 tons, and 79% at 25,000 tons. Values over 90% are reached at 20 knots. Arrangement of equipment inside the hull is discussed. Attention must be given to supporting the coils of the superconducting magnets; separating forces are very large and the restraints must not give excessive heat leakage. Other problems are those of the magnetic field inside the hull and the attraction of foreign iron bodies.

The surface configuration and internal structure of artificial hailstones

Abstract: An experimental study has been made of the external and internal structure of artificial hailstones grown freely supported in a vertical wind tunnel. In addition the nature of ice deposits formed on fixed stationary objects and objects rotating about a horizontal axis has been investigated at airspeeds of 35 to 40 m s−1. Lobe-like growth similar to that found in natural hailstones has been reproduced. The lobes are most pronounced when the accreted droplets are small and when growth takes place near the wet limit. With large droplets and when the growth is very spongy the surface irregularities are far less marked. It is inferred that the lobe-like growth is due to a collection efficiency effect. The drag coefficients of a number of artificial hailstones have been measured. None of the values is greater than 0·66. Some of the moderate sized stones (4 to 6 cm diameter) entered the critical flow regime where their drag coefficients were considerably reduced. This did not occur, however, for large (10 cm diameter) very irregular hailstones.

Note on the numerical solution for unsteady viscous flow past a circular cylinder

Abstract: The starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100 has been obtained by a numerical method. The method used is that developed by Payne (1957) but it has been extended here to cover a larger time interval. At Reynolds number 40 Payne's result for the drag coefficient at time t = 6 is in reasonable agreement with Kawaguti's (1953) result for the steady case but if Payne's computation, is extended to time t ≈ 24, the result is in better agreement with Apelt's (1961) result for the steady case. Also, a further investigation into the case R = 100 shows that Payne's mesh size is too crude. Similar observations can be made concerning the size of the standing vortices downstream of the circular cylinder and how they grow in time.

Fall velocity of irregular shaped particles

Abstract: The determination of the free-fall velocity of irregularly shaped particles in viscous fluids is presented. A shape parameter is proposed which correlates Reynolds number with drag coefficient to describe the motion of irregular shapes. This shape parameter results in a useful Reynolds number-drag coefficient relation. Data for analysis were collected from tests of natural gravel-sized particles of various shapes and sizes supplemented by larger regular geometric shapes. The basic motions of a particle in free-fall are classified and analyzed considering causes such as flow separation and vortex formation.

Drag Reduction by Bacterial Metabolites

Abstract: IN conditions of turbulent flow, relatively low concentrations of linear, high-molecular weight polymers can greatly reduce the frictional drag of a liquid1–4. By measuring the pressure drop along a finebore tube in these conditions, the drag-reducing potential of such a polymer solution can be estimated by comparing with the pressure drop for the pure solvent. This is the principle on which the turbulent flow rheometer5 is based.

An Experimental Determination of the Drag on a Sphere at Low Reynolds Numbers

Abstract: Accurate measurements of the drag on a sphere falling in a viscous medium were carried out for Reynolds numbers between 0.001 and 10.0. When the fractional deviation (D/Ds) − 1 of the actual drag D from the Stokes drag Ds was plotted as a function of the Reynolds number, significant inconsistencies among the results of measurements previously reported in literature and significant differences between these and our own results were revealed. Our experimental results also deviated from most theories available; however, they were consistent with the theory of Proudman and Pearson for vanishingly small Reynolds numbers and at Reynolds numbers between 0.5 and 10 with Carrier's semiempirical modification of Oseen's theory.

Aerodynamic relationships inherent in Newtonian impact theory.

Abstract: Aerodynamic relationships are derived which are inherent in Newtonian impact theory. Some of these relationships are independent of the particular body configuration and some depend only on the projected area of the body. The expressions derived are in a generalized form and apply to any coordinate system. In addition, they are applicable to any threedimensional configuration and for any attitude, subject to the limitations of Newtonian impact theory. The generalized expressions are applied to specific cases: two-dimensional, axisymmetric, and general three-dimensional configurations. In addition to the basic relationships, differential equations defining the drag (and, hence, lift and side force) variation with attitude as a function of the projected area are derived, and the lift-to-drag ratio is shown to be proportional to the rate of change of the drag coefficient. Finally, a comparison of the theory with experiment shows a good correlation.

The static drag on bodies in Bingham plastics

Abstract: A good indication of the static drag force experienced by a body immersed in a Bingham plastic can be obtained by summing the static yield stress over the cross-sectional area of the body normal to the direction of movement of the plastic and multiplying the result by 16.7. The actual drag may be slightly higher in the case of a disc or a sphere than for a cylinder or a rectangular plate, and an additional factor may be required if the length of the body parallel to the flow exceeds its width. The mechanism of transmission of the force from the Bingham plastic to the immersed body is not understood at present.

Effect of boattail juncture shape on pressure drag coefficients of isolated afterbodies

Abstract: Effect of boattail juncture shape on pressure drag coefficients of isolated afterbodies of supersonic engine nacelles

Calculation of Profile Drag of Airfoils at Low Mach Numbers

Abstract: This paper investigates the accuracy of a particular method for calculating the profile drag of airfoils at low Mach numbers. The method consists of 1) calculation of the pressure distribution by any suitable method, 2) calculation of laminar flow near the nose by Thwaites' method, 3) calculation of transition by Michel's method (if it is not known a priori), 4) calculation of turbulent boundary-layer flow by Head's method, and, finally, 5) calculation of momentum deficiency in the far wake by means of the Squire-Young relation. Profile drag has been calculated by this method for several airfoils at various angles of attack and Reynolds numbers. The effects of transition and airfoil thickness on the profile drag are studied. Comparison of calculated and experimental values show generally good agreement. The rms error based on 88 calculated drag values is 2.7%.

Drag Reduction of a Non-Newtonian Fluid by Fluid Injection at the Wall

Abstract: The flat plate boundary-layer equations for a power law model of a non-Newtonian fluid are formulated in a manner to allow similarity solutions with mass injection at the boundary. The variation of injection velocity with longitudinal position along the plate which allows a similarity solution is determined as a function of the power law exponent N. In the analysis, it is shown that the two- point boundary value problem can be reduced to an equivalent initial value problem. Numerical results are presented for velocity profiles, skin-friction coefficient, displacement and momentum thicknesses for a range of values of the power law exponent, and the dimensionless mass injection parameter.

Turbulence measurements in pipe flow of a drag- reducing non-Newtonian fluid.

Abstract: Turbulent shear pipe flow of drag reducing nonNewtonian fluid, measuring streamwise turbulence intensity and energy spectra

Measurement of Particle Drag Coefficients in Flow Regimes Encountered by Particles in a Rocket Nozzle

Abstract: : An experimental investigation was conducted to determine the drag coefficient of particles in flow regimes encountered in a rocket nozzle. The acquisition of these data leads to more reliable predictions of nozzle performance inefficiencies owing to gas-particle flow. The Mach number-Reynolds number regime traversed by a particle in a rocket nozzle is described.