Showing papers on "Drag coefficient published in 1974"

The effects of surface roughness and tunnel blockage on the flow past spheres

Abstract: The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

Turbulent vortex rings

Abstract: We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.

Measurements of velocity distributions in the wake of a circular cylinder at low Reynolds numbers

Abstract: Velocity measurements were made in the flow field behind a circular cylinder at Reynolds numbers from 10 to 80 and results compared with existing numerical solutions. Takami & Keller's solution for the velocity distribution in the wake shows good agreement at low Reynolds numbers and fair agreement at high Reynolds numbers. The drag coefficient of the cylinder and the size of the standing eddies behind the cylinder were also determined. They are compatible with existing experimental and numerical results. Details of the velocity distribution in the standing eddies are clarified.

Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow

Abstract: A method is presented for the automatic synthesis of minimum drag hull shapes for axisymmetric vehicles of specified enclosed volume and constant speed submerged in incompresible, nonseparating, noncavitating flow at zero incidence. The computer-oriented optimization procedure does not consider propulsion or maneuvering; drag reduction is accomplished solely through manipulation of the vehicle hull shape. The selected optimization formulation is a nongradient algorithm in a finite, constrained parameter space. This study considers an eight-parameter class of rounded-nose tailboom bodies constrained to be well behaved as determined by previous hydrodynamic experience. The drag model, for nonseparating flows at zero incidence, is based on classical hydrodynamics and consists of computer programs from work available in the literature; the model is representative of state-of-the-art drag prediction methods. By exploiting laminar flow while avoiding turbulent separation, a body with a drag coefficient one-third below the best existing laminar design has been obtained. The evidence suggests that the method produces realistic hull shapes useful in engineering design. The optimization procedure is independent of any particular drag model so that the effects on minimum drag shapes due to alternate drag models can be studied.

Turbulent drag reduction in polymeric solutions containing suspended fibers

Abstract: Both polymeric solutions and fiber suspensions have separately been known to exhibit drag reduction under turbulent flow conditions. It has recently been shown that the mechanisms of drag reduction differ appreciably in these two kinds of systems. The objective of this study was to show that both mechanisms may be exploited concomitantly to achieve unusually low friction factors. Drag reductions in excess of 95% have been obtained in a 2.4-cm tube and there is no evidence that even more dramatic results could not be obtained under optimal conditions.

Turbulent fluxes of momentum, heat and water vapor in the atmospheric surface layer at sea during ATEX

Abstract: The vertical turbulent fluxes have been determined during the Atlantic Trade Wind Experiment (ATEX) both by direct and profile methods. The drag coefficient obtained from direct measurements was c D = 1.39 × 10−3. A distortion of the wind profile due to wave action could be demonstrated, this produced an increased drag coefficient estimated by the profile method. The dissipation technique using the downwind spectrum gave a lower drag coefficient of 1.26 × 10−3, probably due to non-isotropic conditions (the ratio of vertical to downwind spectrum at high frequencies scattered considerably with an average of 1 instead of 4/3). From direct measurements, the sensible heat flux showed a poor correlation with the bulk parameter product Uδθ, contrary to the heat flux obtained from profiles. It is shown that this is due to the higher frequency part of the cospectrum, say above 0.25 Hz, which contributes more than 50 % of the total flux. Determination of the heat flux from temperature fluctuations by the dissipation method would be in agreement with the direct determination only if the corresponding Kolmogoroff constant were 2.1 instead of 0.8. For the vertical flux of water vapor obtained from profiles, the bulk transfer coefficient was 1.28 × 10−3.

Drag reduction in the turbulent flow of fiber suspensions

Abstract: An analysis of the velocity profile and pressure drop relationships for turbulent flow of fiber suspensions through smooth tubes was evaluated experimentally over a range of flow rates, tube sizes, fiber concentrations, and fiber geometries (aspect ratios). This work shows that drag reduction in these systems, in marked contrast to that in viscoelastic polymeric fluids, involves processes in the turbulent core of the velocity field. As a result the drag reduction achieved is independent of the scale of the system. The implications of these results with respect to rates of heat and mass transport are considered in a preliminary way. The measurement of such transport rates, and of the turbulent velocity profiles in dilute suspensions, is seen to be of mechanistic interest.

Polymer structures and turbulent shear stability of drag reducing solutions

Abstract: THE phenomenon of frictional drag reduction in the turbulent flow of Newtonian fluids, by the addition of high molecular weight polymers, has been known for some time. Because of the great potential it offers in various technological applications this phenomenon has generated considerable engineering interest. Unfortunately, when a limited volume of polymer solution is continuously exposed to mechanical shearing action, either by repeated use1 or by passing through long pipelines2, drag reduction rapidly declines, indicating a rapid breakdown of the polymer molecules3. This polymer degradation greatly limits the application of drag reducing polymers. When considering the use of high molecular weight polymers in operating systems their shear stability must be considered as equally important as their effectiveness in drag reduction. Polymer degradation effect is likely to be caused by the scission of molecular entanglements or the breaking of individual molecules induced by the shear stresses associated with very high local shear rates4. But previous studies were made mainly with linear polymers such as polyethylene oxide (PEO) and polyacrylamide (PAM), because a linear structure was believed to be most effective5. We have studied the effect of polymer structure on turbulent drag reduction by synthesising drag-reducing agents of different structures6. Here we present the results of an investigation of the degradation behaviour of a highly branched PAM, and compare the results with those observed with ordinary linear polymers.

Experimental study of the effectiveness of cylindrical plume simulators for predicting jet-on boattail drag at Mach numbers up to 1.30

Abstract: An investigation has been conducted in a 16-foot transonic tunnel to determine the effectiveness of utilizing solid circular cylinders to simulate the jet exhaust plume for a series of eight nacelle-mounted isolated circular-arc afterbodies. This investigation was conducted at Mach numbers from 0.40 to 1.30 at an angle of attack of 0. Plume simulators with simulator diameter to nozzle-exit diameter ratios of 0.82, 0.88, 0.98, and 1.00 were investigated. Results of this investigation indicate that use of one of the larger diameter simulators at all Mach numbers would generally result in pressure-coefficient distributions and drag coefficients useful for preliminary design work.

Sphere drag coefficient for subsonic speeds in continuum and free-molecule flows

Abstract: An extensive series of measurements of sphere drag coefficients has been made in an aeroballistic range for a broad range of Reynolds and Mach numbers. These measurements have been compared with those obtained in other test facilities. As a result of this comparison it has been possible to suggest reasons for many of the inconsistencies in the earlier measurements and to establish more accurate values of the sphere drag coefficient for M∞ [lsim ] 0·2 and 10−2 [lsim ] Re∞ [lsim ] 107.

Fluid Dynamics of the Circular Porous Slider

Abstract: A fluid of constant density is forced through the porous bottom of a circular slider which is moving laterally on a flat plane. We assume the radius of the slider is much larger than the gap width between the slider and the plane. The Navier-Stokes equations reduce to a set of nonlinear ordinary differential equations. These equations are solved by three methods: series expansion for small crossflow Reynolds number R , matched asymptotic expansions for large R , and also exact numerical integration. The approximate solutions are compared with the numerical results, which is also an exact solution of the Navier-Stokes. Lift and drag are calculated. If everything else is held fixed, both lift and drag increase rapidly although at different rates, with decreasing gap width.

Onset of drag reduction in dilute polymer solutions

Abstract: The onset of drag reduction is observed in a 0.635 cm (0.25 in.) turbulent pipe flow for dilute solutions of Polyox WSR N‐80 in three different glycerine‐water solutions. The time scale onset hypothesis is found to be much more consistent with the data than the length scale onset hypothesis.

Wake Growth and Collapse in Stratified Flow

Abstract: The objective of this research was to obtain data that could be used to predict the effect of stratification on the development of a momentumless wake. Experiments were performed in which a grid was oscillated in a stablystratified flow to produce the steady-state counterpart of the momentumless wake of a self-propelled vehicle. A pH-sensitive indicator was used to produce a neutrally-buoyant tracer to visualize wake development and subsequent vertical collapse. Measured velocity profiles in the simulated wake indicated that it was nearly momentumless, and vertical temperature surveys revealed the degree of mixing in the wake. The wake growth before and after collapse and the distance to collapse were correlated by using power laws and a theoretical analysis of wake collapse. The scaling relations established for predicting stratified flow wake dimensions revealed that the important parameters were the Froude number, defined as the product of the flow velocity and the Brunt-Vaisala period divided by the initial wake size, and the ratio of the time after wake generation to the Brunt-Vaisala period. Through the use of these parameters, two unique curves were obtained for estimating the horizontal width and vertical height of a wake in a stratified flow.

The rise of small bubbles in water

Abstract: Contrary to the conclusions of previous researchers who found the drag coefficients of small bubbles in water to coincide with those expected for solid spheres, we found the drag coefficients of small bubbles in water (Reynolds numbers from 2 to 40) to be significantly less than those expected for solid spheres and close to what we expect are the drag coefficients for ideal fluid spheres. The difference between the present results and those of previous workers is ascribed to velocity measurements nearer to the point of formation, thus giving the surface of a bubble less time to age and collect surfactants.

ON THE LOG-LINEAR WIND PROFILE AND THE RELATIONSHIP BETWEEN SHEAR STRESS AND STABILITY CHARACTERISTICS OVER THE SEA (Research Note)

Abstract: Wind and stability characteristics in the atmospheric surface boundary layer at a height, 2, less than 20 m above the sea were examined in nine oceanic investigations. The analysis lends further support to the utility of the log-linear wind-profile law in the stability region of - 0.4 < Z/L < 0.9, where L is the Monin-Obukhov length. However, it is also shown that, inasmuch as better than 90 % of the measurements fall within the range of /Z/L1 C 0.25, and inasmuch as this correction to the drag coefficient under neutral conditions amounts to less than lo%, the familiar logarithmic wind law may be used rather than the log-linear form. A wind-stress drag coefficient, Cd (= 1.2 x 10-s between 1 .O m < Z $18.3 m), is thus recommended for general deepwater oceanic applications. The situation over shallow water, which is different, is discussed briefly.

A baroclinic planetary boundary-layer model, and its application to the Wangara data

Abstract: Nondimensional parameters characteristic of the outer part of the planetary boundary layer have been determined by fitting a simple, Ekman-type theory to a number of averaged, observed velocity distributions, using the Wangara data of Clarke et al. (1971). The theoretical model is based on constant eddy viscosity in the outer layer and a linear variation of the geostrophic wind with height. At the lower boundary of the outer layer, the condition is applied that stress and velocity are parallel. This yields an equation for the cross-isobar angle as a function of drag coefficient, depth coefficient and nondimensional thermal wind. The data could be sorted into three well-defined, distinct groups, each characterized by a more or less constant value of the depth coefficient. The group with the lowest value of this parameter contains most of the nighttime data, the middle group the remaining nighttime data and most of the daytime ones, and the group with the largest depth, daytime data with cold air advection. The difference between the lowest and highest depth coefficients found here is about a factor of three. Within each group separately, the theoretically derived cross-isobar angle agrees remarkably well with the observed one, as a function of thermal wind.

Early turbulence and drag reduction phenomena in larger pipes

Abstract: SOLUTIONS of certain high molecular weight polymers have been shown to exhibit the phenomena of both early turbulence1–7 and drag reduction4,5,8 depending on whether the measurements were made under laminar flow conditions for the former case or under turbulent flow conditions for the latter. In general, early turbulence has been observed only in capillary tube flows while drag reduction has been observed in a variety of flow geometries, the only requirement being a developing or developed turbulent flow field.

On the log-linear wind profile and the relationship between shear stress and stability characteristics over the sea

Abstract: Wind and stability characteristics in the atmospheric surface boundary layer at a height,Z, less than 20 m above the sea were examined in nine oceanic investigations. The analysis lends further support to the utility of the log-linear wind-profile law in the stability region of −0.4⩽Z/L⩽0.9, whereL is the Monin-Obukhov length. However, it is also shown that, inasmuch as better than 90% of the measurements fall within the range of ¦Z/L¦⩽ 0.25, and inasmuch as this correction to the drag coefficient under neutral conditions amounts to less than 10%, the familiar logarithmic wind law may be used rather than the log-linear form. A wind-stress drag coefficient,Cd (=1.2×10−3 between 1.0 m ⩽Z⩽ 18.3 m), is thus recommended for general deepwater oceanic applications. The situation over shallow water, which is different, is discussed briefly.

Breaking wave forces on a large diameter cell

Abstract: Experiments have been carried out by using non-breaking waves and breaking waves to investigate the wave forces on a vertical circular cell located in the shallow water. Based on the experimental data, the drag coefficient and the inertia coefficient of a circular cylinder and the curling factor of breaking waves are estimated, and the computation methods of wave forces are examined. As a result, it is shown that the phase lag of inertia forces behind the accelerations of water particles should be considered for the estimation of the drag coefficient as well as the inertia coefficient. In addition the previous formula of the maximum breaking wave forces acting on a cell or a pile is revised by introducing the effects of the above-mentioned phase lag and another phase difference, both of which are functions of the ratio of the cell diameter to the wave length. • It is confirmed that the proposed formula is applicable even to the large cell with the diameter comparable to the wave length.

Flight tests of Viking parachute system in three Mach number regimes. 2: Parachute test results

Abstract: Tests of the Viking 16.15-meter nominal-diameter disk-gap-band parachute were conducted at Mach number and dynamic pressure conditions which bracketed the range postulated for the Viking '75 mission to Mars. Parachutes were deployed at supersonic, transonic, and subsonic speeds behind a simulated Viking entry capsule. All parachutes successfully deployed, inflated, and exhibited sufficient drag and stability for mission requirements. Basic parachute data including loads, drag coefficients, pull-off angles, and canopy area ratios are presented. Trajectory reconstruction and onboard camera data methods were combined to yield continuous histories of both parachute and test-vehicle angular motions which are presented for the period from parachute deployment through steady inflation.

Some remarks on the solution of the lifting line equation

Abstract: The present work offers a simplification in the solution of Prandtl's lifting line equation. The equation for the local circulation is usually solved using a sine series in a collocation method. Using the fact that local circulation and local geometric angle of attack are related by a linear operator, an expression can be obtained for the drag coefficient containing only the square of the unknown constants, which implies that the loadings are orthogonal in Graham's sense (1952). Expressions are derived for the unknown constants, making use of the orthogonality of the loadings. The solution gives an approximate solution along the entire span, so that discontinuities, flap deflections, etc., can be accounted for.

Inviscid drag at transonic speeds

Abstract: A systematic asymptotic expansion procedure is introduced into the Euler equations to obtain the transonic, small-disturbance potential equation and corresponding relation for the drag. The relation consists of an integral around any contour enclosing the body and an integral along all shocks contained within the contour. Interpretations are given for the origin of the pressure drag due to shock waves, lift, and wind-tunnel boundaries. Numerical procedures are discussed for evaluating these quantities from finite-difference relaxation calculations. Computed results are included for various contours, and results are compared with some experimental data.

Applications of Steady-State Spray Equations to Combustion Modeling

Abstract: A constant cross-sectional area rocket motor was used to study the combustion of a spray of ethanol drops in oxygen. The steady-state spray equation was solved for monodisperse and distributed initial drop radii and for various drag and vaporization rate equations. The local flux of liquid ethanol drops thus calculated was compared with the experimentally determined one for the purpose of selecting a proper over-all spray combustion model. The main conclusion is that a model made up of a Nukiyama-Tanasawa initial drop radii distribution function, a Stokes drop drag equation, and either a modified Priem-Heidmann or a modified Spalding drop vaporization rate equation reproduced accurately the steady state of the engine tested. The original Priem-Heidmann and Spalding vaporization rate equations, which were suggested for single fuel droplets vaporizing and burning in infinite oxidizing media, were found to overestimate the vaporization rate of the droplets within the spray. Moreover, they would have lead to the erroneous conclusion that most of the vaporization occurs in the first few inches of the combustor, and the remaining lingers on at great length, while the actual vaporization is considerably more uniformly distributed in the axial direction. The monodisperse spray models, corresponding to the acceptable distributed spray models, gave acceptable results as well (in this case r0 = 5r30/3.915).

Velocity lag of solid particles in oscillating gases and in gases passing through normal shock waves

Abstract: The velocity lag of micrometer size spherical particles is theoretically determined for gas particle mixtures passing through a stationary normal shock wave and also for particles embedded in an oscillating gas flow. The particle sizes and densities chosen are those considered important for laser Doppler velocimeter applications. The governing equations for each flow system are formulated. The deviation from Stokes flow caused by inertial, compressibility, and rarefaction effects is accounted for in both flow systems by use of an empirical drag coefficient. Graphical results are presented which characterize particle tracking as a function of system parameters.

Drag reduction obtained by rounding vertical corners on a box-shaped ground vehicle

Abstract: A box-shaped ground vehicle was used to simulate the aerodynamic drag of delivery vans, trucks, and motor homes. A coast-down method was used to define the drag of this vehicle in a configuration with all square corners and a modified configuration with the four vertical corners rounded. The tests ranged in velocity from 30 miles per hour to 65 miles per hour, and Reynolds numbers ranged from 4.4 x 1,000,000 to 1.0 x 10 to the 7th power based on vehicle length. The modified configuration showed a reduction in aerodynamic drag of about 40 percent as compared to the square cornered configuration.