Measured Drag Coefficients Research Articles

Wind profiles, momentum fluxes and roughness lengths at Cabauw revisited

We describe the results of an experiment focusing on wind speed and momentum fluxes in the atmospheric boundary layer up to 200 m. The measurements were conducted in 1996 at the Cabauw site in the Netherlands. Momentum fluxes are measured using the K-Gill Propeller Vane. Estimates of the roughness length are derived using various techniques from the wind speed and flux measurements, and the observed differences are explained by considering the source area of the meteorological parameters. A clear rough-to-smooth transition is found in the wind speed profiles at Cabauw. The internal boundary layer reaches the lowest k-vane (20 m) only in the south-west direction where the obstacle-free fetch is about 2 km. The internal boundary layer is also reflected in the roughness lengths derived from the wind speed profiles. The lower part of the profile (< 40 m) is not in equilibrium and no reliable roughness analysis can be given. The upper part of the profile can be linked to a large-scale roughness length. Roughness lengths derived from the horizontal wind speed variance and gustiness have large footprints and therefore represent a large-scale average roughness. The drag coefficient is more locally determined but still represents a large-scale roughness length when it is measured above the local internal boundary layer. The roughness length at inhomogeneous sites can therefore be determined best from drag coefficient measurements just above the local internal boundary layers directly, or indirectly from horizontal wind speed variance or gustiness. In addition, the momentum and heat fluxes along the tower are analysed and these show significant variation with height related to stability and possibly surface heterogeneity. It appears that the dimensionless wind speed gradients scale well with local fluxes for the variety of conditions considered, including the unstable cases.

Theory and experiments on the stagnant cap regime in the motion of spherical surfactant-laden bubbles

The buoyant motion of a bubble rising through a continuous liquid phase can be retarded by the adsorption onto the bubble surface of surfactant dissolved in the liquid phase. The reason for this retardation is that adsorbed surfactant is swept to the trailing pole of the bubble where it accumulates and lowers the surface tension relative to the front end. The difference in tension creates a Marangoni force which opposes the surface flow, rigidifies the interface and increases the drag coefficient. Surfactant molecules adsorb onto the bubble surface by diffusing from the bulk to the sublayer of liquid adjoining the surface, and kinetically adsorbing from the sublayer onto the surface. The surface surfactant distribution which defines the Marangoni force is determined by the rate of kinetic adsorption and bulk diffusion relative to the rate of surface convection. In the limit in which the rate of either kinetic or diffusive transport of surfactant to the bubble surface is slow relative to surface convection and surface diffusion is also slow, surfactant collects in a stagnant cap at the back end of the bubble while the front end is stress free and mobile. The size of the cap and correspondingly the drag coefficient increases with the bulk concentration of surfactant until the cap covers the entire surface and the drag coefficient is that of a bubble with a completely tangentially immobile surface. Previous theoretical research on the stagnant cap regime has not studied in detail the competing roles of bulk diffusion and kinetic adsorption in determining the size of the stagnant cap angle, and there have been only a few studies which have attempted to quantitatively correlate simulations with measurements.This paper provides a more complete theoretical study of and a validating set of experiments on the stagnant cap regime. We solve numerically for the cap angle and drag coefficient as a function of the bulk concentration of surfactant for a spherical bubble rising steadily with inertia in a Newtonian fluid, including both bulk diffusion and kinetic adsorption. For the case of diffusion-limited transport (infinite adsorption kinetics), we show clearly that very small bulk concentrations can immobilize the entire surface, and we calculate the critical concentrations which immobilize the surface as a function of the surfactant parameters. We demonstrate that the effect of kinetics is to reduce the cap angle (hence reduce the drag coefficient) for a given bulk concentration of surfactant. We also present experimental results on the drag of a bubble rising in a glycerol–water mixture, as a function of the dissolved concentration of a polyethoxylated non-ionic surfactant whose bulk diffusion coefficient and a lower bound on the kinetic rate constants have been obtained separately by measuring the reduction in dynamic tension as surfactant adsorbs onto a clean interface. For low concentrations of surfactant, the experiments measure drag coefficients which are intermediate between the drag coefficient of a bubble whose surface is tangentially mobile and one whose surface is completely immobilized. Using the separately obtained value for the diffusion coefficient of the polyethoxylate, we undertake simulations which provide, upon comparison with the measured drag coefficients, a tighter bound on the kinetic rate constants than were otherwise obtained using dynamic surface tension measurement, and this suggests a new method for the measurement of kinetic rate constants.

Experimental determination of drag coefficient for volcanic materials: Calibration and application of a model to Popocatépetl volcano (Mexico) ballistic projectiles

This study shows the results of experiments performed in a subsonic wind tunnel to measure drag coefficients (Cd) for volcanic particles emitted by Popocatépetl volcano (Mexico). The results indicate that volcanic projectiles move in a range of Reynolds number (Re) values where Cd is independent of Re. Drag coefficients of volcanic fragments were found between the values of spheres and cubes with low values. In this study, initial conditions of the ballistic equations were calibrated with the “launching” kinetic energy from ballistics expelled by Popocatépetl volcano during the eruptive event of December 17, 1998. The maximum range of the projectiles calculated with the experimentally measured drag coefficient is in better agreement with the field and observational data reported here than using the values of geometrical bodies as in previous studies. Our study can be useful for definition of safety zones around volcanoes to protect people and infrastructure adequately.

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 μm and on the order of 1012 particles/m3, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.

Flow resistance of emergent vegetation

Abstract Conventional resistance equations (such as those of Manning, Chezy and Darcy–Weisbach) are inappropriate for flow through emergent vegetation, where resistance is exerted primarily by stem drag throughout the flow depth rather than by shear stress at the bed. An alternative equation form is suggested, in which the resistance coefficient is related to measurable vegetation characteristics and can incorporate bed roughness when this is significant. Equation performance is confirmed by comparison of predicted and measured stage–discharge relationships for flow through artificial cylindrical stems, and by comparison of calibrated and measured drag coefficient values for natural vegetation.

Flow resistance of emergent vegetation

Conventional resistance equations (such as those of Manning, Chézy and Darcy–Weisbach) are inappropriate for flow through emergent vegetation, where resistance is exerted primarily by stem drag throughout the flow depth rather than by shear stress at the bed. An alternative equation form is suggested, in which the resistance coefficient is related to measurable vegetation characteristics and can incorporate bed roughness when this is significant. Equation performance is confirmed by comparison of predicted and measured stage–discharge relationships for flow through artificial cylindrical stems, and by comparison of calibrated and measured drag coefficient values for natural vegetation.

Development of a low electric power 40 cm class magnetic suspension and balance system

We have developed a magnetic suspension and balance system (MSBS) having a test section of 36cm×40cm and being controlled around 5 axes, which can be operated with low electric power. We have developed the control method to support the model in the center of the test section. In order to evaluate the characteristics of this MSBS, we performed the calibration tests of magnetic forces on five axes and interference between these axes. We measured drag coefficients of a sphere and support interference in order to confirm the performance of this MSBS.

Field measurements of drag coefficients for model large woody debris

Woody debris in rivers can be a significant source of roughness and consequently influences flow at both the local and reach scale. In order to develop a better quantitative understanding of the interaction between wood in rivers and stream flow, we thus performed a set of field measurements of the drag on model woody debris for conditions that prevail in typical natural streams. Our model debris consisted of PVC “logs” with diameters between 4 and 30 cm. The field setting allowed us to consider the hydrodynamic influence of a rough stream bottom, and our measurements thus complement previously published flume-based measurements. We found that, owing to the variation of velocity with water depth, some of our results differed appreciably from measurements made in smooth flumes. We determined the effects of (i) the orientation of the log, (ii) the size of the log relative to the water depth, (iii) the depth of the log in the water column, and (iv) leafless branches on the log. We found that the orientation of the log had no significant effect on the apparent drag coefficient. By contrast, because the water velocity varies with depth, the position of the log in the water column influenced the apparent drag for small logs. For large logs (diameter >30% of the water depth), however, the position of the log had little effect on drag. The ratio of the diameter of the log to the water depth, a quantity called “blockage,” also affected drag. As blockage increased, drag increases. For blockages greater than about 0.3, however, the drag becomes independent of blockage. Finally, we found that the presence of leafless branches does not increase the drag (within measurement sensitivity).

HYDRODYNAMIC DAMPING AND QUASI-COHERENT STRUCTURES AT LARGE STOKES NUMBERS

Unsteady flow about solid and perforated cylinders at large Stokes numbers and very small Keulegan–Carpenter numbers has not been sufficiently understood to predict the hydroelastic response of compliant structures subjected to high frequency excitation. It is impossible to compute, difficult to quantify, and extremely difficult to visualize. Here, following a brief review of the previous research, new results for both forced and pluck-induced oscillations are presented. It is shown that: (a) the measured drag coefficients are larger (about double for smooth cylinders) than those predicted from the Stokes–Wang analysis (in the region of its applicability); (b) there is an unstable flow regime in which the oscillatory boundary layer develops quasicoherent structures (QCS) over a range of K values before giving rise to Honji-type coherent structures (HTCS); (c) the drag coefficients for perforated cylinders are much larger than those for solid cylinders and do not follow the Stokes–Wang prediction even at small β. As expected, their inertia coefficients are considerably smaller than those for solid cylinders.

FLOW CHARACTERISTICS IN THE NEAR WAKE OF TANDEM CONES

Experimental measurements in the turbulent wake behind tandem open base cones with four different apex angles of 30, 45, 60 and 90 degrees and the separation distance between the cones fixed at 1.5 cone base diameter (1.5 D) at a Reynolds number of 4x104 were undertaken. Measurements in the wake of single cones at the same Reynolds number have also been performed for comparison. The measurements were extended up to a down stream distance of 10 diameters behind the second cone. All measurements were performed using hot wire anemometer with X-wire probe.Mean velocity, turbulent intensity and shear stress show that the cone angle has an important effect on the wake development, drag force and mixing of the fluid in the near wake behind tandem cones. The measured drag coefficient increases with cone angle. The drag coefficient of tandem cones is lower than that of single open base cone of the same cone angle and Reynolds number. This is in accordance with the observed attenuation of turbulence in the wake of tandem cones.

Study on flow characteristics in gas-molten metal mixture pool

As part of basic research on the flow characteristics of a two-phase mixture pool under severe accident of fast breeder reactor (FBR), visualization and measurement of nitrogen gas-molten lead/bismuth two-phase flow in a rectangular pool were performed by using the neutron radiography technique. Measurements of drag coefficient of a single bubble and bubble shape regime showed that the relationship between the shape, size and the rising velocity of a single isolated nitrogen bubble in the molten lead/bismuth was not much different from that for an ordinary one. Appropriate correlation for drift velocity and drag coefficient between phases were recommended based on the drift flux correlation of measured pool void fraction. One- and two-dimensional analyses were performed by using a next generation computational code for safety analysis of severe accident of FBRs, SIMMER-III with various drag coefficient models. It was revealed that Kataoka–Ishii’s equation was suitable basically for estimation of drift velocity, namely, drag force between phases.

Drag Coefficients for Reactor Loose Parts

To estimate the range of impact velocities of potential reactor loose parts (LPs) requires information on regional flow velocities, LP mass, and LP drag coefficients. Flow velocities and the mass of potential LPs can generally be bounded and therefore are assumed to be known. In this work, drag coefficients for prototype LP shapes, including objects such as bolts, nuts, pins, and hand tools, were measured in the fluid velocity range typical of reactor coolant systems. Unlike drag coefficients measured for stationary objects, or by moving a body through a stagnant fluid, these experiments are performed on objects moving freely in a turbulent flow stream. In general, the measured drag coefficients for all tested LP shapes are shown to be close to the standard drag coefficient for a sphere, especially in the low-Reynolds-number region. However, significant differences exist in the wake transition region, which indicates that the drag coefficient for a freely moving body in turbulent flow is different from the drag coefficient for a confined body under the same flow conditions or for a body moving in a stagnant fluid.

Investigation of interference effects for a group of finite cylinders

Abstract An experimental study of the interference effects between two and three cylinders of finite height immersed in a turbulent boundary layer at subcritical Reynolds numbers has been conducted in a boundary layer wind tunnel, utilizing a pneumatic averaging manifold system to measure the fluctuating force at various levels. Measurements of mean drag and lift force coefficients, mode-generalized RMS drag and lift force coefficients, and mode-generalized drag and lift force spectra, for a range of cylinder spacings, configurations, and various angles of attack, are presented. The interference levels observed were found to depend strongly on the spacing, angle of attack, and the arrangement of the cylinders with respect to each other. The investigation of these relationships for finite cylinders should prove insightful to those interested in such phenomena.

Improved Design of Rod Pump Valves For Thermal And Horizontal Wells-Laboratory And Field Results

Abstract This paper presents results from a multi-participant project conducted by AOSTRA, ARC and industry to improve rod pumping efficiency for thermal and non-thermal oil fields in Alberta. It describes experimental and theoretical investigations on the hydrodynamics of rod pump valves that resulted in improved valve design and increased field production rates; and shows that, two of the most frequent problems encountered in the field are associated with sand and gas/steam inflow and may be alleviated through a better design of pump valves. These problems were examined in the laboratory (ARC) by testing ball-valve hydrodynamics at different GOR and inclination angles. Nineteen different valve designs were investigated using two laboratory facilities. Visual observations regarding critical GOR and inclination angles and quantitative measurements of pressure drop at different pump rates and fluid viscosity were obtained. A diagram, in which measured drag coefficient was plotted versus Reynolds number, was used to capture the steady and unsteady behaviours of the cage-ball systems. This diagram provided a basis for improving valve design. Following discussions of the laboratory findings with the project participants (field operators and manufacturers), and at the instigation of one particular manufacturer, a new valve design (HIVAC) was completed, manufactured and field tested at numerous sites. The field test results showed a significant increase in flow compared to conventional API valves previously used at the same sites. Introduction The design and operation of sucker rod operated bottom hole oil pumps, used in 80 – 90% of artificial lift wells, reached a mature stage during the period 1970 – 1980(1).Improved diagnostic tools for evaluating their performance appeared during the 1980s. These tools included automated dynamometer cards that aided rapid and relatively inexpensive de-convolution and interpretation of load-stroke diagrams(2,3). During the last decade, the development of heavy oil reservoirs in Alberta, Saskatchewan, and Venezuela and the widespread use of horizontal and deviated wells for both conventional and heavy oil reservoirs has imposed additional constraints on sucker rod pump applications. In Alberta, thermal projects have always experienced difficulties with pumping operations. In 1988, a survey conducted by the Alberta Department of Energy-Oil Sands and Research Division (formerly AOSTRA) found that the most common problems encountered were pump seizure (customarily related to sand-laden fluids), and pump inefficiencies due to steam and non-condensible gases(4). A multi-disciplinary team consisting of ADOE-OSRD, ARC, eight major field operators and four rod pump manufacturers in Alberta was formed to address those problems. Although the major objective was to improve existing thermal pumping technology, more general applications to horizontal well and high gas/oil ratio situations were put at a high priority. An overview of the program and its major laboratory achievements during 1988 – 1991 has been discussed elsewhere(4). This paper describes further laboratory observations on valve hydrodynamics with conventional and slanted wells obtained during 1991 – 1992, as well as significant field results achieved using a novel valve design. Equation 1 (available in full paper)

Wind-tunnel tests of conveyer-belt housing structures

The present paper describes a wind-tunnel study aimed at determining the design wind loads for housings of typical conveyer belt structures. Parametric measurements include the influence of several factors (e.g. shape, aspect ratio, solidity ratio, detailing) on the magnitude of the measured drag coefficients. For gantries the influence of the proximity to ground level and the proximity of two parallel lines is also investigated.

Aerodynamic efficiency of wings in rain

Measurements of lift, drag, and moment coefficients were obtained for a rectangular planform wing with wettable and nonwettable surface coatings in light to moderate rain. Comparisons with surfacewater flow patterns show that the degradation of aerodynamic efficiency caused by rain depended on the location of rivulet formation and on the diameter of these rivulets. Drag forces increase with increasing diameter of rivulets. Lift forces decrease with a longer film-convection region. Wing surfaces with wettable coatings had thinner films, flatter thinner rivulets, and flatter droplets that resulted in the least loss in lift-to-drag ratio caused by rain, despite longer film-convection regions. Droplet and rivulet diameters are found to be more important to aerodynamic performance than the location of rivulet formation.

On the Virtual Nonexistence of Multiple Instability Regions for Some Heat-Exchanger Arrays in Crossflow

In fluidelastic analyses involving a time delay (or phase lag) between the motions of cylinders in an array and the resultant unsteady fluid forces on the cylinders, a succession of instability-stability regions is predicted theoretically at low values of the mass-damping parameter, mδ/ρD2, below the “ultimate” fluidelastic instability, beyond which the system is not restabilized. However, as experimenters have had difficulty in verifying the existence of these regions of instability, it is legitimate to ask (i) do these regions really exist, and (ii) why are they so rarely observed? In this paper, with the aid of the quasi-steady model of Price and Pai¨doussis and with expanded measurements of lift and drag coefficients for a parallel triangular array with P/D = 1.375, it is shown that (a) the stability of the array strongly depends on geometric asymmetries; (b) whereas for a perfectly symmetric geometry the system may have several sub-ultimate instability regions, an asymmetry of as little as 0.02D may quench them and leave only the ultimate instability region intact. This suggests a possible explanation as to why the instability regions in question are so difficult to “find” experimentally. It also suggests that they may be of rather less practical importance for operating engineering systems than had heretofore been assumed, at least for some array geometries.

Testing Three-Dimensional Bluff-Body Models in a Low-Speed Two-Dimensional Adaptive Wall Test Section

Thin, sharp-edged disk models were evaluated in a low-speed two-dimensional adaptive flexible wall test section to determine the optimum adaptive wall testing environment for three-dimensional bluff-body models, by providing model testing recommendations for nominal solid blockage ratio and model span ratio. Drag coefficient measurements obtained under straight wall and adapted wall conditions showed that for a two-dimensional adaptive wall test section, the model span ratio imposes a more severe restriction upon model size than does the nominal solid blockage ratio. Minimum wall interference conditions were achieved with adapted walls for nominal solid blockage ratios less than 3 percent and model span ratios less than 21 percent, independent of the nominal test section aspect ratio, based on favorable comparison with previously-published experimental data. Data obtained under straight wall conditions confirmed that wall interference effects can only be neglected in conventional, straight-walled test sections for solid blockage ratios less than 0.5 percent and model span ratios less than 10 percent. The post-test boundary correction method of Maskell was successfully used to adjust the straight wall test section drag coefficient measurements of the larger models for wall interference effects, but no direct measurements of wall interference are used with this method. The results support the careful use of a two-dimensional wall adjustment strategy for three-dimensional nonlifting flows.

Spontaneous symmetry-breaking in the 3-D wake of a long cylinder simulated by the lattice gas method and drag coefficient measurements

Spontaneous symmetry-breaking in the 3-D wake of a long cylinder simulated by the lattice gas method and drag coefficient measurements

Aerodynamic drag reduction of goods trains

Tests on one-tenth scale hopper and gondola rail cars have been undertaken in a closed-circuit wind tunnel with a fixed floor. By varying the number of wagons in the train length, it was concluded that simulation of a typical wagon away from end effects (i.e. the influences of the locomotive(s) and trailing wagon) could be achieved with one and a half “dummy” wagons upstream and one half a “dummy” wagon downstream. An active model coupled to a drag balance was used to measure drag coefficients and drag reductions from geometric modifications on a typical wagon. The largest drag savings arose from fitting an enclosing top. Other effects, including inter-wagon gap and end fairings were also investigated. It was found that a practical wagon design, that was based on an existing wagon and allowed the current methods of loading and unloading, would reduce averaged drag coefficients by 27% for an unladen wagon. Considerably larger savings (up to 50%) could be made with more substantial wagon redesign.