Showing papers on "Drag coefficient published in 1985"

Creeping motion of a sphere through a Bingham plastic

Abstract: A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stress Yg below which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only when Yg is below 0.143 For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of Yg there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations For the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit.

Effect of Ultra-Stokesian Drag and Particle Interception on Impaction Characteristics

Abstract: The characteristics of impactors with round or rectangular nozzles have been determined by the numerical solution of the Navier-Stokes equations and of the equation of motion of the particles. The sensitivity of this solution to the system of grid lines was investigated by decreasing the spacing between them; these studies yielded sharper curves and higher √St50 for finer grids. The particle trajectory calculation program included an empirical ultra-Stokesian drag coefficient and a facility for handling particle interception. Studies comparing the results of runs made using the ultra-Stokesian drag law with those assuming Stokes law indicated that the latter underpredicts the √St20 by 5 to 10%. The influence of particle interception was found to be small except at very low Reynolds numbers, the characteristics for which demon strated low-efficiency tails. Dimensional analysis of the impactor system required the introduction of a second dimensionless quantity (in addition to the St) to char acterize the pa...

Particle dynamics and particle heat and mass transfer in thermal plasmas. Part I. The motion of a single particle without thermal effects

Abstract: A particle injected into a thermal plasma will experience a number of effects which are not present in an ordinary gas. In this paper effects exerted on the motion of a particle will be reviewed and analyzed in the context of thermal plasma processing of materials. The primary purpose of this paper is an assessment of the relative importance of various effects on particle motion. Computer experiments are described, simulating motion of a spherical particle in a laminar, confined plasma jet or in a turbulent, free plasma jet. Particle sizes range from 5 to 50 µm, and as sample materials alumina and tungsten are considered. The results indicate that (i) the correction term required for the viscous drag coefficient due to strongly varying properties is the most important factor; (ii) non-continuum effects are important for particle sizes <10 µm at atmospheric pressure and these effects will be enhanced for smaller particles and/or reduced pressures; (iii) the Basset history term is negligible, unless relatively large and light particles are considered over long processing distances; (iv) thermophoresis is not crucial for the injection of particles into thermal plasmas; (v) turbulent dispersion becomes important for particle <10 µm in diameter.

Wall-layer structure and drag reduction

Abstract: When drag-reducing additives are confined entirely to the linear sublayer of a turbulent channel flow of water, both the spanwise spacing and bursting rate of the wall-layer structure are the same as those for a water flow and there is no evidence of drag reduction. Drag reduction is measured downstream of the location where the additives injected into the sublayer begin to mix in significant quantities with the buffer region (10 y + The superscript + denotes a dimensionless quantity scaled with the kinematic viscosity ν and the wall shear velocity v * = (τ w /ρ) ½ . of the channel flow. At streamwise locations where drag reduction does occur and where the injected fluid is not yet uniformly mixed with the channel flow, the dimensionless spanwise streak spacing increases and the average bursting rate decreases. The decrease in bursting rate is larger than the corresponding increase in streak spacing. The wall-layer structure is like the structure in the flow of a homogeneous, uniformly mixed, drag-reducing solution. Thus, the additives have a direct effect on the flow processes in the buffer region and the linear sublayer appears to have a passive role in the interaction of the inner and outer portions of a turbulent wall layer.

The drag on a sphere in a power-law fluid

Abstract: Using a finite-element program, the drag on an unbounded fluid in an (inelastic) power-law fluid is estimated. Comparison with upper and lower bounds, and with experimental data is given. Some remarks on wall effects are also made, and it is shown that wall effects are negligible forn ⩽ 0.5.

Navier-Stokes computations of projectile base flow with and without mass injection

Abstract: A computational capability has been developed for predicting the flowfield about projectiles, including the recirculatory base flow at transonic speeds. In addition, the developed code allows mass injection at the projectile base and hence is used to show the effects of base bleed on base drag. Computations have been made for a secant-ogive-cylinder projectile for a series of Mach numbers in the transonic flow regime. Computed results show the qualitative and quantitative nature of base flow with and without base bleed. Base drag is computed and compared with the experimental data and semiempirical predictions. The reduction in base drag with base bleed is clearly predicted for various mass injection rates. Results are also presented that show the variation of total aerodynamic drag both with and without mass injection for Mach numbers of 0.9 < M< 1.2. The results obtained indicate that, with further development, this computational technique may provide useful design guidance for projectiles. MAJOR area of concern in shell design is the accurate prediction of the total aerodynamic drag. Both the range and terminal velocity of a projectile (two critical factors in shell design) are directly related to the total aerodynamic drag. The total drag for projectiles can be divided into three components: 1) pressure drag (excluding the base region), 2) viscous (skin friction) drag, and 3) base drag. At transonic speeds, base drag constitutes a major portion of the total drag. For a typical shell at M = 0.90, the relative magnitudes of the aerodynamic drag components are: 20% pressure drag, 30% viscous drag, and 50% base drag. The critical aerodynamic behavior of projectiles, indicated by rapid changes in the aerodynamic coefficients, occurs in the transonic speed regime and can be attributed in part to the complex shock structure existing on projectiles at transonic speeds. Therefore, in order to predict the total drag for projectiles, computation of the full flowfield (including the base flow) must be made. There are few reliable semiempirical procedures that can be used to predict shell drag; however, these procedures cannot predict the effects of mass injection. The objective of this research effort was to develop a numerical capability, using the Navier-Stokes computational technique, to compute the flowfield in the base region of projectiles at transonic speeds and thus to be able to compute the total aerodynamic drag with and without mass injection. The pressure and viscous components of drag generally cannot be reduced significantly without adversely affecting the stability of the shell. Therefore, recent attempts to reduce the total drag have been directed toward reducing the base drag. A number of studies have been made to examine the total drag reduction due to the addition of a boattail.1 Although this is very effective in reducing the total drag, it has a negative impact on the aerodynamic stability, especially at transonic

Effects of quadratic drag on convection in a saturated porous medium

Abstract: The effects of inertia (involving a drag which is quadratic in the velocity) on convection in a fluid‐saturated porous medium are considered. It is shown that the effect of quadratic drag is physically significant for natural convection, at realistic values of the Rayleigh number, in a thin layer of a medium whose overall Prandtl number is small. The qualitative effect of quadratic drag on the global stability of the conduction regime, and on bifurcation into the convection regime, is reported. Convection in an inclined slab of material is also discussed.

Drag reduction effectiveness and shear stability of polymer-polymer and polymer-fibre mixtures in recirculatory turbulent flow of water

Abstract: The turbulent drag reduction caused by polymer-polymer and polymerfibre mixtures has been measured in recirculatory flow of water. Shear stability studies have also been made on a number of drag reducing polymers, asbestos fibres and their mixtures in recirculatory turbulent flow of water. Reynolds numbers ranged from 20,000 to 57,000. Both positive and negative deviations from linear additive behaviour have been observed in drag reduction caused by the polymer-polymer mixtures depending upon their compositions, flow rate and polymer species in the mixture. The drag reduction by the mixtures has been predicted by using simple mixture rule equations including an interaction parameter. This interaction parameter is believed to depend upon the polymer interaction in the polymer mixture. The random coil size and rigidity of the polymer molecules appear to be responsible for the synergism observed in the drag reduction caused by the mixture. In general, mixtures having larger solvation number seem to give positive synergism.

Supercritical airfoil drag reduction by passive shock wave/boundary layer control in the Mach number range .75 to .90

Abstract: Airfoils operating in the transonic region are subject to large increases in drag due to shock wave/boundary layer interactions. The concept of passive shock wave/boundary layer control seeks drag reduction by placing a thin cavity with a porous top surface at the airfoil chordwise position where a shock wave would normally occur. The higher pressure behind the shock wave circulates flow through the cavity to the lower pressure ahead of the shock wave. The effects from this circulation prevent boundary layer separation and reduce entropy increases through the shock wave. In this investigation this concept is studied at a freestream Mach number range of .75 and .90. The Mach number distributions over the model, the wake impact pressure surveys used to determine profile drag and schlieren photographs for 2.8 percent porosity and solid airfoil cases are presented and compared. Results indicate that the profile drag coefficient can be reduced by as much as 40 percent through the use of this passive drag control system.

Surface wetting effects on a laminar flow airfoil in simulated heavy rain

Abstract: Wind tunnel experiments have been conducted on a natural laminar flow airfoil in a simulated heavy rain of 440 mm/h at a Reynolds number of 310,000 to assess the effect of surface wettability on the performance degradation due to rain. A significant loss of performance was observed for each of the three surfaces tested with the nonwettable, waxed surface being the most degraded (-75% reduction in maximum L/D) and the incompletely wettable epoxy gel coat being the least (-45% reduction). Accompanying the L/D loss was an effective reduction in angle of attack of up to 2 deg resulting from a downward translation of the CL polar. In photographic observations, the runback water layer was found to bead on the wax surface and sheet on the wettable surfaces. The strong dependence on surface wettability of both the airfoil performance and the water behavior indicates that the degradation due to heavy rain is primarily a result of the roughening of the airfoil surface by the runback water layer. The observed performance loss could only be partially emulated by causing premature transition from a laminar to a turbulent boundary layer. Nomenclature CL =lift coefficient, based on chord CD =drag coefficient, based on chord D = drop or bead diameter h = height of water layer L/D = lift-to-drag ratio U = flow velocity We = Weber number OL = angle of attack 0 = contact angle p = air density a = surface tension

Steady flows inside and around a fluid sphere at low Reynolds numbers

Abstract: The effects of internal circulation in bubbles and droplets have been analysed by means of a semi-analytical series-truncation method. The equations of motion are transformed into a series of coupled, ordinary, nonlinear differential equations by use of orthogonal sets. These infinite-series equations are then truncated adequately and solved numerically. Using this series-truncation method, we have evaluated the effects of different ratios (between the continuous and dispersed phases) of both density and viscosity for the flows of low Reynolds numbers. For all the density ratios investigated, the density difference has almost no effect on the drag coefficient at low Reynolds numbers. The shear stress and the drag coefficient increase with increasing viscosity ratio of droplet to ambience and decrease with increasing Reynolds number.

Isothermal flow past a blowing sphere

Abstract: Steady, axisymmetric, isothermal, incompressible flow past a sphere with uniform blowing out of the surface is investigated for Reynolds numbers in the range 1 to 100 and surface velocities up to 10 times the free stream value. A stream-function-velocity formulation of the flow equations in spherical polar co-ordinates is used and the equations are solved by a Galerkin finite-element method. Reductions in the drag coefficients arising from blowing are computed and the effects on the viscous and pressure contributions to the drag considered. Changes in the surface pressure, surface vorticity and flow patterns for two values of the Reynolds number (1 and 40) are examined in greater detail. Particular attention is paid to the perturbation to the flow field far from the sphere.

The effects of a strongly temperature-dependent viscosity on Stokes's drag law: experiments and theory

Abstract: This is an experimental and theoretical study of the slow translation of a hot sphere through a fluid at rest at infinity The viscosity depends strongly on temperature, ie, if Δ T = T 0 − T ∞ is the applied temperature difference and γ = |(d/d T 0 ) lnμ( T 0 )|, then the parameter θ = γ Δ T is large: it is about 65 in the experiments and is taken as infinite in the theory The flow is determined by two large parameters, namely the Nusselt number N and the modified viscosity ratio e −1 = ν ∞ /(ν 0 θ 3 ) The qualitative state of the flow is observed to depend on the relation between N and e If e −1 → ∞ ( N fixed, possibly large) previous analysis (Morris 1982) shows that all the shear occurs in a thin low-viscosity film coating the sphere; this film and the associated thermal layer separate at the equator, and a separation bubble of low-viscosity fluid trails the sphere (ii) If N → ∞ (e −1 ) large but fixed) even the most viscous fluid deforms, and both the drag and heat losses are found to be controlled by this highly viscous flow The present work maps the major asymptotic states which separate these two end-states for small e The drag and heat-transfer laws are determined experimentally and theoretically: in addition it is shown that separation of the thermal layer ceases when the drag is controlled by the most viscous fluid, even though the heat transfer in this case can be still controlled by the dynamics of the least-viscous fluid The heat-transfer and drag laws are also given for a sphere moving in a spherical container of finite radius This model is shown to give a close estimate of wall effects for a sphere moving in a cylindrical container For state (i) the theory predicts the heat transfer to within 20% and, for the smallest e, the drag to within 30% In the experiments e is small enough for all limiting states to be evident but, apart from state (i), a design flaw prevents a quantitative test of the theory For the other states, the theory is compared with numerical results from Daly & Raefsky (1985) Although the values of e in the calculations are not small enough for the limiting states to be achieved, the theory predicts the drag to within 8% and the heat transfer to within 10 %

Crab carapace hydrodynamics

Abstract: The hydrodynamic properties of the carapace of the swimming crab, (Callinectes sapidus, Portunidae) and two dissimilar benthic species, Cancer productus and Lopholithodes mandtii, are investigated employing flow visualization and low-speed wind tunnel techniques. Drag and lift forces for different orientations are determined for angles of attack ranging from 0–20. For Callinectes and Cancer productus drag is least at all angles of attack for sideways placement of the carapace, which corresponds to the position during locomotion in both species. Values of the drag Coefficient (based on plan form area) for Reynolds numbers greater than 104 for C. sapidus and C. productus are of the order of 0.2 0.35. Maximum values of the lift coefficient are of the order of 1.2 and 0.6 -0.7 for C. supidus and C.productus, respectively, giving maximum lift to drag ratios of about 4.0 for C. sapidus and 2.0 for C. productus. In contrast, L. mandtii is characterized by relatively high drag coefficients, low lift coefficients (about 1.0 and 0.2, respectively) and a lift to drag ratio that is an order of magnitude less than that of C. productus. The adaptive significance of the different lift to drag ratios of the animals is discussed in the context of simple hydromechanical models of carapace design in relation to flow velocity. It is argued that the carapace of Callinectes is adapted for minimum resistance and to generate sufficient lift to counter excess weight over buoyancy (specific gravity, S.G. = 1.14) at low forward speeds. Assuming that all of the lift required is produced passively by the carapace, minimum swimming speeds of the order of 0.15 ms-1 are calculated. The model applied to the benthic species focuses on two critical velocities, the slipping speed (speed at which lateral displacement first occurs) and the lift-off speed (speed at which the animal is lifted off the bottom). The ratio of lift-off speed to slipping speed for C. productus is approximately 1.9 and similar to that for plaice. Values for L. mandtii are about 3.3. It is suggested that the carapace of C. productus is adapted to maximize slipping speed and that displacement in L. mandtii is resisted actively by holding on to the substratum. The influence of flow on crabs in general is briefly discussed in relation to morphological design and habitat.

Drag on a sphere moving slowly in a rotating viscous fluid

Abstract: The mobility of a sphere moving slowly along the axis of a rotating, viscous, imcompressible fluid has been calculated for zero Reynolds number R and values of the Taylor number T ranging from zero to infinity, using a method of induced forces. For small values of T the mobility has been expanded in a power series in T½; the first seven terms of this series have been evaluated. Very good agreement is found with experimental data, which are only available for T [les ] 0.75.

Embedded cavity drag in steady laminar flow

Abstract: The numerical solution of the laminar boundary-layer flow over an embedded cavity is studied. The purpose of the study is to examine the relevant drag characteristics of laminar cavity flow. The solution field is obtained in terms of velocity and vorticity variables, with the stream function and pressure derivable from the directly computed variables. An analysis and comparison is made among four square cavities, ranging in size from 0.25 to 1.00 boundary-layer thickness deep. The dominant flow features are examined in the vicinity of the cavity by means of the stream function and isovorticity contours. The dominant physics in the overall drag characteristics of the flow are examined by an analysis of the pressure and wall shear-stress distributions in the cavity, and upstream and downstream of the cavity. Pressure forces and frictional forces in, and in the vicinity of, the cavity are determined. Stress relaxation distances, both upstream and downstream of the cavity, are calculated and analyzed. The dynamics of the boundary-layer flow over an embedded cavity are summarized. Finally, the relevance of the present results to the control of flow separation in such flows is discussed.

Icing flight research: Aerodynamic effects of ice and ice shape documentation with stereo photography

Abstract: Aircraft icing flight research was performed in natural icing conditions. A data base consisting of icing cloud measurements, ice shapes, and aerodynamic measurements is being developed. During research icing encounters the icing cloud was continuously measured. After the encounter, the ice accretion shapes on the wing were documented with a stereo camera system. The increase in wing section drag was measured with a wake survey probe. The overall aircraft performance loss in terms of lift and drag coefficient changes was obtained by steady level speed/power measurements. Selective deicing of the airframe components was performed to determine their contributions to the total drag increase. Engine out capability in terms of power available was analyzed for the iced aircraft. It was shown that the stereo photography system can be used to document ice shapes in flight and that the wake survey probe can measure increases in wing section drag caused by ice. On one flight, the wing section drag coefficient (c sub d) increased approximately 120 percent over the uniced baseline at an aircraft angle of attack of 6 deg. On another flight, the aircraft darg coefficient (c sub d) increased by 75 percent over the uniced baseline at an aircraft lift coefficient (C sub d) of 0.5.

The normal-force coefficient of a thin closed fence

Abstract: In a full-scale field study, the drag coefficient of a thin closed fence was estimated. A measurement plate was constructed more or less in the center of the barrier in order to estimate the normal-force on the fence. The normal-force coefficient was studied under near-neutral stratification for various Reynolds numbers and different angles of attack.

Comparison of on-road and wind-tunnel tests for tractor-trailer aerodynamic devices, and fuel savings predictions

Abstract: Wind tunnels which are large enough for full-scale trucks are rare, and the cost of satisfactorily-detailed models for smaller tunnels is high. The work presented shows the results from the application of a method which provides an over-the-road evaluation of the incremental changes in fuel consumption and drag coefficient produced following the addition of a variety of aerodynamic drag reducing devices to a tractor-trailer truck combination. The devices tested were an aerodynamic sunvisor, a roof-mounted air deflector, cab extenders, cab skirts, a trailer nose fairing, a set of trailer quads (quarter-rounds), and trailer skirts which were mounted on a low-forward-entry tractor and high box-van trailer. The significant differences between the wind tunnel and on-road drag reductions suggest that the effects of on-road wind turbulence can substantially reduce the wind tunnel results even though a 1.5% turbulence intensity level was used in the tunnel experiments. These experiments have highlighted that the wind tunnel results were optimistic and suggest a need for on-road testing to more accurately evaluate the benefit of aerodynamic devices for trucks. The on-road results finally are used to predict the resultant fuel economies for various loads and speed conditions.

Effect of Flow Oscillations on Cavity Drag and a Technique for Their Control

Abstract: Experiments to relate the state of the shear layer to cavity drag have been performed in a water channel using a 4" axisymmetric cavity model. Detailed flow measurements in various cavity flow oscillation phases, amplitude amplification along the flow direction, distribution of shear stress, and other momentum flux obtained by laser Doppler velocimeter are presented. Measurements show exponential dependence of cavity drag on the length of the cavity. A jump in the cavity drag coefficient is observed as the cavity flow shows a bluff body wake type behavior. Natural and forced oscillations are introduced by a sinusoidally heated thin-film strip which excites the Tollmein-Schlichting waves in the boundary layer upstream of the gap. For a large gap, self-sustained periodic oscillations are observed, while for smaller gaps, which do not oscillate naturally, periodical oscillations can be obtained by external forcing through the strip heater. The drag of the cavity can be increased by one order of magnitude in the non-oscillating case through external forcing. Also, it is possible to completely eliminate mode switching by external forcing. For the first time, it is demonstrated that amplitude of cavity flow Kelvin-Helmholtz wave is dampened or cancelled by introduction of external perturbation of natural flow frequency but different phase.

Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

Abstract: The drag coefficient for bubbles with mobile or immobile interface rising in shear-thinning elastic fluids described by an Ellis or a Carreau model is discussed Approximate solutions based on linearization of the equations of motion are presented for the highly elastic region of flow These solutions are in reasonably good agreement with the theoretical predictions based on variational principles and with published experimental data

Drag of Bodies in Rarefied Hypersonic Flow

Abstract: The drag behavior of simple -shaped two-dimensional and axisymmetric bodies in hypersonic rarefied flow is summarized. The experimental data used were mainly obtained in the DFVLR hypersonic low density tunnels during the past 15 years. The body shapes analyzed include spheres, disks, cones, cylinders, and flat plates parallel to the flow. These shapes include bodies that have only pressure or frictional drag. Special attention is given to the frictional drag overshoot of flat plates in the near free molecular flow regime. Simple qualitative explanations for this overshoot and for the different behavior of two- and threedimensional bodies are given. Nomenclature