Showing papers on "Drag coefficient published in 1999"

Drag, turbulence, and diffusion in flow through emergent vegetation

Abstract: Aquatic plants convert mean kinetic energy into turbulent kinetic energy at the scale of the plant stems and branches. This energy transfer, linked to wake generation, affects vegetative drag and turbulence intensity. Drawing on this physical link, a model is developed to describe the drag, turbulence and diffusion for flow through emergent vegetation which for the first time captures the relevant underlying physics, and covers the natural range of vegetation density and stem Reynolds' numbers. The model is supported by laboratory and field observations. In addition, this work extends the cylinder-based model for vegetative resistance by including the dependence of the drag coefficient, CD, on the stem population density, and introduces the importance of mechanical diffusion in vegetated flows.

Robust nonlinear control of a hypersonic aircraft

Abstract: For the longitudinal motion of a hypersonic aircraft containing twenty-eight inertial and aerodynamic uncertain parameters, robust flight control systems with nonlinear dynamic inversion structure are synthesized. The system robustness is characterized by the probability of instability and probabilities of violations of thirty-eight performance criteria, subjected to the variations of the uncertain system parameters. The design cost function is defined as a weighted quadratic sum of these probabilities. The control system is designed using a genetic algorithm to search a design parameter space of the nonlinear dynamic inversion structure. During the search iteration, Monte Carlo evaluation is used to estimate the system robustness and cost function. This approach explicitly takes into account the design requirements and makes full use of engineering knowledge in the design process to produce practical and efficient control systems. A4 MY, m 4 Nomenclatm-e speed of sound, ftls drag coefficient lift coefficient moment coefficient due to pitch rate moment coefficient due to angle of attack moment coefficient due to elevator deflection thrust coefficient reference length, 80 ft drag, lbf altitude, ft moment of inertia, 7 X lo6 slug-ft2 lift, lbf Mach number pitching moment, lbf-ft mass, 9375 slugs pitch rate, radis radius of the Earth, 20,903,500 ft radial distance from Earth’s center, ft reference area, 3603 ft2 thrust, lbf velocity, ft/S angle of attack, rad throttle setting flight-path angle, rad elevator deflection, rad gravitational constant, 1.39 X 1Or6 ft3/s2~ density of air, slugsIft

Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall

Abstract: Drag reduction phenomena, in which 14% drag reduction of tap water flowing in a 16 mm-diameter pipe occurs in the laminar flow range, have been clarified. Experiments were carried out to measure the pressure drop and the velocity profile of tap water and an aqueous solution of glycerin flowing in pipes with highly water-repellent walls, by using a pressure transducer and a hot-film anemometer, respectively. The same drag reduction phenomena also occurred in degassed tap water when using a vacuum tank. The velocity profile measured in this experiment gives the slip velocity at the pipe wall, and it was shown that the shear stress is directly proportional to the slip velocity.The friction factor formula for a pipe with fluid slip at the wall has been obtained analytically from the exact solution of the Navier–Stokes equation, and it agrees well qualitatively with the experimental data.The main reasons for the fluid slip are that the molecular attraction between the liquid and the solid surface is reduced because the free surface energy of the solid is very low and the contact area of the liquid is decreased compared with a conventional smooth surface because the solid surface has many fine grooves. Liquid cannot flow into the fine grooves owing to surface tension. These concepts are supported by the experimental result that drag reduction does not occur in the case of surfactant solutions.

Variation of Roughness Coefficients for Unsubmerged and Submerged Vegetation

Abstract: This paper investigates the variation of the vegetative roughness coefficient with the depth of flow. A horsehair mattress is used in the experimental study to simulate the vegetation on the watercourses. Test results reveal that the roughness coefficient reduces with increasing depth under the unsubmerged condition. However, when fully submerged, the vegetative roughness coefficient tends to increase at low depths but then decrease to an asymptotic constant as the water level continues to rise. A simplified model based on force equilibrium is developed to evaluate the drag coefficient of the vegetal element; Manning's equation is then employed to convert the drag coefficient into the roughness coefficient. The data of this study are compared with those of selected previous laboratory and field tests. The results show a consistent trend of variation for the drag coefficient versus the Reynolds number. This trend can be represented by a vegetative characteristic number k. Given information such as the bed ...

Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers

Abstract: Direct numerical simulations of two-dimensional (2D) and 3-D unsteady flow around a square cylinder for moderate Reynolds numbers (Re=150–500) are performed, employing an implicit fractional step method finite-volume code with second-order accuracy in space and time. The simulations, which are carried out with a blockage ratio of 5.6%, indicate a transition from 2-D to 3-D shedding flow between Re=150 and Re=200. Both spanwise instability modes, A and B, are present in the wake transitional process, similar to the flow around a circular cylinder. However, seemingly in contrast to a circular cylinder, the transitional flow around a square cylinder exhibits a phenomenon of distinct low-frequency force pulsations (Re=200–300). For 3-D simulations, the Strouhal number and the mean drag coefficient are in general agreement with existing experiments. Between Re=300 and 500, an increase in the spanwise coupling of fluctuating forces is indicated. The influence of the spanwise aspect ratio using periodic boundary conditions, a finer grid, and a finer time step is also investigated.

Drag and lift forces on a rotating sphere in a linear shear flow

Abstract: The drag and lift forces acting on a rotating rigid sphere in a homogeneous linear shear flow are numerically studied by means of a three-dimensional numerical simulation. The effects of both the fluid shear and rotational speed of the sphere on the drag and lift forces are estimated for particle Reynolds numbers of 1[les ]Rep[les ]500.The results show that the drag forces both on a stationary sphere in a linear shear flow and on a rotating sphere in a uniform unsheared flow increase with increasing the fluid shear and rotational speed. The lift force on a stationary sphere in a linear shear flow acts from the low-fluid-velocity side to the high-fluid-velocity side for low particle Reynolds numbers of Rep 60. The change of the direction of the lift force can be explained well by considering the contributions of pressure and viscous forces to the total lift in terms of flow separation. The predicted direction of the lift force for high particle Reynolds numbers is also examined through a visualization experiment of an iron particle falling in a linear shear flow of a glycerin solution. On the other hand, the lift force on a rotating sphere in a uniform unsheared flow acts in the same direction independent of particle Reynolds numbers. Approximate expressions for the drag and lift coefficients for a rotating sphere in a linear shear flow are proposed over the wide range of 1[les ]Rep[les ]500.

Blunt-Body Wave Drag Reduction Using Focused Energy Deposition

Abstract: A parametric computational study of energy deposition upstream of generic two-dimensional and axisymmetric blunt bodies at Mach numbers of 6.5 and 10 is performed utilizing a full Navier-Stokes computational fluid dynamics code. The energy deposition modifies the upstream shock structure and results in large wave drag reduction and very high power effectiveness. Specifically, drag is reduced to values as low as 30% of baseline drag (no energy deposited into flow) and power effectiveness ratios (ratio of thrust power saved to power deposited into the flow) of up to 33 are obtained. The fluid dynamic and thermodynamic bases of the observed drag reduction are examined

Multi-phase CFD analysis of natural and ventilated cavitation about submerged bodies

Abstract: A multi-phase CFD method has been developed and is applied here to model the flow about submerged bodies subject to natural and ventilated cavitation. The method employs an implicit, dual-time, pre-conditioned, multi-phase Navier-Stokes algorithm and is three-dimensional, multi-block and parallel. It incorporates mixture volume and constituent volume fraction transport/generation for liquid, condensable vapor and non-condensable gas fields. Mixture momentum and turbulence scalar equations are also solved. Mass transfer modeling provides exchange between liquid and vapor phases. The model accounts for buoyancy effects and the presence/interaction of condensable and non-condensable fields. In this paper, the theoretical formulation of the method is summarized. Results are presented for steady-state and transient axisymmetric flows with natural and ventilated cavitation about several bodies. Comparisons are made with available measurements of surface pressure distribution, cavitation bubble geometry and drag coefficient. Three-dimensional results are presented for a submerged body running at several angles of attack. The underlying three-species formulation and the specific models employed for mass transfer and momentum diffusion are demonstrated to provide good correspondence with measurements; however, several weaknesses in the current modeling are identified and discussed.

Rising speed and dissolution rate of a carbon dioxide bubble in slightly contaminated water

Abstract: The rising speed and dissolution rate of a carbon dioxide bubble in slightly contaminated water were investigated experimentally and numerically. We developed an experimental system that uses a charged-coupled device (CCD) camera coupled with a microscope to track the rising bubble. By precisely measuring the bubble size and rising speed, we were able to accurately estimate the drag coefficient and the Sherwood number for the dissolution rate of gas bubbles at Reynolds numbers below 100 in the transient regime, where the bubble changes from behaving as a fluid sphere to behaving as a solid particle. We also numerically estimated the drag coefficient and Sherwood number of the ‘stagnant cap model’ by directly solving the coupled Navier–Stokes and convection–diffusion equations. We compared our experimental results with our numerical results and proposed equations for estimating the drag coefficient and Sherwood number of the bubble affected by contamination and clarified that the gas–liquid interface of the carbon dioxide bubble in water is immobile. We also show that the experimental and numerical results are in good agreement and the stagnant cap model can explain the mechanism of the transient process where the bubble behaviour changes from that of a fluid sphere to that of a solid particle.

Wake Integration for Three-Dimensional Flowfield Computations: Theoretical Development

Abstract: This paper examines the analytical, experimental, and computational aspects of the determination of the drag acting on an aircraft in flight, with or without powered engines, for subsonic/transonic flow. Using a momentum balance approach, the drag is represented by an integral over a crossflow plane at an arbitrary distance behind the aircraft. Asymptotic evaluation of the integral shows the drag can be decomposed into three components corresponding to streamwise vorticity and variations in entropy and stagnation enthalpy. These are related to the established engineering concepts of induced drag, wave drag, profile drag, and engine power and efficiency. This decomposition of the components of drag is useful in formulating techniques for accurately evaluating drag using computational fluid dynamics calculations or experimental data.

Similarity Statistics from a Direct Numerical Simulation of the Neutrally Stratified Planetary Boundary Layer.

Abstract: The turbulent flow in the unstratified Ekman layer over a smooth surface for the case of no horizontal rotation has been simulated. All relevant scales of motion are resolved so that no subgrid-scale parameterization is needed. The Reynolds number Re, while much smaller than those found in the atmosphere, is large enough that the flow exhibits a distinct logarithmic surface layer and yields shear-stress statistics that, to a good approximation, satisfy Reynolds number similarity. Agreement with shear-stress profiles from large eddy simulations is good, especially when latitude and geostrophic wind direction are taken into account. Results are used to estimate the ratio of the boundary layer depth to the Ekman scale u∗/f and the similarity constants needed to determine the geostrophic drag coefficient u∗/G and surface-stress angle α0 in the Re → ∞ limit characteristic of the neutral planetary boundary layer.

Pressure Drag in Linear and Nonlinear Quantum Fluids

Abstract: We study the flow of a weakly interacting Bose-Einstein condensate around an obstacle by numerical solution of the Gross-Pitaevskii equation. We observe vortex emission and the formation of bow waves leading to pressure drag. We compare the drag law with that of an ideal Bose gas, and show that interactions reduce the drag force. This reduction can be explained in terms of a ``collisional screening'' of the obstacle.

Motion of tracer particles in supersonic flows

Abstract: Factors that may act on particle motion in high-speed flow are investigated. The classical expressions of drag coefficient C D for a sphere are reviewed. Then, a drag expression is proposed, extending Cunningham’s method to higher velocities and Knudsen numbers. This law, valid from continuum to free molecule conditions, for Re≲200 and M≲1 (where Re and M are, respectively, the Reynolds and Mach numbers based on relative velocity), is used to compare calculated and experimental values of the drag coefficient, as well as the particle velocities across an oblique shock wave. Calculated results are found to be in agreement with experiments.

Gravitational settling of particles through density interfaces

Abstract: Gravitational settling of dense particles through density interfaces is common in many environmental and engineering flow situations, yet very little research has been done to understand the mechanics of particle–stratification interactions. To this end, a detailed experimental study was carried out to investigate the settling of solid spherical particles through density interfaces. In these experiments, the solid particles first descended through a deep homogeneous layer, entered a thick pycnocline and then descended to another denser homogeneous layer. It was found that the stratification has a significant impact on the settling of particles in the approximate parameter range 1.5

On the rise and fall of a ball with linear or quadratic drag

Abstract: We review the problem of a vertically thrown ball, with a drag force which is either linear or quadratic in the speed. It is stressed from the outset that these two types of drag correspond to specific ranges of the Reynolds number (Re<1 and 103

Estimates of bottom roughness length and bottom shear stress in South San Francisco Bay, California

Abstract: A field investigation of the hydrodynamics and the resuspension and transport of particulate matter in a bottom boundary layer was carried out in South San Francisco Bay (South Bay), California, during March-April 1995. Using broadband acoustic Doppler current profilers, detailed measurements of turbulent mean velocity distribution within 1.5 m above bed have been obtained. A global method of data analysis was used for estimating bottom roughness length zo and bottom shear stress (or friction velocities u*). Field data have been examined by dividing the time series of velocity profiles into 24-hour periods and independently analyzing the velocity profile time series by flooding and ebbing periods. The global method of solution gives consistent properties of bottom roughness length zo and bottom shear stress values (or friction velocities u*) in South Bay. Estimated mean values of zo and u* for flooding and ebbing cycles are different. The differences in mean zo and u* are shown to be caused by tidal current flood-ebb inequality, rather than the flooding or ebbing of tidal currents. The bed shear stress correlates well with a reference velocity; the slope of the correlation defines a drag coefficient. Forty-three days of field data in South Bay show two regimes of zo (and drag coefficient) as a function of a reference velocity. When the mean velocity is >25–30 cm s−1, the ln zo (and thus the drag coefficient) is inversely proportional to the reference velocity. The cause for the reduction of roughness length is hypothesized as sediment erosion due to intensifying tidal currents thereby reducing bed roughness. When the mean velocity is <25–30 cm s−1, the correlation between zo and the reference velocity is less clear. A plausible explanation of scattered values of zo under this condition may be sediment deposition. Measured sediment data were inadequate to support this hypothesis, but the proposed hypothesis warrants further field investigation.

Evidence for the Effects of Swell and Unsteady Winds on Marine Wind Stress

Abstract: Over the past four decades much effort has been directed toward determining a parameterization of the sea surface drag coefficient on readily measurable quantities, such as mean wind speed and atmospheric stability. Although such a parameterization would have obvious operational advantages, the considerable scatter present between experiments, or within any one experiment, indicates that it is not easily achievable. One likely candidate for much of the scatter is the underlying wave field. Unfortunately, few campaigns over the years have included spectral measurements of the waves. Among those that have, the results are inconclusive. Here data are presented from the Surface Wave Dynamics Experiment and High Resolution Remote Sensing Program campaigns in which 3-m discus buoys were instrumented with K-Gill and sonic anemometers and complete motion packages to measure the direct (eddy correlation) stress and, concurrently, the directional ocean wave spectrum. These data are examined for the effects of swell on the drag coefficient. It is found that much of the scatter in the drag coefficient can be attributed to geophysical effects, such as the presence of swells or nonstationary conditions.

The flow of an Oldroyd-B fluid past a cylinder in a channel: adaptive viscosity vorticity (DAVSS-ω) formulation

Abstract: A parallel unstructured finite volume method (FVM) is developed and implemented under a distributed computing environment through the parallel virtual machine (PVM) libraries, and is used to simulate the channel flow of the Oldroyd-B fluid past a circular cylinder. Differing from our previous work [11, 12] , a discrete elastic viscous split stress (DEVSS) formulation together with an independent interpolation of the vorticity (DEVSS- ω ) is proposed in this paper. This method has almost the same stability behavior as the elastic viscous split stress (EVSS) formulation, and is suitable for complex constitutive models. To further improve the stability at high Deborah numbers, we combine the idea of the discrete adaptive elastic viscous split stress (DAVSS) formulation [7] with the independent interpolation of the vorticity to arrive at the DAVSS- ω method. The numerical implementation is based on the unstructured FVM method and the semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm. The parallelization of the program is implemented by a domain decomposition strategy and using PVM software libraries. The results are compared with those by the EVSS, DEVSS, and the plain Oldroyd-B formulation (without splitting the stress). It is found that the drag coefficient first decreases and then increases with the De number, for a channel half width to cylinder radius ratio of h / R = 2. It is also confirmed that the drag enhancement at high Deborah number is due to the increasing extension effect in the regions near the front and the rear stagnation points.

Experimental studies of strongly stratified flow past three-dimensional orography

Abstract: Stably stratified flows past three-dimensional orography have been investigated using a stratified towing tank. Flows past idealized axisymmetric orography in which the Froude number, F h = U/Nh (where U is the towing speed, N is the buoyancy frequency and h is the height of the obstacle) is less than unity have been studied. The orography considered consists of two sizes of hemisphere and two cones of different slope. For all the obstacles measurements show that as F h decreases, the drag coefficient increases, reaching between 2.8 and 5.4 times the value in neutral flow (depending on obstacle shape) for F h ≤ 0.25. Local maxima and minima in the drag also occur. These are due to the finite depth of the tank and can be explained by linear gravity-wave theory. Flow visualization reveals a lee wave train downstream in which the wave amplitude is O(F h h), the smallest wave amplitude occurring for the steepest cone. Measurements show that for all the obstacles, the dividing-streamline height, Z s , is described reasonably well by the formula Z s /h = 1 - F h . Flow visualization and acoustic Doppler velocimeter measurements in the wake of the obstacles show that vortex shedding occurs when F h ≤ 0.4 and that the period of the vortex shedding is independent of height. Based on velocity measurements in the wake of both sizes of hemisphere (plus two additional smaller hemispheres), it is shown that a blockage-corrected Strouhal number, S 2c = f L 2 /U c , collapses onto a single curve when plotted against the effective Froude number, F hc = U c /Nh. Here, U c is the blockage-corrected free-stream speed based on mass-flux considerations, f is the vortex shedding frequency and L 2 is the obstacle width at a height z s /2. Collapse of the data is also obtained for the two different shapes of cone and for additional measurements made in the wake of triangular and rectangular flat plates. Indeed, the values of S 2c for all these obstacles are similar and this suggests that despite the fact that the obstacle widths vary with height, a single length scale determines the vortex-street dynamics. Experiments conducted using a splitter plate indicate that the shedding mechanism provides a major contribution to the total drag (∼ 25%). The addition of an upstream pointing 'verge region' to a hemisphere is also shown to increase the drag significantly in strongly stratified flow. Possible mechanisms for this are discussed.

Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions.

Abstract: Microbially produced polysaccharides have properties which are extremely useful in different applications. Polysaccharide producing fermentations start with liquid broths having Newtonian rheology and end as highly viscous non-Newtonian solutions. Since aerobic microorganisms are used to produce these polysaccharides, it is of great importance to know the mass transfer rate of oxygen from a rising air bubble to the liquid phase, where the microorganisms need the oxygen to grow. One of the most important parameters determining the oxygen transfer rate is the terminal rise velocity of air bubble. The dynamics of the rise of air bubbles in the aqueous solutions of different, mostly microbially produced polysaccharides was studied in this work. Solutions with a wide variety of polysaccharide concentrations and rheological properties were studied. The bubble sizes varied between 0.01 mm3 and 10 cm3. The terminal rise velocities as a function of air bubble volume were studied for 21 different polysaccharide solutions with different rheological properties. It was found that the terminal velocities reached a plateau at higher bubble volumes, and the value of the plateau was nearly constant, between 23 and 27 cm/s, for all solutions studied. The data were analyzed to produce the functional relationship between the drag coefficient and Reynolds number (drag curves). It was found out that all the experimental data obtained from 21 polysaccharide solutions (431 experimental points), can be represented by a new single drag curve. At low values of Reynolds numbers, below 1.0, this curve could be described by the modofoed Hadamard–Rybczynski model, while at Re > 60 the drag coefficient was a constant, equal to 0.95. The latter finding is similar to that observed for bubble rise in Newtonian liquids which was explained on the basis of the “solid bubble” approach. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 64: 257–266, 1999.

A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures

Abstract: A continuum theory of a multiphase mixture is formulated. In the basic balance laws we introduce an additional balance of equilibrated forces to describe the microstructural response according to Goodman & Cowin [11] and Passman et al. [23] for each constituent. Based on the Muler-Liu form of the second law of thermodynamics a set of constitutive equations for a viscous solid-fluid mixture with microstructure is derived. These relatively general equations are then reduced to a system of ordinary differential equations describing a steady flow of the solid-fluid mixture between two horizontal plates. The resulting boundary value problem is solved numerically and results are presented for various values of parameters and boundary conditions. It is shown that simple shearing generally does not occur. Typically, for the solid phase, in the vicinity of a boundary, if the solid-volume fraction is low, a layer of high shear rate occurs, whose thickness is nearly between 5 and 15 grain diameters, while if the solid-volume fraction is high, an interlock phenomenon occurs. The fluid velocity depends largely on the drag force between the constituents. If the drag coefficient is sufficiently large, the fluid flow is nearly the same as that of the solid, while for a small drag coefficient, the fluid shearing flow largely decouples from that of the solid in the entire flow region. Apart from this, there is a tendency for solid particles to accumulate in regions of low shear rate.

Axisymmetric creeping flow past a porous prolate spheroidal particle using the Brinkman model

Abstract: A boundary-value solution to axisymmetric creeping flow past and through a porous prolate spheroidal particle is presented. The Brinkman model for the flow inside the porous medium and the Stokes model for the free-flow region in their stream function formulations are used. As boundary conditions, continuity of velocity, pressure and tangential stresses across the interface are employed. A mainly analytical procedure for calculating the required eigenvalues and eigenfunctions for the porous region part of the solution is proposed. The coefficients of the convergent series expansions of the general solutions for the stream functions, and thus for the velocity, pressure, vorticity and stress fields, both for the flow inside and outside the porous particle, can be calculated to any desired degree of accuracy as the solution of a truncated algebraic system of linear equations, once the eigenvalues to the Brinkman equation for a given focal distance and permeability have been computed. The drag force experienced by the porous particle is then given as a function of only one of these coefficients. Streamline-pattern and drag-force dependence on permeability and focal distance are presented and discussed

The influence of sediment load on tidal dynamics, a case study : Cádiz Bay

Abstract: A two-dimensional, non-linear, finite-difference, hydrodynamic model was applied to Cadiz Bay to study the influence of sediment load on tidal dynamics. The sediment load effect is represented parametrically as a dependence of the drag coefficient on the relative settling velocity (the ratio of the settling velocity of suspended particles to the bottom friction velocity) and the relative friction velocity (the ratio of the bottom friction velocity to its critical value at which sediment particles begin to go into suspension). This dependence is derived from a solution of the equations describing the vertical structure of the sediment-stratified bottom logarithmic layer. A comparison of the model predictions with and without allowance for the sediment load effect shows that the latter is responsible for small local changes of the amplitude and phase of tidal elevation and the maximum depth-averaged tidal velocity, the result counting in favour of the conventional approach whereby the influence of sediment load on tidal dynamics is considered to be negligible. However, it is apparent after close inspection of the model predictions that the sediment load effect tends to enhance the time-space variability of the tidal characteristics. In particular, it results in an increase in the maximum depth-averaged velocity and a decrease in the drag coefficient for the periods of flood and ebb currents, thus reducing the shear bottom stress and the tidal energy dissipation by about half.

Numerical simulations of a sphere settling through a suspension of neutrally buoyant fibres

Abstract: The sedimentation of a small dense sphere through a suspension of neutrally buoyant fibres is investigated via a numerical simulation technique that includes both fibre–fibre contact forces and long-range hydrodynamic interactions. In situations where the diameter of the sphere is smaller than the length of the fibres, calculations that exclude the effect of contacts between fibres severely underestimate the drag force on the sphere measured in experiments. By including fibre–fibre contacts in our simulations we are to able to account for this discrepancy, and also the strong dependence of the drag on the initial orientation of the fibres. At low and moderate values of nL3, where n is the number of fibres per unit volume and L the fibre length, hydrodynamic interactions are found to be important in moderating the effect of contacts between fibres.An asymptotic solution is presented for the limit when the sphere diameter is much smaller than both the fibre length and inter-fibre spacing, but large compared to the fibre thickness. This is found to be in good agreement with the simulations.Results of calculations on sedimentation through a monolayer of fibres are also presented, as a model of a semi-concentrated suspension. Collisions between fibres are much more frequent, due to the geometric confinement.