Computed Drag Coefficients Research Articles

Sea-ice drag as a function of deformation and ice cover: Effects on simulated sea ice and ocean circulation in the Arctic

Many state-of-the-art coupled sea ice-ocean models use atmospheric and oceanic drag coefficients that are at best a function of the atmospheric stability but otherwise constant in time and space. Constant drag coefficients might lead to an incorrect representation of the ice-air and ice-ocean momentum exchange, since observations of turbulent fluxes imply high variability of drag coefficients. We compare three model runs, two with constant drag coefficients and one with drag coefficients varying as function of sea-ice characteristics. The computed drag coefficients range between 0.88 ×10−3 and 4.68 ×10−3 for the atmosphere, and between 1.28 ×10−3 and 13.68 ×10−3 for the ocean. They fall in the range of observed drag coefficients and illustrate the interplay of ice deformation and ice concentration in different seasons and regions. The introduction of variable drag coefficients improves the realism of the model simulation. In addition, using the average values of the variable drag coefficients improves simulations with constant drag coefficients. When drag coefficients depend on sea-ice characteristics, the average sea-ice drift speed in the Arctic basin increases from 6.22 cm s−1 to 6.64 cm s−1. This leads to a reduction of ice thickness in the entire Arctic and particularly in the Lincoln Sea with a mean value decreasing from 7.86 m to 6.62 m. Variable drag coefficients lead also to a deeper mixed layer in summer and to changes in surface salinity. Surface temperatures in the ocean are also affected by variable drag coefficients with differences of up to 0.06 °C in the East Siberian Sea. Small effects are visible in the ocean interior

Application of the Lattice Boltzmann Method to the flow past a sphere

The results of fully resolved simulations and large eddy simulations of bluff-body flows obtained by means of the Lattice Boltzmann Method (LBM) are reported. A selection of Reynolds numbers has been investigated in unsteady laminar and transient flow regimes. Computed drag coefficients of a cube have been compared with the available data for validation purposes. Then, a more detailed analysis of the flow past a sphere is presented, including also the determination of vortex shedding frequency and the resulting Strouhal numbers. Advantages and drawbacks of the chosen geometry implementation technique, so called “staircase geometry”, are discussed. For the quest of maximum computational efficiency, all simulations have been carried out with the use of in-house code executed on GPU.

Flow fields of graupel falling in air

The flow fields of conical graupel of diameters 0.5–5mm falling in air of 800hPa and −20°C are studied by solving the relevant Navier–Stokes equations numerically using the ANSYS Fluent as the solver. The range of Reynolds numbers investigated in this study is from 20.12 to 1084.16. A steady state solution is obtained first and is perturbed by adding an instantaneous velocity perturbation. The flow solutions for the cases of 0.5, 1 and 2mm graupel return to steady state after a brief transient period. The solutions for 3, 4 and 5mm become unsteady with eddy shedding. The eddy shedding appears to become more turbulent for larger graupel. The characters of the flow fields are illustrated using the velocity, pressure distribution, and streamtrace fields. The computed drag coefficients are compared with that for spheres and disks of the same Reynolds number range and are found to be closer to spheres rather than disks.

Membrane-assisted fluidized beds—part 1: Development of an Immersed Boundary Discrete Particle Model

Many novel reactor concepts based on the integration of membranes in fluidized beds have been proposed. For the detailed numerical investigation of such systems, a method is required describing the motion of the particles while accounting for (i) the gas motion and (ii) the encounters between particles and confining walls/membranes. In this paper a novel hybrid computational method is presented, combining the Discrete Particle Model (DPM) and the Immersed Boundary Method (IBM). The first part focuses on the implementation and validation of these models. The IBM component of the model has been verified by comparing the computed drag coefficients for Simple Cubic (SC) arrays of cylinders with data of Sangani and Acrivos (1982) at creeping flow conditions. For higher Reynolds numbers the code has been compared to Ferziger and Peric (2002) for a single off-center cylinder, after which simulations with addition and extraction of gas through the membrane surface have been conducted.In the second part of this work we will focus on actual fluidized bed membrane systems, and will report results of simulations for several membrane geometries as well as permeation ratios.

Numerical Study on Choked Flow over Grid-Fin Configurations

An improved configuration, which we term a swept-back grid fin, is proposed in the present study to reduce the detrimental effects of high drag caused by the flow choking within the transonic regime. Viscous computational fluid dynamics simulationswere performed to investigateflows over amissilewith baseline and swept-back gridfins under supersonic and transonic conditions at zero incidence. The computed drag coefficients for the baseline missile agree well with those in the literature. Our numerical results indicate that flow choking can be reduced by using the sweptback gridfin.As a result, the drag coefficient on thefins is decreased by approximately 13% for all theMachnumbers investigated in the present study.

Comparison among sea surface roughness schemes

Based on the measurements from the US National Data Buoy Center 3-m discus buoy site No. 44004 (38.5°N, 70.47°W) from January 1 to March 31 of 2003, with the COARE algorithm (Version 3.0), the results from four parameterization schemes developed recently for sea surface aerodynamic roughness length were compared with each other. Calculations of frictional speedu*, drag coefficientC d and wind stress τ indicate that the calculated frictional velocities from the four schemes (8.50%–16.20%, the normalized standard error estimate, or NSEE), the computed drag coefficients and wind stress (respectively 15.08%–28.67% and 17.26%–50.59% NSEE) are reasonable. Schemes YT96 and GW03 are consistent. The O02 scheme gives over-estimated values foru* andC d. Schemes TY01 and GW03 display discontinuous characteristics in handling young wave data.

Computations of the drag coefficients for low-Reynolds-number flow past rings

The variation in the drag coefficient for low-Reynolds-number flow past rings orientated normal to the direction of flow is investigated numerically. An aspect ratio parameter is used for a ring, which describes at its limits a sphere and a circular cylinder. This enables a continuous range of bodies between a sphere and a circular cylinder to be studied.The computed drag coefficients for the flow past rings at the minimum and maximum aspect ratio limits are compared with the measured and computed drag coefficients reported for the sphere and the circular cylinder. Some interesting features of the behaviour of the drag coefficients with variation of Reynolds number and aspect ratio emerge from the study. These include the decrease in the aspect ratio at which the minimum drag coefficient occurs as the Reynolds number is increased, from are provided, which are accurate within approximately 2%.

Computational study of influences of a seam line of a ball for baseball on flows

Flows around a ball used in baseball games are calculated using third-order upwind-difference method with various seam positions determined by two rotation angles. Those are four-seam rotation with an angle: a and two-seam rotation with an angle: b. The computed results of the four-seam rotation are compared with experimental data measured in a wind tunnel and computed drag coefficients qualitatively agree well with experiments. However, lift coefficients do not agree well. The computed results and geometrical symmetry suggest that a supporting rod in the wind tunnel would have strong influence on the accuracy of the measurement. Flow changes in two-seam rotation are also simulated. It is found that the lowest drag force is observed at b=90 and that the value is less than half of the largest drag force at a=30 and 60 degrees. The largest lift force is observed at b=20 degree. In this case, a projection of the seam line on the top causes a large separation while smooth surface without the seam at the bottom dose not separate the flow. A pair of longitudinal vortices are found in the wake, which make wake slant and generate large lift force.

Simulations of sedimentation of a sphere in a viscoelastic fluid using molecular based constitutive models

Numerical computations using an adaptive finite element technique have been performed to simulate the experimental studies of sedimentation of a sphere in a polyisobutylene based Boger fluid performed by Arigo et al. [M.T. Agrio, D.R. Rajagopalan, N.T. Shapely and G.H. McKinley, J. Non-Newtonian Fluid Mech., 60, (1995) 225–257]. The Chillcott–Rallison, FENE-P, multimode Giesekus and the single and multimode versions of the model recently proposed by Verhoef et al. [M.R.J. Verhoef, B.H.A.A. vanden Brule and M.A. Hulsen, On the Modeling of a PIB/PB Boger Fluid in Extensional Flow, J. Non-Newtonian Fluid Mech., in press] were used to describe the rheological data of the Boger fluid. Overall, the multimode Giesekus and the multimode version of the Verhoef et al. [M.R.J. Verhoef, B.H.A.A. vanden Brule and M.A. Hulsen, On the Modeling of a PIB/PB Boger Fluid in Extensional Flow, J. Non-Newtonian Fluid Mech., in press] model provide the best representation of the steady shear and transient uniaxial extensional viscosity of the Boger fluid. A comparison of experimentally measured and computed drag coefficients demonstrate that all the models are capable of qualitatively describing the experimental measured drag as a fraction of We. However, none of these dumbbell based models is capable of describing the experimental data quantitatively over a wide range of We and in different tube to sphere radius ratio geometries. In fact, the agreement between the computed and experimental results in this study is much more limited than prior studies of semi-concentrated polymeric solutions in flows with a single acceleration or deceleration of the fluid elements [J-M. Li, W.R. Burghardt, B. Yang and B. Khomami, J. Non-Newtonian Fluid Mech., 74, (1998) 151–193]. In addition, it has been shown that inclusion of dissipative stresses in dumbbell based constitutive equations does give rise to an increase in the predicted drag in comparison to dumbbell models which do not include this contribution. However, inclusion of these dissipative stresses is not sufficient to describe the experimental data quantitatively. Overall, the results of this study indicate that elastic dumbbell based constitutive equations do not contain all of the underlying physics required to describe the fluid dynamics of dilute polymeric solutions in complex flows.

Numerical Simulation of Three-Dimensional Unsteady Flow past Ice Crystals

The unsteady flow fields around falling columnar ice crystals, hexagonal ice plates, and broad-branch crystals are simulated by numerically solving the time-dependent Navier–Stokes equations appropriate for these geometries in the primitive equation form. A predictor–corrector method and a quadratic interpolation for convective kinematics (QUICK) scheme are applied on nonuniform grids to determine the velocity fields. The ice crystals are held in fixed orientation but time-dependent behaviors such as eddy shedding are allowed to occur by imposing an initial perturbation with a magnitude 30% of the free-stream velocity. The computed flow fields cover a Reynolds number range from 0.1 to about 200, being slightly different for different crystal habits. Examples of velocity fields are illustrated. The computed drag coefficients for cylinders agree with experimental values to within a few percent, while those for hexagonal plates agree with experimental values and previous calculations by Pitter et al. to less than 15% even though the aspect ratios are different. The drag coefficients for broad-branch crystals are higher than those for hexagonal plates at the same Reynolds numbers. Special features of flow passing through the branch gaps of broad-branch crystals suggest that it may be possible to use a creeping flow assumption to treat flow passing through spaces in complicated dendritic crystals.

Laminar flow past a permeable sphere

AbstractFlow past an isolated permeable sphere has been studied. The complete Navier‐Stokes equation governs the fluid motion outside the sphere, while Brinkman's extension of Darcy's Law is assumed to hold within the porous sphere. The Navier‐Stokes equation is solved using a finite difference scheme. The flow within the porous sphere is solved in two different ways, each being efficient over a particular range of Reynolds number. Drag Coefficients are presented for dimensionless permeability, β, of 5, 10, 15, and 30 and for Reynolds numbers up to 50. The computed drag coefficients are within 10% of the experimental values observed by Masliyah and Polikar for 15 < β > 33, the range covered in their work. Separation was observed only for β > 10. The onset of separation is delayed considerably in porous spheres.