The slow motion of a sphere in a rotating, viscous fluid.
Uniform slow spherical body motion in constant velocity rotating viscous fluid, correcting Stokes drag formula
DRAG EFFECT↗
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The flow created by a sphere moving along the axis of a rotating, slightly-viscous fluid
Flow field around and drag on sphere rising axially through rotating viscous fluid
Maxworthy, T.↗
Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence
In this article, this study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Re T = 300. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.
42 ENGINEERING↗
The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation
We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.
42 ENGINEERING↗
Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions
Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.
42 ENGINEERING↗
Assessment of the Unstructured Grid Software TetrUSS for Drag Prediction of the DLR-F4 Configuration
An application of the NASA unstructured grid software system TetrUSS is presented for the prediction of aerodynamic drag on a transport configuration. The paper briefly describes the underlying methodology and summarizes the results obtained on the DLR-F4 transport configuration recently presented in the first AIAA computational fluid dynamics (CFD) Drag Prediction Workshop. TetrUSS is a suite of loosely coupled unstructured grid CFD codes developed at the NASA Langley Research Center. The meshing approach is based on the advancing-front and the advancing-layers procedures. The flow solver employs a cell-centered, finite volume scheme for solving the Reynolds Averaged Navier-Stokes equations on tetrahedral grids. For the present computations, flow in the viscous sublayer has been modeled with an analytical wall function. The emphasis of the paper is placed on the practicality of the methodology for accurately predicting aerodynamic drag data.
Pirzadeh, Shahyar Z.↗
Theoretical study on the massively augmented electro-osmotic water transport in polyelectrolyte brush functionalized nanoslits
In this paper, we demonstrate that functionalizing nanoslits with pH-responsive polyelectrolyte (PE) brushes can lead to extremely fast electroosmotic (EOS) water transport, where the maximum centreline velocity and the volume ow rate can be an order of magnitude larger than these quantities in identically charged brush-free nanochannels for a wide range of system parameters. Such an enhancement is most remarkable given that the brushes have been known to retard the transport by imparting additional drag on the fluid flow. We argue that this enhancement stems from the localization of the charge density of the brush-induced electric double layer (and hence the EOS body force) away from the nanochannel wall (or the location of the wall-induced drag force). This ensures a much larger impact of the EOS body force triggering such fast water transport. Lastly, the calculated flux values for the present brush-grafted nanochannels are found to be signi ficantly larger than those for a wide range of nanofluidic membranes and channels, suggesting that the brush functionalization can be considered as a mechanism for enabling such superfast nanofluidic transport.
42 ENGINEERING↗
Mathematical modeling of the flow field and particle motion in a rotating bioreactor at unit gravity and microgravity
The biotechnology group at NASA Johnson Space Center is developing systems for culturing mammalian cells that stimulate some aspect of microgravity and provide a low shear environment for microgravity-based studies on suspension and anchorage dependent cells. The design of these vessels for culturing cells is based on the need to suspend cells and aggregates of cells and microcarrier beads continually in the culturing medium. The design must also provide sufficient circulation for adequate mass transfer of nutrients to the cells and minimize the total force on the cells. Forces, resulting from sources such as hydrodynamic fluid shear and collisions of cells and walls of the vessels, may damage delicate cells and degrade the formation of three dimensional structures. This study examines one particular design in both unit gravity and microgravity based on two concentric cylinders rotating in the same direction at different speeds to create a Couette flow between them. A numerical simulation for the flow field and the trajectories of particles in the vessel. The flow field for the circulation of the culturing medium is modeled by the Navier-Stokes equations. The forces on a particle are assumed to be drag from the fluid's circulation, buoyancy from the gravitational force and centrifugal force from the rotation of the vessel. The problem requires first solving the system of partial differential equations for the fluid flow by a finite difference method and then solving the system of ordinary differential equations for the trajectories by Gear's stiff method. Results of the study indicate that the trajectories in unit gravity and microgravity are very similar except for small spatial deviations on the fast time scale in unit gravity. The total force per unit cross sectional area on a particle in microgravity, however, is significantly smaller than the corresponding value in unit gravity, which is also smaller than anticipated. Hence, this study indicates that this design for a bioreactor with optimal rates of rotation can provide a good environment for culturing cells in microgravity with adequate circulation and minimal force on the cells.
Boyd, Ernest J.↗
Tutorial: Langevin Dynamics methods for aerosol particle trajectory simulations and collision rate constant modeling
The Langevin Dynamics (LD) method (also known in the literature as Brownian Dynamics) is routinely used to simulate aerosol particle trajectories for transport rate constant calculations as well as to understand aerosol particle transport in internal and external fluid flows. This tutorial intends to explain the methodological details of setting up a LD simulation of a population of aerosol particles and to deduce rate constants from an ensemble of classical trajectories. We discuss the applicability and limitations of the translational Langevin equation to model the combined stochastic and deterministic motion of particles in fields of force or fluid flow. The drag force and stochastic “diffusion” force terms that appear in the Langevin equation are discussed elaborately, along with a summary of common forces relevant to aerosol systems (electrostatic, gravity, van der Waals, …); a commonly used first order and a fourth order Runge-Kutta time stepping schemes for linear stochastic ordinary differential equations are presented. A MATLAB® implementation of a LD code for simulating particle settling under gravity using the first order scheme is included for illustration. Scaling analysis of aerosol transport processes and the selection of timestep and domain size for trajectory simulations are demonstrated through two specific aerosol processes: particle diffusion charging and coagulation. Fortran® implementations of the first order and fourth order time-stepping schemes are included for simulating the 3D motion of a particle in a periodic domain. Lastly, potential applications and caveats to the usage of LD are included as a summary.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A theoretical model for determining turbine flowmeter sensitivity
Analytical model of turbine-type flowmeter guides in the selection of valid extrapolation of available calibration data. An expression for flowmeter performance is developed to include the effects of fluid friction, bearing drag, and magnetic drag upon helical rotor design.
Smith, R. L.↗
Heat Transfer and Fluid Mechanics Institute, Meeting, 25th, University of California, Davis, Calif., June 21-23, 1976, Proceedings
Major research advances in heat transfer and fluid dynamics are outlined, with particular reference to relevant energy problems. Of significant importance are such topics as synthetic fuels in combustion, turbulence models, combustion modeling, numerical methods for interacting boundary layers, and light-scattering diagnostics for gases. The discussion covers thermal convection, two-phase flow and boiling heat transfer, turbulent flows, combustion, and aerospace heat transfer problems. Other areas discussed include compressible flows, fluid mechanics and drag, and heat exchangers. Featured topics comprise heat and salt transfer in double-diffusive systems, limits of boiling heat transfer in a liquid-filled enclosure, investigation of buoyancy-induced flow stratification in a cylindrical plenum, and digital algorithms for dynamic analysis of a heat exchanger. Individual items are announced in this issue.
Mckillop, A. A.↗
Morphometry of streamlined forms in terrestrial and Martian channels
Streamlined erosional forms in the Channeled Scabland are compared with streamline features recognized in the region of the Kasei Vallis on Mars shown in Viking imagery. The morphometric analysis considers three physical parameters, length, measured parallel to the suggested flow direction; width, taken as the maximum width of the streamlined form perpendicular to the flow direction; and area, measured with a grid placed over the surface. These parameters are used to calculate a dimensionless parameter k, defined as the square of the length multiplied by pi over four times the area. For the 137 Scabland forms studied k values range from 1.0 to 8.3 with an average of 3.2. The k values for 47 Martian streamlined forms range from 1.5 to 12.0 with an average of 3.8. The rough similarity of these results suggests that the terrestrial and Martian features were formed by similar processes. The forms appear to have developed an ideal shape, sufficiently elongated to reduce pressure drag in the fluid creating them, but not so long as to create excessive skin resistance.
Baker, V. R.↗
On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field
The use of a magnetic field to control the motion of electrically conducting fluids is studied. The incompressible boundary-layer solutions are found for flow over a flat plate when the magnetic field is fixed relative to the plate or to the fluid. The equations are integrated numerically for the effect of the transverse magnetic field on the velocity and temperature profiles, and hence, the skin friction and rate of heat transfer. It is concluded that the skin friction and the heat-transfer rate are reduced when the transverse magnetic field is fixed relative to the plate and increased when fixed relative to the fluid. The total drag is increased in all of the areas.
Rossow, Vernon J↗
Numerical simulation of non-Newtonian free shear flows
Free shear flows, like those of mixing layers, are encountered in aerodynamics, in the atmosphere, and in the ocean as well as in many industrial applications such as flow reactors or combustion chambers. It is, therefore, crucial to understand the mechanisms governing the process of transition to turbulence in order to predict and control the evolution of the flow. Delaying transition to turbulence as far downstream as possible allows a gain in energy expenditure while accelerating the transition can be of interest in processes where high mixing is desired. Various methods, including the use of polymer additives, can be effective in controlling fluid flows. The drag reduction obtained by the addition of small amounts of high polymers has been an active area of research for the last three decades. It is now widely believed that polymer additives can affect the stability of a large variety of flows and that dilute solutions of these polymers have been shown to produce drag reductions of over 80 percent in internal flows and over 60 percent in external flows under a wide range of conditions. The major thrust of this work is to study the effects of polymer additives on the stability of the incompressible mixing layer through large scale numerical simulations. In particular, we focus on the two dimensional flow and examine how the presence of viscoelasticity may affect the typical structures of the flow, namely roll-up and pairing of vortices.
Homsy, G. M.↗
Special Course on Skin Friction Drag Reduction
Lecture notes for the AGARD Fluid Dynamics Panel (FDP) Special Course on 'Skin Friction Drag Reduction' have been assembled in this report. The aim and scope of this course was to provide an overview of the state of the art of current technology programs focused on reducing aircraft drag caused by skin friction. This report provides a review of recent progress in the field of skin friction drag reduction for transport aircraft. It provides a general introduction to the technology and then focuses on two specific aspects of drag reduction: maintaining laminar flow by controlling transition and manipulating the turbulence structure in boundary layers to help reduce skin friction. Technology associated with the use of riblets, LEBU, polymers, additives, etc., is also reviewed.
Advisory Group for Aerospace Research and Developm↗
Aerodynamic Drag and Drag Reduction: Energy and Energy Savings (Invited)
An assessment of the role of fluid dynamic resistance and/or aerodynamic drag and the relationship to energy use in the United States is presented. Existing data indicates that up to 25% of the total energy consumed in the United States is used to overcome aerodynamic drag, 27% of the total energy used in the United States is consumed by transportation systems, and 60% of the transportation energy or 16% of the total energy consumed in the United States is used to overcome aerodynamic drag in transportation systems. Drag reduction goals of 50% are proposed and discussed which if realized would produce a 7.85% total energy savings. This energy savings correlates to a yearly cost savings in the $30Billion dollar range.
Wood, Richard M.↗
Aerodynamic Drag and Drag Reduction: Energy and Energy Savings (Invited)
An assessment of the role of fluid dynamic resistance and/or aerodynamic drag and the relationship to energy use in the United States is presented. Existing data indicates that up to 25% of the total energy consumed in the United States is used to overcome aerodynamic drag, 27% of the total energy used in the United States is consumed by transportation systems, and 60% of the transportation energy or 16% of the total energy consumed in the United States is used to overcome aerodynamic drag in transportation systems. Drag reduction goals of 50% are proposed and discussed which if realized would produce a 7.85% total energy savings. This energy savings correlates to a yearly cost savings in the $30Billion dollar range.
Wood, Richard M.↗
Improved Aerodynamic Analysis for Hybrid Wing Body Conceptual Design Optimization
This paper provides an overview of ongoing efforts to develop, evaluate, and validate different tools for improved aerodynamic modeling and systems analysis of Hybrid Wing Body (HWB) aircraft configurations. Results are being presented for the evaluation of different aerodynamic tools including panel methods, enhanced panel methods with viscous drag prediction, and computational fluid dynamics. Emphasis is placed on proper prediction of aerodynamic loads for structural sizing as well as viscous drag prediction to develop drag polars for HWB conceptual design optimization. Data from transonic wind tunnel tests at the Arnold Engineering Development Center s 16-Foot Transonic Tunnel was used as a reference data set in order to evaluate the accuracy of the aerodynamic tools. Triangularized surface data and Vehicle Sketch Pad (VSP) models of an X-48B 2% scale wind tunnel model were used to generate input and model files for the different analysis tools. In support of ongoing HWB scaling studies within the NASA Environmentally Responsible Aviation (ERA) program, an improved finite element based structural analysis and weight estimation tool for HWB center bodies is currently under development. Aerodynamic results from these analyses are used to provide additional aerodynamic validation data.
Gern, Frank H.↗