Mean Force Coefficients Research Articles

Force coefficients and Strouhal numbers of three circular cylinders subjected to a cross-flow

In this paper, wind tunnel experiments were conducted to measure the mean force coefficients and Strouhal numbers for three circular cylinders of equal diameters in an equilateral-triangular arrangement when subjected to a cross-flow. These experiments were carried out at five subcritical Reynolds numbers ranging from 1.26 × 104 to 6.08 × 104. The pressure distributions on the surface of the cylinders were measured using pressure transducers. Furthermore, the hot-wire anemometer was employed to measure the vortex shedding frequencies behind each cylinder. Six spacing ratios (l/d) varying from 1.5 to 4 were investigated. It is observed that for l/d > 2, the upstream cylinder experiences a lower mean drag coefficient compared with the downstream cylinders. The minimum values of the drag coefficient for the downstream cylinders occur at l/d = 1.5 and l/d = 2, because there is no vortex shedding from the foregoing cylinders. Also, the value of the pressure coefficient behind the upstream cylinder reduces by increasing l/d. Moreover, by decreasing the value of l/d, the Strouhal number for the upstream cylinder increases. It can be concluded that the flow pattern and aerodynamic coefficients are basically dependent on l/d; in other words, decreasing l/d results in an increase in the effects of the flow interference between the cylinders.

Numerical investigation of boundary layer effects on vortex shedding frequency and forces acting upon marine pipeline

In this study the force components and vortex shedding frequency of a pipe exposed to a steady current were numerically investigated in terms of the drag coefficient, lift coefficient and Strouhal number. The effects of the bed proximity and boundary layer thickness on these parameters were studied extensively. The Reynolds-averaged-Navier–Stokes equations with a k – ε turbulence closure model were numerically solved to approximate both the flow pattern and pressure distribution around the pipe. The instantaneous drag and lift coefficients were calculated based on the pressure distribution around the pipe, while the Strouhal number was estimated by the spectral analysis of the predicted instantaneous lift force. Evaluation of the numerical model revealed that the model well predicted the velocity profile around the pipe, force coefficients and Strouhal number. The results showed that the model slightly over-predicts the mean force coefficients and Strouhal number. It is concluded that the mean force coefficients and the root-mean-square (RMS) lift coefficient are strongly affected by the gap to diameter ratio while the Strouhal number is slightly affected by the gap ratio. The results also indicated that the mean lift force acting on the pipe is upward in all boundary layers and is rapidly decreased by increasing the gap ratio, whereas the mean drag force is slightly increased as the gap ratio is increased up to a certain value. The RMS lift force also increased as the gap ratio increased up to a certain value and remained approximately constant for further increase of the gap ratio. The mean force coefficients and Strouhal number calculated in terms of the flow velocity at the pipe axis are marginally influenced by the boundary layer thickness, while the parameters calculated in terms of the free-stream velocity are strongly affected by the boundary layer thickness.

Wind tunnel tests for mean wind loads on partially clad structures

Many structures, such as buildings under construction, industrial process structures, and manufacturing and storage facilities, are temporarily or permanently partially clad. Scant wind load data for these structures are available in the literature and wind codes. An investigation was undertaken at the L.S.U. Wind Tunnel Laboratory to study the aerodynamic behavior of these structures. Mean force coefficients for various cladding arrangements are reported for models of a 10-storey structure for two plan aspect ratios (1:1 and 3:1) in smooth, grid turbulent, and boundary layer flow. Three flow regimes were tested to validate results against published data and to investigate the possibility of reducing the number of key variables. Results for the fully clad and unclad cases compared well with available data for ground-mounted prisms and lattice frames, respectively. It was found that force coefficients for some of the cladding configurations significantly exceeded those for a fully clad structure of the same overall geometry. Additionally, the manner in which the force coefficients varied with wind direction was found to differ dramatically from the fully clad cases for some of the cladding arrangements. The conditioning of the approach flow was found to be less important for unclad models than for partially or fully clad configurations.

Ion Selectivity of α-Hemolysin with β-Cyclodextrin Adapter. II. Multi-Ion Effects Studied with Grand Canonical Monte Carlo/Brownian Dynamics Simulations

In a previous study of ion selectivity of alpha-hemolysin (alphaHL) in complex with beta-cyclodextrin (betaCD) adapter, we calculated the potential of mean force (PMF) and characterized the self-diffusion coefficients of isolated K(+) and Cl(-) ions using molecular dynamics simulations (Y. Luo et al., "Ion Selectivity of alpha-Hemolysin with beta-Cyclodextrin Adapter: I. Single Ion Potential of Mean Force and Diffusion Coefficient"). In the present effort, these results pertaining to single isolated ions in the wide aqueous pore are extended to take into account multi-ion effects. The grand canonical Monte Carlo/Brownian dynamics (GCMC/BD) algorithm is used to simulate ion currents through the wild-type alphaHL ion channel, as well as two engineered alphaHL mutants, with and without the cyclic oligosaccaride betaCD lodged in the lumen of the pore. The GCMC/BD current-voltage curves agree well with experimental results and show that betaCD increases the anion selectivity of alphaHL. Comparisons between multi-ion PMFs from GCMC/BD simulations and single-ion PMFs demonstrate that multi-ion effects and pore shape are crucial for explaining this behavior. It is concluded that the narrow betaCD adapter increases the anion selectivity of alphaHL because it reduces the pore radius locally, which decreases the ionic screening and the dielectric shielding of the strong electrostatic field induced by a nearby ring of positively charged alphaHL side chains.

Fluid forces on a square cylinder in oscillating flows with non‐zero‐mean velocities

AbstractThe unsteady forces on a square cylinder in sinusoidally oscillating flows with non‐zero‐mean velocities are investigated numerically by using a weakly compressible‐flow method with three‐dimensional large eddy simulations. The major parameters in the analysis are Keulegan–Carpenter number (KC) and the ratio between the amplitude and the mean velocities of the approaching flow (AR). By varying the values of KC and AR the resulting drag and lift of the cylinders are analyzed systematically at two selected approaching‐flow attack angles (0 and 22.5∘). In the case of the non‐zero attack angle, results show that both the drag and lift histories can be adequately described by Morison equations. However, Morison equations fail to correctly describing the lift history as the attack angle is zero. In addition, when the ratio of AR/KC is near the Strouhal number of the bluff‐body flow, the resulting drag is promoted due to the occurrence of resonance. Based on the results of systematic analyses, finally, the mean and inertia force coefficients at the two selected attack angles are presented as functions of KC and AR based on the Morison relationships. Copyright © 2008 John Wiley & Sons, Ltd.

Theoretical investigation of imidazolium based ionic liquid/alcohol mixture: a molecular dynamic simulation

In this work, molecular dynamic simulation of the mixture of imidazolium based ionic liquids with alcohols is implemented in order to investigate mixing excess properties and some structural and physical properties of the mixture. Excess volumes and enthalpies are evaluated for 11 different mole fractions of ionic liquids at each 0.1, in the range of 0 to 1. Radial distribution function, cohesive energy density, potential of mean force, solvation energy, and diffusion coefficient are reported and analysed. The effects of the cationic alkyl chain length, in comparison with changes of the anions, on these properties are reported. Results reveal that the methanol molecule participates with its hydrophilic characteristics in the mixing process and tends to aggregate around anion part of the ionic liquids, especially in the case of Cl.

Flow-induced forces on two circular cylinders in proximity

Flow-induced forces on two nearby circular cylinders of equal diameter immersed in the cross flow at Re = 100 were numerically studied. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. It turns out that significant changes in the characteristics of flow-induced forces are noticed depending on how the two circular cylinders are positioned, resulting in quantitative changes of force coefficients on both cylinders. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and rms values of force coefficient fluctuations for each of the two cylinders. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main flow direction.

두 개의 원형 실린더를 지나는 유동의 레이놀즈 수 효과

As a follow-up of our previous studies on flow-induced forces on two identical nearby circular cylinders immersed in the cross flow at Re=100 and flow patterns past them,(1,2) we present Reynolds-number effects on the forces and patterns by further computing flows with Re=40, 50, 160. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the angle inclined with respect to the main flow direction. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and their rms of fluctuation as well as for flow patterns and Strouhal number for each Re. These diagrams shed light on a comprehensive picture on how the wake interaction between the two cylinders alters depending on Re.

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.

Integral equation theory study on the structure and effective interactions in star polymer nanocomposite melts

The polymer reference interaction site model theory is used to investigate the radial distribution function, potential of mean force, depletion force, and second virial coefficient in star polymer nanocomposite melts. The contact aggregation of nanoparticles for relatively weak nanoparticle-monomer attraction and the bridging aggregation of nanoparticles for very large nanoparticle-monomer attraction are observed. The star architecture can well suppress the organization states of direct contact and bridging structure for the moderate nanoparticle-monomer attraction, and promote the bridging-type organization for relatively large nanoparticle-monomer attraction. At constant particle volume fraction, the arm length quantitatively affects the organization states of star polymer nanocomposite melt, and larger repulsive barriers are existent to prevent the contact aggregation of larger nanoparticles. These observations provide useful information for the development of new nanocomposite materials.

Calculating potentials of mean force and diffusion coefficients from nonequilibrium processes without Jarzynski’s equality

In general, the direct application of the Jarzynski equality (JE) to reconstruct potentials of mean force (PMFs) from a small number of nonequilibrium unidirectional steered molecular-dynamics (SMD) paths is hindered by the lack of sampling of extremely rare paths with negative dissipative work. Such trajectories that transiently violate the second law of thermodynamics are crucial for the validity of JE. As a solution to this daunting problem, we propose a simple and efficient method, referred to as the FR method, for calculating simultaneously both the PMF U(z) and the corresponding diffusion coefficient D(z) along a reaction coordinate z for a classical many-particle system by employing a small number of fast SMD pullings in both forward (F) and time reverse (R) directions, without invoking JE. By employing Crooks [Phys. Rev. E 61, 2361 (2000)] transient fluctuation theorem (that is more general than JE) and the stiff-spring approximation, we show that (i) the mean dissipative work W(d) in the F and R pullings is the same, (ii) both U(z) and W(d) can be expressed in terms of the easily calculable mean work of the F and R processes, and (iii) D(z) can be expressed in terms of the slope of W(d). To test its viability, the FR method is applied to determine U(z) and D(z) of single-file water molecules in single-walled carbon nanotubes (SWNTs). The obtained U(z) is found to be in very good agreement with the results from other PMF calculation methods, e.g., umbrella sampling. Finally, U(z) and D(z) are used as input in a stochastic model, based on the Fokker-Planck equation, for describing water transport through SWNTs on a mesoscopic time scale that in general is inaccessible to MD simulations.

A computational study of the aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight

The aerodynamics and forewing-hindwing interaction of a model dragonfly in forward flight are studied, using the method of numerically solving the Navier-Stokes equations. Available morphological and stroke-kinematic parameters of dragonfly (Aeshna juncea) are used for the model dragonfly. Six advance ratios (J; ranging from 0 to 0.75) and, at each J, four forewing-hindwing phase angle differences (gamma(d); 180 degrees, 90 degrees, 60 degrees and 0 degree) are considered. The mean vertical force and thrust are made to balance the weight and body-drag, respectively, by adjusting the angles of attack of the wings, so that the flight could better approximate the real flight. At hovering and low J (J=0, 0.15), the model dragonfly uses separated flows or leading-edge vortices (LEV) on both the fore- and hindwing downstrokes; at medium J (J=0.30, 0.45), it uses the LEV on the forewing downstroke and attached flow on the hindwing downstroke; at high J (J=0.6, 0.75), it uses attached flows on both fore- and hindwing downstrokes. (The upstrokes are very lightly loaded and, in general, the flows are attached.) At a given J, at gamma(d)=180 degrees, there are two vertical force peaks in a cycle, one in the first half of the cycle, produced mainly by the hindwing downstroke, and the other in the second half of the cycle, produced mainly by the forewing downstroke; at gamma(d)=90 degrees, 60 degrees and 0 degree, the two force peaks merge into one peak. The vertical force is close to the resultant aerodynamic force [because the thrust (or body-drag) is much smaller than vertical force (or the weight)]. 55-65% of the vertical force is contributed by the drag of the wings. The forewing-hindwing interaction is detrimental to the vertical force (and resultant force) generation. At hovering, the interaction reduces the mean vertical force (and resultant force) by 8-15%, compared with that without interaction; as J increases, the reduction generally decreases (e.g. at J=0.6 and gamma(d)=90 degrees, it becomes 1.6%). A possible reason for the detrimental interaction is as follows: each of the wings produces a mean vertical force coefficient close to half that needed for weight support, and a downward flow is generated in producing the vertical force; thus, in general, a wing moves in the downwash-velocity field induced by the other wing, reducing its aerodynamic forces.

Intramolecular Janus Segregation of a Heteroarm Star Copolymer

Conformations of heteroarm star copolymers AnBn are investigated by off-lattice Monte Carlo simulations. Intramolecular segregation is always observed in selective solvents. It can also be found in a common good solvent, which however gives block incompatibility. The degree of Janus segregation is characterized by the mean-square separation between A and B blocks, 〈(xA - xB) 2 〉, or by the orientation correlation between the two blocks, 〈xA‚xB〉, where xi denotes the relative position of the center of mass associated with the block arms i from the star core. The degree of segregation grows with increasing arm numbers while the effect of arm lengths is insignificant. The influence of the intramolecular segregation on the aggregation behavior in solution can be revealed through interactions between two star copolymers. The potential of mean force and second virial coefficient are calculated for various solvent qualities. In a selective solvent, the blockarm star copolymer can form a unimolecular micelle structure and always shows intermolecular repulsions. In contrast, the heteroarm star copolymer may display the Janus segregation, which leads to intermolecular attractions. This consequence facilitates the formation of multimolecular micelles.

Characteristics of wind forces acting on tall buildings

Nine models with different rectangular cross-sections were tested in a wind tunnel to study the characteristics of wind forces on tall buildings. The data was briefly reported (Local wind forces acting on rectangular prisms. Proceedings of 14th National Symposium on Wind Engineering, 4–6 December 1996, Japan Association for Wind Engineering, Tokyo, pp. 263–268.). In the present paper, local wind forces on tall buildings are investigated in terms of mean and RMS force coefficients, power spectral density, and spanwise correlation and coherence. The effects of three parameters, elevation, aspect ratio, and side ratio, on bluff-body flow and thereby on the local wind forces are discussed. The overall loads and base moments are obtained by integration of local wind forces. Comparisons are made with results obtained from high-frequency force balances in two wind tunnels.

Forces on oscillating foils for propulsion and maneuvering

Experiments were performed on an oscillating foil to assess its performance in producing large forces for propulsion and effective maneuvering. First, experiments on a harmonically heaving and pitching foil were performed to determine its propulsive efficiency under conditions of significant thrust production, as function of the principal parameters: the heave amplitude, Strouhal number, angle of attack, and phase angle between heave and pitch. Planform area thrust coefficients of 2.4 were recorded for 35° maximum angle of attack and efficiencies of up to 71.5% were recorded for 15° maximum angle of attack. A plateau of good efficiency, in the range of 50–60%, is noted. A phase angle of 90–100° between pitch and heave is found to produce the best thrust performance. Also, the introduction of higher harmonics in the heave motion, so as to ensure a sinusoidal variation in the angle of attack produced much higher thrust coefficient at high Strouhal numbers. Second, experiments on a harmonically oscillating foil with a superposed pitch bias, as well as experiments on impulsively moving foils in still water, were conducted to assess the capability of the foil to produce large lateral forces for maneuvering. Mean side force coefficients of up to 5.5, and instantaneous lift coefficients of up to 15 were recorded, demonstrating an outstanding capability for maneuvering force production.

WIND LOADS ON FREE-STANDING CANOPY ROOFS: A REVIEW

Previous studies of wind loads on free-standing canopy roofs have been surveyed. Focus is on the data obtained from wind-tunnel measurements in simulated atmospheric boundary layers as well as from full-scale measurements. Comparisons are made between these studies for some aerodynamic characteristics, such as mean and peak wind force coefficients. The wind load provisions in the current Building Standard Law of Japan are also compared with the experimental results. The comparisons are restricted to the clear flow case with no obstructions under the roof. A discussion is made of the subjects to be investigated for making the provisions more appropriate.

The Production of Elevated Flight Force Compromises Manoeuvrability in the Fruit Fly Drosophila Melanogaster

In this study, we have investigated how enhanced total flight force production compromises steering performance in tethered flying fruit flies, Drosophila melanogaster. The animals were flown in a closed-loop virtual-reality flight arena in which they modulated total flight force production in response to vertically oscillating visual patterns. By simultaneously measuring stroke amplitude and stroke frequency, we recorded the ability of each fly to modulate its wing kinematics at different levels of aerodynamic force production. At a flight force that exactly compensates body weight, the temporal deviations with which fruit flies vary their stroke amplitude and frequency are approximately 2.7 degrees and 4.8 Hz of their mean value, respectively. This variance in wing kinematics decreases with increasing flight force production, and at maximum force production fruit flies are restricted to a unique combination of stroke amplitude, stroke frequency and mean force coefficient. This collapse in the kinematic envelope during peak force production could greatly attenuate the manoeuvrability and stability of animals in free flight.

A Combined Molecular Dynamics and Diffusion Model of Single Proton Conduction through Gramicidin

We develop a model for proton conduction through gramicidin based on the molecular dynamics simulations of Pomès and Roux ( Biophys. J. 72:A246, 1997). The transport of a single proton through the gramicidin pore is described by a potential of mean force and diffusion coefficient obtained from the molecular dynamics. In addition, the model incorporates the dynamics of a defect in the hydrogen bonding structure of pore waters without an excess proton. Proton entrance and exit were not simulated by the molecular dynamics. The single proton conduction model includes a simple representation of these processes that involves three free parameters. A reasonable value can be chosen for one of these, and the other two can be optimized to yield a good fit to the proton conductance data of Eisenman et al. (1980, Ann. N. Y. Acad. Sci. 339:8–20) for pH ≥ 1.7. A sensitivity analysis shows the significance of this fit.

Prediction of unsteady flow around square and rectangular section cylinders using a discrete vortex method

A discrete vortex method has been developed at the Department of Aerospace Engineering, University of Glasgow to predict unsteady, incompressible, separated flows around closed bodies. The basis of the method is the discretisation of the vorticity field, rather than the velocity field, into a series of vortex particles which are free to move in the flow. The grid free nature of the method allows analysis of a wide range of problems for both stationary and moving bodies. This report presents a brief description of the numerical implementation, and presents the results of an extensive validation of the method on bluff body flow fields. Results are presented for the mean force coefficients, surface pressure coefficients and Strouhal numbers on a square section cylinder at varying angle of incidence. Also presented are the mean force coefficients and Strouhal numbers on rectangular cylinders. The results from the vortex method show good agreement, both qualitative and quantitative, with results taken from various experimental data.

The control of wing kinematics and flight forces in fruit flies (Drosophila spp.).

By simultaneously measuring flight forces and stroke kinematics in several species of fruit flies in the genus Drosophila, we have investigated the relationship between wing motion and aerodynamic force production. We induced tethered flies to vary their production of total flight force by presenting them with a vertically oscillating visual background within a closed-loop flight arena. In response to the visual motion, flies modulated their flight force by changing the translational velocity of their wings, which they accomplished via changes in both stroke amplitude and stroke frequency. Changes in wing velocity could not, however, account for all the modulation in flight force, indicating that the mean force coefficient of the wings also increases with increasing force production. The mean force coefficients were always greater than those expected under steady-state conditions under a variety of assumptions, verifying that force production in Drosophila spp. must involve non-steady-state mechanisms. The subtle changes in kinematics and force production within individual flight sequences demonstrate that flies possess a flexible control system for flight maneuvers in which they can independently control the stroke amplitude, stroke frequency and force coefficient of their wings. By studying four different-sized species, we examined the effects of absolute body size on the production and control of aerodynamic forces. With decreasing body size, the mean angular wing velocity that is required to support the body weight increases. This change is due almost entirely to an increase in stroke frequency, whereas mean stroke amplitude was similar in all four species. Despite the elevated stroke frequency and angular wing velocity, the translational velocity of the wings in small flies decreases with the reduction in absolute wing length. To compensate for their small size, D. nikananu must use higher mean force coefficients than their larger relatives.