Modeling vortex-shedding effects for the stochastic response of tall buildings in non-synoptic winds

This study derives a model for the vortex-induced vibration and the stochastic response of a tall building in strong non-synoptic wind regimes. The vortex-induced stochastic dynamics is obtained by combining turbulent-induced buffeting force, aeroelastic force and vortex-induced force. The governing equations of motion in non-synoptic winds account for the coupled motion with nonlinear aerodynamic damping and non-stationary wind loading. An engineering model, replicating the features of thunderstorm downbursts, is employed to simulate strong non-synoptic winds and non-stationary wind loading. This study also aims to examine the effectiveness of the wavelet-Galerkin (WG) approximation method to numerically solve the vortex-induced stochastic dynamics of a tall building with complex wind loading and coupled equations of motions. In the WG approximation method, the compactly supported Daubechies wavelets are used as orthonormal basis functions for the Galerkin projection, which transforms the time-dependent coupled, nonlinear, non-stationary stochastic dynamic equations into random algebraic equations in the wavelet space. An equivalent single-degree-of-freedom building model and a multi-degree-of-freedom model of the benchmark Commonwealth Advisory Aeronautical Research Council (CAARC) tall building are employed for the formulation and numerical analyses. Preliminary parametric investigations on the vortex-shedding effects and the stochastic dynamics of the two building models in non-synoptic downburst winds are discussed. The proposed WG approximation method proves to be very powerful and promising to approximately solve various cases of stochastic dynamics and the associated equations of motion accounting for vortex shedding effects, complex wind loads, coupling, nonlinearity and non-stationarity.     

On the nonlinear effects of the mean wind force on the galloping onset in shallow cables

Nonlinear Dynamics - The critical aeroelastic behavior of horizontal, suspended, and shallow cables is analyzed via a continuous model accounting for both external and internal damping....     

A physically based correlation for the effects of power law rheology and inclination on slug bubble rise velocity

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoretical expression for the rise velocity of air bubbles in water is derived on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise speeds at high Reynolds number. The effects of increasing Newtonian viscosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble Froude number. Results from an experimental survey in seven different non-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface tension and viscosity. An empirical relation is proposed for the effective shear rate in the fluid travelling around the bubble nose. Our correlation is compared to literature data from a broad range of Reynolds numbers with excellent agreement except at shallow angles.     

Combined effects of topography and bottom friction on shoaling internal solitary waves in the South China Sea

A numerical study to a generalized Korteweg-de Vries (KdV) equation is adopted to model the propagation and disintegration of large-amplitude internal solitary waves (ISWs) in the South China Sea (SCS). Based on theoretical analysis and in situ measurements, the drag coefficient of the Chezy friction is regarded as inversely proportional to the initial amplitude of an ISW, rather than a constant as assumed in the previous studies. Numerical simulations of ISWs propagating from a deep basin to a continental shelf are performed with the generalized KdV model. It is found that the depression waves are disintegrated into several solitons on the continental shelf due to the variable topography. It turns out that the amplitude of the leading ISW reaches a maximum at the shelf break, which is consistent with the field observation in the SCS.Moreover, a dimensionless parameter defining the relative importance of the variable topography and friction is presented.     

The effect of incidence angle on the mean wake of surface-mounted finite-height square prisms

The mean wake of a surface-mounted finite-height square prism was studied experimentally in a low-speed wind tunnel to explore the combined effects of incidence angle (α) and aspect ratio (AR). Measurements of the mean wake velocity field were made with a seven-hole pressure probe for finite square prisms of AR = 9, 7, 5 and 3, at a Reynolds number of Re = 3.7 × 10⁴, for incidence angles from α = 0° to 45°. The relative thickness of the boundary layer on the ground plane, compared to the prism width, was δ/D = 1.5. As the incidence angle increases from α = 0° to 15°, the mean recirculation zone shortens and the mean wake shifts in the direction opposite to that of the mean lift force. The downwash is also deflected to this side of the wake and the mean streamwise vortex structures in the upper part of the wake become strongly asymmetric. The shortest mean recirculation zone, and the greatest asymmetry in the mean wake, is found at the critical incidence angle of α_critical ≈ 15°. As the incidence angle increases from α = 15° to 45°, the mean recirculation zone lengthens and the mean streamwise vortex structures regain their symmetry. These vortices also elongate in the wall-normal direction and become contiguous with the horseshoe vortex trailing arms. The mean wake of the prism of AR = 3 has some differences, such as an absence of induced streamwise vorticity near the ground plane, which support its classification as lying below the critical aspect ratio for the present flow conditions.     

Effects of mean shear on the vortex identification and the orientation statistics

This work compares the threshold applied to the swirling strength as well as the vortex orientation statistics in the total and fluctuating velocity fields using direct numerical simulations of compressible and incompressible turbulent channel flows. It is concluded that the difference in the swirling strength for vortex identification is minimal in the logarithmic region such that these two situations share the same threshold. Regarding the vortex orientation, the inclination angle remains similar. However, as the wall-normal distance increases, a more and more obvious distinction is noticed for its orientation with respect to the spanwise ($z$) direction. It is mainly due to their intrinsic differences and attendant contrasting preference for the vortex identification, i.e., vortices rotating in the $-z$ direction for the total velocity field and in the $z$ direction for the fluctuating one. These observations function as a reasonable explanation for various remarks in previous studies.     

Bounds on the distribution of extreme values for the stress in composite materials

Suitable macroscopic quantities beyond effective elastic properties are used to assess the distribution of stress within a composite. The composite is composed of N anisotropic linearly elastic materials and the length scale of the microstructure relative to the loading is denoted by ε. The stress distribution function inside the composite λ^ε(t) gives the volume of the set where the norm of the stress exceeds the value t. The analysis focuses on the case when 0<ε?1. A rigorous upper bound on lim_ε→0λ^ε(t) is found. The bound is given in terms of a macroscopic quantity called the macro stress modulation function. It is used to provide a rigorous assessment of the volume of over stressed regions near stress concentrators generated by reentrant corners or by an abrupt change of boundary loading.     

Localization of the mean and mean squared intensities, and intensity fluctuations, of waves propagating in a one-dimensional random medium

A theoretical analysis of the wave field radiated by a point source in an infinite, one-dimensional, weakly inhomogeneous, weakly dissipative random medium is presented. The approach is based on the quasi-Rytov method, and includes both multiple forward scatter and multiple backscatter effects. Approximate expressions are derived for the mean squared intensity and for the mean squared fluctuating intensity of the field. (The intensity is defined to be the square of the modulus of the complex wave amplitude). The expression for the mean squared intensity shows that, as a result of backscattering by the random inhomogeneities of the medium, this quantity is localized; i.e., in a neighborhood of the source it is amplified, whereas outside of this neighborhood it is diminished. These results are similar to those obtained previously for the mean intensity. The latter results are discussed here briefly, and are shown to agree qualitatively with analogous results obtained by other investigators. The expression for the mean squared fluctuating intensity shows that this quantity (normalized to eliminate the effect of absorption) is a maximum at the source point and decays exponentially with distance from the source. This expression shows also that, in a neighborhood of the source, the fluctuating intensity increases monotonically as the backscatter strength of the medium increases, whereas outside of this region it first increases to a maximum value, then decreases to zero. Finally, it is found that, everywhere in the medium, the fluctuating intensity tends to dominate the mean intensity with increasing backscatter strength. These results are also consistent with those of other investigators.     

A study on the measurement of mean velocity and its convergence in molecular dynamics simulations

In many particle‐based simulations, measurement of local mean flow velocity and other continuum‐based properties are of utmost importance. Macroscopic quantities, such as mean flow velocity, temperature, and density, can be estimated by averaging the corresponding microscopic behavior of the particles. The two main subjects that should be considered in the averaging over the particles in a specific problem are spatial and temporal behaviors of them. In this paper, we study the latter. Because of the chaotic nature of the collisions among the molecules and consequently their random path, extracted macroscopic values fluctuate about their average values causing statistical errors. In this paper, an averaging method called SAM‐Modified‐CAM (SMC) will be proposed for the measurement of mean velocity that reduces statistical errors in its calculation. This proposal is based on the study conducted here on the implementations of two common averaging methods, sample‐averaged measurement (SAM) and cumulative average measurement (CAM) in molecular dynamics. In addition, convergence of mean flow velocity measurement is thoroughly discussed, and a convergence criterion is proposed for this purpose. Implementation of the proposed method in different test cases has approved its reliable performance. Copyright © 2010 John Wiley & Sons, Ltd.     

The effects of confinement and inertia on the production of droplets

Recent experiments of Sibillo et al., Phys. Rev. Lett. 97:054502, (2006) investigate the effect of walls on flow-induced drop deformation for Stokes flow. The drop and the fluid in which it is suspended have the same viscosities. The capillary numbers vary from 0.4 to 0.46. They find that complex start-up transients are observed with overshoots and undershoots in drop deformation. Drop breakup is inhibited by lowering the gap. The ratio of initial drop radius to wall separation is fixed at 0.34. We show that inertia can enhance elongation to break the drop by examining Reynolds numbers in the range of 1 to 10. The volumes of the daughter drops can be larger than in the unbounded case, and even result in the production of monodisperse droplets.      

The effects of blood viscoelasticity on the pulse wave in arteries

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈａｔｔｈｅｂｌｏｏｄｈａｓｖｉｓｃｏｅｌａｓｔｉｃｐｒｏｐｅｒｔｉｅｓｉｓａｗｅｌｌ＿ｋｎｏｗｎｆａｃｔ.ＴｈｅｒｅｓｅａｒｃｈｅｓｆｏｒｔｈｅｂｌｏｏｄｖｉｓｃｏｅｌａｓｔｉｃｉｔｙｂｙＧ .Ｂ .Ｔｈｕｒｓｔｏｎ[1～4]ａｎｄＳ .Ｃｈｉｅｎ[5 ]ｓｈｏｗｔｈａｔｔｈｅｂｌｏｏｄｎｏｔｏｎｌｙａｐｐｅａｒｓｔｈｅｖｉｓｃｏｅｌａｓｔｉｃｉｔｙｉｎｖａｒｉｏｕｓｏｓｃｉｌｌａｔｏｒｙｂｌｏｏｄｆｌｏｗｓ,ｂｕｔａｌｓｏｈａｓｑｕｉｔｅｓｔｒｏｎｇｅｌａｓｔｉｃｉｔｙｉｎｓｏｍｅ…     

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the FukagataIwamoto-Kasagi(FIK) identity(FUKAGATA, K., IWAMOTO, K., and KASAGI, N.Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows.Physics of Fluids, 14(11), L73–L76(2002)) and the Renard-Deck(RD) identity(DECK,S., RENARD, N., LARAUFIE, R., and WEISS, P.′E. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650.Journal of Fluid Mechanics, 743, 202–248(2014)). The direct numerical simulation(DNS) data provided by Lee and Moser(LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics,774, 395–415(2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers.The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.     

Measurements of mean and turbulence quantities in the curved wake of an airfoil

Measurements of mean and turbulence quantities are presented for a curved wake of an airfoil. The wake is generated by placing a NACA 0012 airfoil of 0.150 m chord length at one chord length upstream of a 90° bend. The bend has a square cross-section of 0.457 m × 0.457 m, a mean radius-to-height ratio of R/H=1.17, and concave and convex radii of curvature 0.764 and 0.307 m, respectively. In addition to streamwise curvature, the wake is subjected to varying streamwise and radial pressure. The measurements were carried out at mainstream air velocities of 10, 15 and 20 m/s. The results are presented for the mean streamwise velocity, five components of turbulence stresses, the calculated wake half-width and the maximum velocity defect. The results showed the formation of an asymmetric wake about the wake centreline, with a larger wake half-width on the inner side. The wake half-width on both inner side and outer side of the wake decrease with mainstream velocity, whereas the maximum velocity defect, turbulence stresses increase with mainstream velocity. The turbulence stresses are enhanced on the inner side but suppressed on the outer side.     

THE CREEP EFFECTS ON THE BUCKLING OF SHALLOW SHELLS

An analysis of the creep effects on the buckling of concreteshallow shells is presented in this paper.Based on the non-linear theory of thin elastic shells.it is found that forthose of the elliptical paraboloidal type.the upper cri-tical load of the load-deflection curve will decrease whilethe lower limit Will increase with time.As to the problemof local buckling of the shell.the critical load is de-pendent only upon the modulus of elasticity at the instantit occurs.     

The effects of flow rate and distance travelled on the mobility of phosphate in soils

Effects of flow rate and distance travelled on average mobilities of phosphate in a soil are estimated from breakthrough curves of phosphate at the outlets of small columns of soil, following step increases in the concentration at the inlets. Experimental results are compared with results from a computer simulation model of leached columns of soil.Average mobilities of phosphate in columns of soil, following a step increase in the input concentration, decrease with decreasing rate of flow and with increasing distance travelled and appear to be linearly correlated on a logarithmic scale with both flow rate and distance travelled. An empirical equation, describing these relationships, is fitted to data from leaching experiments at flow rates between 30 and 600 cm/day in 10 cm long columns of soil. Coefficients are obtained by curve fitting breakthrough curves, calculated with a numerical computer simulation model, to experimental breakthrough curves. The fitted equation enables extrapolation to flow rates and travel distances that are more relevant to a field situation.