Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Computational study of viscous effects on lobed mixer flow features and performance

This article describes a computational study of viscous effects on lobed mixer flowfields. The computations, which were carried out using a compressible, three-dimensional, unstructured-mesh Navier-Stokes solver, were aimed at assessing the impacts on mixer performance of inlet boundary-layer thickness and boundary-layer separation within the lobe. The geometries analyzed represent a class of lobed mixer configurations used in turbofan engines. Parameters investigated included lobe penetration angles from 22 to 45 deg, stream-to-stream velocity ratios from 0.5 to 1.0, and two inlet boundary-layer displacement thicknesses. The results show quantitatively the increasing influence of viscous effects as lobe penetration angle is increased. It is shown that the simple estimate of shed circulation given by Skebe et al. (Experimental Investigation of Three-Dimensional Forced Mixer Lobe Flow Field, AIAA Paper 88-3785, July, 1988) can be extended even to situations in which the flow is separated, provided an effective mixer exit angle and height are defined. An examination of different loss sources is also carried out to illustrate the relative contributions of mixing loss and of boundary-layer viscous effects in cases of practical interest.

A Numerical Study for Turbulent Flow and Thermal Influence Over Inhomogenous Canopy of Roughness Elements

A large-eddy simulation with transitional structure function(TSF) subgrid model we previously proposed was performed to investigate the turbulent flow with thermal influence over an inhomogeneous canopy, which was represented as alternative large and small roughness elements. The aerodynamic and thermodynamic effects of the presence of a layer of large roughness elements were modelled by adding a drag term to the three-dimensional Navier-Stokes equations and a heat source/sink term to the scalar equation, respectively. The layer of small roughness elements was simply treated using the method as described in paper (Moeng 1984, J. Atmos Sci. 41, 2052-2062) for homogeneous rough surface. The horizontally averaged statistics such as mean vertical profiles of wind velocity, air temperature, et al., are in reasonable agreement with Gao et al.(1989, Boundary layer meteorol. 47, 349-377) field observation (homogeneous canopy). Not surprisingly, the calculated instantaneous velocity and temperature fields show that the roughness elements considerably changed the turbulent structure within the canopy. The adjustment of the mean vertical profiles of velocity and temperature was studied, which was found qualitatively comparable with Belcher et al. (2003, J Fluid Mech. 488, 369-398)'s theoretical results. The urban heat island(UHI) was investigated imposing heat source in the region of large roughness elements. An elevated inversion layer, a phenomenon often observed in the urban area (Sang et al., J Wind Eng. Ind. Aesodyn. 87, 243-258)'s was successfully simulated above the canopy. The cool island(CI) was also investigated imposing heat sink to simply model the evaporation of plant canopy. An inversion layer was found very stable and robust within the canopy.

Size effects in the constrained deformation of metallic foams

The constrained deformation of an aluminium alloy foam sandwiched between steel substrates has been investigated. The sandwich plates are subjected to through-thickness shear and normal loading, and it is found that the face sheets constrain the foam against plastic deformation and result in a size effect: the yield strength increases with diminishing thickness of foam layer. The strain distribution across the foam core has been measured by a visual strain mapping technique, and a boundary layer of reduced straining was observed adjacent to the face sheets. The deformation response of the aluminium foam layer was modelled by the elastic-plastic finite element analysis of regular and irregular two dimensional honeycombs, bonded to rigid face sheets; in the simulations, the rotation of the boundary nodes of the cell-wall beam elements was set to zero to simulate full constraint from the rigid face sheets. It is found that the regular honeycomb under-estimates the size effect whereas the irregular honeycomb provides a faithful representation of both the observed size effect and the observed strain profile through the foam layer. Additionally, a compressible version of the Fleck-Hutchinson strain gradient theory was used to predict the size effect; by identifying the cell edge length as the relevant microstructural length scale the strain gradient model is able to reproduce the observed strain profiles across the layer and the thickness dependence of strength. © 2002 Elsevier Science Ltd. All rights reserved.

Assessment of the contribution of surface roughness to airframe noise

The generation of sound by turbulent boundary-layer flow at low Mach number over a rough wall is investigated by applying a theoretical model that describes the scattering of the turbulence near field into sound by roughness elements. Attention is focused on the numerical method to approximately quantify the absolute level of far-field radiated roughness noise. Models for the source statistics are obtained by scaling smooth-wall data by the increased skin friction velocity and boundary-layer thickness for a rough surface. Numerical integration is performed to determine the roughness noise, and it reproduces the spectral characteristics of the available empirical formula and experimental data. Experiments are conducted to measure the radiated sound from two rough plates in an open jet The measured noise spectra of the rough plates are above that of a smooth plate in 1-2.5 kHz frequency and exhibit reasonable agreement with the predicted level. Estimates of the roughness noise for a Boeing 757 sized aircraft wing with idealized levels of surface roughness show that hi the high-frequency region the sound radiated from surface roughness may exceed that from the trailing edge, and higher overall sound pressure levels are observed for the roughness noise. The trailing edge noise is also enhanced by surface roughness somewhat A parametric study indicates that roughness height and roughness density significantly affect the roughness noise with roughness height having the dominant effect The roughness noise directivity varies with different levels of surface roughness. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Effects of surface roughness on airframe noise

The generation of sound by turbulent boundary layer flow at low Mach number over a rough wall is investigated by applying the theoretical model which describes the scattering of the turbulence near field into sound by roughness elements. Attention is focused on the numerical method to approximately quantify the absolute level of the roughness noise radiated to far field. Empirical models for the source statistics are obtained by scaling smooth-wall data through increased skin friction velocity and boundary layer thickness for the rough surface. Numerical integration is performed to determine the roughness noise, and it reproduces the spectral characteristics of the available empirical formula and experimental data. Experiments are conducted to measure the radiated sound from two rough plates in an open jet by four 1/2'' free-field condenser microphones. The measured noise spectra of the rough plates are above that of a smooth plate in 1-2.5 kHz frequency and exhibits encouraging agreement with the predicted spectra. Also, a phased microphone array is utilized to localize the sound source, and it confirms that the rough plates generate higher source strengthes in this frequency range. A parametric study illustrates that the roughness height and roughness density significantly affect the far-field radiated roughness noise with the roughness height having the dominant effect. The estimates of the roughness noise for a Boeing 757 sized aircraft wing show that in high frequency region the sound radiated from surface roughness may exceed that from the trailing edge, and higher overall sound pressure levels for the roughness noise are also observed.

An overview of air-sea interface process studies

Recent progress in the study of air-sea interface processes for momentum, heat, moisture and mass transfer are reviewed in the present article. Except for turbulent structure, we have analysed the other physical mechanisms occurring in the wave boundary layer, such as the roles of the sea surface state, droplets and bubbles due to wave breaking, which at least partly account for the existing discrepancies between theory and observations. The experiments, both over the ocean and in the laboratory, are described briefly. In conclusion, a few perspective trends in this area are suggested for further investigation.

Measurement and simulation of surface roughness noise using phased microphone arrays

A turbulent boundary-layer flow over a rough wall generates a dipole sound field as the near-field hydrodynamic disturbances in the turbulent boundary-layer scatter into radiated sound at small surface irregularities. In this paper, phased microphone arrays are applied to the measurement and simulation of surface roughness noise. The radiated sound from two rough plates and one smooth plate in an open jet is measured at three streamwise locations, and the beamforming source maps demonstrate the dipole directivity. Higher source strengths can be observed on the rough plates which also enhance the trailing-edge noise. A prediction scheme in previous theoretical work is used to describe the strength of a distribution of incoherent dipoles and to simulate the sound detected by the microphone array. Source maps of measurement and simulation exhibit satisfactory similarities in both source pattern and source strength, which confirms the dipole nature and the predicted magnitude of roughness noise. However, the simulations underestimate the streamwise gradient of the source strengths and overestimate the source strengths at the highest frequency. © 2008 Elsevier Ltd. All rights reserved.

Variation of drag coefficient with wind wave development

Turbulent air flows over developing wind waves in the air-sea boundary layer are numerically simulated without considering wave breaking. Influences of wind waves on air flows are considered using a model of significant wave and surface roughness, with a formula proposed for calculating the surface roughness, k - epsilon model is adopted to simulate turbulent flows. The results of the drag coefficient and turbulence characteristics agree well with the observations.

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 <= Pr <= 50). We focus on the relationships between the critical Reynolds number Re-c, the azimuthal wave number m, the aspect ratio F and the Prandtl number Pr. A detailed Re-c-Pr stability diagram is given for liquid bridges with various Gamma. In the region of Pr > 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR.

Reconstructing The Vertical Distribution Of The Aeolian Saltation Mass Flux Based On The Probability Distribution Of Lift-Off Velocity

The probability distribution of lift-off velocity of the saltating grains is a bridge to linking microscopic and macroscopic research of aeolian sand transport. The lift-off parameters of saltating grains (i.e., the horizontal and vertical lift-off velocities, resultant lift-off velocity, and lift-off angle) in a wind tunnel are measured by using a Phase Doppler Particle Analyzer (PDPA). The experimental results show that the probability distribution of horizontal lift-off velocity of saltating particles on a bed surface is a normal function, and that of vertical lift-off velocity is an exponential function. The probability distribution of resultant lift-off velocity of saltating grains can be expressed as a log-normal function, and that of lift-off angle complies with an exponential function. A numerical model for the vertical distribution of aeolian mass flux based on the probability distribution of lift-off velocity is established. The simulation gives a sand mass flux distribution which is consistent with the field data of Namikas (Namikas, S.L., 2003. Field measurement and numerical modelling of acolian mass flux distributions on a sandy beach, Sedimentology 50, 303-326). Therefore, these findings are helpful to further understand the probability characteristics of lift-off grains in aeolian sand transport. (c) 2007 Elsevier B.V. All rights reserved.

Using wavelet transform to study the Lipschitz local singular exponent in wall turbulence

In this paper, wavelet,transform is introduced to study the Lipschitz local singular exponent for characterising the local singularity behavior of fluctuating velocity in wall turbulence. I, is found that the local singular exponent is negative when the ejections and sweeps of coherent structures occur in a turbulent boundary layer.

Effects of Mach number on turbulent separation behaviours induced by blunt fin

An experimental study of the interaction between shock wave and turbulent boundary layer induced by blunt fin has been carried out at M-infinity = 7.8 using oil flow visualization and simultaneous measurements of fluctuating wall pressure and heat transfer. This paper presents the effects of Mach number on turbulent separation behaviours induced by blunt fin.

Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel

Two-time scale perturbation expansions were developed in weakly viscous fluids to investigate surface wave motions by linearizing the Navier-Stokes equation in a circular cylindrical vessel which is subject to a vertical oscillation. The fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates a damping term and external excitation, was derived for the weakly viscid fluids. The condition for the appearance of stable surface waves was obtained and the critical curve was determined. In addition, an analytical expression for the damping coefficient was determined and the relationship between damping and other related parameters (such as viscosity, forced amplitude, forced frequency and the depth of fluid, etc.) was presented. Finally, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent.