scholarly journals A Two-Scale Approach for Lubricated Soft-Contact Modeling: An Application to Lip-Seal Geometry

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Michele Scaraggi ◽  
Giuseppe Carbone
Keyword(s):  
Large Scale ◽  
Mixed Lubrication ◽  
Small Scale ◽  
Length Scale ◽  
Contact Modeling ◽  
Soft Contact ◽  
Lip Seal ◽  
Contact Algorithm ◽  
Scale Roughness ◽  
Lubrication Conditions

We consider the case of soft contacts in mixed lubrication conditions. We develop a novel, two scales contact algorithm in which the fluid- and asperity-asperity interactions are modeled within a deterministic or statistic scheme depending on the length scale at which those interactions are observed. In particular, the effects of large-scale roughness are deterministically calculated, whereas those of small-scale roughness are included by solving the corresponding homogenized problem. The contact scheme is then applied to the modeling of dynamic seals. The main advantage of the approach is the tunable compromise between the high-computing demanding characteristics of deterministic calculations and the much lower computing requirements of the homogenized solutions.

Reverberation Intensity Decaying in Range-Dependent Waveguide

2019 ◽  
Vol 27 (03) ◽  
pp. 1950007
Author(s):  
J. R. Wu ◽  
T. F. Gao ◽  
E. C. Shang
Keyword(s):  
Large Scale ◽  
Back Propagation ◽  
Normal Modes ◽  
Small Scale ◽  
Signal Pulse ◽  
First Order ◽  
Orthogonal Property ◽  
Short Signal ◽  
Scale Roughness ◽  
Special Case

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

scholarly journals A MODIFIED TWO-SCALE MICROWAVE SCATTERING MODEL FOR A GAUSSIAN-DISTRIBUTED CONDUCTING ROUGH SURFACE

2018 ◽  
Vol XLII-3 ◽  
pp. 2141-2146
Author(s):  
F. Yu ◽  
H. Wang ◽  
Z. Y. Chen
Keyword(s):  
Surface Roughness ◽  
Rough Surface ◽  
Large Scale ◽  
Incident Angle ◽  
Wavelet Packet ◽  
Small Scale ◽  
Backscattering Coefficient ◽  
Microwave Scattering ◽  
Scattering Model ◽  
Scale Roughness

A modified two-scale microwave scattering model (MTSM) was presented to describe the scattering coefficient of natural rough surface in this paper. In the model, the surface roughness was assumed to be Gaussian so that the surface height <i>z(x, y)</i> can be split into large-scale and small-scale components relative to the electromagnetic wavelength by the wavelet packet transform. Then, the Kirchhoff Model (KM) and Small Perturbation Method (SPM) were used to estimate the backscattering coefficient of the large-scale and small-scale roughness respectively. Moreover, the ‘tilting effect’ caused by the slope of large-scale roughness should be corrected when we calculated the backscattering contribution of the small-scale roughness. Backscattering coefficient of the MTSM was the sum of backscattering contribution of both scale roughness surface. The MTSM was tested and validated by the advanced integral equation model (AIEM) for dielectric randomly rough surface, the results indicated that, the MTSM accuracy were in good agreement with AIEM when incident angle was less than 30&amp;deg; (<i>&amp;theta;<sub>i</sub></i>&amp;thinsp;&amp;lt;30&amp;deg;) and the surface roughness was small (<i>ks</i>&amp;thinsp;=&amp;thinsp;0.354).

scholarly journals A multifractal model for the momentum transfer process in wall-bounded flows

2017 ◽  
Vol 824 ◽  
Author(s):  
X. I. A. Yang ◽  
A. Lozano-Durán
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Small Scale ◽  
Length Scale ◽  
Cascade Process ◽  
Outer Length ◽  
Multifractal Formalism ◽  
Multiplicative Process ◽  
Stress Fluctuation

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation $\unicode[STIX]{x1D70F}_{l}^{\prime }$, where $l$ is the filtering length scale. According to the multifractal formalism, $\langle {\unicode[STIX]{x1D70F}^{\prime }}^{2}\rangle \sim \log (Re_{\unicode[STIX]{x1D70F}})$ and $\langle \exp (p\unicode[STIX]{x1D70F}_{l}^{\prime })\rangle \sim (L/l)^{\unicode[STIX]{x1D701}_{p}}$ in the log-region, where $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, $p$ is a real number, $L$ is an outer length scale and $\unicode[STIX]{x1D701}_{p}$ is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at $Re_{\unicode[STIX]{x1D70F}}=4200$.

Amplitude and frequency modulation of the small scales in a jet

2015 ◽  
Vol 772 ◽  
pp. 756-783 ◽  
Author(s):  
D. Fiscaletti ◽  
B. Ganapathisubramani ◽  
G. E. Elsinga
Keyword(s):  
Amplitude Modulation ◽  
Frequency Modulation ◽  
High Speed ◽  
Large Scale ◽  
Spectral Band ◽  
Physical Space ◽  
Small Scale ◽  
Length Scale ◽  
Air Jet ◽  
Amplitude And Frequency Modulation

The present study is an experimental investigation of the relationship between the large- and small-scale motions in the far field of an air jet at high Reynolds number. In the first part of our investigation, the analysis is based on time series of hot-wire anemometry (HWA), which are converted into space series after applying the Taylor hypothesis. By using a spectral filter, two signals are constructed, one representative of the large-scale motions ($2{\it\lambda}_{T}-L$, where ${\it\lambda}_{T}$ is the Taylor length scale, and $L$ is the integral length scale) and the other representative of the small-scale motions ($1.5{-}5{\it\eta}$, where ${\it\eta}$ is the Kolmogorov length scale). The small-scale signal is found to be modulated both in amplitude and in frequency by the energy-containing scales in an analogous way, both at the centreline and around the centreline. In particular, for positive fluctuations of the large-scale signal, the small-scale signal is locally stronger in amplitude (amplitude modulation), and it locally exhibits a higher number of local maxima and minima (frequency modulation). The extent of this modulation is quantified based on the strength of the large-scale fluctuations. The response of the small-scale motions to amplitude modulation can be considered instantaneous, being on the order of one Kolmogorov time scale. In the second part of our investigation we use long-range ${\it\mu}$PIV to study the behaviour of the small-scale motions in relation to their position in either high-speed or low-speed regions of the flow. The spatially resolved velocity vector fields allow us to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25 % of the value measured from HWA. The remaining 75 % comes from the fixed spectral band filter used to obtain the large- and small-scale signals, which does not consider the local convection velocity. A very similar overestimation of amplitude modulation when quantified in the time-frame is also obtained analytically. Furthermore, the size of the structures of intense vorticity does not change significantly in relation to the large-scale velocity fluctuation, meaning that there is no significant spatial frequency modulation. The remaining amplitude modulation in space can be explained as a statistical coupling between the strength of the structures of vorticity and their preferential location inside large-scale high-velocity regions. Finally, the implications that the present findings have on amplitude and frequency modulation in turbulent boundary layers (TBLs) are discussed.

scholarly journals Non-Repeatability, Scale- and Model Effects in Laboratory Measurement of Impact Loads Induced by an Overtopped Bore on a Dike Mounted Wall

2019 ◽  
Author(s):  
Maximilian Streicher ◽  
Andreas Kortenhaus ◽  
Corrado Altomare ◽  
Steven Hughes ◽  
Krasimir Marinov ◽  
...  
Keyword(s):  
Large Scale ◽  
Scale Effects ◽  
Vertical Wall ◽  
Scale Factor ◽  
Scale Model ◽  
Small Scale ◽  
Length Scale ◽  
Force Measurements ◽  
Impact Forces ◽  
Small Scale Model

Abstract Overtopping bore impact forces on a dike mounted vertical wall were measured in similar large-scale (Froude length scale factor 1-to-4.3) and small-scale (Froude length scale factor 1-to-25) models. The differences due to scale effects were studied, by comparing the up-scaled force measurements from both models in prototype. It was noted that if a minimum layer thickness, velocity of the overtopping flow and water depth at the dike toe were maintained in the small-scale model, the resulting differences in impact force due to scale effects are within the range of differences due to non-repeatability and model effects.

WAVE AND CURRENT INTERACTIONS IN SHALLOW WATER

1986 ◽  
Vol 1 (20) ◽  
pp. 125
Author(s):  
Sung B. Yoon ◽  
Philip L.F. Liu
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Large Scale ◽  
Evolution Equations ◽  
Small Scale ◽  
Length Scale ◽  
Rip Currents ◽  
Coastal Currents ◽  
Protection Measures ◽  
Incident Cases

Interactions between waves and currents are common and important phenomena in the coastal zone. Coastal currents, such as longshore currents, rip currents, and river flows, can significantly change wave heights and directions of wave propagation. Consequently, the design for shoreline protection measures must be adjusted accordingly. Various theories for wave-current interactions exist and have been reviewed by Peregrine and Jonsson (1983). Most of these theories are developed for large-scale currents where the length-scale for the current variation is much greater than the typical wavelength. These theories cannot be applied to the coastal currents which are small-scale currents. In this paper, the interactions between currents and nonlinear shallow water waves are investigated. Boussinesq equations are used to derive evolution equations for spectral wave components. The current intensity is assumed to be larger than the leading wave orbital velocity and smaller than the group velocity. The length-scale of the current is much shorter than those assumed in the existing large-scale theories. To facilitate numerical computations, the parabolic approximation is applied and a simplified model is developed. A numerical example is given for the refraction and diffraction of cnoidal waves over a rip current on a sloping topography. Both normal and oblique incident cases are examined.

scholarly journals Modelling turbulent boundary layer flow over fractal-like multiscale terrain using large-eddy simulations and analytical tools

2017 ◽  
Vol 375 (2091) ◽  
pp. 20160098 ◽  
Author(s):  
X. I. A. Yang ◽  
C. Meneveau
Keyword(s):  
Large Scale ◽  
Wind Farm ◽  
Ground Surface ◽  
Small Scale ◽  
Subgrid Scale ◽  
Mean Velocity ◽  
Roughness Model ◽  
Roughness Elements ◽  
Large Eddy ◽  
Scale Roughness

In recent years, there has been growing interest in large-eddy simulation (LES) modelling of atmospheric boundary layers interacting with arrays of wind turbines on complex terrain. However, such terrain typically contains geometric features and roughness elements reaching down to small scales that typically cannot be resolved numerically. Thus subgrid-scale models for the unresolved features of the bottom roughness are needed for LES. Such knowledge is also required to model the effects of the ground surface ‘underneath’ a wind farm. Here we adapt a dynamic approach to determine subgrid-scale roughness parametrizations and apply it for the case of rough surfaces composed of cuboidal elements with broad size distributions, containing many scales. We first investigate the flow response to ground roughness of a few scales. LES with the dynamic roughness model which accounts for the drag of unresolved roughness is shown to provide resolution-independent results for the mean velocity distribution. Moreover, we develop an analytical roughness model that accounts for the sheltering effects of large-scale on small-scale roughness elements. Taking into account the shading effect, constraints from fundamental conservation laws, and assumptions of geometric self-similarity, the analytical roughness model is shown to provide analytical predictions that agree well with roughness parameters determined from LES. This article is part of the themed issue ‘Wind energy in complex terrains’.

Inferring Earth’s discontinuous chemical layering from the 660-kilometer boundary topography

Science ◽  
2019 ◽  
Vol 363 (6428) ◽  
pp. 736-740 ◽  
Author(s):  
Wenbo Wu ◽  
Sidao Ni ◽  
Jessica C. E. Irving
Keyword(s):  
Solid Earth ◽  
Long Range ◽  
Upper Mantle ◽  
Lower Mantle ◽  
Seismic Waves ◽  
Short Length ◽  
Small Scale ◽  
Length Scale ◽  
Scale Roughness ◽  
Topographic Variation

Topography, or depth variation, of certain interfaces in the solid Earth can provide important insights into the dynamics of our planet interior. Although the intermediate- and long-range topographic variation of the 660-kilometer boundary between Earth’s upper and lower mantle is well studied, small-scale measurements are far more challenging. We found a surprising amount of topography at short length scale along the 660-kilometer boundary in certain regions using scatteredP'P'seismic waves. Our observations required chemical layering in regions with high short-scale roughness. By contrast, we did not see such small-scale topography along the 410-kilometer boundary in the upper mantle. Our findings support the concept of partially blocked or imperfect circulation between the upper and lower mantle.

On the scaling of air entrainment from a ventilated partial cavity

2013 ◽  
Vol 732 ◽  
pp. 47-76 ◽  
Author(s):  
Simo A. Mäkiharju ◽  
Brian R. Elbing ◽  
Andrew Wiggins ◽  
Sarah Schinasi ◽  
Jean-Marc Vanden-Broeck ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Weber Number ◽  
Large Scale ◽  
Air Entrainment ◽  
Small Scale ◽  
Length Scale ◽  
Entrainment Rate ◽  
Two Dimensional ◽  
Wide Range ◽  
Stable Cavity

AbstractThe behaviour of a nominally two-dimensional ventilated partial cavity was examined over a wide range of size scales and flow speeds to determine the influence of Froude, Reynolds, and Weber number on the cavity shape, dynamics, and gas entrainment rate. Two geometrically similar experiments were conducted with a 14:1 length scale ratio. The results were compared to a two-dimensional semi-analytical model of the cavity flow, and Froude scaling was found to be sufficient to match basic cavity shapes. However, the air flux required to maintain a stable cavity did not scale with Froude number alone, as the dynamics of the cavity closure changed with increasing Reynolds number. The required air flux differed over one order of magnitude between the lowest and highest Reynolds number flows. But, for sufficiently high Reynolds numbers, the rate of scaled entrainment appeared to approach Reynolds number independence. Modest changes in surface tension of the small-scale experiment suggested that the Weber number was important only at the lowest speeds and smaller length scale. Otherwise, the Weber numbers of the flows were sufficiently high to make the effects of interfacial tension negligible. We also observed that modest unsteadiness in the inflow to the large-scale cavity led to a significant increase in the required air flux needed to maintain a stable cavity, with the required excess gas flux nominally proportional to the flow’s perturbation amplitude. Finally, discussion is provided on how these results relate to model testing of partial cavity drag reduction (PCDR) systems for surface ships.

scholarly journals Combined effects of homogenization and singular perturbations: Quantitative estimates

2021 ◽  
pp. 1-34
Author(s):  
Weisheng Niu ◽  
Zhongwei Shen
Keyword(s):  
Large Scale ◽  
Convergence Rates ◽  
Elliptic Systems ◽  
Small Scale ◽  
Length Scale ◽  
Combined Effects ◽  
Periodic Homogenization ◽  
Quantitative Estimates ◽  
Lipschitz Estimate ◽  
Scale Estimate

We investigate quantitative estimates in periodic homogenization of second-order elliptic systems of elasticity with singular fourth-order perturbations. The convergence rates, which depend on the scale κ that represents the strength of the singular perturbation and on the length scale ε of the heterogeneities, are established. We also obtain the large-scale Lipschitz estimate, down to the scale ε and independent of κ. This large-scale estimate, when combined with small-scale estimates, yields the classical Lipschitz estimate that is uniform in both ε and κ.

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