Correction Function

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Olga I Vinogradova - One of the best experts on this subject based on the ideXlab platform.

  • hydrodynamic interaction with super hydrophobic surfaces
    Soft Matter, 2010
    Co-Authors: Aleksey V Belyaev, Olga I Vinogradova
    Abstract:

    Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a Correction Function to the Reynolds equation, which is shown to be the harmonic mean of Corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (compared to texture characteristic length) gap. It is not really sensitive to the pattern geometry, but depends strongly on the fraction of the gas phase and local slip length at the gas area.

  • hydrodynamic interaction with super hydrophobic surfaces
    arXiv: Fluid Dynamics, 2010
    Co-Authors: Aleksey V Belyaev, Olga I Vinogradova
    Abstract:

    Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a Correction Function to the Reynolds equation, which is shown to be the harmonic mean of Corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (compared to texture period) gap. It is not really sensitive to the pattern geometry, but depends strongly on the fraction of the gas phase and local slip length at the gas area.

Gabriel G Katul - One of the best experts on this subject based on the ideXlab platform.

  • A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer
    Journal of the Atmospheric Sciences, 2015
    Co-Authors: Tirtha Banerjee, Jehn-yih Juang, Gabriel G Katul
    Abstract:

    AbstractA spectral budget model is developed to describe the scaling behavior of the longitudinal turbulent velocity variance with the stability parameter and the normalized height in an idealized stably stratified atmospheric surface layer (ASL), where z is the height from the surface, L is the Obukhov length, and δ is the boundary layer height. The proposed framework employs Kolmogorov’s hypothesis for describing the shape of the longitudinal velocity spectra in the inertial subrange, Heisenberg’s eddy viscosity as a closure for the pressure redistribution and turbulent transfer terms, and the Monin–Obukhov similarity theory (MOST) scaling for linking the mean longitudinal velocity and temperature profiles to ζ. At a given friction velocity , reduces with increasing ζ as expected. The model is consistent with the disputed z-less stratification when the stability Correction Function for momentum increases with increasing ζ linearly or as a power law with the exponent exceeding unity. For the Businger–Dye...

  • buoyancy effects on the integral lengthscales and mean velocity profile in atmospheric surface layer flows
    Physics of Fluids, 2013
    Co-Authors: Scott T Salesky, Gabriel G Katul, Marcelo Chamecki
    Abstract:

    Within the diabatic atmospheric surface layer (ASL) under quasi-stationary and horizontal homogeneous conditions, the mean velocity profile deviates from its conventional logarithmic shape by a height-dependent universal stability Correction Function ϕm(ζ) that varies with the stability parameter ζ. The ζ parameter measures the relative importance of mechanical to buoyant production or destruction of turbulent kinetic energy (TKE) within the ASL. A link between ϕm(ζ) and the spectrum of turbulence in the ASL was recently proposed by Katul et al. [“Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer,” Phys. Rev. Lett. 107, 268502 (2011)]. By accounting for the stability-dependence of TKE production, Katul et al. were able to recover scalings for ϕm with the anticipated power-law exponents for free convective, slightly unstable, and stable conditions. To obtain coefficients for the ϕm(ζ) curve in good agreement with empirical formulas, they introduced a Correction for the ...

  • mean velocity profile in a sheared and thermally stratified atmospheric boundary layer
    Physical Review Letters, 2011
    Co-Authors: Gabriel G Katul, Alexandra G Konings, Amilcare Porporato
    Abstract:

    : A stability Correction Function φ(m)(ζ) that accounts for distortions to the logarithmic mean velocity profile (MVP) in the lower atmosphere caused by thermal stratification was proposed by Monin and Obukhov in the 1950s using dimensional analysis. Its universal character was established from many field experiments. However, theories that describe the canonical shape of φ(m)(ζ) are still lacking. A previous link between the spectrum of turbulence and the MVP is expanded here to include the effects of thermal stratification on the turbulent kinetic energy dissipation rate and eddy-size anisotropy. The resulting theory provides a novel explanation for the power-law exponents and coefficients already reported for φ(m)(ζ) from numerous field experiments.

Aleksey V Belyaev - One of the best experts on this subject based on the ideXlab platform.

  • hydrodynamic interaction with super hydrophobic surfaces
    Soft Matter, 2010
    Co-Authors: Aleksey V Belyaev, Olga I Vinogradova
    Abstract:

    Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a Correction Function to the Reynolds equation, which is shown to be the harmonic mean of Corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (compared to texture characteristic length) gap. It is not really sensitive to the pattern geometry, but depends strongly on the fraction of the gas phase and local slip length at the gas area.

  • hydrodynamic interaction with super hydrophobic surfaces
    arXiv: Fluid Dynamics, 2010
    Co-Authors: Aleksey V Belyaev, Olga I Vinogradova
    Abstract:

    Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a Correction Function to the Reynolds equation, which is shown to be the harmonic mean of Corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (compared to texture period) gap. It is not really sensitive to the pattern geometry, but depends strongly on the fraction of the gas phase and local slip length at the gas area.

Xin Luo - One of the best experts on this subject based on the ideXlab platform.

  • a multi module electrodynamic exciter with a variable pole arc ratio disk halbach array for a high bandwidth dynamic torsional stiffness test
    Sensors, 2019
    Co-Authors: Fang Yuan, Lizhan Zeng, Xuedong Chen, Chengyuan Liang, Xiaojun Ding, Xin Luo
    Abstract:

    In this paper, a multi-module electrodynamic exciter based on moving-magnet disk voice coil motor is presented to meet the demands of high torque and high bandwidth in a dynamic torsional stiffness test. A variable pole-arc ratio disk Halbach array (VPAR-DHA) is proposed, so that both high torque density and low rotor inertia can be obtained through enhancing the magnetic field in the working range. The analytical quasi-3-D model of VPAR-DHA was set up by using the harmonic Function method, with the consideration of end-effects by a Correction Function. Electromagnetic structure optimization was carried out with the analytical model, and verified by 3-D finite-element (FEM) results. The proposed design was experimentally tested and verified with a prototype that achieved a peak dynamic torque output of 40 Nm at a frequency of 120 Hz, and a stroke of ±1°. The proposed method can also be easily extended to satisfy various demands of dynamic torsional stiffness test.

  • A Multi-Module Electrodynamic Exciter with a Variable Pole-Arc Ratio Disk Halbach Array for a High-Bandwidth Dynamic Torsional Stiffness Test
    MDPI AG, 2019
    Co-Authors: Fang Yuan, Lizhan Zeng, Xuedong Chen, Chengyuan Liang, Xiaojun Ding, Xin Luo
    Abstract:

    In this paper, a multi-module electrodynamic exciter based on moving-magnet disk voice coil motor is presented to meet the demands of high torque and high bandwidth in a dynamic torsional stiffness test. A variable pole-arc ratio disk Halbach array (VPAR-DHA) is proposed, so that both high torque density and low rotor inertia can be obtained through enhancing the magnetic field in the working range. The analytical quasi-3-D model of VPAR-DHA was set up by using the harmonic Function method, with the consideration of end-effects by a Correction Function. Electromagnetic structure optimization was carried out with the analytical model, and verified by 3-D finite-element (FEM) results. The proposed design was experimentally tested and verified with a prototype that achieved a peak dynamic torque output of 40 Nm at a frequency of 120 Hz, and a stroke of ±1°. The proposed method can also be easily extended to satisfy various demands of dynamic torsional stiffness test

Marcelo Chamecki - One of the best experts on this subject based on the ideXlab platform.

  • buoyancy effects on the integral lengthscales and mean velocity profile in atmospheric surface layer flows
    Physics of Fluids, 2013
    Co-Authors: Scott T Salesky, Gabriel G Katul, Marcelo Chamecki
    Abstract:

    Within the diabatic atmospheric surface layer (ASL) under quasi-stationary and horizontal homogeneous conditions, the mean velocity profile deviates from its conventional logarithmic shape by a height-dependent universal stability Correction Function ϕm(ζ) that varies with the stability parameter ζ. The ζ parameter measures the relative importance of mechanical to buoyant production or destruction of turbulent kinetic energy (TKE) within the ASL. A link between ϕm(ζ) and the spectrum of turbulence in the ASL was recently proposed by Katul et al. [“Mean velocity profile in a sheared and thermally stratified atmospheric boundary layer,” Phys. Rev. Lett. 107, 268502 (2011)]. By accounting for the stability-dependence of TKE production, Katul et al. were able to recover scalings for ϕm with the anticipated power-law exponents for free convective, slightly unstable, and stable conditions. To obtain coefficients for the ϕm(ζ) curve in good agreement with empirical formulas, they introduced a Correction for the ...