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Jacques Magnaudet - One of the best experts on this subject based on the ideXlab platform.
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oscillatory motion and wake instability of freely rising axisymmetric bodies
Journal of Fluid Mechanics, 2007Co-Authors: Pedro C Fernandes, Frederic Risso, Patricia Ern, Jacques MagnaudetAbstract:This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρ b close to the density ρ f of the fluid. We have investigated the role of the Reynolds Number based on the mean rise velocity u m in the range 80 ≤ Re = u md /ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d / h ≤ 20. Beyond a critical Reynolds Number, Re c , which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Re cf 1 (χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Re cf 2 (χ), and frequency, ω f , of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds Numbers, Re cf 1 and Re cf 2 , decrease. Introducing a Reynolds Number Re * based on the velocity in the recirculating wake makes it possible to obtain thresholds and that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ Re c (χ) is equal to Re cf 1 (χ) and ω is close to ω f . However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Re c to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d , , respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the Modified Reynolds Number, Re *; they no longer depend on the body shape.
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oscillatory motion and wake instability of freely rising axisymmetric bodies
Journal of Fluid Mechanics, 2007Co-Authors: Pedro C Fernandes, Frederic Risso, Patricia Ern, Jacques MagnaudetAbstract:This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρb close to the density ρf of the fluid. We have investigated the role of the Reynolds Number based on the mean rise velocity um in the range 80 ≤ Re = umd/ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d/h ≤ 20. Beyond a critical Reynolds Number, Rec, which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Recf1(χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(χ), and frequency, ωf, of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds Numbers, Recf1 and Recf2, decrease. Introducing a Reynolds Number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds and that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ < 6) are essentially triggered by the wake instability observed for a fixed body: Rec(χ) is equal to Recf1(χ) and ω is close to ωf. However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Rec to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, , respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the Modified Reynolds Number, Re*; they no longer depend on the body shape.
Pedro C Fernandes - One of the best experts on this subject based on the ideXlab platform.
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oscillatory motion and wake instability of freely rising axisymmetric bodies
Journal of Fluid Mechanics, 2007Co-Authors: Pedro C Fernandes, Frederic Risso, Patricia Ern, Jacques MagnaudetAbstract:This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρ b close to the density ρ f of the fluid. We have investigated the role of the Reynolds Number based on the mean rise velocity u m in the range 80 ≤ Re = u md /ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d / h ≤ 20. Beyond a critical Reynolds Number, Re c , which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Re cf 1 (χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Re cf 2 (χ), and frequency, ω f , of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds Numbers, Re cf 1 and Re cf 2 , decrease. Introducing a Reynolds Number Re * based on the velocity in the recirculating wake makes it possible to obtain thresholds and that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ Re c (χ) is equal to Re cf 1 (χ) and ω is close to ω f . However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Re c to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d , , respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the Modified Reynolds Number, Re *; they no longer depend on the body shape.
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oscillatory motion and wake instability of freely rising axisymmetric bodies
Journal of Fluid Mechanics, 2007Co-Authors: Pedro C Fernandes, Frederic Risso, Patricia Ern, Jacques MagnaudetAbstract:This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρb close to the density ρf of the fluid. We have investigated the role of the Reynolds Number based on the mean rise velocity um in the range 80 ≤ Re = umd/ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d/h ≤ 20. Beyond a critical Reynolds Number, Rec, which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Recf1(χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(χ), and frequency, ωf, of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds Numbers, Recf1 and Recf2, decrease. Introducing a Reynolds Number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds and that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ < 6) are essentially triggered by the wake instability observed for a fixed body: Rec(χ) is equal to Recf1(χ) and ω is close to ωf. However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Rec to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, , respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the Modified Reynolds Number, Re*; they no longer depend on the body shape.
Evgeni Fedorovich - One of the best experts on this subject based on the ideXlab platform.
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ARTICLE A Boundary-Layer Scaling for Turbulent Katabatic Flow
2016Co-Authors: Alan Shapiro, Evgeni FedorovichAbstract:Abstract Scaling relationships are proposed for the turbulent katabatic flow of a stably stratified fluid down a homogeneously cooled planar slope—the turbulent analogue of a Prandtl-type slope flow. The Theorem predicts that such flows are controlled by three non-dimensional parameters: the slope angle, the Prandtl Number, and a Reynolds Number defined in terms of the surface thermal forcing (surface buoyancy or surface buoyancy flux), Brunt-Väisälä frequency, slope angle, and molecular viscosity and diffusivity coefficients. However, by exploiting the structure of the governing differential equations in a boundary-layer form, scaled equations are deduced that involve only two non-dimensional parameters: the Prandtl Number and a Modified Reynolds Number. In the proposed scaling framework, the slope angle does not appear as an independent governing parameter, but merely acts as a stretching factor in the scales for the dependent and independent variables, and appears in the Reynolds Number. Based on the boundary-layer analysis, we hypothesize that the full katabatic-flow problem is largely controlled by two rather than three parameters. Preliminary tests of the scaling hypothesis using data from direct numerical simulations provide encouraging results
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A Boundary-Layer Scaling for Turbulent Katabatic Flow
Boundary-Layer Meteorology, 2014Co-Authors: Alan Shapiro, Evgeni FedorovichAbstract:Scaling relationships are proposed for the turbulent katabatic flow of a stably stratified fluid down a homogeneously cooled planar slope—the turbulent analogue of a Prandtl-type slope flow. The $$\Pi $$ Π Theorem predicts that such flows are controlled by three non-dimensional parameters: the slope angle, the Prandtl Number, and a Reynolds Number defined in terms of the surface thermal forcing (surface buoyancy or surface buoyancy flux), Brunt-Väisälä frequency, slope angle, and molecular viscosity and diffusivity coefficients. However, by exploiting the structure of the governing differential equations in a boundary-layer form, scaled equations are deduced that involve only two non-dimensional parameters: the Prandtl Number and a Modified Reynolds Number. In the proposed scaling framework, the slope angle does not appear as an independent governing parameter, but merely acts as a stretching factor in the scales for the dependent and independent variables, and appears in the Reynolds Number. Based on the boundary-layer analysis, we hypothesize that the full katabatic-flow problem is largely controlled by two rather than three parameters. Preliminary tests of the scaling hypothesis using data from direct numerical simulations provide encouraging results.
K R Rajagopal - One of the best experts on this subject based on the ideXlab platform.
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numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing
Meccanica, 2018Co-Authors: Martin Lanzendorfer, Josef Malek, K R RajagopalAbstract:We provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing. We study the influence of several parameters, namely the ratio of the characteristic lengths $$\varepsilon >0$$ (with $$\varepsilon \searrow 0$$ representing the Reynolds lubrication approximation); the coefficient of the exponential pressure–viscosity relation $$\alpha ^*\ge 0$$ ; the parameter $$G^*\ge 0$$ related to the Carreau–Yasuda shear-thinning model and the Modified Reynolds Number $${\mathrm {Re}}_\varepsilon \ge 0$$ . The finite element approximations to the steady isothermal flows are computed without resorting to the lubrication approximation. We obtain the numerical solutions as long as the variation of the viscous stress $$\varvec{S}=2\eta (p,{{\mathrm{tr}}}\,\varvec{D}^2)\varvec{D}$$ with the pressure is limited, say $$|\partial \varvec{S}/\partial p|\le 1$$ . We show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter. We observe that the piezoviscous rheology generates pressure differences across the fluid film.
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numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing
arXiv: Fluid Dynamics, 2017Co-Authors: Martin Lanzendorfer, Josef Malek, K R RajagopalAbstract:We provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing. We study the influence of several parameters, namely the ratio of the characteristic lengths $\varepsilon>0$ (with $\varepsilon\searrow0$ representing the Reynolds lubrication approximation); the coefficient of the exponential pressure--viscosity relation $\alpha^*\geq0$; the parameter $G^*\geq0$ related to the Carreau--Yasuda shear-thinning model and the Modified Reynolds Number $\mathrm{Re}_\varepsilon\geq0$. The finite element approximations to the steady isothermal flows are computed without resorting to the lubrication approximation. We obtain the numerical solutions as long as the variation of the viscous stress $\mathbf{S}=2\eta(p,\mathrm{tr}\mathbf{D}^2)\mathbf{D}$ with the pressure is limited, say $|\partial\mathbf{S}/\partial p|\leq1$. We show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter. We observe that the piezoviscous rheology generates pressure differences across the fluid film.
Patricia Ern - One of the best experts on this subject based on the ideXlab platform.
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oscillatory motion and wake instability of freely rising axisymmetric bodies
Journal of Fluid Mechanics, 2007Co-Authors: Pedro C Fernandes, Frederic Risso, Patricia Ern, Jacques MagnaudetAbstract:This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρ b close to the density ρ f of the fluid. We have investigated the role of the Reynolds Number based on the mean rise velocity u m in the range 80 ≤ Re = u md /ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d / h ≤ 20. Beyond a critical Reynolds Number, Re c , which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Re cf 1 (χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Re cf 2 (χ), and frequency, ω f , of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds Numbers, Re cf 1 and Re cf 2 , decrease. Introducing a Reynolds Number Re * based on the velocity in the recirculating wake makes it possible to obtain thresholds and that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ Re c (χ) is equal to Re cf 1 (χ) and ω is close to ω f . However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Re c to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d , , respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the Modified Reynolds Number, Re *; they no longer depend on the body shape.
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oscillatory motion and wake instability of freely rising axisymmetric bodies
Journal of Fluid Mechanics, 2007Co-Authors: Pedro C Fernandes, Frederic Risso, Patricia Ern, Jacques MagnaudetAbstract:This paper reports on an experimental study of the motion of freely rising axisym- metric rigid bodies in a low-viscosity fluid. We consider flat cylinders with height h smaller than the diameter d and density ρb close to the density ρf of the fluid. We have investigated the role of the Reynolds Number based on the mean rise velocity um in the range 80 ≤ Re = umd/ν ≤ 330 and that of the aspect ratio in the range 1.5 ≤ χ = d/h ≤ 20. Beyond a critical Reynolds Number, Rec, which depends on the aspect ratio, both the body velocity and the orientation start to oscillate periodically. The body motion is observed to be essentially two-dimensional. Its description is particularly simple in the coordinate system rotating with the body and having its origin fixed in the laboratory; the axial velocity is then found to be constant whereas the rotation and the lateral velocity are described well by two harmonic functions of time having the same angular frequency, ω. In parallel, direct numerical simulations of the flow around fixed bodies were carried out. They allowed us to determine (i) the threshold, Recf1(χ), of the primary regular bifurcation that causes the breaking of the axial symmetry of the wake as well as (ii) the threshold, Recf2(χ), and frequency, ωf, of the secondary Hopf bifurcation leading to wake oscillations. As χ increases, i.e. the body becomes thinner, the critical Reynolds Numbers, Recf1 and Recf2, decrease. Introducing a Reynolds Number Re* based on the velocity in the recirculating wake makes it possible to obtain thresholds and that are independent of χ. Comparison with fixed bodies allowed us to clarify the role of the body shape. The oscillations of thick moving bodies (χ < 6) are essentially triggered by the wake instability observed for a fixed body: Rec(χ) is equal to Recf1(χ) and ω is close to ωf. However, in the range 6 ≤ χ ≤ 10 the flow corrections induced by the translation and rotation of freely moving bodies are found to be able to delay the onset of wake oscillations, causing Rec to increase strongly with χ. An analysis of the evolution of the parameters characterizing the motion in the rotating frame reveals that the constant axial velocity scales with the gravitational velocity based on the body thickness, , while the relevant length and velocity scales for the oscillations are the body diameter d and the gravitational velocity based on d, , respectively. Using this scaling, the dimensionless amplitudes and frequency of the body's oscillations are found to depend only on the Modified Reynolds Number, Re*; they no longer depend on the body shape.