The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia

2015 ◽  
Vol 771 ◽  
pp. 115-158 ◽  
Author(s):  
T. Rosén ◽  
M. Do-Quang ◽  
C. K. Aidun ◽  
F. Lundell
Keyword(s):  
Shear Flow ◽  
External Boundary ◽  
Full Description ◽  
Spheroidal Particle ◽  
Fluid Inertia ◽  
Prolate Spheroidal ◽  
Particle Inertia ◽  
Inertia Effects ◽  
Rotational States ◽  
Neutrally Buoyant

The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that the case of a single neutrally buoyant particle is a surprisingly rich dynamical system that exhibits several bifurcations between rotational states due to inertial effects. It was observed that the rotational states were associated with either fluid inertia effects or particle inertia effects, which are always in competition. The effects of fluid inertia are characterized by the particle Reynolds number $\mathit{Re}_{p}=4Ga^{2}/{\it\nu}$, where $G$ is the shear rate, $a$ is the length of the particle major semi-axis and ${\it\nu}$ is the kinematic viscosity. Particle inertia is associated with the Stokes number $\mathit{St}={\it\alpha}\,\mathit{Re}_{p}$, where ${\it\alpha}$ is the solid-to-fluid density ratio. Previously, the neutrally buoyant case ($\mathit{St}=\mathit{Re}_{p}$) was studied extensively. However, little is known about how these results are affected when $\mathit{St}\neq \mathit{Re}_{p}$, and how the aspect ratio $r_{p}$ (major axis/minor axis) influences the competition between fluid and particle inertia in the absence of gravity. This work gives a full description of how prolate spheroidal particles in the range $2\leqslant r_{p}\leqslant 6$ behave depending on the chosen $\mathit{St}$ and $\mathit{Re}_{p}$. Furthermore, consequences for the rheology of a dilute suspension containing such particles are discussed. Finally, grid resolution close to the particle is shown to affect the quantitative results considerably. It is suggested that this resolution is a major cause of quantitative discrepancies between different studies. Thus, the results of this work and previous direct numerical simulations of this problem should be regarded as qualitative descriptions of the physics involved, and more refined methods must be used to quantitatively pinpoint the transitions between rotational states.

Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow

2013 ◽  
Vol 738 ◽  
pp. 563-590 ◽  
Author(s):  
T. Rosén ◽  
F. Lundell ◽  
C. K. Aidun
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Aspect Ratio ◽  
Shear Flow ◽  
Stokes Number ◽  
Spheroidal Particle ◽  
Fluid Inertia ◽  
Prolate Spheroidal ◽  
Particle Inertia ◽  
Neutrally Buoyant

AbstractThe basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (${\mathit{Re}}_{p} $) and Stokes number ($\mathit{St}$), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by ${\mathit{Re}}_{p} = 4G{a}^{2} / \nu $, where $G$ is the shear rate, $a$ is the length of the spheroid major semi-axis and $\nu $ is the kinematic viscosity. The Stokes number is defined as $\mathit{St}= \alpha \boldsymbol{\cdot} {\mathit{Re}}_{p} $, where $\alpha $ is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle ($\mathit{St}= {\mathit{Re}}_{p} $) of aspect ratio (major axis/minor axis) ${r}_{p} = 4$ is considered. The long-term rotational motion for different initial orientations and ${\mathit{Re}}_{p} $ is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high ${\mathit{Re}}_{p} $, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as $\vert {\mathit{Re}}_{p} - {\mathit{Re}}_{c} {\vert }^{- 1/ 2} $. Analyses in this paper show that if a transition from tumbling to steady state occurs at ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $, then any parameter $\beta $ (e.g. confinement or particle spacing) that influences the value of ${\mathit{Re}}_{c} $, such that ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $ as $\beta = {\beta }_{c} $, will lead to a period that scales as $\vert \beta - {\beta }_{c} {\vert }^{- 1/ 2} $ and is independent of particle shape or any geometric aspect ratio in the flow.

Motion of spheroid particles in shear flow with inertia

2014 ◽  
Vol 749 ◽  
pp. 145-166 ◽  
Author(s):  
Wenbin Mao ◽  
Alexander Alexeev
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Shear Flow ◽  
Rotation Period ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Simple Shear Flow ◽  
Fluid Inertia ◽  
Particle Rotation ◽  
Particle Inertia

AbstractIn this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.

Rheology of suspensions with high particle inertia and moderate fluid inertia

2003 ◽  
Vol 480 ◽  
pp. 95-118 ◽  
Author(s):  
JONATHAN J. WYLIE ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Fluid Inertia ◽  
Particle Inertia ◽  
High Particle

Dynamic Characterization of an Integral Squeeze Film Bearing Support Damper for a Supercritical CO2 Expander

2017 ◽  
Author(s):  
Bugra Ertas ◽  
Adolfo Delgado ◽  
Jeffrey Moore
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Mechanical Impedance ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Damping Behavior ◽  
Impedance Testing ◽  
Stiffness And Damping ◽  
Onset Of Cavitation

The present work advances experimental results and analytical predictions on the dynamic performance of an integral squeeze film damper (ISFD) for application in a high-speed super-critical CO2 (sCO2) expander. The test campaign focused on conducting controlled orbital motion mechanical impedance testing aimed at extracting stiffness and damping coefficients for varying end seal clearances, excitation frequencies, and vibration amplitudes. In addition to the measurement of stiffness and damping; the testing revealed the onset of cavitation for the ISFD. Results show damping behavior that is constant with vibratory velocity for each end seal clearance case until the onset of cavitation/air ingestion, while the direct stiffness measurement was shown to be linear. Measurable added inertia coefficients were also identified. The predictive model uses an isothermal finite element method to solve for dynamic pressures for an incompressible fluid using a modified Reynolds equation accounting for fluid inertia effects. The predictions revealed good correlation for experimentally measured direct damping, but resulted in grossly overpredicted inertia coefficients when compared to experiments.

Annular Squeeze Films With Inertial Effects

1983 ◽  
Vol 105 (3) ◽  
pp. 361-363 ◽  
Author(s):  
S. R. Turns
Keyword(s):  
Annular Plate ◽  
Equation Of Motion ◽  
Plate Motion ◽  
Squeezing Flow ◽  
Approximation Technique ◽  
Inertial Effects ◽  
Fluid Inertia ◽  
Governing Equations ◽  
Inertia Effects ◽  
Incompressible Newtonian Fluid

An analysis of the laminar squeezing flow of an incompressible Newtonian fluid between parallel plane annuli is presented in which a successive approximation technique is used to account for fluid inertia effects. An expression for the force generated by the fluid is developed and coupled to the equation of motion for the annular plate. Results are presented from the numerical integration of the governing equations for the plate motion.

Extended Finite Element Analysis of Journal Bearing Dynamic Forced Performance to Include Fluid Inertia Force Coefficients

2012 ◽  
Author(s):  
Luis San Andrés
Keyword(s):  
Finite Element ◽  
Test Data ◽  
Small Amplitude ◽  
Forced Response ◽  
Inertia Force ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Force Coefficients ◽  
Reaction Forces ◽  
Bearing Stiffness

Reynolds equation governs the generation of hydrodynamic pressure in oil lubricated fluid film bearings. The static and dynamic forced response of a bearing is obtained from integration of the film pressure on the bearing surface. For small amplitude journal motions, a linear analysis represents the fluid film bearing reaction forces as proportional to the journal center displacements and velocity components through four stiffness and four damping coefficients. These force coefficients are integrated into rotor-bearing system structural analysis for prediction of the system stability and the synchronous response to imbalance. Fluid inertia force coefficients, those relating reaction forces to journal center accelerations, are routinely ignored because most oil lubricated bearings operate at relatively low Reynolds numbers, i.e., under slow flow conditions. Modern rotating machinery operates at ever increasing surface speeds to deliver more power in smaller size units. Under these operating conditions fluid inertia effects need to be accounted for in the forced response of oil lubricated bearings, as recent experimental test data also reveal. The paper presents a finite element formulation to predict added mass coefficients in oil lubricated bearings by extending a basic formulation that already calculates the bearing stiffness and damping force coefficients. That is, a small amplitude perturbation analysis of the lubrication flow equations keeps the temporal fluid inertia effects and develops a set of equations to obtain the bearing stiffness, damping and inertia force coefficients. The method does not impose on the cost of the original formulation which makes it very attractive for ready implementation in existing software. Predictions of the computational model are benchmarked against archival test data for an oil-lubricated pressure dam bearing supporting large compressors. The comparisons show fluid inertia effects cannot be ignored for operation at high rotor speeds and with small static loads.

The motion of a droplet subjected to linear shear flow including the presence of a plane wall

1995 ◽  
Vol 302 ◽  
pp. 45-63 ◽  
Author(s):  
W. S. J. Uijttewaal ◽  
E. J. Nijhof
Keyword(s):  
Shear Flow ◽  
Flow Field ◽  
Theoretical Models ◽  
Boundary Integral ◽  
Plane Wall ◽  
Time Dependent ◽  
Fluid Inertia ◽  
Linear Shear ◽  
Material Element ◽  
Migration Velocities

A fluid droplet subjected to shear flow deforms and rotates in the flow. In the presence of a wall the droplet migrates with respect to a material element in the undisturbed flow field. Neglecting fluid inertia, the Stakes problem for the droplet is solved using a boundary integral technique. It is shown how the time-dependent deformation, orientation, circulation and droplet viscosity. The migration velocities are calculated in the directions parallel and perpendicular to the wall, and compared with theoretical models and expeeriments. The results reveal some of the shortcomings of existiong models although not all diserepancies between our calculations and known experiments could be clarified.

scholarly journals Squeeze-Film Damper Technology: Part 1 — Prediction of Finite Length Damper Performance

1983 ◽  
Author(s):  
J. W. Lund ◽  
A. J. Smalley ◽  
J. A. Tecza ◽  
J. F. Walton
Keyword(s):  
Finite Length ◽  
Gas Turbines ◽  
Squeeze Film ◽  
Fluid Inertia ◽  
Inertia Effects ◽  
Strongly Coupled ◽  
Squeeze Film Damper ◽  
Rotor Systems ◽  
Squeeze Film Dampers ◽  
Calculation Results

Squeeze-film dampers are commonly used in gas turbine engines and have been applied successfully in a great many new designs, and also as retrofits to older engines. Of the mechanical components in gas turbines, squeeze-film dampers are the least understood. Their behavior is nonlinear and strongly coupled to the dynamics of the rotor systems on which they are installed. The design of these dampers is still largely empirical, although they have been the subject of a large number of past investigations. To describe recent analytical and experimental work in squeeze-film damper technology, two papers are planned. This abstract outlines the first paper, Part 1, which concerns itself with squeeze-film damper analysis. This paper will describe an analysis method and boundary conditions which have been developed recently for modelling dampers, and in particular, will cover the treatment of finite length, feed and drain holes and fluid inertia effects, the latter having been shown recently to be of great importance in predicting rotor system behavior. A computer program that solves the Reynolds equation for the above conditions will be described and sample calculation results presented.

Sign in / Sign up

Export Citation Format

Share Document