scholarly journals Settling of an asymmetric dumbbell in a quiescent fluid

2016 ◽  
Vol 802 ◽  
pp. 174-185 ◽  
Author(s):  
F. Candelier ◽  
B. Mehlig
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Size Difference ◽  
Fluid Inertia ◽  
Horizontal Orientation ◽  
Vertically Aligned ◽  
Rigid Rod ◽  
Quiescent Fluid

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different, the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small, then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal, then fluid inertia causes the dumbbell to settle in a horizontal orientation.

Effect of Fluid Inertia on Stability of Oil Journal Bearings

1999 ◽  
Vol 122 (4) ◽  
pp. 741-745 ◽  
Author(s):  
S. K. Kakoty ◽  
B. C. Majumdar
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Transient Analysis ◽  
Mass Parameter ◽  
Journal Bearings ◽  
Fluid Inertia ◽  
Viscous Forces ◽  
Fluid Inertia Effect ◽  
The Stability ◽  
Negligible Contribution

In the analysis of hydrodynamic journal bearings the effect of fluid inertia is generally neglected in view of its negligible contribution compared to viscous forces. However, the fluid inertia effect is to be taken in the analysis when modified Reynolds number is around one. Though there are a few attempts to analyze steady-state and dynamic characteristics of finite journal bearings, stability of the journal under the effect of fluid inertia is yet to be investigated. An attempt has been made to evaluate the mass parameter (a measure of stability) besides finding out the steady-state characteristics of finite journal bearings considering the effects of fluid inertia. The analysis is carried out for modified Reynolds number ∼O(1.), which is assumed to be laminar. A nonlinear time transient analysis is carried out for the stability analysis. [S0742-4787(00)00204-6]

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.

An airfoil theory of bifurcating laminar separation from thin obstacles

1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Steady State ◽  
Steady State Solution ◽  
Equation System ◽  
Branch Points ◽  
Laminar Separation ◽  
Kutta Condition ◽  
Numerical Studies ◽  
Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

Characterization of Metallically Bonded Carbon Nanotube-Based Thermal Interface Materials Using a High Accuracy 1D Steady-State Technique

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Joseph R. Wasniewski ◽  
David H. Altman ◽  
Stephen L. Hodson ◽  
Timothy S. Fisher ◽  
Anuradha Bulusu ◽  
...  
Keyword(s):  
Steady State ◽  
High Performance ◽  
Applied Pressure ◽  
Test Facility ◽  
Thermal Interface Materials ◽  
Thermal Interface ◽  
Thermal Interface Resistance ◽  
Vertically Aligned ◽  
Performance Results ◽  
Interface Materials

The next generation of thermal interface materials (TIMs) are currently being developed to meet the increasing demands of high-powered semiconductor devices. In particular, a variety of nanostructured materials, such as carbon nanotubes (CNTs), are interesting due to their ability to provide low resistance heat transport from device-to-spreader and compliance between materials with dissimilar coefficients of thermal expansion (CTEs), but few application-ready configurations have been produced and tested. Recently, we have undertaken major efforts to develop functional nanothermal interface materials (nTIMs) based on short, vertically aligned CNTs grown on both sides of a thin interposer foil and interfaced with substrate materials via metallic bonding. A high-precision 1D steady-state test facility has been utilized to measure the performance of nTIM samples, and more importantly, to correlate performance to the controllable parameters. In this paper, we describe our material structures and the myriad permutations of parameters that have been investigated in their design. We report these nTIM thermal performance results, which include a best to-date thermal interface resistance measurement of 3.5 mm2 K/W, independent of applied pressure. This value is significantly better than a variety of commercially available, high-performance thermal pads and greases we tested, and compares favorably with the best results reported for CNT-based materials in an application-representative setting.

Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder

2013 ◽  
Vol 722 ◽  
pp. 159-186 ◽  
Author(s):  
Sukalyan Bhattacharya ◽  
Dil K. Gurung ◽  
Shahin Navardi
Keyword(s):  
Reynolds Number ◽  
Particle Diameter ◽  
Axial Direction ◽  
Perturbation Scheme ◽  
Fluid Inertia ◽  
Regular Perturbation ◽  
Cross Sectional ◽  
First Order ◽  
Reynolds Number Flow ◽  
Freely Suspended

AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

Time-Dependent Laminar Backward-Facing Step Flow in a Two-Dimensional Duct

1988 ◽  
Vol 110 (3) ◽  
pp. 289-296 ◽  
Author(s):  
F. Durst ◽  
J. C. F. Pereira
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Steady State Flow ◽  
Backward Facing Step ◽  
Step Flow ◽  
Recirculating Flow ◽  
State Flow

This paper presents results of numerical studies of the impulsively starting backward-facing step flow with the step being mounted in a plane, two-dimensional duct. Results are presented for Reynolds numbers of Re = 10; 368 and 648 and for the last two Reynolds numbers comparisons are given between experimental and numerical results obtained for the final steady state flow conditions. In the computational scheme, the convective terms in the momentum equations are approximated by a 13-point quadratic upstream weighted finite-difference scheme and a fully implicit first order forward differencing scheme is used to discretize the temporal derivatives. The computations show that for the higher Reynolds numbers, the flow starts to separate on the lower and upper corners of the step yielding two disconnected recirculating flow regions for some time after the flow has been impulsively started. As time progresses, these two separated flow regions connect up and a single recirculating flow region emerges. This separated flow region stays attached to the step, grows in size and approaches, for the time t → ∞, the dimensions measured and predicted for the separation region for steady laminar backward-facing flow. For the Reynolds number Re = 10 the separation starts at the bottom of the backward-facing step and the separation region enlarges with time until the steady state flow pattern is reached. At the channel wall opposite to the step and for Reynolds number Re = 368, a separated flow region is observed and it is shown to occur for some finite time period of the developing, impulsively started backward-facing step flow. Its dimensions change with time and reduce to zero before the steady state flow pattern is reached. For the higher Reynolds number Re = 648, the secondary separated flow region opposite to the wall is also present and it is shown to remain present for t → ∞. Two kinds of the inlet conditions were considered; the inlet mean flow was assumed to be constant in a first study and was assumed to increase with time in a second one. The predicted flow field for t → ∞ turned out to be identical for both cases. They were also identical to the flow field predicted for steady, backward-facing step flow using the same numerical grid as for the time-dependent predictions.

scholarly journals Deformation of a magnetic liquid drop in an applied non-stationary uniform magnetic field

2018 ◽  
Vol 185 ◽  
pp. 09006
Author(s):  
Alexander Tyatyushkin
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Steady State ◽  
Uniform Magnetic Field ◽  
Liquid Drop ◽  
Magnetic Liquid ◽  
Stationary Approximation ◽  
The Magnetic Field

Small steady-state deformational oscillations of a drop of magnetic liquid in a nonstationary uniform magnetic field are theoretically investigated. The drop is suspended in another magnetic liquid immiscible with the former. The Reynolds number is so small that the inertia can be neglected. The variation of the magnetic field is so slow that the quasi-stationary approximation for the magnetic field and the quasi-steady approximation for the flow may be used.

scholarly journals Axisymmetric viscous gravity currents flowing over a porous medium

2009 ◽  
Vol 622 ◽  
pp. 135-144 ◽  
Author(s):  
MELISSA J. SPANNUTH ◽  
JEROME A. NEUFELD ◽  
J. S. WETTLAUFER ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Gravity Current ◽  
Gravity Currents ◽  
Constant Input ◽  
Radial Extent ◽  
Vertically Aligned ◽  
Analytical Expressions ◽  
Permeability Structure ◽  
Good Agreement

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant input from a point source. In this case, a steady state is possible in which drainage balances the input, and we present analytical expressions for the resulting steady profile and radial extent. We demonstrate good agreement between our experiments, which use a bed of vertically aligned tubes as the porous medium, and the theoretically predicted evolution and steady state. However, analogous experiments using glass beads as the porous medium exhibit a variety of unexpected behaviours, including overshoot of the steady-state radius and subsequent retreat, thus highlighting the importance of the porous medium geometry and permeability structure in these systems.

Effect of Twist Ratio on Heat Transfer Enhancement by Swirl Impingement

2019 ◽  
Author(s):  
Kishore Ranganath Ramakrishnan ◽  
Srivatsan Madhavan ◽  
Prashant Singh ◽  
Srinath V. Ekkad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Steady State ◽  
Heat Transfer Enhancement ◽  
Experimental Work ◽  
Working Fluid ◽  
Transfer Enhancement ◽  
Average Heat ◽  
Twist Ratio ◽  
Single Jet

Abstract Steady state experimental work has been carried out to compare a conventional single jet of diameter 12.7mm with a swirling impinging jet. In this study swirl inserts with three different twist ratios 3, 4.5 and 6 were used to induce the swirling motion to the working fluid. The Reynolds number based on conventional impinging jet’s diameter is varied from 10000 to 16000. It is observed that with increase in twist ratio, the average heat transfer enhancement is reduced. However, with higher twist ratios more uniform distribution of heat transfer enhancement is observed.

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