Instabilities of a freely moving spherical particle in a Newtonian fluid: Direct Numerical Simulation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yuxiu Li ◽  
Shashank S. Tiwari ◽  
Geoffrey M. Evans ◽  
Krishnaswamy Nandakumar ◽  
Jyeshtharaj B. Joshi
Keyword(s):  
Spherical Particle ◽  
Bluff Body ◽  
Chaotic Regime ◽  
Lagrangian Multiplier ◽  
Transitional Regime ◽  
Heavy Particles ◽  
Density Ratios ◽  
Fft Analysis ◽  
Good Agreement ◽  
Quiescent Fluid

Abstract Direct Numerical Simulations (DNS) were carried out for a freely falling/rising rigid particle in an otherwise quiescent fluid, using a non-Lagrangian multiplier based fictitious domain (FD) method. Validation studies showed that the proposed FD based DNS are in good agreement with the existing experimental results in the transition regime of falling/rising spheres. Simulations done in the transitional regime (50 < Reynolds number (Re) < 1800 and solid-to-fluid density ratios Γ = ρ p / ρ f ${\Gamma}={\rho }_{p}/{\rho }_{f}$ from 0.08 to 4), confirmed that (i) a falling spherical particle (Γ = 4) exhibits a helical trajectory in the range 270 < Re < 320, and (ii) a rising particle (Γ = 0.5) shows a zig-zagging trajectory in the same range of Re. This finding closes the uncertainty to the question as to whether or not rising/falling particles exhibit a helical and a zig-zagging trajectory. In addition to this, a total of seven distinctive flow regimes were identified, which are as follows: (I) vertical straight path (II) steady oblique path (III) Wavy oblique path (IV) zig-zagging path (for 0.08 < Γ < 1) (V) helical path (for 1 < Γ < 4) (VI) early transition to chaos and (VII) chaotic regime. Regime IV occurs only for light particles (Γ < 1), whereas Regime V occurs only for heavy particles (Γ > 1). Fast Fourier Transform (FFT) analysis characterized the presence of a bimodal frequency similar to that exhibited by flow past an isolated stationary bluff body.

Analysis of general creeping motion of a sphere inside a cylinder

2009 ◽  
Vol 642 ◽  
pp. 295-328 ◽  
Author(s):  
SUKALYAN BHATTACHARYA ◽  
COLUMBIA MISHRA ◽  
SONAL BHATTACHARYA
Keyword(s):  
Vector Field ◽  
Spherical Particle ◽  
Asymptotic Methods ◽  
Flow Equation ◽  
Creeping Flow ◽  
Separable Form ◽  
Angular Velocities ◽  
Moving Particle ◽  
Parabolic Flow ◽  
Quiescent Fluid

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

scholarly journals THE UNIT OF ELECTRIC CHARGE AND THE MASS HIERARCHY OF HEAVY PARTICLES

2007 ◽  
Vol 22 (38) ◽  
pp. 2909-2916
Author(s):  
G. LÓPEZ CASTRO ◽  
J. PESTIEAU
Keyword(s):  
Standard Model ◽  
Mass Hierarchy ◽  
Empirical Formulas ◽  
Heavy Particles ◽  
The Standard Model ◽  
Experimental Values ◽  
The One ◽  
Simple Ratio ◽  
The Masses ◽  
Good Agreement

We propose some empirical formulas relating the masses of the heaviest particles in the standard model (the W, Z, H bosons and the t quark) to the charge of the positron e and the Higgs condensate v. The relations for the masses of gauge bosons mW = (1+e)v/4 and [Formula: see text] are in good agreement with experimental values. By requiring the electroweak standard model to be free from quadratic divergences at the one-loop level, we find: [Formula: see text] and [Formula: see text], or the very simple ratio (mt/mH)2 = e.

Convective and Absolute Instabilities in Reacting Bluff Body Wakes

2011 ◽  
Author(s):  
Benjamin Emerson ◽  
Julia Lundrigan ◽  
Jacqueline O’Connor ◽  
David Noble ◽  
Tim Lieuwen
Keyword(s):  
Reynolds Number ◽  
Bluff Body ◽  
Flow Behavior ◽  
Density Ratio ◽  
Intermittent Flow ◽  
Flow Problems ◽  
High Reynolds ◽  
Bluff Body Flow ◽  
Density Ratios ◽  
Parameter Values

This paper describes the variation of bluff body wake structure with flame density ratio. It is known that the bluff body flow structure at “high” and “low” flame density ratios is fundamentally different, being dominated by the convectively unstable shear layers or absolutely unstable Von Karman vortex street, respectively. This paper characterizes the aforementioned transition and shows that the bifurcation in flow behavior does not occur abruptly at some ρu/ρb value. Rather, there exists a range of transitional density ratios at which the flow exists intermittently in both flow states, abruptly shifting back and forth between the two. The fraction of time that the flow spends in either state is a monotonic function of ρu/ρb. This behavior is to be contrasted with lower Reynolds number, laminar flow problems where the convective/absolute instability transition occurs at a well defined value of bifurcation parameter. With this distinction in mind, however, this paper also shows that local parallel stability analyses developed for laminar base wake flows can capture many of the observed flow dependencies. These results have important implications on the dynamics of high Reynolds number, vitiated flows, where typical parameter values fall into the highly intermittent flow regime characterized in this study. This suggests that such flows exhibit two co-existing dynamical states, intermittently jumping between the two.

scholarly journals Study on a Change in the Behavior of Flame on Bluff-Body under the Transitional Regime by Swirled Air Flow

2013 ◽  
Vol 79 (803) ◽  
pp. 1196-1207 ◽  
Author(s):  
Tatsuo NISHIMURA ◽  
Koji KUNITSUGU ◽  
Genryu OOE ◽  
Ken-ichiro TANOUE
Keyword(s):  
Bluff Body ◽  
Air Flow ◽  
Transitional Regime

Flows produced by the combined oscillatory rotation and translation of a circular cylinder in a quiescent fluid

2014 ◽  
Vol 764 ◽  
pp. 148-170 ◽  
Author(s):  
Christopher Koehler ◽  
Philip Beran ◽  
Marcos Vanella ◽  
Elias Balaras
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Bluff Body ◽  
Stokes Equations ◽  
Time Windows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Immersed Boundary ◽  
Dimensionless Time ◽  
Quiescent Fluid

AbstractFlows produced by a circular cylinder undergoing oscillatory rotation and translation in a quiescent fluid have been studied via direct numerical simulations. The incompressible Navier–Stokes equations were solved for large dimensionless time windows using an immersed boundary method with adaptive Cartesian grid refinement. Parametric studies were conducted in two dimensions on the Reynolds number, Keulegan–Carpenter number and phase shift. In addition to the previously reported net thrust case (Blackburn et al., Phys. Fluids, vol. 11, 1999, pp. 4–6), the study catalogued the appearance of several streaming jet regimes with varying deflection angles, deflected and horizontal vortex shedding regimes, and a double mirrored jet regime with varying inter-jet angles, as well as several chaotic cases. Visualizations are presented to clarify each observed flow regime and to illustrate the parameter space. Connections are drawn between these canonical bluff-body deflected wakes and a similar phenomenon observed in aerofoils oscillating at high reduced frequencies in a cross-flow. Also, the discovery of the streaming jet regimes with varying deflection angles opens the door for using these flows as a low-Reynolds-number propulsive mechanism requiring only a two-degree-of-freedom actuator. Simulation results suggest that the flow phenomena observed in two dimensions persist in three dimensions, despite spanwise fluctuations.

scholarly journals Numerical and Experimental Investigations of the Cavitating Behavior of an Inducer

2004 ◽  
Vol 10 (1) ◽  
pp. 15-25 ◽  
Author(s):  
F. Bakir ◽  
R. Rey ◽  
A. G. Gerber ◽  
T. Belamri ◽  
B. Hutchinson
Keyword(s):  
Bubble Dynamics ◽  
Three Dimensional ◽  
Experimental Investigations ◽  
Cfd Model ◽  
Flow Rates ◽  
Solution Approach ◽  
Robust Solutions ◽  
Density Ratios ◽  
Scalar Equations ◽  
Good Agreement

A robust CFD model is described, suitable for general three-dimensional flows with extensive cavitation at large density ratios. The model utilizes a multiphase approach, based on volume-scalar-equations, a truncated Rayleigh-Plesset equation for bubble dynamics, and specific numerical modifications (in a finite-volume solution approach) to promote robust solutions when cavitation is present. The model is implemented in the CFD software CFX TASCflow 2.12. The validation of the model was done on an inducer designed and tested at LEMFI. First, The physical model and the numerical aspects are described. Then, the experimental and numerical methodologies, at cavitating regime, are presented. Finally, for several flow rates, the comparisons between experimental and simulated results on the overall performances, head drop and cavitation figures, are discussed. For a range of flow rates, good agreement between experiment and prediction was found.

Stratified wake of a tilted cylinder. Part 2. Lee internal waves

2012 ◽  
Vol 699 ◽  
pp. 198-215 ◽  
Author(s):  
Patrice Meunier
Keyword(s):  
Circular Cylinder ◽  
Internal Waves ◽  
Bluff Body ◽  
Theoretical Study ◽  
Horizontal Cylinder ◽  
Quantitative Prediction ◽  
Dispersive Waves ◽  
Lee Waves ◽  
The Waves ◽  
Good Agreement

AbstractThis experimental, numerical and theoretical study considers the lee internal waves generated by the wake of a circular cylinder, whose axis is tilted with respect to a stable density gradient. The main difference with the case of a horizontal cylinder is that the lee waves contain a large axial velocity, which are located in a row of lobes extending downstream from the cylinder. At small tilt angles, the wavelength is equal to $2\lrm{\pi} U/ N$, $U$ being the velocity of the cylinder and $N$ the Brunt–Väisälä frequency, which can be explained by the fact that the group velocity of the waves is small. The amplitude of the waves can be predicted using the Lighthill theory for dispersive waves applied to the case of a tilted bluff body. The flow around the cylinder is modelled empirically in order to reach a quantitative prediction in good agreement with the experimental and numerical results. The spatial structure of the predicted internal waves is qualitatively correct although some discrepancies arise because the advection by the flow around the cylinder is neglected.

Prediction of a Turbulent Flow in Bluff Body Stabilized Burner by Using Two Classical Models of Turbulence

2017 ◽  
Vol 32 ◽  
pp. 112-123
Author(s):  
Merouane Habib
Keyword(s):  
Turbulent Flow ◽  
Bluff Body ◽  
Diameter Ratio ◽  
Governing Equations ◽  
Quadrilateral Elements ◽  
Annular Jet ◽  
Classical Models ◽  
Resolution Scheme ◽  
Volume Method ◽  
Good Agreement

In present study, a detailed investigation of an annular jet at high diameter ratio r = 0,905 has been reported numerically. The numerical simulation was performed by making use of the commercial CFD code which discretizes the solution domain into quadrilateral elements and use a numerical finite volume method coupled with a multigrid resolution scheme. In this research the applications of k-epsilon and k-omega models for prediction of a turbulent flow in annular jet are described. The flow governing equations are solved by using a performed coupled algorithm. The results of predicted axial velocity profiles are compared with the experimental data. The computations indicated that the results predicted by k-epsilon model are in good agreement with the experiment.

scholarly journals Feature-Parameter-Criterion for Predicting Lean Blowout Limit of Gas Turbine Combustor and Bluff Body Burner

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Hongtao Zheng ◽  
Zhibo Zhang ◽  
Yajun Li ◽  
Zhiming Li
Keyword(s):  
Gas Turbine ◽  
Bluff Body ◽  
Flow Distribution ◽  
Gas Turbine Combustor ◽  
Experiment Data ◽  
Lean Blowout ◽  
Feature Parameter ◽  
Computational Fluid Dynamics Cfd ◽  
Mixture Velocity ◽  
Good Agreement

Lean blowout (LBO) limit is one of the most important combustor parameters. A new method named Feature-Parameter-Criterion (FPC) for predicting LBO limit has been put forward in the present work. A computational fluid dynamics (CFD) software FLUENT has been used to simulate the process of LBO of gas turbine combustor and bluff body burner. And “M” flame has been proposed as the portent for predicting lean blowout of gas turbine combustor. Effects of flow velocity, air temperature, droplet averaged-diameter, and flow distribution between swirlers and primary holes on the LBO limit of gas turbine combustor have been researched by use of Feature-Parameter-Criterion in this paper. The effects of fuel air mixture velocity and different structures on bluff body LBO limit have also been analyzed in the present work by use of FPC. The results show that the simulation of LBO limit based on FPC is in good agreement with the experiment data (the errors are about 5%) and this method is reliable for engineering applications.

Transient Free Convection About Vertical Plates and Circular Cylinders

1964 ◽  
Vol 86 (4) ◽  
pp. 490-500 ◽  
Author(s):  
R. J. Goldstein ◽  
D. G. Briggs
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Transfer Problem ◽  
Convection Heat Transfer ◽  
Circular Cylinders ◽  
Flat Plates ◽  
One Dimensional ◽  
Free Convection Heat ◽  
Good Agreement ◽  
Quiescent Fluid

An analysis is made of the transient free-convection, heat-transfer problem from vertical flat plates and vertical circular cylinders to a surrounding initially quiescent fluid. The transient is initiated by a change in wall temperature of the plate or cylinder. A method of predicting the length of time for which a one-dimensional regime of velocity and heat transfer will exist is proposed and solutions are presented. Good agreement is found with the few existing data.

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