A Model for an Acoustically Driven Microbubble Inside a Rigid Tube

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Adnan Qamar ◽  
Ravi Samtaney
Keyword(s):  
Bubble Radius ◽  
Coupled Model ◽  
Tube Diameter ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Rigid Tube ◽  
Basic Model ◽  
Proposed Model ◽  
D 12 ◽  
Bubble Fragmentation

A theoretical framework to model the dynamics of acoustically driven microbubble inside a rigid tube is presented. The proposed model is not a variant of the conventional Rayleigh–Plesset category of models. It is derived from the reduced Navier–Stokes equation and is coupled with the evolving flow field solution inside the tube by a similarity transformation approach. The results are computed, and compared with experiments available in literature, for the initial bubble radius of Ro = 1.5 μm and 2 μm for the tube diameter of D = 12 μm and 200 μm with the acoustic parameters as utilized in the experiments. Results compare quite well with the existing experimental data. When compared to our earlier basic model, better agreement on a larger tube diameter is obtained with the proposed coupled model. The model also predicts, accurately, bubble fragmentation in terms of acoustic and geometric parameters.

Analytical Solution of Hydrostatic Pocket Tilting

2016 ◽  
Vol 821 ◽  
pp. 113-119 ◽  
Author(s):  
Eduard Stach ◽  
Jiří Falta ◽  
Matěj Sulitka
Keyword(s):  
Computational Models ◽  
Load Capacity ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Detailed Model ◽  
Limit Values ◽  
Inertia Effects ◽  
Proposed Model ◽  
Machine Tool Structure

Tilting (parallelism error) of guiding surfaces may cause reduction of load capacity of hydrostatic (HS) guideways and bearings in machine tools (MT). Using coupled finite element (FE) computational models of MT structures, it is nowadays possible to determine the extent of guiding surfaces deformation caused by thermal effects, gravitational force, cutting forces and inertia effects. Assessment of maximum allowable tilt has so far been based merely on experience. The paper presents a detailed model developed for description of the effect of HS bearing tilt on the load capacity characteristics of HS guideways. The model allows an evaluation of the tilt influence on the change of the characteristics as well as determination of the limit values of allowable tilt in interaction with compliant machine tool structure. The proposed model is based on the model of flow over the land of the HS pocket under extended Navier-Stokes equation. The model is verified using an experimental test rig.

Melting of Powder Particles in a Low Pressure Plasma Jet

1983 ◽  
Vol 30 ◽  
Author(s):  
D. Wei ◽  
D. Apelian ◽  
S. M. Correa ◽  
M. Paliwal
Keyword(s):  
Plasma Jet ◽  
Low Pressure ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Navier Stokes Equation ◽  
Free Jet ◽  
Binary Model ◽  
Proposed Model ◽  
Powder Particles ◽  
Heat And Momentum Transfer

ABSTRACTA numerical model has been developed to predict the temperature profile of particles injected in a D.C. plasma jet. The equations governing particle melting were applied to spherical powders of binary model alloys. Thermophysical properties of the gas and the powder material have been taken to be temperature dependent. In the proposed model, the latent heat of melting was taken into account by introducing apparent enthalpy as a function of the fraction of liquid formed which can be derived from equations describing non-equilibrium melting. The temperature and velocity profiles of the plasma jet used in this analysis are for a free jet (without target interference) and were calculated using the parabolic Navier-Stokes equation with a K-E turbulence model. Correction factors have been introduced to take into account non-continuum effects encountered in the low pressure environment and the results show that both heat and momentum transfer between the plasma gas and the injected particles are reduced.

scholarly journals Closure model for homogeneous isotropic turbulence in the Lagrangian specification of the flow field

2018 ◽  
Vol 841 ◽  
pp. 521-551
Author(s):  
Makoto Okamura
Keyword(s):  
Flow Field ◽  
Isotropic Turbulence ◽  
Longitudinal Velocity ◽  
Navier Stokes ◽  
Homogeneous Isotropic Turbulence ◽  
Closure Model ◽  
Navier Stokes Equation ◽  
Closed Set ◽  
Proposed Model ◽  
Velocity Derivative

This paper proposes a new two-point closure model that is compatible with the Kolmogorov$-5/3$power law for homogeneous isotropic turbulence in an incompressible fluid using the Lagrangian specification of the flow field. A closed set of three equations was derived from the Navier–Stokes equation with no adjustable free parameters. The Kolmogorov constant and the skewness of the longitudinal velocity derivative were evaluated to be 1.779 and$-0.49$, respectively, using the proposed model. The bottleneck effect was also reproduced in the near-dissipation range.

Pulsatile Flow in Tapered Tubes: A Model of Blood Flow With Large Disturbances

1983 ◽  
Vol 105 (2) ◽  
pp. 112-119 ◽  
Author(s):  
E. Kimmel ◽  
U. Dinnar
Keyword(s):  
Blood Flow ◽  
Pulsatile Flow ◽  
Mean Value ◽  
Navier Stokes ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Navier Stokes Equation ◽  
Rigid Tube ◽  
Flow Through ◽  
Uniform Tube

Blood flow-through segments of large arteries of man, between adjacent bifurcations, can be modeled as pulsatile flow in tapered converging tubes, of small angle of convergence, up to 2 deg. Assuming linearity, rigid tube and homogeneous Newtonian fluid, the physiological flow field is governed by the Navier-Stokes equation with dominant nonlinear and unsteady terms. Analytical solution of this problem is presented based on an integral method technique. The solution shows that even for small tapering the flow pattern is markedly different from the flow obtained for a uniform tube. The periodic shear stresses at the wall and pressure gradients increase both in their mean value and amplitude with increased distance downstream. These results are highly significant in the process of atherogenesis.

Numerical Computation of Hydrodynamically and Thermally Developing Liquid Flow in Microchannels With Electrokinetics Effects

2004 ◽  
Vol 126 (1) ◽  
pp. 70-75 ◽  
Author(s):  
X. Y. Chen ◽  
K. C. Toh ◽  
C. Yang ◽  
J. C. Chai
Keyword(s):  
Liquid Flow ◽  
Electrical Potential ◽  
Planck Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Electrokinetic Effect ◽  
Proposed Model ◽  
Parallel Slit ◽  
Temperature Dependent Properties ◽  
Volume Method

Developing fluid flow and heat transfer with temperature dependent properties in microchannels with electrokinetic effects is investigated numerically. The electrokinetic effect on liquid flow in a parallel slit is modeled by the general Nernst-Planck equation describing anion and cation distributions, the Poisson equation determining the electrical potential profile, the continuity equation, and the modified Navier-Stokes equation governing the velocity field. A Finite-Volume Method is utilized to solve the proposed model.

scholarly journals An Incompressible Polymer Fluid Interacting with a Koiter Shell

2021 ◽  
Vol 31 (1) ◽  
Author(s):  
Dominic Breit ◽  
Prince Romeo Mensah
Keyword(s):  
Moving Boundary ◽  
Classical Model ◽  
Elastic Shell ◽  
Planck Equation ◽  
Navier Stokes ◽  
Flexible Shell ◽  
Navier Stokes Equation ◽  
Shell System ◽  
Forward Equation ◽  
Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

scholarly journals Effects of Salt Tracer Volume and Concentration on Residence Time Distribution Curves for Characterization of Liquid Steel Behavior in Metallurgical Tundish

Metals ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 430
Author(s):  
Changyou Ding ◽  
Hong Lei ◽  
Hong Niu ◽  
Han Zhang ◽  
Bin Yang ◽  
...  
Keyword(s):  
Residence Time ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Mass Concentration ◽  
Distribution Curve ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Residence Time Distribution Curve ◽  
Tracer Solution ◽  
Time Distribution Curve

The residence time distribution (RTD) curve is widely applied to describe the fluid flow in a tundish, different tracer mass concentrations and different tracer volumes give different residence time distribution curves for the same flow field. Thus, it is necessary to have a deep insight into the effects of the mass concentration and the volume of tracer solution on the residence time distribution curve. In order to describe the interaction between the tracer and the fluid, solute buoyancy is considered in the Navier–Stokes equation. Numerical results show that, with the increase of the mass concentration and the volume of the tracer, the shape of the residence time distribution curve changes from single flat peak to single sharp peak and then to double peaks. This change comes from the stratified flow of the tracer. Furthermore, the velocity difference number is introduced to demonstrate the importance of the density difference between the tracer and the fluid.

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