Micro-Channels: Reality and Myth

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
G. Hetsroni ◽  
A. Mosyak ◽  
E. Pogrebnyak ◽  
L. P. Yarin
Keyword(s):  
Measurement Accuracy ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Ionic Composition ◽  
Experimental Studies ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Physical Mechanisms ◽  
Sufficient Detail ◽  
Micro Channels

Many important problems connected to flows in micro-heat exchangers were not studied in sufficient detail. In particular, the governing physical mechanisms are still not well understood for flows in pipes and channels with hydraulic diameter ranging from 5 to 103 μm, which are often defined as micro-tubes or micro-channels. Experimental and numerical results of pressure driven laminar, continuous, incompressible, flow in different scale and shape channels are analyzed to highlight variations between various studies and these discrepancies are considered. The main objective is to determine whether the classical fluid flow theory based on the Navier- Stokes equations is valid to predict velocity distribution, pressure drop and transition from laminar to turbulent flow in micro-channels. No differences were found between results in micro-channels, unaffected by fluid ionic composition and the nature of the wall, and conventional size channels. The distinctions between different experimental studies must be attributed to different initial conditions, difference between actual conditions of a given experiment and conditions corresponding to the theoretical model, and measurement accuracy.

Computational Characterization of Passive Fluid Mixing in Microfluidics

Volume 3 ◽  
2004 ◽  
Author(s):  
Erik D. Svensson
Keyword(s):  
Stokes Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Fluid Mixing ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Systems ◽  
Sensitive Dependence ◽  
Microfluidic Mixers

In this work we computationally characterize fluid mixing in a number of passive microfluidic mixers. Generally, in order to systematically study and characterize mixing in realistic fluid systems we (1) compute the fluid flow in the systems by solving the stationary three-dimensional Navier-Stokes equations or Stokes equations with a finite element method, and (2) compute various measures indicating the degree of mixing based on concepts from dynamical systems theory, i.e., the sensitive dependence on initial conditions and mixing variance.

scholarly journals PARALLEL COMPUTATIONS IN STUDIES OF DEPENDENCE OF GAS DYNAMIC PARAMETERS OF UPWARD SWIRLING FLOW OF GAS ON BLOWING VELOCITY

2016 ◽  
pp. 92-97
Author(s):  
R. E. Volkov ◽  
A. G. Obukhov
Keyword(s):  
Stokes Equations ◽  
Swirling Flow ◽  
Initial Conditions ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Computational Domain ◽  
Navier Stokes Equations ◽  
Gas Dynamic

The rectangular parallelepiped explicit difference schemes for the numerical solution of the complete built system of Navier-Stokes equations. These solutions describe the three-dimensional flow of a compressible viscous heat-conducting gas in a rising swirling flows, provided the forces of gravity and Coriolis. This assumes constancy of the coefficient of viscosity and thermal conductivity. The initial conditions are the features that are the exact analytical solution of the complete Navier-Stokes equations. Propose specific boundary conditions under which the upward flow of gas is modeled by blowing through the square hole in the upper surface of the computational domain. A variant of parallelization algorithm for calculating gas dynamic and energy characteristics. The results of calculations of gasdynamic parameters dependency on the speed of the vertical blowing by the time the flow of a steady state flow.

scholarly journals Direct Numerical Simulation of Liquid Flow in a Horizontal Microchannel

2005 ◽  
Author(s):  
Cenk Evren Ku¨krer ◽  
I˙lker Tarı
Keyword(s):  
Liquid Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Micro Channel ◽  
Governing Equations ◽  
Qualitative Comparison ◽  
Navier Stokes Equations ◽  
Axial Conduction ◽  
Micro Channels

Numerical Simulations of liquid flow in a micro-channel between two horizontal plates are performed. The channel is infinite in streamwise and spanwise directions and its height is taken as 3.1×10−4 m which falls within the dimension ranges of micro-channels. The Navier-Stokes equations with the addition of Brinkman number (Br) to the energy equation are used as the governing equations and a spectral methods based approach is applied to obtain the required accuracy to handle liquid flow in the micro-channel. It is known for micro-channels that Br combines the effects of conduction and viscous dissipation in liquids and is also a way of comparing the importance of later relative to former. A laminar flow of a liquid in a micro-channel shows different characteristics compared to a similar flow in a macro-channel. To observe the differences, three different cases are run over each of a range of Reynolds numbers: one with no axial conduction assumption that correspond to a case similar to macro-channel flow, another case with axial conduction included in the energy equation to simulate one of the main differences and lastly a case with inclusion of Br number in the governing equations. The results are compared with each other to see the effects of axial conduction and Br inclusion. A qualitative comparison is made with the previous results in literature.

scholarly journals COMPARISON OF DIFFERENT METHODS FOR GENERATION AND ABSORPTION OF WATER WAVES

2019 ◽  
Vol 18 (1) ◽  
pp. 71 ◽  
Author(s):  
J. M. P. Conde
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Numerical Models ◽  
Experimental Studies ◽  
Wave Generation ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Wave Absorption ◽  
Water Level Rise

The knowledge of water wave characteristics (generation, propagation, transformation and breaking) is fundamental for hydrodynamic studies and the design of ocean, coastal and port structures. In addition to the small-scale experimental studies, the use of numerical models is also a very important tool in hydrodynamic studies. To have reliable numerical results a proper validation is required. The main objective of this paper is to compare different methods of wave generation and wave absorption in a numerical flume, and to find what is the most suited to simulate non-breaking regular wave propagation in a two-dimensional flume in deep water condition. The numerical simulations were made using the OpenFOAM® software package. Two solvers, waves2Foam and IHFoam/OlaFlow, the utility GroovyBC and a mesh stretching technique are compared. These numerical codes solve the transient Navier-Stokes equations and use a VoF (Volume of Fluid) method to identify the free surface. A solution dependence study with the methods of wave generation and wave absorption is presented. The results are also compared with the theoretical wave and experimental data. The results show that the different methods of generation produce waves similar to the theoretical and the experimental ones, only slightly differences were visible. The three method of wave dissipation considered produce very different results: IHFoam/OlaFlow is not able to dissipate the wave tested; the mesh stretching technique is able to dissipate the waves but produces a water level rise; the waves2Foam solver is able to dissipate properly the wave tested.

scholarly journals Numerical study of cascading dam-break characteristics using SWEs and RANS

2019 ◽  
Vol 20 (1) ◽  
pp. 348-360 ◽  
Author(s):  
Shubing Dai ◽  
Yong He ◽  
Jijian Yang ◽  
Yulei Ma ◽  
Sheng Jin ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Initial Conditions ◽  
Numerical Study ◽  
Air Entrainment ◽  
Dam Break ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Depth Ratio ◽  
Surface Profiles ◽  
Run Up

Abstract This paper investigates the cascading dam-break flood propagation on the downstream sloping channel and reservoir using the shallow water equations (SWEs) and the Reynolds-average Navier-Stokes equations (RANS). The calculated surface profiles, stage hydrographs and maximum run-up heights for 24 sets of initial conditions are elaborately compared with the experimental measurements, which show the SWEs reproduce the wave oscillation evolution and the maximum run-up height inaccurately. The maximum run-up heights calculated by the SWEs are all smaller than those by the RANS and the measured results, the maximum errors are within −10% to −25%, which may predict delay of the downstream dam-break. However, the maximum errors calculated by the RANS are within ±10%. So the RANS predict more accurate results than the SWEs. Additionally, the generation of short waves must be below a certain upstream-to-downstream ‘depth ratio’, roughly the ‘depth ratio’ <2/3 in this study. If the ratio is too high, it is difficult to form a wavy push due to air entrainment and turbulence. The SWEs predict more accurate results for shallow initial depths than deep initial depths. Therefore, the advantage of the RANS can be more obvious for deep initial depths.

scholarly journals On the motion of small spheroidal particles in a viscous liquid

1956 ◽  
Vol 1 (5) ◽  
pp. 540-553 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Experimental Evidence ◽  
Viscous Liquid ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dissipation Of Energy

Small spheroidal particles suspended in a sheared viscous liquid are sometimes observed to take up slowly preferred orientations, relative to the motion of the undisturbed liquid, which are independent of the initial conditions of release. These obsevations cannot be accounted for by the solution, obtained by Jeffery (1922), of the linearized Navier-Stokes equations. It is shown in this paper that the effect of the inertia of the liquid is to alter slowly the orbit of the particle in accordance with Jeffery's hypothesis that the particle ultimately moves in such a way that the dissipation of energy is a minimum, but that this effect is orders of magnitude too small to account for any of the experimental observations.It is suggested that non-Newtonian properties of the liquid account for the observations. It is shown that the rate of orientation of a particle would then be independent of its size, and this prediction is verified experimentally. Other experimental evidence in support of this suggestion is also described.Some remarks are also made about the possible effect of collisions between the particles when more than one particle is present.

On the initial-value problem in the kinetic theory of gases

1971 ◽  
Vol 50 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Howard R. Baum
Keyword(s):  
Kinetic Theory ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Mean Free Path ◽  
Spatial Dimension ◽  
Collision Integral ◽  
Navier Stokes ◽  
Kinetic Theory Of Gases ◽  
Navier Stokes Equations ◽  
Scale Perturbation

The relaxation of an initially non-uniform gas to equilibrium is studied within the framework of the kinetic theory of gases. The macroscopic gas properties are taken to depend on one spatial dimension as well as the time. The amplitude of the non-uniformity is assumed to be small with a length scale large compared with the mean free path, and the Krook model of the Boltzmann collision integral is employed.By applying multi-time scale perturbation methods to this reduced problem, uniformly valid analytical solutions for the macroscopic velocity, density and temperature are obtained. The macroscopic equations appropriate to each stage of the relaxation process are obtained in a straightforward and unambiguous manner. The distribution function obtained is shown to be a re-expansion of the Chapman–Enskog solution of the Krook equation, with additional terms accounting for the relaxation of the initial conditions to a near equilibrium form. The results indicate that the uniformly valid frst approximation to the macroscopic velocity, density and temperature can be obtained from the Navier–Stokes equations, but that no purely macroscopic set of equations will suffice for the determination of higher approximations.

Axisymmetric Inertial Oscillations in Transient Rotating Flows in a Cylinder

1997 ◽  
Vol 119 (2) ◽  
pp. 390-396
Author(s):  
Jae Won Kim ◽  
Jae Min Hyun
Keyword(s):  
Large Time ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Experimental Studies ◽  
Numerical Results ◽  
Navier Stokes ◽  
Inertial Oscillations ◽  
Time Duration ◽  
Navier Stokes Equations

A numerical study is made of axisymmetric inertial oscillations in a fluid-filled cylinder. The entire cylinder undergoes a spin-up process from rest with an impulsively started rotation rate Ω(t) = Ω0 + εω cos(ωt). Numerical solutions are obtained to the axisymmetric, time-dependent Navier-Stokes equations. Identification of the inertial oscillations is made by inspecting the evolution of the pressure difference between two pre-set points on the central axis, Cp. In the limit of large time, the inertial frequency thus determined is in close agreement with the results of the classical inviscid theory for solid-body rotation. As in previous experimental studies, the t* − (Ω0/ω) plots are constructed for inertial oscillations, where t* indicates the time duration until the maximum Cp is detected. These detailed numerical results are in broad agreement with the prior experimental data. Flow intensifications under the resonance conditions are illustrated based on the numerical results. Depictions are made of the increase in the amplitude of oscillating part of the total angular momentum under the resonance conditions. Also, the patterns of t* − (Ω0/ω) curves are displayed for different inertial frequency modes.

scholarly journals Viscous motion in an oceanic circulation model

1981 ◽  
Vol 23 (3) ◽  
pp. 443-460
Author(s):  
A. F. Bennett ◽  
P. E. Kloeden
Keyword(s):  
Ocean Circulation ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Numerical Procedure ◽  
Circulation Model ◽  
Laboratory Simulation ◽  
Generalized Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Equations

The barotropic motion of a viscous fluid in a laboratory simulation of ocean circulation may be modelled by Beards ley's vorticity equations. It is established here that these equations have unique smooth solutions which depend continuously on initial conditions. To avoid a boundary condition which involves an integral operator, the vorticity equations are replaced by an equivalent system of momentum equations. The system resembles the two-dimensional incompressible Navier-Stokes equations in a rotating reference frame. The existence of unique generalized solutions of the system in a square domain is established by modifying arguments used by Ladyzhenskaya for the Navier-Stokes equations. Smoothness of the solutions is then established by modifying Golovkin's arguments, again originally for the Navier- Stokes equations. A numerical procedure for solving the vorticity equations is discussed, as are the effects of reentrant corners in the domain modelling islands and peninsulae.

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