Parametric Study of a Micromixer with Convergent-Divergent Sinusoidal Walls

2013 ◽  
Vol 479-480 ◽  
pp. 220-224
Author(s):  
Arshad Afzal ◽  
Kwang Yong Kim
Keyword(s):  
Reynolds Number ◽  
Parametric Study ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Geometrical Parameters ◽  
Number Range ◽  
Mixing Performance ◽  
Dean Vortices ◽  
Reynolds Number Range ◽  
Divergent Channel

A Parametric study of a passive micromixer with convergent-divergent channel walls of sinusoidal variation is conducted numerically using combined Navier-Stokes equations and convection-diffusion model for a Reynolds number range, 10 ≤ Re ≤ 70. Water and ethanol are used as working fluids for mixing analysis. Mixing performance was used to compare different configurations (layout) of the micromixer. In comparison with previously published design, which was based on Dean vortices in the sub-channels, the new configurations offered Dean vortices in the sub-channels and recirculation zones in the recesses of the channel for effective mixing. The proposed configurations are competitive in terms mixing performance and pressure loss. Finally, effect of two geometrical parameters viz. the ratio of throat-width to diameter of circular wall and the ratio of diameter of circular wall to amplitude, on mixing performance was studied over a chosen Reynolds number range.

scholarly journals Asymmetrical Split-and-Recombine Micromixer with Baffles

Micromachines ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 844 ◽  
Author(s):  
Wasim Raza ◽  
Kwang-Yong Kim
Keyword(s):  
Reynolds Number ◽  
Geometrical Parameters ◽  
Mixed Species ◽  
Mixing Index ◽  
Number Range ◽  
Mixing Performance ◽  
Curved Channels ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Reynolds Number Range

The present work proposes a planar micromixer design comprising hybrid mixing modules of split-and-recombine units and curved channels with radial baffles. The mixing performance was evaluated numerically by solving the continuity and momentum equations along with the advection-diffusion equation in a Reynolds number range of 0.1–80. The variance of the concentration of the mixed species was considered to quantify the mixing index. The micromixer showed far better mixing performance over whole Reynolds number range than an earlier split-and-recombine micromixer. The mixer achieved mixing indices greater than 90% at Re ≥ 20 and a mixing index of 99.8% at Re = 80. The response of the mixing quality to the change of three geometrical parameters was also studied. A mixing index over 80% was achieved within 63% of the full length at Re = 20.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Geometrical Effects on Fluid Mixing of Pulsatile Flow in Convergent-Divergent Micromixer

2015 ◽  
Author(s):  
Arshad Afzal ◽  
Kwang-Yong Kim
Keyword(s):  
Pulsatile Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Geometrical Parameters ◽  
Navier Stokes Equations ◽  
Mixing Performance ◽  
Throat Width ◽  
Pulsatile Flows ◽  
Geometrical Effects ◽  
Diffusion Convection

Time-dependent pulsatile flows have been used by many researchers for fast and efficient mixing at micro-scale [1–2]. In a recent study, a convergent-divergent microchannel with sinusoidal walls showed a strong coupling with pulsatile flow for enhanced mixing performance over a short mixing length [3]. In the present study, effects of two geometrical parameters, i.e., the ratio of amplitude to wavelength and ratio of throat-width to depth on mixing performance, were analyzed with the Strouhal number and the ratio of pulsing amplitude to steady flow velocity at a fixed Reynolds number, Re = 0.5. The flow and mixing analyses were performed using unsteady Navier-Stokes equations and a diffusion-convection model for species concentration.

Calculations of self-excited impinging jet flow

1986 ◽  
Vol 163 ◽  
pp. 69-98 ◽  
Author(s):  
Samuel Ohring
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Frequency ◽  
Numerical Results ◽  
The Self ◽  
Experimental Results ◽  
Number Range ◽  
Planar Jet ◽  
Reynolds Number Range ◽  
Stream Function Formulation

This paper presents numerical calculations of the self-excited oscillations of an incompressible planar jet impinging upon a wedge for a Reynolds-number range of 250–650. For this Reynolds-number range these flows are experimentally observed to be two-dimensional and laminar. A finite-difference vorticity/stream-function formulation of the Navier-Stokes equations is employed. The self-sustained flow oscillations result in not just one but several well-defined flow frequency components due to nonlinear interaction of two primary components: the most unstable frequency (β) of the jet shear layer and a low-frequency modulating component ($\frac{1}{3}\beta $). The modulating component results from vortex-vortex interaction at the impingement edge of both like and counter-rotating vortices. Although the interaction pattern varies through the Reynolds-number range studied, the pattern adjusts itself to maintain the modulating component $\frac{1}{3}\beta $ which has a strong upstream influence. The numerical results, in agreement with experimental results, strongly suggest the occurrence of such phenomena as frequency jumps and hysteresis. Pressure at the wedge surface has been calculated and compared with experimental results. Numerical results for wedge torque and lift, which have not been experimentally measured, have also been obtained.

Numerical Investigation of Micro-Channeled Louver Fin Aluminum Heat Exchangers at Low Reynolds Number

2016 ◽  
Author(s):  
Pradeep Shinde ◽  
Mirko Schäfer ◽  
Cheng-Xian Lin
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Exchanger ◽  
Heat Exchangers ◽  
Low Reynolds Number ◽  
Poor Performance ◽  
Geometrical Parameters ◽  
Number Range ◽  
Reynolds Number Range ◽  
Low Reynolds

Extensive studies are being carried out by several researchers on the performance prediction of aluminum heat exchangers with different fin and tube geometrical configurations mostly for Reynolds number higher than 100. In the present study, the air-side heat transfer and pressure drop characteristics of the louvered fin micro-channeled, Aluminum heat exchangers are systematically analyzed by a 3D numerical simulation for very low Reynolds number from 25 to 200. Three different heat exchanger geometries obtained for the experimental investigation purposes with constant fin pitch (14 fins per inch) but varied fin geometrical parameters (fin height, fin thickness, louver pitch, louver angle, louver length and flow depth) are numerically investigated. The performance of the heat exchangers is predicted by calculating Colburn j factor and Fanning friction f factor. The effect of fin geometrical parameters on the heat exchanger performance at the Reynolds number range specified is evaluated. The air-side performance of the studied heat exchangers for the specified Reynolds number range is compared with experimental heat exchanger performance data available in the open literature and a good agreement is observed. The present results show that at the studied range of Reynolds number the flow through the heat exchanger is fin directed rather than the louver directed and therefore the heat exchanger shows poor performance. The effect of geometrical parameters on the average heat transfer coefficient is computed and design curves are obtained which can be used to predict the heat transfer performance for a given geometry.

Approximations in Hydrodynamic Lubrication

1992 ◽  
Vol 114 (1) ◽  
pp. 14-25 ◽  
Author(s):  
R. X. Dai ◽  
Q. Dong ◽  
A. Z. Szeri
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Hydrodynamic Lubrication ◽  
Lubrication Theory ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Bearing Stiffness

In this numerical study of the approximations that led Reynolds to the formulation of classical Lubrication Theory, we compare results from (1) the full Navier-Stokes equations, (2) a lubrication theory relative to the “natural,” i.e., bipolar, coordinate system of the geometry that neglects fluid inertia, and (3) the classical Reynolds Lubrication Theory that neglects both fluid inertia and film curvature. By applying parametric continuation techniques, we then estimate the Reynolds number range of validity of the laminar flow assumption of classical theory. The study demonstrates that both the Navier-Stokes and the “bipolar lubrication” solutions converge monotonically to results from classical Lubrication Theory, one from below and the other from above. Furthermore the oil-film force is shown to be invariant with Reynolds number in the range 0 < R < Rc for conventional journal bearing geometry, where Rc is the critical value of the Reynolds number at first bifurcation. A similar conclusion also holds for the off-diagonal components of the bearing stiffness matrix, while the diagonal components are linear in the Reynolds number, in accordance with the small perturbation theory of DiPrima and Stuart.

A Parametric Study on the Effects of Reynolds Number on the Topology Optimization of Navier-Stokes Flows

2020 ◽  
Author(s):  
Joel C. Najmon ◽  
Tong Wu ◽  
Andres Tovar
Keyword(s):  
Reynolds Number ◽  
Topology Optimization ◽  
Stokes Flow ◽  
Dynamic Viscosity ◽  
Parametric Study ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Design Domain ◽  
Flow Topology ◽  
Flow Channels

Abstract Fluid-flow topology optimization (FTO) allows the generation of innovative flow-channel layouts with minimal pressure drop (power dissipation) between inlet and outlet ports in a given design domain. FTO was first explored using Stokes flow with the material in the design domain modeled as a porous medium governed by Darcy’s law. More recently, Navier-Stokes flow has been implemented to consider higher Reynolds numbers. The objective of this work is to demonstrate the effect of the Reynolds number on the FTO results and generate a set of design rules. To this end, a density-based FTO algorithm and an in-house finite element analysis code for incompressible Navier-Stokes flow are developed. The optimization process is updated using the method of moving asymptotes so that the flow’s potential power is maximized. The nonlinear Navier-Stokes equations are solved using a trust region Newton’s method. Sensitivity analysis is carried out using the adjoint method. A parametric study of the underlying parameters of the Reynolds number in two numerical examples shows the effect of the fluid’s dynamic viscosity and velocity on the optimized flow channels. The results show that fluids with the same Reynolds number, but with different dynamic viscosity or velocity values, can generate significantly different flow channels.

Evaluation of Various Channel Shapes of a Microchannel Heat Sink

2016 ◽  
Vol 24 (03) ◽  
pp. 1650018 ◽  
Author(s):  
Aatif Ali Khan ◽  
Kwang-Yong Kim
Keyword(s):  
Reynolds Number ◽  
Thermal Resistance ◽  
Heat Sink ◽  
Stokes Equations ◽  
Hydraulic Diameter ◽  
Navier Stokes ◽  
Average Height ◽  
Microchannel Heat Sink ◽  
Navier Stokes Equations ◽  
Number Range

Thermal and hydraulic performances of various geometric shapes of a microchannel heat sink were evaluated numerically using Navier–Stokes equations. A heat sink comprised of a [Formula: see text][Formula: see text]cm2 silicon wafer was investigated with water as the cooling fluid. The performances of seven microchannel shapes were compared at the same microchannel hydraulic diameter and the same average height of the bottom silicon substrate. The thermal resistance, friction coefficient, and Nusselt number were calculated for a Reynolds number range of 50 to 500. The results show that an inverse trapezoidal shape gives the lowest thermal resistance for a Reynolds number up to 300. The values of [Formula: see text]Re are almost similar for all the shapes because of the constant hydraulic diameter.

Four-dimensional turbulence in a plane channel

2011 ◽  
Vol 680 ◽  
pp. 67-79 ◽  
Author(s):  
NIKOLAY NIKITIN
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Stokes Equations ◽  
Plane Channel ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Wall Friction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range

The four-dimensional (4D) incompressible Navier–Stokes equations are solved numerically for the plane channel geometry. The fourth spatial coordinate is introduced formally to be homogeneous and mathematically orthogonal to the others, similar to the spanwise coordinate. Exponential growth of small 4D perturbations superimposed onto 3D turbulent solutions was observed in the Reynolds number range from Re = 4000 to Re = 10000. The growth rate of small 4D perturbations expressed in wall units was found to be λ+4D = 0.016 independent of Reynolds number. Nonlinear evolution of 4D perturbations leads either to attenuation of turbulence and relaminarization or to establishment of a self-sustained 4D turbulent solution (4D turbulent flow). Both results on flow evolution were obtained at the lowest Reynolds number, depending on the grid resolution, pointing to the proximity of Re = 4000 as the critical Reynolds number for 4D turbulence. Self-sustained 4D turbulence appeared to be less intense compared with 3D turbulence in terms of mean wall friction, which is about 55% of that predicted by the empirical Dean law for turbulent channel flow at all Reynolds numbers considered. Thus, the law of resistance of 4D turbulent channel flow can be expressed as Cf = 0.04Re−0.25.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

Sign in / Sign up

Export Citation Format

Share Document