scholarly journals Hydrodynamic Entrance Length for Laminar Flow in Microchannels with Rectangular Cross Section

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 240
Author(s):  
Germán Ferreira ◽  
Artur Sucena ◽  
Luís L. Ferrás ◽  
Fernando T. Pinho ◽  
Alexandre M. Afonso
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Low Reynolds Numbers ◽  
Viscous Forces ◽  
Aspect Ratios ◽  
Judicious Choice ◽  
Microsystem Design

This work presents a detailed numerical investigation on the required development length (L=L/B) in laminar Newtonian fluid flow in microchannels with rectangular cross section and different aspect ratios (AR). The advent of new microfluidic technologies shifted the practical Reynolds numbers (Re) to the range of unitary (and even lower) orders of magnitude, i.e., creeping flow conditions. Therefore, accurate estimations of L at Re≤O(1) are important for microsystem design. At such low Reynolds numbers, in which inertial forces are less dominant than viscous forces, flow characteristics become necessarily different from those at the macroscale where Re is typically much larger. A judicious choice of mesh refinement and adequate numerical methods allowed obtaining accurate results and a general correlation for estimating L, valid in the ranges 0≤Re≤2000 and 0.1≤AR≤1, thus covering applications in both macro and microfluidics.

Modeling and Numerical Simulation of Flow Resistance Characteristics in Slowly-Varying Rectangular Cross-Section Microchannel

2016 ◽  
Author(s):  
Shen Teng ◽  
Wang Jiong ◽  
Sun Dong ◽  
Liu Yafeng ◽  
Tian Zhouyu
Keyword(s):  
Numerical Simulation ◽  
Theoretical Calculation ◽  
Cross Section ◽  
Flow Resistance ◽  
Rectangular Cross Section ◽  
Flow Characteristics ◽  
Aspect Ratios ◽  
Good Accord ◽  
Simulation Results ◽  
Poiseuille Number

In this paper, flow characteristics in slowly-varying rectangular microchannels with different aspect ratios and Re numbers ranging from 7 to 200 are investigated. The obtained simulation results are compared with theoretics values based on the Bernoulli equations. The results show that the simulation results just hold an average discrepancy of 10% with the theoretical calculation value whichis presents a good accord. All the research of microchannel, the Poiseuille number of the flow is inconstant within the range of Re number, except when the contract angle is small where Poiseuille number is essentially unchanged.

Sound Radiation From Two Side-by-Side Rectangular Cylinders With Slightly Different Aspect Ratios

2015 ◽  
Author(s):  
Ressa Octavianty ◽  
Masahito Asai
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Sound Radiation ◽  
Reynolds Numbers ◽  
Low Mach Number ◽  
Aspect Ratios ◽  
Square Cylinders ◽  
Vortex Streets ◽  
Rectangular Cylinders ◽  
Center Distance

Sound radiation from two side-by-side rectangular cylinders, one of which had a square cross-section and the other had a rectangular cross-section with aspect ratio AR = 1.2 to 1.5, was examined experimentally at Reynolds numbers Re = 1.0 × 104 - 3.3 × 104 in low Mach number flows. The center-to-center distance between two cylinders T/D was 3.6, 4.5 and 6.0. When the center-to-center distance was small, T/d = 3.6, vortex streets from two different cylinders were synchronized with the same frequency as that for a pair of identical square cylinders, even for the cylinder pair of ARs = 1.0 and 1.5. Sound radiation was dipole-like (planar-anti-symmetric), unlike in the case of square-cylinders-pair where sound radiation was in-phase. For larger cylinder spacing T/d = 6, highly modulated sound was radiated with two different frequencies due to non-synchronized vortex shedding from two cylinders.

Stokes Flow Characteristics in a Cylindrical Quadrant Duct With Rotating Outer Wall

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Zongyong Wang ◽  
Jiayu Zhao ◽  
Jianhua Wu
Keyword(s):  
Stokes Flow ◽  
Flow Characteristics ◽  
Outer Wall ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Low Reynolds Numbers ◽  
Chaotic Flow ◽  
Rotating Wall ◽  
Analytical Results ◽  
Analytical Expressions

The Stokes flow in a cylindrical quadrant duct with a rotating wall was analytically and numerically studied. Based on mathematics and fluid dynamics theory, the analytical expressions of three velocity components were achieved by solving a Poisson's equation and a biharmonic equation. Especially, a closed-form analytical expression of axial velocity was obtained, which can greatly improve the calculating accuracy and speed in analyzing Stokes flow. The velocity distributions for different Reynolds numbers were investigated numerically to insure the accuracy of the analytical results at low Reynolds numbers and to confirm the error range of the analytic results at higher Reynolds numbers. The conclusion indicates that there exists an infinite sequence of eddies that decrease exponentially in size towards the sectorial vertex. The width of the first eddy region reached 99.4% of the sector radius; the sum of the width of other eddies is only 0.6% of the sector radius, which cannot be easily displayed graphically, while the sequence of eddies contributes to form the chaotic flow. The maximum deviations of the velocity components between the analytical results and simulated ones are all less than 1% when Re < 0.1, which verifies the validity and accuracy of the analytical expressions in the creeping flow regime. The analytical expressions are not only suitable for creeping flow but also for laminar flow with smaller Reynolds number (Re < 50).

Heat Transfer for Laminar Flow in Spiral Ducts of Rectangular Cross Section

2005 ◽  
Vol 127 (3) ◽  
pp. 352-356 ◽  
Author(s):  
Michael W. Egner ◽  
Louis C. Burmeister
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Aspect Ratios ◽  
Small Pitch

Laminar flow and heat transfer in three-dimensional spiral ducts of rectangular cross section with aspect ratios of 1, 4, and 8 were determined by making use of the FLUENT computational fluid dynamics program. The peripherally averaged Nusselt number is presented as a function of distance from the inlet and of the Dean number. Fully developed values of the Nusselt number for a constant-radius-of-curvature duct, either toroidal or helical with small pitch, can be used to predict those quantities for the spiral duct in postentry regions. These results are applicable to spiral-plate heat exchangers.

Correlated Compressible and Incompressible Channel Flows

1997 ◽  
Vol 119 (4) ◽  
pp. 911-915 ◽  
Author(s):  
C. Crnojevic´ ◽  
V. D. Djordjevic´
Keyword(s):  
Cross Section ◽  
High Reynolds Number ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Isothermal Flow ◽  
Governing Equations ◽  
Adiabatic Flow ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Reynolds Number Flows

Compressible flow in channels of slowly varying cross section at moderately high Reynolds numbers is treated in the paper by employing some Stewartson-type transformations that convert the problem into an incompressible one. Both adiabatic flow and isothermal flow are considered, and a Poiseuille-type incompressible solution is mapped onto compressible plane in order to generate some exact solutions of the compressible governing equations. The results show striking effects that viscosity may have upon the flow characteristics in this case, in comparison with more conventional high Reynolds number flows.

Topology of vortex breakdown in closed polygonal containers

2017 ◽  
Vol 820 ◽  
pp. 263-283 ◽  
Author(s):  
Igor V. Naumov ◽  
Irina Yu. Podolskaya
Keyword(s):  
Aspect Ratio ◽  
Cross Section ◽  
Vortex Breakdown ◽  
Laser Doppler Anemometry ◽  
Reynolds Numbers ◽  
Cylindrical Container ◽  
Stagnation Points ◽  
Aspect Ratios ◽  
Particle Visualization ◽  
Cross Section Geometry

The topology of vortex breakdown in the confined flow generated by a rotating lid in a closed container with a polygonal cross-section geometry has been analysed experimentally and numerically for different height/radius aspect ratios $h$ from 0.5 to 3.0. The locations of stagnation points of the breakdown bubble emergence and corresponding Reynolds numbers were determined experimentally and numerically by STAR-CCM+ computational fluid dynamics software for square, pentagonal, hexagonal and octagonal cross-section configurations. The flow pattern and velocity were observed and measured by combining seeding particle visualization and laser Doppler anemometry. The vortex breakdown size and position on the container axis were identified for Reynolds numbers ranging from 500 to 2800 in steady flow conditions. The obtained results were compared with the flow structure in the closed cylindrical container. The results allowed revealing regularities of formation of the vortex breakdown bubble depending on $Re$ and $h$ and the cross-section geometry of the confined container. It was found in a diagram of $Re$ versus $h$ that reducing the number of cross-section angles from eight to four shifts the breakdown bubble location to higher Reynolds numbers and a smaller aspect ratio. The vortex breakdown bubble area for octagonal cross-section was detected to correspond to the one for the cylindrical container but these areas for square and cylindrical containers do not overlap in the entire range of aspect ratio.

Improving Adhesion Density and Coverage Uniformity of Antibody-Antigen Binding on a Sensor Surface Using U-Type, T-Type and W-Type Microfluidic Devices

2011 ◽  
Author(s):  
Chia-Che Wu ◽  
Ping-Kuo Tseng ◽  
Ching-Hsiu Tsai
Keyword(s):  
Quantum Dots ◽  
Microfluidic Channel ◽  
Microfluidic Devices ◽  
Reynolds Numbers ◽  
Yellow Mosaic Virus ◽  
Fluorescent Intensity ◽  
Low Reynolds Numbers ◽  
Viscous Forces ◽  
Drag Forces ◽  
Low Reynolds

Usually microorganisms, molecules, or viruses in the fluidic environment are at very low Reynolds numbers because of tiny diameters. At very low Reynolds numbers, viscous forces of molecules and viruses will dominate. Those micro- or nanoparticles will stop moving immediately when flows cease and drag forces disappear, those phenomena were discovered by the fluorescent particle experiment. Of course, molecules and viruses are still subject to Brownian motion and move randomly. In order to increase the adhesion density of micro- and nanoparticles on sensor’s surface, designs of the flow movements in microfluidic channel is proposed. Adhesion density of linker 11-mercaptoundecanoic acid (MUA) and Turnip yellow mosaic virus (TYMV) with specific quantum dots were measured by confocal microscope. Fluorescent intensity and coverage of quantum dots are used to identify the adhesion density quantitatively. Results show that TYMV and MUA layers disperse randomly by dipping method. Fluorescent intensity of quantum dots; i.e. relative to the amount of MUA and TYMV; were 2.67A.U. and 19.13A.U., respectively, in W-type microfluidic devices to contrast just 1.00A.U. and 1.00A.U., respectively, by dipping method. Coverage of MUA and TYMV were 80∼90% and 70∼90%, respectively, in W-type microfluidic channel to contrast just 20∼50% and 0∼10%, respectively, by dipping method.

Novel Low Reynolds Number Mixers for Microfluidic Applications

2003 ◽  
Author(s):  
S. P. Vanka ◽  
C. M. Winkler ◽  
J. Coffman ◽  
E. Linderman ◽  
S. Mahjub ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Rhodamine 6G ◽  
Rectangular Cross Section ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Low Reynolds Numbers ◽  
Sucrose Solutions ◽  
Low Reynolds ◽  
Rhodamine 6G Dye ◽  
Microfabrication Techniques

We present two new designs of compact mixers that can provide good mixing at low Reynolds numbers encountered in many microfluidic devices. The new designs benefit from curvature induced cross-stream vortices to enhance mixing of two co-flowing streams of fluids arranged side by side. One of the designs is a spiral of rectangular cross-section, while the other is a series of concentric circular channels arranged as a labyrinth. Both utilize the formation of sustained secondary flows to enhance mixing between two streams. Currently, the devices are fabricated in aluminum using standard machining techniques. However, they can be reduced further in size using standard microfabrication techniques. Mixing experiments were conducted in these channels at a Reynolds number of 6.8 using two sucrose solutions, one of which was laced with Rhodamine 6G dye. Compared to a experiment in an equivalent straight channel, a significant enhancement in the mixing of the two streams, as indicated by the intensity of the second fluid’s color, was observed. The present designs provide a compact and easy-to-fabricate alternative to various other concepts proposed in literature.

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