scholarly journals A NUMERICAL SCHEME FOR SOLVING CREEPING FLOWS

2003 ◽  
Vol 2 (2) ◽  
pp. 35
Author(s):  
H. A. Navarro ◽  
V. G. Ferreira
Keyword(s):  
Numerical Scheme ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Low Reynolds Numbers ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Creeping Flows ◽  
Adi Schemes ◽  
Adi Scheme

This work shows an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows at low Reynolds numbers. The conservation equations are solved in stream function - vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient to simulate a creeping flow. Numerical results demonstrating the applicability of this technique are also presented.

scholarly journals A NUMERICAL SCHEME FOR SOLVING CREEPING FLOWS

2003 ◽  
Vol 2 (2) ◽  
Author(s):  
H. A. Navarro ◽  
V. G. Ferreira
Keyword(s):  
Numerical Scheme ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Creeping Flow ◽  
Low Reynolds Numbers ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Creeping Flows ◽  
Adi Schemes ◽  
Adi Scheme

This work shows an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows at low Reynolds numbers. The conservation equations are solved in stream function - vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient to simulate a creeping flow. Numerical results demonstrating the applicability of this technique are also presented.

Numerical Study of Transient and Steady Induced Symmetric Flows in Rectangular Cavities

1977 ◽  
Vol 99 (3) ◽  
pp. 526-530 ◽  
Author(s):  
B. S. Jagadish
Keyword(s):  
Steady State ◽  
Stream Function ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Aspect Ratios ◽  
Alternating Direction ◽  
Vorticity Transport ◽  
Steady State Solutions

Symmetric flows induced in rectangular cavities by a pair of moving walls are studied numerically. Solutions are obtained by solving the coupled transient vorticity transport and stream function relations using the alternating direction implicit method. Steady state solutions are obtained as limiting cases of the transients. The study covers Reynolds numbers of 1 100 and 1000 for cavities having aspect ratios of 0.5 and 1.0.

scholarly journals Improvement of a 2-D SIA ice-flow model: application to Glacier de Saint-Sorlin, France

2007 ◽  
Vol 53 (183) ◽  
pp. 713-722 ◽  
Author(s):  
Martina Schäfer ◽  
Emmanuel Le Meur
Keyword(s):  
Flow Model ◽  
Mass Conservation ◽  
Ice Thickness ◽  
Dynamic Effects ◽  
Ice Flow ◽  
Alpine Glacier ◽  
Alternating Direction Implicit ◽  
Initial Deviation ◽  
Alternating Direction ◽  
Adi Scheme

A number of improvements have been made to an existing two-dimensional ice-flow model applied to an alpine glacier. Analysis of the results of the existing model revealed several shortcomings. The first concerns the lack of mass conservation of the applied alternating-direction-implicit (ADI) scheme. A semi-implicit (SI) scheme is therefore proposed and the effects on mass conservation assessed by a comparison with the ADI scheme. The comparison is first carried out with a simple theoretical glacier for which the improvement is significant. Concerning the real case of Glacier de Saint-Sorlin, France, the initial deviation in mass conservation was much less pronounced such that the new scheme, although improving mass conservation, does not significantly change the modelled dynamics. However, other shortcomings that have a more profound impact on the modelling of glacier behaviour have been identified. The ice thickness may become negative over some gridpoints, leading to an inconsistency. The problem is partly resolved by incorporating extra checks on critical gridpoints at the glacier border. Finally, with the help of ice particle tracking, unrealistic ice settlement above the bergschrund has been identified as the main reason for spurious dynamic effects and has been corrected.

scholarly journals Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model

2017 ◽  
Vol 904 ◽  
pp. 012014 ◽  
Author(s):  
L. Calatroni ◽  
C. Estatico ◽  
N. Garibaldi ◽  
S. Parisotto
Keyword(s):  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Adi Schemes

scholarly journals Bioinspired cilia arrays with programmable nonreciprocal motion and metachronal coordination

2020 ◽  
Vol 6 (45) ◽  
pp. eabc9323
Author(s):  
Xiaoguang Dong ◽  
Guo Zhan Lum ◽  
Wenqi Hu ◽  
Rongjing Zhang ◽  
Ziyu Ren ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Design Method ◽  
Complex Fluids ◽  
Fluid Flows ◽  
Quantitative Relationship ◽  
Reynolds Numbers ◽  
Living Systems ◽  
Low Reynolds Numbers ◽  
Metachronal Waves ◽  
Miniature Devices

Coordinated nonreciprocal dynamics in biological cilia is essential to many living systems, where the emergentmetachronal waves of cilia have been hypothesized to enhance net fluid flows at low Reynolds numbers (Re). Experimental investigation of this hypothesis is critical but remains challenging. Here, we report soft miniature devices with both ciliary nonreciprocal motion and metachronal coordination and use them to investigate the quantitative relationship between metachronal coordination and the induced fluid flow. We found that only antiplectic metachronal waves with specific wave vectors could enhance fluid flows compared with the synchronized case. These findings further enable various bioinspired cilia arrays with unique functionalities of pumping and mixing viscous synthetic and biological complex fluids at low Re. Our design method and developed soft miniature devices provide unprecedented opportunities for studying ciliary biomechanics and creating cilia-inspired wireless microfluidic pumping, object manipulation and lab- and organ-on-a-chip devices, mobile microrobots, and bioengineering systems.

Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations

2015 ◽  
Vol 17 (2) ◽  
pp. 487-509 ◽  
Author(s):  
Guang-Hua Gao ◽  
Hai-Wei Sun
Keyword(s):  
Diffusion Equations ◽  
Two Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Alternating Direction Implicit ◽  
Truncation Errors ◽  
Advection Diffusion ◽  
Alternating Direction ◽  
Implicit Difference Schemes ◽  
Adi Schemes

AbstractThis paper is devoted to the discussion of numerical methods for solving two-dimensional time-fractional advection-diffusion equations. Two different three-point combined compact alternating direction implicit (CC-ADI) schemes are proposed and then, the original schemes for solving the two-dimensional problems are divided into two separate one-dimensional cases. Local truncation errors are analyzed and the unconditional stabilities of the obtained schemes are investigated by Fourier analysis method. Numerical experiments show the effectiveness and the spatial higher-order accuracy of the proposed methods.

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).

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.

Investigation on the effect of leading edge tubercles of sweptback wing at low reynolds number

2020 ◽  
Vol 21 (6) ◽  
pp. 621
Author(s):  
Veerapathiran Thangaraj Gopinathan ◽  
John Bruce Ralphin Rose ◽  
Mohanram Surya
Keyword(s):  
Leading Edge ◽  
Reynolds Numbers ◽  
Sweep Angle ◽  
Laminar Separation ◽  
Low Reynolds Numbers ◽  
Flow Energy ◽  
Airplane Wing ◽  
Low Reynolds ◽  
Naca 0015 ◽  
Wing Performance

Aerodynamic efficiency of an airplane wing can be improved either by increasing its lift generation tendency or by reducing the drag. Recently, Bio-inspired designs have been received greater attention for the geometric modifications of airplane wings. One of the bio-inspired designs contains sinusoidal Humpback Whale (HW) tubercles, i.e., protuberances exist at the wing leading edge (LE). The tubercles have excellent flow control characteristics at low Reynolds numbers. The present work describes about the effect of tubercles on swept back wing performance at various Angle of Attack (AoA). NACA 0015 and NACA 4415 airfoils are used for swept back wing design with sweep angle about 30°. The modified wings (HUMP 0015 A, HUMP 0015 B, HUMP 4415 A, HUMP 4415 B) are designed with two amplitude to wavelength ratios (η) of 0.1 & 0.24 for the performance analysis. It is a novel effort to analyze the tubercle vortices along the span that induce additional flow energy especially, behind the tubercles peak and trough region. Subsequently, Co-efficient of Lift (CL), Co-efficient of Drag (CD) and boundary layer pressure gradients also predicted for modified and baseline (smooth LE) models in the pre & post-stall regimes. It was observed that the tubercles increase the performance of swept back wings by the enhanced CL/CD ratio in the pre-stall AoA region. Interestingly, the flow separation region behind the centerline of tubercles and formation of Laminar Separation Bubbles (LSB) were asymmetric because of the sweep.

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