Numerical Study of a Conjecture in the Self-avoiding Random Walk Problem

1973 ◽  
Vol 26 (2) ◽  
pp. 207 ◽  
Author(s):  
AJ Guitmann ◽  
MF Sykes
Keyword(s):  
Random Walk ◽  
Numerical Study ◽  
Three Dimensional ◽  
The Self ◽  
Series Expansions ◽  
Honeycomb Lattice ◽  
Exact Inequality ◽  
Good Agreement

It has been conjectured that the sum of the critical attritions p. and v of a selfavoiding random walk on a triangular and a honeycomb lattice respectively should be precisely six. Estimates of the critical attrition obtained from the analysis of exact series expansions support this conjecture. Assuming the conjecture, estimates of the two critical attritions are made and found to be in good agreement with those obtained by other methods. The exact inequality v2 ~ p.2/(1 + p.) is proved, and it is shown that an analogous inequality applies to a pair of three-dimensional lattices.

The Effect of the Steady Flow Potential on the Motions of a Moving Ship in Waves

2000 ◽  
Vol 44 (01) ◽  
pp. 14-32
Author(s):  
Ming-Chung Fang
Keyword(s):  
Steady Flow ◽  
Present Method ◽  
Three Dimensional ◽  
Source Distribution ◽  
Series Expansions ◽  
Ship Motions ◽  
Double Integral ◽  
Flow Potential ◽  
Principal Value ◽  
Good Agreement

A three-dimensional method to analyze the motions of a ship running in waves is presented, including the effects of the steady-flow potential. Basically, the general formulations are based on the source distribution technique by which the ship hull surface is regarded as the assembly of many panels. The present study includes three algorithms for treating the corresponding Green function:the Hess & Smith algorithm for the part of simple source I/r,the complex plane contour integral of the Shen & Farell algorithm for the double integral of steady flow, andthe series expansions of the Telste & Noblesse algorithm for the Cauchy principal value integral of unsteady flow. The study reveals that the effect of steady flow on ship motions is generally small, but it still cannot be neglected in some cases, especially for the ship running in oblique waves. The effect also depends on the fore-aft configuration of the ship. The results predicted by the present method are found to be in fairly good agreement with existing experiments and other theories.

Numerical Study on Supersonic Combustor with an Allotype Cavity

2014 ◽  
Vol 694 ◽  
pp. 187-192
Author(s):  
Jin Xiang Wu ◽  
Jian Sun ◽  
Xiang Gou ◽  
Lian Sheng Liu
Keyword(s):  
Alternative Model ◽  
Numerical Study ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Experimental Result ◽  
Navier Stokes ◽  
Cold Flow ◽  
Hypersonic Inlet ◽  
Good Agreement

The three-dimensional coupled explicit Reynolds Averaged Navier–Stokes (RANS) equations and the two equation shear-stress transport k-w (SST k-w) model has been employed to numerically simulate the cold flow field in a special-shaped cavity-based supersonic combustor. In a cross-section shaped rectangular, hypersonic inlet with airflow at Mach 2.0 chamber, shock structures and flow characteristics of a herringbone-shaped boss and a herringbone-shaped cavity models were discussed, respectively. The results indicate: Firstly, according to the similarities of bevel-cutting shock characteristics between the boss case and the cavity case, the boss structure can serve as an ideal alternative model for shear-layer. Secondly, the eddies within cavity are composed of herringbone-spanwise vortexes, columnar vortices in the front and main-spanwise vortexes in the rear, featuring tilting, twisting and stretching. Thirdly, the simulated bottom-flow of cavity is in good agreement with experimental result, while the reverse flow-entrainment resulting from herringbone geometry and pressure gradient. However, the herringbone-shaped cavity has a better performance in fuel-mixing.

PREDICTION OF UNSTEADY STATES IN LID-DRIVEN CAVITIES FILLED WITH AN INCOMPRESSIBLE VISCOUS FLUID

2012 ◽  
Vol 23 (04) ◽  
pp. 1250030 ◽  
Author(s):  
FAYÇAL HAMMAMI ◽  
NADER BEN-CHEIKH ◽  
ANTONIO CAMPO ◽  
BRAHIM BEN-BEYA ◽  
TAIEB LILI
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Three Dimensional Flow ◽  
Driven Cavity ◽  
Flow Evolution ◽  
2D And 3D ◽  
Benchmark Solutions ◽  
Good Agreement

In this work, a numerical study devoted to the two-dimensional and three-dimensional flow of a viscous, incompressible fluid inside a lid-driven cavity is undertaking. All transport equations are solved using the finite volume formulation on a staggered grid system and multi-grid acceleration. Quantitative aspects of two and three-dimensional flows in a lid-driven cavity for Reynolds number Re = 1000 show good agreement with benchmark results. An analysis of the flow evolution demonstrates that, with increments in Re beyond a certain critical value Rec, the steady flow becomes unstable and bifurcates into unsteady flow. It is observed that the transition from steadiness to unsteadiness follows the classical Hopf bifurcation. The time-dependent velocity distribution is studied in detail and the critical Reynolds number is localized for both 2D and 3D cases. Benchmark solutions for 2D and 3D lid-driven cavity flows are performed for Re = 1500 and 6000.

scholarly journals Numerical study on snow transport and drift formation

1993 ◽  
Vol 18 ◽  
pp. 135-141 ◽  
Author(s):  
Takahiko Uematsu
Keyword(s):  
Continuity Equation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Density Field ◽  
Particle Movement ◽  
Snow Density ◽  
Fall Velocity ◽  
Snow Transport ◽  
Good Agreement

A three-dimensional, numerical simulation model for snow transport and drift formation is proposed in which saltation as well as suspension are considered as dynamic behavioral factors of moving snow particles. The procedure for simulation is as follows: (1) Air flow field is simulated solving the Reynolds equations and the continuity equation. (2) Using the result of the air field flow simulation, the blown-snow density field is simulated using the diffusion equations in which the fall velocity of blown snow particles is considered. In the boundary conditions, the particle movement of saltation is taken into consideration. (3) Finally, the snowdrift rate is computed based on the amount of snow particles not transported by saltation. This model was quantitatively tested for the phenomenon of snowdrift development. The computed results showed good agreement with observations.

scholarly journals Water transport and absorption in pharmaceutical tablets – a numerical study

Meccanica ◽  
2019 ◽  
Vol 55 (2) ◽  
pp. 421-433 ◽  
Author(s):  
Povilas Vaitukaitis ◽  
Dario Maggiolo ◽  
Johan Remmelgas ◽  
Susanna Abrahmsén-Alami ◽  
Diana Bernin ◽  
...  
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Coating Process ◽  
Droplet Impingement ◽  
Pharmaceutical Tablets ◽  
Pharmaceutical Tablet ◽  
Capillary Spreading ◽  
Spreading Time ◽  
Good Agreement

AbstractThe quality of a coated pharmaceutical tablet can be strongly affected by the interactions of water droplets with the porous substrate during processes such as coating process. Three different mechanisms co-exist in the coating process: water spreading, absorption and evaporation. Disentangling the fundamental understanding of these phenomena can therefore be crucial for achieving a higher quality of the products (e.g. a longer shelf-life of the tablets) and for controlling the efficiency of the process. This paper aims to investigate the spreading and absorption mechanisms after droplet impingement on a tablet using a Lattice-Boltzmann methodology. Our numerical results (droplet height and spreading, penetration depth and absorbed volume) are in a good agreement with experimental data and numerical simulations available in the literature. In particular, the spreading phase is characterised by the capillary spreading time scale, as confirmed by previous studies. In contrast to previous studies, we find that the absorption process begins at times shorter than the capillary spreading time but with a different power-law in the absorbed volume. We explain this behaviour through a modified Washburn law that takes into account three-dimensional effects. Our data can be used as a benchmark to test novel mathematical models.

Numerical Study of the Three-Dimensional Structure of a Bubble Plume

2000 ◽  
Vol 122 (4) ◽  
pp. 754-760 ◽  
Author(s):  
Y. Murai ◽  
Y. Matsumoto
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Lagrangian Model ◽  
Dimensional Structure ◽  
Bubble Motion ◽  
Bubble Plume ◽  
Two Phase ◽  
Simulated Flow ◽  
Good Agreement

The whole behavior and the micro scale flow characteristics of a three-dimensional bubble plume are investigated numerically. The bubble plume drives liquid convection in a tank due to strong local two-phase interaction so that the Eulerian-Lagrangian model is formulated with emphasis on the translational motions of the bubble. In this model, each bubble motion is tracked in a bubbly mixture which is treated as a continuum. The three-dimensional numerical results reveal several particular structures, such as swaying and swirling structures of the bubble plume. These simulated flow structures show qualitatively good agreement with the experimental observations. Furthermore, the detailed behavior in the bubble plume is clarified by various analysis to discuss the dominant factors causing such the strong three-dimensionality. [S0098-2202(00)00904-4]

Numerical Study of the Turbulent Wake of a Towed or Auto-Propelled Axisymmetrical Body in a Stratified Medium Using LES-VMS

2013 ◽  
Author(s):  
B. Sainte-Rose ◽  
X. Lenhardt ◽  
O. Allain ◽  
A. Dervieux
Keyword(s):  
Numerical Study ◽  
Three Dimensional ◽  
Turbulent Wake ◽  
Flow Dynamics ◽  
Stratified Medium ◽  
Two Dimensional ◽  
Multi Scale ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Good Agreement

Numerical simulations of close and far wakes behind an axisymmetrical body in a stratified medium are carried out. Towed and auto-propelled regimes are considered. The parameters of the flow are Pr = 7, Re = 10000 based on the diameter of the cylinder and F = 25. Turbulence is modelled with a Large Eddy Simulation - Variational Multi-Scale approach. Realistic results are obtained for the towed case where the so-called three-dimensional (3D), non-equilibrium (NEQ) and quasi two-dimensional (Q2D) regimes are exhibited with very good agreement with the experiments. In addition, the effect of auto-propulsion on the flow dynamics is satisfactorily addressed.

Computation of Three-Dimensional Turbulent Flows in a Pipe Junction with Reference to Engine Inlet Manifolds

1992 ◽  
Vol 206 (4) ◽  
pp. 285-296 ◽  
Author(s):  
H Fu ◽  
M J Tindal ◽  
A P Watkins ◽  
M Yianneskis
Keyword(s):  
Turbulent Flows ◽  
Combustion Engine ◽  
Laser Doppler Anemometry ◽  
Numerical Study ◽  
Three Dimensional ◽  
Turbulence Energy ◽  
Numerical Predictions ◽  
Split Ratio ◽  
Inlet Manifold ◽  
Good Agreement

This paper presents a numerical study of the flows in an internal combustion engine inlet manifold. The three-dimensional turbulent flows through a single branched manifold were simulated using the κ-ɛ model of turbulence. The flow structure was characterized in detail and the effects of the flow split ratio and inlet flowrate were investigated. Detailed measurements were performed to validate the numerical predictions, using laser Doppler anemometry. Good agreement was obtained between the predicted and the measured mean velocities. The predicted levels of turbulence energy are in qualitative agreement with the measurements.

scholarly journals Experimental and computational investigation for three dimensional duct flow with modified arrangement ribs turbulators

2020 ◽  
pp. 93-93
Author(s):  
Khudheyer Mushatet ◽  
Sarah Nashee
Keyword(s):  
Friction Factor ◽  
Numerical Study ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Duct Flow ◽  
Computational Investigation ◽  
Performance Factor ◽  
Pitch Ratio ◽  
Overall Performance ◽  
Good Agreement

A combined numerical and experimental study is conducted to test the heat transfer enhancement and friction factor characteristics for a rectangular duct fitted with three cases of ribs turbulators: continuous ribs (CR), intermittent-continuous-intermittent ribs (ICIR) and intermittent ribs (IR). Experiments are conducted within a turbulent flow for Reynolds numbers values varied from 10000 to 35000, pitch ratio (p/e) equal to 5 and height ratio (e/H) of 0.33. The numerical study carried out using ANSYS FlUENT17.2. The turbulence is modeled by using k-? model. The results showed that the case of intermittent ribs provide the highest over performance factor while the continuous ribs indicate less overall performance factor among the considered cases. In addition, the results show that the highest values of the friction factor are marked from the case of intermittent ribs (IR) and then the case of intermittent-continuous-intermittent ribs (ICIR) followed by continuous rib case (CR). The continuous rib case showed the lowest friction factor. The experimental results showed a good agreement with the computational results.

Numerical study of droplet breakup in an asymmetric T-junction microchannel with different cross-section ratios

2021 ◽  
pp. 2250023
Author(s):  
Milad Isanejad ◽  
Keivan Fallah
Keyword(s):  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Droplet Breakup ◽  
Width Ratio ◽  
Two Phase ◽  
Droplet Motion ◽  
Daughter Droplets ◽  
Breakup Time ◽  
Good Agreement

In this study, numerical simulations are conducted to investigate droplet breakup in an asymmetric [Formula: see text]-junction microchannel with different cross-section ratios. To this approach, a two-phase model based on the volume of fluid (VOF) method is adopted to study the three-dimensional feature of droplet motion inside [Formula: see text]-junctions. The comparison reveals that the present results are in good agreement with previous studies. The effects of the capillary number (Ca), the non-dimensional droplet length ([Formula: see text]), and the non-dimensional width ratio ([Formula: see text]) on the breakup time and splitting ratio of daughter droplets are studied. Five distinct regimes are observed involving the non-breakup, breakup with tunnel, breakup without tunnel, asymmetric breakup, and sorting. Achieved results indicate that the time of breakup ([Formula: see text]) increases about 15% when the Ca is increased from 0.0134 to 0.0268 (about 100%). It is also found that the mass center of the mother droplet in the primary channel is shifted to a larger wide branch, which facilitates the asymmetric breakup of the droplet in a [Formula: see text]-junction microchannel.

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