Simulation of Lid Cavity Flow in Rectangular, Half-Circular and Beer Bucket Shapes using Quasi-Molecular Modeling

We developed a new method based on quasimolecular modeling to simulate the cavity flow in three cavity shapes: rectangular, half-circular and bucket beer in cgs units. Each quasi-molecule was a group of particles that interacted in a fashion entirely analogous to classical Newtonian molecular interactions. When a cavity flow was simulated, the instantaneous velocity vector fields were obtained by using an inverse distance weighted interpolation method. In all three cavity shapes, fluid motion was rotated counter-clockwise. The velocity vector fields of the three cavity shapes showed a primary vortex located near the upstream corners at time t ~ 0.500 s, t ~ 0.450 s and t ~ 0.350 s, respectively. The configurational kinetic energy of the cavities increased as time increased until the kinetic energy reached a maximum at time t ~ 0.02 s and, then, the kinetic energy decreased as time increased. The rectangular cavity system showed the lowest kinetic energy, while the half-circular cavity system showed the highest kinetic energy. The kinetic energy of rectangular, beer bucket and half-circular cavities fluctuated about stable average values 35.62 x 103, 38.04 x 103 and 40.80 x 103 ergs/particle, respectively. This indicated that the half-circular shapes were the most suitable shape for a shrimp pond because the water in shrimp pond flows best when we compared with rectangular and beer bucket shape.




References:
[1] E Erturk. "Nature of driven cavity flow at high Re and benchmark
solution on fine grid mesh," Int. J. Numer. Meth. Fluids. Submitted for
publication 2005.
[2] A. J. Chorin. "Numerical study of slightly viscous flow," J. Fluid MechI,
vol. 57, pp. 785-796, 1973.
[3] C. K. Aidun, and N. G. Triantafllopoulos, In Inter national symposium
on mechanics of thin-film coating. Spring National Meeting of the
AICHE. 1991.
[4] C. K. Aidun, N. G. Triantafllopoulos and J. D. Benson, "Global stability
of a lid driven cavity with through flow: flow visualization studies," J.
Phys. Fluids A, vol.3, pp.2081-2091, 1991.
[5] N. Ramanan, and G. M. Homsy,."Linear Stability of lid-driven cavity
flow," Phys. J. Phys. Fluids, vol. 6, pp.2690, 1994.
[6] C. J. Freitas, and R. L, "Street. Non-Linear Transport Phenomena in a
Complex Recirculating Flow: A Numerical Investigation," Int. J. Numer.
Method Fluids, vol. 8, pp 769-802, 1988.
[7] U. Ghia, K. N. Ghia, and C. T. Shin, "High-Re Solutions for
Incompressible Flow Using the Navier-Stokes Equations and a Multigrid
Method," J. Comp. Physics, vol. 48, pp. 387-411, 1982.
[8] V. M. Theodossiou and A. C. M, "Sousa. An efficient algorithm for
solving the incompressible fluid flow equations," Int. J. Numer. Meth.
Fluids, vol. 6, pp. 557-72, 1986.
[9] A. J. Chorin, "Numerical study of slightly viscous flow," J. Fluid Mech,
vol. 57, pp. 785-96, 1973.
[10] J. Ehlers, K. Hepp and H. A. Weidinmuller. Lecture note in physics #8.
In: Proceeding of the 2nd International conference on numerical methods
in fluid dynamics, New York, 1971.
[11] A. E. Gill and K. Bryen, "Effect of geometry on the circulation of threedimensional
southern-hemisphere ocean model,". Deep-sea Research
vol. 18, pp. 685-721, 1971.
[12] P. Jamet, P. Lascaux and P. A. Raviart, "Method de resolution
numerique des equation de Navier-Stokes,". Numer. Math, vol. 16, pp.
93-144, 1970.
[13] D. Greenspan. Quasi-molecular modelling. JBW Printers and Binders
Ptd. Ltd., Singapore, 1991.
[14] Interpolation: inverse distance weighting, Available at:
http://www.ncgia.ucsb.edu/pubs/spherekit/inverse.html, accessed March
2006.
[15] D. Greenspan, "Particle Modelling of the cavity problem for liquids," J.
Com. Math. Appl, vol. 45, pp. 715-22, 2003.
[16] D. Greenspan, "Molecular Mechanics-type approach to turbulence,"
Math. Comput. Model, vol. 26, pp. 85-96, 1997.
[17] S. Kulsri, M. Jaroensutasinee and K. Jaroensutasinee, "Simulation of lid
cavity flow using quasi-molecular modeling," Walailak J. Sci. & Tech.,
(to be published)
[18] C. Migon, A. Texier, and G. Pineau, "Effect of lid driven cavity shape
on the flow establishment phase," J Fluid Struc., vol. 14, pp. 469-488,
2002.