Numerical Simulation of Oscillatory Convection in Low-Pr Fluids

For the last ten years, there has been an ever-increasing awareness that fluid motion and transport processes influenced by buoyancy are of interest in many fields of science and technology. In particular, a lot of research has been devoted to the oscillatory behaviour of metallic melts (low-Pr fluids) due to the very crucial impact of such flow oscillations on the quality of growing crystals, semi-conductors or metallic alloys, for advanced technology applications. Test cases on the 2D oscillatory convection in differentially heated cavities containing low-Pr fluids have been defined by the organizing committee, and proposed to the community in 1987. The GAMM-Worshop was attended by 55 scientists from 12 countries, in Oct. 1988 in Marseille (France). Twenty-eight groups contributed to the mandatory cases coming from France (12), other European countries (7) and other countries: USA, Japan and Australia (9). Several groups also presented solutions of various related problems such as accurate determination of the threshold for the onset of oscillations, thermocapillary effect in open cavities, and 3D simulations. Period doubling, quasi- periodic behaviour, reverse transition and hysteresis loops have been reported for high Grashof numbers in closed cavities. The workshop was also open to complementary contributions (5), from experiments and theory (stability and bifurcation analysis). The book contains details about the various methods employed and the specific results obtained by each contributor.

Contenu

Benchmark Definition.- 1. Finite Difference Methods.- Fine Mesh Solutions Using Stream Function-Vorticity Formulation.- A Comparison of Velocity-Vorticity and Stream Function-Vorticity Formulations for Pr=0.- Buoyancy-Driven Oscillatory Flows in Shallow Cavities Filled With Low-Prandtl Number Fluids.- A Finite-Difference Method With Direct Solvers for Thermally-Driven Cavity Problems.- Contribution to the GAMM Workshop.- Low Prandtl Number Convection in a Shallow Cavity.- Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids With the TURBIT Code.- Marangoni Flows in a Cylindrical Liquid Bridge of Silicon.- Numerical Simulation of Oscillatory Convection in a Low Prandtl Fluid.- Steady-State Natural Convection in a Rectangular Cavity Filled With Low Prandtl Number Fluids.- Numerical Simulation of Oscillatory Convection in Low Prandtl Number Fluids Using AQUA Code.- Pressure Correction Splitting Methods for the Computation of Oscillatory Free Convection in Low Pr Fluids.- Influence of Thermocapillarity on the Oscillatory Convection in Low-Pr Fluids.- 2. Finite Volume Methods.- Numerical Simulation of Oscillatory Convection in Low-Pr Fluids.- An Implicit Pressure Velocity Algorithm Applied to Oscillatory Convection in Low Prandtl Fluid.- Oscillatory Natural Convection in a Long Horizontal Cavity.- Contribution of the Heat-Transfer Group at DELFT University.- Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids.- 3. Finite Element Methods.- Application of the N3S Finite Element Code to Simulation of Oscillatory Convection in Low Prandtl Fluids.- Two- and Three-Dimensional Finite Element Simulations of Buoyancy-Driven Convection in a Confined Pr=0.015 Liquid Layer.- Two and Three-Dimensional Study of Convection in Low Prandtl Number Fluids.- Numerical Simulation of Oscillatory Convection in Low Prandtl Fluids.- The Solution of the Boussinesq Equations by the Finite Element Method.- Numerical Simulation of Oscillatory Convection in Low Pr Fluids by Using the Galerkin Finite Element Method.- 4. Spectral Methods.- Oscillatory Convection in Low Prandtl Fluids: A Chebyshev Solution With Special Treatment of the Pressure field.- Contribution to the GAMM Workshop With a Pseudo-Spectral Chebyshev Algorithm on a Staggered Grid.- Spectral Calculations of Convection in Low-Pr Fluids.- Spectral Method for Two-Dimensional Time-Dependent Pr?0 Convection.- Steady-State Solution of a Convection Benchmark Problem by Multidomain Chebyshev Collocation.- 5. Synthesis.- Synthesis of Finite Difference Methods.- Synthesis of the Results With the Finite-Volume Method.- Analysis of Finite Element Results.- Analysis of Spectral Results.- General Synthesis of the Numerical Results.- 6. Stability Results.- Linear and Non-Linear Analysis of the Hadley Circulation.- A Bifurcation Analysis of Oscillatory Convection in Liquid Metals.- 7. Experimental Results.- A Laboratory Study of Oscillations in Differentially Heated Layers of Mercury.- Subharmonic Transitions in Convection in a Moderately Shallow Cavity.- Convection in a Shallow Cavity.- Conclusions.- List of Participants.- Support and Sponsoring Acknowledgements.