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    Rayleigh-Benard convection in limited domains: Part 2 - Transition to chaos

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    Transitions to chaos in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, have been examined by direct numerical simulation as the Rayleigh number is varied. Two different problems have been considered: the first is related to a domain 3.5 X 1 X 2.1 filled with water at 70°C (Prandtl number 2.5); the second is related to a domain 2.4 X 1 X 1.2 filled with water at 33°C (Prandtl number 5). The Rayleigh number has been varied from 45,000 up to 300,000. Three different bifurcation sequences have been detected, but only two individual mechanisms for the transition to the nonperiodic motion have been identified: the subharmonic cascade and the quasi-periodicity with three incommensurate frequencies. Effects of different regimes and flow structures on heat transfer have been discussed

    Rayleigh-Benard convection in limited domains: Part 1 - Oscillatory flow

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    Transition from the steady state to an oscillatory regime in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, has been examined by direct numerical simulation. Two different physical problems have been considered: the first is related to a domain 3.5 X 1 X 2.1 filled with water at 70° C (Prandtl number 2.5); the second considers a domain 2.4 X1 X1.2 filled with water at 33°C (Prandtl number 5). The Rayleigh number has been varied from 20,000 to 80,000. A new procedure based on a statistical approach for ev aluation of the critical Rayleigh number for transition from steady state to oscillatory flow Ra has been introduced in order to reduce numerical errors and estimate the error bars. A systematic study for the determination of Ra has been conducted as a function of the geometries considered and the different flow structures observed

    True transient vorticity-velocity method using preconditioned Bi-CGSTAB

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    A fully implicit method for the solution of time-dependent Navier-Stokes equations written in terms of vorticity and velocity is presented. The field equations are discretized using second-order finite-difference technique and cast into a large sparse linear system. The numerical solution of the algebraic problem generated is obtained using a preconditioned Bi-CGSTAB method. The numerical method, developed mainly for the solution of true transient problems, also shows good stability behavior at high Rayleigh numbers. Sample results are presented for the window cavity at 10(4) less than or equal to Ra less than or equal to 10(8) and art oscillatory flow in liquid metal

    A partition method for the solution of coupled liquid-structure interaction problem

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    A numerical code is presented to study the motion of an incompressible inviscid flow in a deformable tank. It is based on a method belonging to the partition treatment class, as the fluid and structural fields are solved by coupling two distinct models. The fluid field is modeled by the Laplace equation and numerically solved by a Finite Volume technique. The computational grid is updated at each time step to take into account the movements of the free surface and the deformations of the vertical walls. An unsteady finite element formulation is used for modeling the tank on a grid discretized by triangular elements and linear shape functions. Results are presented for two different cases: a flow induced by a perturbation on the free surface in a tank motionless; a flow in a tank forced to oscillate periodically in the horizontal direction
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