Bok-Cheol Sim

Oscillatory thermocapillary convection in open cylindrical annuli. Part 2. Simulations

Oscillatory thermocapillary convection in open cylindrical annuli heated from the outer wall is investigated numerically. Results at fixed inner/outer radius ratio of 0.5, aspect ratios (Ar )o f 1, 2.5, 3.33, and 8 ,zero Biot number, and a Prandtl number of 6.84 are obtained and compared with experiments (Part 1 of this paper). Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re). Transition to oscillatory states occurs at critical values of Re which depend on Ar. With Ar =1 ,2 .5 and 3.33, we observe 5, 9 and 12 azimuthal wavetrains, respectively, travelling clockwise at the free surface near the critical Re .W ith Ar =8 , there are 20 standing waves near the critical Re .E xperimental results in Part 1 support this finding. A multi-roll structure appears beyond the critical Re in shallow liquid layers with Ar =3 .33 and 8. The critical Re and frequency are in qualitative but not in quantitative agreement with the experimental ones. Either heat loss from the free surface or heating from the surroundings to the free surface stabilizes the flow, and the critical Re increases with increasing Biot number while the critical period goes down. The numerical results agree better with the experimental ones if the free surface is assumed to be heated as shown in Part 1. We have also computed supercritical time-dependent states and find that while the non-dimensional frequency increases with increasing Re near the critical region, it approaches an asymptote at super- critical Re.

STUDY OF THERMAL BEHAVIOR AND FLUID FLOW DURING LASER SURFACE HEATING OF ALLOYS

Abstract Transient and steady state laser melting problems are numerically simulated for steel and Al-4.5% Cu. Enthalpy and apparent capacity methods are used to solve the energy equation, and the momentum equations are solved in the liquid domain and mushy zone with the SOLA-VOF algorithm. Using a laser with a top-hat profile, a wide range of studies are performed by varying the beam power density and the beam radius. The streamline plots show that the flow pattern is dependent on the strength of the rotating cell along with heat flux. It is found that the shape of the pool, the surface velocity, and the surface temperature are quite different from those without convection in the mushy zone. Convection in the mushy zone plays an important role in heat transfer and fluid flow during laser melting.

Thermocapillary convection in liquid bridges with undeformable curved surfaces

Thermocapillary convection in differentially heated cylindrical liquid bridges is investigated by two- and threedimensional numerical simulations. The nondeformable free surface is either e at or curved as determined by the e uid volume and the Young ‐Laplace equation. With Prandtl numbers of 1 and 4 and a e at surface, our computed results for onset of oscillations are in good agreement with linear theory. Convection is steady and axisymmetric at sufe ciently low values of Reynolds number with either e at or curved interfaces. Only steady convection is possibleat all Reynoldsnumbersconsidered in strictly axisymmetriccomputations. Transition to oscillatory threedimensional motions occurs as the Reynolds number increases beyond a critical value, dependent on the Prandtl number and liquid volume. Rotating waves with wave numbers of 1 or 2 are observed. The critical wave number depends on the Biot number. Heat loss from the free surface stabilizes the e ow, and the critical Reynolds number increases with increasing Biot number. With nonzero Biot number, two different branches can exist in the stability diagram. The numerical results are in reasonable agreement with experiments.

Thermocapillary Convection in Cylindrical Geometries

Thermocapillary convection in two types of cylindrical geometries is studied by three-dimensional numerical simulations: an open cylindrical annulus heated from the outside wall and a liquid bridge. The non-deformable free surfaces are either flat or curved as determined by the fluid volume, V, and the Young-Laplace equation. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number, Re, with either flat or curved surfaces. For the parameter ranges considered, it is found that only steady convection is possible at any Re in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on the aspect ratio, the Prandtl number, and V. Good agreement with available experiments is achieved in all cases.

Oscillatory thermocapillary-Coriolis convection in open cylindrical annuli

Oscillatory thermocapillary convection in open cylindrical annuli heated from the inside wall is investigated numerically. Results for aspect ratio of 1 and Prandtl number of 30 are obtained to compare the simulations with available experiments. The influence of space craft or orbital rotation on the critical Reynolds number and pattern of convection through the Coriolis force, as measured by a vector Taylor number of magnitude Ta, is investigated. The flow is steady and axisymmetric at sufficiently low values of Re. In the absence of rotation, we observe a twolobed, isotherm pattern travelling clockwise at the free surface near Recr. Thus the frequency of temperature oscillations is twice that of the isotherm rotation. At supercritical jRe, a two-lobed pulsating isotherm pattern is observed instead. Isotherm patterns on the free surface are in good agreement with experimental results. With Ta less than 1, which is relevant to space applications, the effect of rotation on Recr and flow field is small. Recr is found to decrease with increasing Ta. When the rotation vector is orthogonal to the cylinder axis, the isotherms take a three-lobed pulsating pattern. When the rotation vector is parallel to the cylinder axis, a two-lobed rotating isotherm pattern is observed. It is found that rotation has a stronger influence on the flow field when parallel to the cylinder axis.