Scale Analysis of Thermocapillary Weld Pool Shape With High Prandtl Number

2011 ◽  
Author(s):  
P. S. Wei ◽  
C. L. Lin ◽  
H. J. Liu
Keyword(s):  
Prandtl Number ◽  
Boundary Layers ◽  
Molten Pool ◽  
Surface Flow ◽  
Transport Processes ◽  
Surface Boundary ◽  
Scale Analysis ◽  
Melting Front ◽  
Pool Shape ◽  
High Prandtl Number

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from parametric scale analysis for the first time. Determination of the molten pool shape is crucial due to its close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative values, indicating an outward surface flow, whereas high Prandtl number represents the thermal boundary layer thickness to be less than that of momentum. Since Marangoni number is usually very high, the scaling of transport processes is divided into the hot, intermediate and cold corner regions on the flat free surface, boundary layers on the solid-liquid interface and ahead of the melting front. Coupling among distinct regions and thermal and momentum boundary layers, the results find that the width and depth of the pool can be determined as functions of Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The predictions agree with numerical computations and available experimental data.

Scaling Weld or Melt Pool Shape Affected by Thermocapillary Convection With High Prandtl Numbers

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
P. S. Wei ◽  
C. L. Lin ◽  
H. J. Liu ◽  
T. DebRoy
Keyword(s):  
Boundary Layer ◽  
Molten Pool ◽  
Thermocapillary Convection ◽  
Surface Flow ◽  
Beam Power ◽  
Melting Front ◽  
Pool Shape ◽  
Close Relationship ◽  
Prandtl Numbers ◽  
Maximum Temperatures

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to their close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative, indicating an outward surface flow, whereas high Prandtl number represents a reduced thickness of the thermal boundary layer compared to that of the momentum boundary layer. Since the Marangoni number is usually very high, the domain of scaling is divided into hot, intermediate and cold corner regions, boundary layers along the solid–liquid interface and ahead of the melting front. The results show that the width and depth of the pool, peak and secondary surface velocities, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables, or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The scaled results agree with numerical results and available experimental data.

Transient Thermocapillary Convection in a Molten or Weld Pool

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
P. S. Wei ◽  
C. L. Lin ◽  
H. J. Liu ◽  
C. N. Ting
Keyword(s):  
Prandtl Number ◽  
Molten Pool ◽  
Thermocapillary Convection ◽  
Welding Process ◽  
Melting Process ◽  
Scanning Speed ◽  
Surface Velocity ◽  
Vortex Cell ◽  
Incident Flux ◽  
High Prandtl Number

This study presents a numerical scenario for the effect of thermocapillary convection on the transient, two-dimensional molten pool shape during welding or melting. Tracing the melting process is necessary to achieve a better and more complete understanding of the physical mechanism of welding. This model is used to simulate a steady state, three-dimensional welding process, by introducing an incident flux with a Gaussian distribution with a time-dependent radius determined by scanning speed and distribution parameter. Aside from presenting the variations of peak surface velocities and temperature, and depth and width of the molten pool with time, the predicted results of this work show that surface velocity and temperature profiles for a high Prandtl number strongly deform in the course of melting. The velocity profile eventually exhibits two peaks, located near the edges of the incident flux and the pool, respectively. Conversely, only one peak velocity occurs near the pool edge for a small Prandtl number. In all cases, surface temperature can ultimately be divided into hot, intermediate, and cold regions. The pool becomes deep due to an induced secondary vortex cell near the bottom of the pool for a small Prandtl number. For a high Prandtl number, the pool edge is thin and shallow, as a result of penetration into the solid near the top surface. The predicted results agree with those obtained using a commercial computer code.

Theoretical Analysis of Thermocapillary Flow in Cylindrical Columns of High Prandtl Number Fluids

1998 ◽  
Vol 120 (3) ◽  
pp. 758-764 ◽  
Author(s):  
Y. Kamotani ◽  
S. Ostrach
Keyword(s):  
Prandtl Number ◽  
Driving Force ◽  
Deformation Parameter ◽  
Scaling Laws ◽  
Physical Mechanism ◽  
Surface Deformation ◽  
Surface Flow ◽  
Scaling Analysis ◽  
Thermocapillary Flows ◽  
High Prandtl Number

Steady and oscillatory thermocapillary flows of high Prandtl number fluids in the half-zone configuration are analyzed theoretically. Scaling analysis is performed to determine the velocity and length scales of the basic steady flow. The predicted scaling laws agree well with the numerically computed results. The physical mechanism of oscillations is then discussed. It is shown that the deformation of free surface plays an important role for the onset of oscillations in that it alters the main thermocapillary driving force of the flow by changing the temperature field near the hot-corner region. This phenomenon triggers oscillation cycles in which the surface flow undergoes active and slow periods. Based on that concept a surface deformation parameter is derived by scaling analysis. The deformation parameter correlates available data for the onset of oscillations well.

scholarly journals Boundary layers in turbulent vertical convection at high Prandtl number

2021 ◽  
Vol 930 ◽  
Author(s):  
Christopher J. Howland ◽  
Chong Shen Ng ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Environmental Flows ◽  
Three Dimensional ◽  
Vertical Channel ◽  
Vertical Surface ◽  
Wide Range ◽  
High Prandtl Number ◽  
Prandtl Numbers

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers ${Pr}$ . This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $\mbox {{Ra}}$ and Prandtl number ${Pr}$ . For the considered parameter range $1\leq {Pr} \leq 100$ , $10^{6} \leq \mbox {{Ra}} \leq 10^{9}$ , we find the flow to be consistent with a ‘buoyancy-controlled’ regime where the heat flux is independent of the wall separation. For given ${Pr}$ , the heat flux is found to scale linearly with the friction velocity $V_\ast$ . Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice–ocean interfaces.

Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions

2004 ◽  
Vol 16 (5) ◽  
pp. 1746-1757 ◽  
Author(s):  
D. E. Melnikov ◽  
V. M. Shevtsova ◽  
J. C. Legros
Keyword(s):  
Prandtl Number ◽  
Liquid Bridge ◽  
High Prandtl Number
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