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.

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.

Numerical simulations of Rayleigh–Bénard convection for Prandtl numbers between 10−1 and 104 and Rayleigh numbers between 105 and 109

2010 ◽  
Vol 662 ◽  
pp. 409-446 ◽  
Author(s):  
G. SILANO ◽  
K. R. SREENIVASAN ◽  
R. VERZICCO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Numerical Simulations ◽  
Multiple Solutions ◽  
Large Scale ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Numbers ◽  
Rayleigh Benard

We summarize the results of an extensive campaign of direct numerical simulations of Rayleigh–Bénard convection at moderate and high Prandtl numbers (10−1 ≤ Pr ≤ 104) and moderate Rayleigh numbers (105 ≤ Ra ≤ 109). The computational domain is a cylindrical cell of aspect ratio Γ = 1/2, with the no-slip condition imposed on all boundaries. By scaling the numerical results, we find that the free-fall velocity should be multiplied by $1/\sqrt{{\it Pr}}$ in order to obtain a more appropriate representation of the large-scale velocity at high Pr. We investigate the Nusselt and the Reynolds number dependences on Ra and Pr, comparing the outcome with previous numerical and experimental results. Depending on Pr, we obtain different power laws of the Nusselt number with respect to Ra, ranging from Ra2/7 for Pr = 1 up to Ra0.31 for Pr = 103. The Nusselt number is independent of Pr. The Reynolds number scales as ${\it Re}\,{\sim}\,\sqrt{{\it Ra}}/{\it Pr}$, neglecting logarithmic corrections. We analyse the global and local features of viscous and thermal boundary layers and their scaling behaviours with respect to Ra and Pr, and with respect to the Reynolds and Péclet numbers. We find that the flow approaches a saturation state when Reynolds number decreases below the critical value, Res ≃ 40. The thermal-boundary-layer thickness increases slightly (instead of decreasing) when the Péclet number increases, because of the moderating influence of the viscous boundary layer. The simulated ranges of Ra and Pr contain steady, periodic and turbulent solutions. A rough estimate of the transition from the steady to the unsteady state is obtained by monitoring the time evolution of the system until it reaches stationary solutions. We find multiple solutions as long-term phenomena at Ra = 108 and Pr = 103, which, however, do not result in significantly different Nusselt numbers. One of these multiple solutions, even if stable over a long time interval, shows a break in the mid-plane symmetry of the temperature profile. We analyse the flow structures through the transitional phases by direct visualizations of the temperature and velocity fields. A wide variety of large-scale circulation and plume structures has been found. The single-roll circulation is characteristic only of the steady and periodic solutions. For other regimes at lower Pr, the mean flow generally consists of two opposite toroidal structures; at higher Pr, the flow is organized in the form of multi-jet structures, extending mostly in the vertical direction. At high Pr, plumes mainly detach from sheet-like structures. The signatures of different large-scale structures are generally well reflected in the data trends with respect to Ra, less in those with respect to Pr.

Doppler Profiler and Radar Observations of Boundary Layer Variability during the Landfall of Tropical Storm Gabrielle

2006 ◽  
Vol 63 (1) ◽  
pp. 234-251 ◽  
Author(s):  
Kevin R. Knupp ◽  
Justin Walters ◽  
Michael Biggerstaff
Keyword(s):  
Boundary Layer ◽  
Doppler Radar ◽  
Layer Structure ◽  
Flow Direction ◽  
Surface Flow ◽  
Tropical Storm ◽  
Mean Flow ◽  
Boundary Layer Structure ◽  
Stratiform Precipitation ◽  
Wind Profiles

Abstract Detailed observations of boundary layer structure were acquired on 14 September 2001, prior to and during the landfall of Tropical Storm Gabrielle. The Mobile Integrated Profiling System (MIPS) and the Shared Mobile Atmospheric Research and Teaching Radar (SMART-R) were collocated at the western Florida coastline near Venice, very close to the wind center at landfall. Prior to landfall, the boundary layer was rendered weakly stable by a long period of evaporational cooling and mesoscale downdrafts within extensive stratiform precipitation that started 18 h before landfall. The cool air mass was expansive, with an area within the 23°C surface isotherm of about 50 000 km2. East-northeasterly surface flow transported this cool air off the west coast of Florida, toward the convergent warm core of the Gabrielle, and promoted the development of shallow warm and cold fronts that were prominent during the landfall phase. Airflow properties of the boundary layer around the coastal zone are examined using the MIPS and SMART-R data. Wind profiles exhibited considerable temporal variability throughout the period of observations. The stable offshore flow within stratiform precipitation exhibited a modest jet that descended from about 600 to 300 m within the 20-km zone centered on the coastline. In contrast, the onshore flow on the western side of the wind center produced a more turbulent boundary layer that exhibited a well-defined top varying between 400 and 1000 m MSL. The horizontal variability of each boundary layer is examined using high-resolution Doppler radar scans at locations up to 15 km on either side of the coastline, along the mean flow direction of the boundary layer. These analyses reveal that transitions in boundary layer structure for both the stable and unstable regimes were most substantial within 5 km of the coastline.

scholarly journals The effect of uniform magnetic field on spatial-temporal evolution of thermocapillary convection with the silicon oil based ferrofluid

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 4159-4171
Author(s):  
Shuo Yang ◽  
Rui Ma ◽  
Qiaosheng Deng ◽  
Guofeng Wang ◽  
Yu Gao ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Transverse Magnetic Field ◽  
Liquid Bridge ◽  
Thermocapillary Convection ◽  
Surface Deformation ◽  
Axial Magnetic Field ◽  
Transverse Magnetic ◽  
Surface Flow ◽  
Silicon Oil

A uniform axial or transverse magnetic field is applied on the silicon oil based ferrofluid of high Prandtl number fluid (Pr ? 111.67), and the effect of magnetic field on the thermocapillary convection is investigated. It is shown that the location of vortex core of thermocapillary convection is mainly near the free surface of liquid bridge due to the inhibition of the axial magnetic field. A velocity stagnation region is formed inside the liquid bridge under the axial magnetic field (B = 0.3-0.5 T). The disturbance of bulk reflux and surface flow is suppressed by the increasing axial magnetic field. There is a dynamic response of free surface deformation to the axial magnetic field, and then the contact angle variation of the free surface at the hot corner is as following, ?hot, B = 0.5 T = 83.34? > ?hot, B = 0.3 T = 72.16? > > ?hot,B = 0.1 T = 54.21? > ?hot, B = 0 T = 43.33?. The results show that temperature distribution near the free surface is less and less affected by thermocapillary convection with the increasing magnetic field, and it presents a characteristic of heat-conduction. In addition, the transverse magnetic field does not realize the fundamental inhibition for thermocapillary convection, but it transfers the influence of thermocapillary convection to the free surface.

Free-convection effects in the boundary layer along a vertically stretching flat surface

1992 ◽  
Vol 70 (12) ◽  
pp. 1253-1260 ◽  
Author(s):  
John E. Daskalakis
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Convection ◽  
Skin Friction ◽  
Flat Surface ◽  
Relaxation Method ◽  
Boussinesq Approximation ◽  
Axial Coordinate ◽  
Prandtl Numbers ◽  
Energy Equations

We assess the effects of free convection on the boundary layer formed along a flat surface stretching vertically in a quiescent fluid. The flow is laminar and incompressible, the buoyancy forces conform to the Boussinesq approximation and the surface temperature is variable. The two-point boundary value problem of the coupled momentum and energy equations is solved using a simple and accurate relaxation method that provides the general nonsimilar solution to the flow. The effect of free-convection currents on velocity and temperature profiles, skin friction, and heat transfer is studied by varying the flow Grashof and Prandtl numbers. Zero shear stress and heat-transfer rate are predicted at some axial coordinate on a surface with decreasing wall temperature. Also the skin friction is markedly modified by the buoyancy while the heat transfer at the surface is correspondingly only moderately influenced.

Convective and Absolute Instabilities Induced by Viscous Dissipation in the Thermocapillary Convection with Through-Flow

2021 ◽  
Author(s):  
Eduardo V. M. dos Reis ◽  
Leonardo S. de B. Alves
Keyword(s):  
Viscous Dissipation ◽  
Shooting Method ◽  
Thermocapillary Convection ◽  
Thin Liquid Film ◽  
Internal Heating ◽  
Limited Region ◽  
Through Flow ◽  
Liquid Film Flow ◽  
Prandtl Numbers ◽  
Unstable Temperature

Abstract The mixed convection in a thin liquid film flow over a horizontal plate is investigated under finite Prandtl numbers. The gas-liquid interface is considered free, non-deformable and subject to surface tension gradients and convection, while gravity is assumed negligible. Therefore, Marangoni instead of buoyancy effects appear due to the unstable temperature stratification induced by the internal heating generated by viscous dissipation. A linear and modal stability analysis of this model is then performed to identify its convective/absolute nature. This is achieved by solving the resulting differential eigenvalue problem with a shooting method. Longitudinal rolls are the most unstable at the onset of instability for most parametric conditions. Otherwise, transverse rolls are the first to become convectively unstable. Finally, longitudinal rolls are absolutely stable. A transition to absolute instability occurs through transverse rolls, but only within a limited region in parametric space.

Research on Molten Pool Shape during Laser Rapid Forming through the Close-Range Continuous Photography

2005 ◽  
pp. 2615-2618
Author(s):  
Jing Chen ◽  
Haiou Yang ◽  
Meng Wang ◽  
Yun Peng Su ◽  
Wei Dong Huang
Keyword(s):  
Molten Pool ◽  
Pool Shape ◽  
Close Range ◽  
Laser Rapid Forming

Development of Wall and Free Plumes Above a Heated Vertical Plate

1978 ◽  
Vol 100 (2) ◽  
pp. 184-190 ◽  
Author(s):  
E. M. Sparrow ◽  
S. V. Patankar ◽  
R. M. Abdel-Wahed
Keyword(s):  
Boundary Layer ◽  
Vertical Plate ◽  
Leading Edge ◽  
Convection Boundary Layer ◽  
Heated Plate ◽  
Adiabatic Wall ◽  
Similarity Type ◽  
Vertical Extension ◽  
Prandtl Numbers ◽  
Wall Plume

An analysis has been made to determine the successive stages of development as the natural convection boundary layer on a steadily heated vertical plate evolves into a plume. Both the wall plume and the free plume are investigated. The wall plume develops along an adiabatic wall which is the vertical extension of the heated plate. The free plume is created as the boundary layer streams away from the upper edge of the plate. Since the plate is heated on only one of its faces, the free plume is initially unsymmetric. The development of these plumes does not admit similarity-type boundary layer solutions, and numerical techniques were, therefore, employed, with results being obtained for Prandtl numbers of 0.7, 2, 5, and 10. It was found that at sufficient downstream distances both plumes attain their respective fully developed behaviors (i.e., similar profiles at successive streamwise stations). For the wall plume, the development for all Prandtl numbers is completed at a position that is about five plate lengths above the leading edge of the heated plate. The development length for the free plume for Pr = 0.7 is about the same as that for the wall plume, but about 30 plate lengths are required for the development of the free plume when Pr = 10. The fully developed free plume is symmetric.

Surface Flow Patterns as Visualised by Dust Deposits on the Blades of a Fan

1963 ◽  
Vol 67 (633) ◽  
pp. 589-594 ◽  
Author(s):  
E. T. Hignett ◽  
M. M. Gibson
Keyword(s):  
Boundary Layer ◽  
Wind Tunnel ◽  
Leading Edge ◽  
Surface Flow ◽  
Scale Model ◽  
Flow Visualisation ◽  
Pressure Gradients ◽  
Suction Surface ◽  
Layer Flow ◽  
Dust Deposits

Investigations by one of the authors in connection with the design of a fan for a blower type of wind tunnel showed that regular and repeatable dust patterns occurred on the blades of a one-quarter scale model fan of 18 inches diameter. Dust was deposited on the fan blades along the leading-edge and on the suction surface over an area thought to be the turbulent region of the boundary layer. The introduction of isolated protuberances on the dust free area of a blade gave rise to turbulence wedges in which dust was also deposited and this was interpreted as confirmation of the coincidence of the dust deposits with regions of turbulent boundary-layer flow. These deposits showed the existence of a considerable extent of laminar flow on the suction surface of each blade close to the root, a region where high lift coefficients would be expected with associated adverse pressure gradients. Two-dimensional wind tunnel experiments were made to confirm the interpretation of the observed dust patterns by comparison with the smoke filament and volatile liquid methods of flow visualisation and these are reported in Reference 2.

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