Study on Flight Dynamics and Heat Transfer Solidification of Metal Droplets during Centrifugal Spray Deposition Forming Process
Abstract
:1. Introduction
2. Model Establishment
2.1. Introduction of Physical Model
- (1)
- Due to the small diameter of the droplet, the droplet is regarded as a uniform sphere under surface tension.
- (2)
- Due to the short flight time, as a rough estimate, the specific heat of the droplet at room temperature is taken as the research parameter.
- (3)
- The relationship between the Weber number and droplet fragmentation is not considered. Droplets are granulated at the edge of the centrifugal disc.
- (4)
- The velocity of the ambient gas is zero.
- (5)
- The droplets do not collide with each other in flight.
2.2. Kinetic Model
2.3. Heat Transfer Solidification Model
- (1)
- Liquid-phase cooling
- (2)
- Nucleation and recalescence
- (3)
- Segregation solidification
- (4)
- Eutectic transformation
- (5)
- Solid-phase cooling
3. Numerical Experiment
4. Results and Discussion
4.1. The Relationship between Rotational Speed and Droplet Diameter
4.2. Droplet Flight Trajectory
4.3. The Relationship between Droplet Flight Time and Motion Parameters
4.4. Relationship between Droplet Flight Time and Convective Heat Transfer Coefficient
4.5. The Relationship between Flight Time and Heat Transfer Solidification
4.6. The Relationship between Droplet Solidification and Flight Time at Different Speeds
4.7. Effect of Superheat on Heat Transfer Solidification
4.8. The Relationship between Droplet Solidification and Flight Time under Different Superheats
5. Conclusions
- The droplet diameter decreases with an increase in rotational speed. When the rotational speed is lower than a certain value, the droplet diameter is greatly affected by the rotational speed. When the rotational speed is higher than this value, the influence of rotational speed on the droplet diameter is weakened.
- The flight trajectory of the droplet is parabolic; the flight displacement, initial velocity, ambient gas resistance and convective heat transfer coefficient increase with an increase in speed, and the vertical displacement of the droplet is not influenced by the movement of the substrate during the forming process.
- In the forming process, the superheat has no obvious effect on the cooling and solidification process of the droplet, which is mainly affected by the speed of the centrifugal disc, and the time required for cooling and solidification decreases with the increase in speed.
- Under the same superheat, the speed of the centrifugal disc is negatively correlated with the time required for droplet solidification, where the droplet starts to solidify in a linear relationship with the speed, and the time required for complete solidification is a quadratic function of the speed.
- In the case of the same centrifugal disc speed, the superheat is positively correlated with the time required for the droplet to solidify, where the time required for the droplet to start solidifying and complete solidification is linear with the temperature.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
initial velocity of the droplet (m/s) | |
tangential velocity of the droplet (m/s) | |
average radial velocity of droplets (m/s) | |
rotation speed of the centrifugal disc (r/min) | |
diameter of the centrifugal disc (m) | |
metal density (kg/m3) | |
flow rate of the liquid metal (m3/s) | |
viscosity of the liquid metal (Pa·s) | |
diameter of the droplet (μm) | |
surface tension of the metal (N/m) | |
gravity of the droplet (N) | |
resistance of the droplets (N) | |
mass of the droplets (kg) | |
gas density (kg/m3) | |
drag coefficient (-) | |
velocity of the droplet (m·s−1) | |
velocity projection of droplet in the x direction (m·s−1) | |
velocity projection of the droplet in the y direction (m·s−1) | |
velocity of the ambient gas (m·s−1) | |
velocity projection of the ambient gas in the x direction (m·s−1) | |
velocity projection of the ambient gas in the y direction (m·s−1) | |
convective heat transfer coefficient (W·m−2·K−1) | |
thermal conductivity of gas (W·m−1·K−1) | |
specific heat capacity of the metal (J·kg−1·K−1) | |
specific heat capacity of the gas (J·kg−1·K−1) | |
angle between the velocity and horizontal direction (°) | |
temperature of the metal droplet (K) | |
temperature of the ambient gas (K) | |
Stefan–Boltzmann constant (W·m−2·K−4) | |
latent heat of metal melting (J·kg−1) | |
solid–liquid interface energy (J·m−2) | |
liquidus temperature of the metal (K) | |
wetting angle (°) | |
droplet cooling rate (K·s−1) | |
nucleation temperature (K) | |
droplet volume (m3) | |
recalescence temperature (K) | |
melting point of the pure alloy solvent (K) | |
eutectic temperature (K) | |
interfacial adhesion coefficient (m·s−1·K−1) | |
constant value (-) | |
Reynolds number (-) | |
melting point of the pure alloy solvent (-) | |
Prandtl number (-) | |
maximum solid fraction (-) | |
correlation coefficient (-) | |
solid fraction (-) | |
Boltzmann constant (-) | |
emissivity of metal droplets (-) |
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Li, P.; Wei, S.; Lei, X.; Yang, L.; Sun, B. Study on Flight Dynamics and Heat Transfer Solidification of Metal Droplets during Centrifugal Spray Deposition Forming Process. Metals 2023, 13, 1446. https://doi.org/10.3390/met13081446
Li P, Wei S, Lei X, Yang L, Sun B. Study on Flight Dynamics and Heat Transfer Solidification of Metal Droplets during Centrifugal Spray Deposition Forming Process. Metals. 2023; 13(8):1446. https://doi.org/10.3390/met13081446
Chicago/Turabian StyleLi, Peng, Shizhong Wei, Xianqing Lei, Lu Yang, and Bo Sun. 2023. "Study on Flight Dynamics and Heat Transfer Solidification of Metal Droplets during Centrifugal Spray Deposition Forming Process" Metals 13, no. 8: 1446. https://doi.org/10.3390/met13081446