![Sample our Engineering & Technology journals, sign in here to start your access, latest two full volumes FREE to you for 14 days]({"type":"image" , "src" : "/sda/5933/TOC-Subject-Sample-2021-Engineering-Tech.jpg"})
ABSTRACT
To simulate bubble dynamic behaviors under an electric field conveniently and accurately, a volume-of-fluid, level set, and smoothed physical parameter (VOF+LS+SPP) method based on FLUENT is first proposed. Compared with the VOF and VOF+LS methods based on FLUENT, the VOF+LS+SPP method has very high precision and the maximum deviation is only 7%. In addition, its simulation results are superior to those results obtained by the front tracking, LS and phase field methods in the literature and almost the same with the data acquired by the VOSET method. Finally, the proposed method is used to investigate the law and mechanism of bubble deformation with different permittivity ratios.
Nomenclature
| B | = | maximum width of the bubble, m |
| Boe | = | electric Bond number |
| Co | = | Courant number |
| d | = | distance to the interface, m |
| D | = | deformation rate |
| E | = | electric field intensity, N · C−1 |
| Fσ | = | surface tension force, N · m−3 |
| Fe | = | electric force, N · m−3 |
| g | = | gravitational acceleration, m · s−2 |
| H (φ) | = | Heaviside function |
| L | = | maximum length of the bubble, m |
| p | = | pressure, Pa |
| r | = | position vector, m |
| R | = | radius, m |
| t | = | time, s |
| v | = | velocity vector, m · s−1 |
| α | = | volume fraction |
| ϕ | = | electric potential, V |
| δ(φ) | = | Dirac distribution function, m−1 |
| ε | = | relative permittivity |
| ε0 | = | permittivity of vacuum, F · m−1 |
| κ | = | interface curvature, m−1 |
| λε | = | permittivity ratio |
| λρ | = | density ratio |
| λμ | = | viscosity ratio |
| μ | = | dynamic viscosity, Pa · s |
| ρ | = | density, kg · m−3 |
| σ | = | surface tension coefficient, N · m−1 |
| φ | = | level set function, m |
| Δ | = | grid size, m |
| Subscript | = | |
| b | = | bottom boundary |
| g | = | gas phase |
| l | = | liquid phase |
| t | = | top boundary |
Nomenclature
| B | = | maximum width of the bubble, m |
| Boe | = | electric Bond number |
| Co | = | Courant number |
| d | = | distance to the interface, m |
| D | = | deformation rate |
| E | = | electric field intensity, N · C−1 |
| Fσ | = | surface tension force, N · m−3 |
| Fe | = | electric force, N · m−3 |
| g | = | gravitational acceleration, m · s−2 |
| H (φ) | = | Heaviside function |
| L | = | maximum length of the bubble, m |
| p | = | pressure, Pa |
| r | = | position vector, m |
| R | = | radius, m |
| t | = | time, s |
| v | = | velocity vector, m · s−1 |
| α | = | volume fraction |
| ϕ | = | electric potential, V |
| δ(φ) | = | Dirac distribution function, m−1 |
| ε | = | relative permittivity |
| ε0 | = | permittivity of vacuum, F · m−1 |
| κ | = | interface curvature, m−1 |
| λε | = | permittivity ratio |
| λρ | = | density ratio |
| λμ | = | viscosity ratio |
| μ | = | dynamic viscosity, Pa · s |
| ρ | = | density, kg · m−3 |
| σ | = | surface tension coefficient, N · m−1 |
| φ | = | level set function, m |
| Δ | = | grid size, m |
| Subscript | = | |
| b | = | bottom boundary |
| g | = | gas phase |
| l | = | liquid phase |
| t | = | top boundary |