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ABSTRACT
The present work deals with the development of a compressible phase-change solver and implementation toward the numerical modeling and investigation of a part-unit cell of a pulsating heat pipe (PHP). The fundamental understanding of the working of the part-unit cell is imperative in the development of a complete Computational Fluid Dynamics (CFD) model of a PHP. The compressible model developed in the present work is based on the Volume-of-Fluid solver of the open source CFD software, OpenFOAM, in which the contour-based interface reconstruction algorithm and the contact-line evaporation model have been incorporated. Owing to the lack of a single standard benchmark validation case for a compressible phase-change solver, a huge emphasis in the present work is laid on the solver development and validation, the latter part of which is conducted in stages. Furthermore, simulations for the formation of a Taylor-Bubble through a constrained bubble growth are performed and the fallacy of an incompressible solver is shown distinctly. The validated solver is used to model a part-unit cell of a PHP and a parametric study is performed on the part-unit cell. The effect of variation of evaporator length, evaporator superheat, and liquid fill ratio on the performance of the PHP is discussed.
Nomenclature
| a | = | major-axis length of ellipse, m |
| b | = | minor-axis length of ellipse, m |
| c | = | specific heat capacity, J/(kg K) |
| D | = | diameter, m |
| F | = | volume fraction of the liquid phase, - |
| Fs | = | surface tension force, N |
| f1 | = | objective function 1, - |
| g | = | acceleration due to gravity, m/s2 |
| = | phase-change mass flux, kg/(m2 s) | |
| k | = | thermal conductivity, W/(m K) |
| L | = | length, m |
| p | = | pressure, Pa |
| R | = | heat resistance, K m2/W |
| = | radius, m | |
| s | = | second, s |
| T | = | temperature, K |
| t | = | time, s |
| U | = | velocity vector, m/s |
| u | = | magnitude of velocity, m/s |
| V | = | volume, m3 |
| Δh | = | change in enthalpy, J/kg |
| Δt | = | time step, s |
| Δτ | = | artificial time step, s |
| Δx | = | length interval, m |
| ρ | = | density, kg/m3 |
| = | sharp mass source term field, kg/(m3s) | |
| = | smeared mass source term field, kg/(m3s) | |
| γ | = | polytropic constant, - |
| μ | = | dynamic viscosity, Pa s |
| σ | = | surface tension, N/m |
| κ | = | interface curvature, 1/m |
| ϕ | = | any arbitrary vector field, - |
| Subscripts | = | |
| A | = | adiabatic section |
| E | = | evaporator |
| F | = | liquid fill region |
| I | = | component/phase |
| L | = | liquid |
| V | = | vapor |
| Int | = | interface |
| Lv | = | difference of the parameter between liquid and vapor phases |
| Max | = | maximum |
| Sat | = | saturation |
| ∞ | = | infinity |
Nomenclature
| a | = | major-axis length of ellipse, m |
| b | = | minor-axis length of ellipse, m |
| c | = | specific heat capacity, J/(kg K) |
| D | = | diameter, m |
| F | = | volume fraction of the liquid phase, - |
| Fs | = | surface tension force, N |
| f1 | = | objective function 1, - |
| g | = | acceleration due to gravity, m/s2 |
| = | phase-change mass flux, kg/(m2 s) | |
| k | = | thermal conductivity, W/(m K) |
| L | = | length, m |
| p | = | pressure, Pa |
| R | = | heat resistance, K m2/W |
| = | radius, m | |
| s | = | second, s |
| T | = | temperature, K |
| t | = | time, s |
| U | = | velocity vector, m/s |
| u | = | magnitude of velocity, m/s |
| V | = | volume, m3 |
| Δh | = | change in enthalpy, J/kg |
| Δt | = | time step, s |
| Δτ | = | artificial time step, s |
| Δx | = | length interval, m |
| ρ | = | density, kg/m3 |
| = | sharp mass source term field, kg/(m3s) | |
| = | smeared mass source term field, kg/(m3s) | |
| γ | = | polytropic constant, - |
| μ | = | dynamic viscosity, Pa s |
| σ | = | surface tension, N/m |
| κ | = | interface curvature, 1/m |
| ϕ | = | any arbitrary vector field, - |
| Subscripts | = | |
| A | = | adiabatic section |
| E | = | evaporator |
| F | = | liquid fill region |
| I | = | component/phase |
| L | = | liquid |
| V | = | vapor |
| Int | = | interface |
| Lv | = | difference of the parameter between liquid and vapor phases |
| Max | = | maximum |
| Sat | = | saturation |
| ∞ | = | infinity |
Acknowledgments
The authors would like to acknowledge the technical support provided by Prof. Dr.-Ing. Peter Stephan and Dr.-Ing. Stefan Batzdorf of Technische Universitat Darmstadt toward successful completion of the present work.