Modeling evaporation in the rarefied gas regime by using macroscopic transport equations

dc.contributor.authorBeckmann, Alexander Felix
dc.contributor.supervisorStruchtrup, Henning
dc.date.accessioned2018-04-19T20:01:38Z
dc.date.available2018-04-19T20:01:38Z
dc.date.copyright2018en_US
dc.date.issued2018-04-19
dc.degree.departmentDepartment of Mechanical Engineeringen_US
dc.degree.levelMaster of Applied Science M.A.Sc.en_US
dc.description.abstractDue to failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the direct simulation Monte Carlo method (DSMC) to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. To gain a better understanding of evaporation physics, a non-steady simulation for slow evaporation in a microscopic system, based on the Navier-Stokes-Fourier equations, is conducted. The one-dimensional problem consists of a liquid and vapor layer (both pure water) with respective heights of 0.1mm and a corresponding Knudsen number of Kn=0.01, where vapor is pumped out. The simulation allows for calculation of the evaporation rate within both the transient process and in steady state. The main contribution of this work is the derivation of new evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with proven applicability in the transition regime. The approach for deriving the boundary conditions is based on an entropy balance, which is integrated around the liquid-vapor interface. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier-Stokes-Fourier solutions for two steady-state, one-dimensional problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement to DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to Navier-Stokes-Fourier (NSF) solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed which suggest continuation of this work.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/9238
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectEvaporationen_US
dc.subjectModelingen_US
dc.subjectMechanical Engineeringen_US
dc.subjectPartial Differential Equationsen_US
dc.subjectMacroscopic Transport Equationsen_US
dc.subjectBoltzmann Equationen_US
dc.subjectMoment Methodsen_US
dc.subjectOnsager Theoryen_US
dc.subjectBoundary Conditionsen_US
dc.subjectNumericsen_US
dc.subjectNumerical Simulationen_US
dc.subjectNon-steady Simulationen_US
dc.subjectNavier Stokesen_US
dc.subjectEvaporation of Wateren_US
dc.subjectMatlaben_US
dc.subjectTemperature Jumpen_US
dc.subjectApplied Mathematicsen_US
dc.subjectDSMCen_US
dc.subjectKnudsen Layeren_US
dc.subjectRarefied Gas Dynamicsen_US
dc.subjectFluid Mechanicsen_US
dc.subjectThermodynamicsen_US
dc.subjectHeat and Mass Transporten_US
dc.subjectNon-Equilibrium Thermodynamicsen_US
dc.titleModeling evaporation in the rarefied gas regime by using macroscopic transport equationsen_US
dc.typeThesisen_US

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