Modeling two-phase flow with stochastic coalescence/breakage model

Ki Sun Park, Purdue University

Abstract

Gas-particle flows were modeled to account for coalescence and breakup of liquid metal oxide droplets dispersed within the gas phase. The one-way coupled population balance equation (PBE) describing the evolution of number concentration due to particle-particle interactions and aerodynamic forces was solved using the direct quadrature method of moments (DQMOM) along with Reynolds averaged Navier-Stokes equation (RANS). The turbulent feature was assessed by Wilcox's k-ω equations. The fast Eulerian method was used to assess the slip velocity of the dispersed phase which holds a significant inertia. Orthokinetic collision was considered under laminar and turbulent flow where the radial component of relative velocity between two colliding particles is a source of collision. Hydrodynamic and aerodynamic collision frequency functions for turbulent flow were obtained from prior studies and modified to take into account inertia of particles. For a general laminar movement of flow, hydrodynamic and aerodynamic collision frequency functions were derived for spherical particles. The laminar hydrodynamic collision frequency kernel was derived for application to high speed (high Reynolds number) flows. The inclusion of influence of multidimensional and mean flow behavior permits application to flows in which shear layers are present and high Reynolds number flow which necessitates inclusion of compressibility effects. The new model agrees well with prior incompressible formulations. Results indicate that the compressible part of new shearing collision frequency has a significant effect on the collision kernel due to the contraction and dilatation effects of a fluid element. The model was validated using historical data from particle collection experiments (and a correlation based on these data) in solid rocket motors. Considering the error bounds of correlation, the predicted mass mean diameter was in agreement with the measurements/correlation. Further validations performed to assess effects of chamber pressure, particle mass concentration, and nozzle scale showed a good agreement with empirical correlation and mass mean diameter variation trends were very similar to the behavior of the empirical correlation. Parametric studies were performed on typical converging-diverging nozzles attached to rocket motors. The results of series of computations were presented to assess the effects of mean flow state (laminar vs turbulent), chamber pressure, inlet particle concentration and size, nozzle scale, contraction angle, divergence angle, and shock wave on resulting particle size evolution for nozzle simulations. The comparisons of laminar and turbulent effects on coalescence/breakup process showed that both effects are significant for these supersonic flows. As chamber pressure, inlet particle concentration, inlet particle size, and nozzle throat diameter increased, the resultant particle size also increased. The effect of nozzle geometries which is assessed based on contraction and divergence angle of nozzle wall showed that the particle size increases as the angles increases. Finally, it was found that there are periodic breakup-coalescence structures along the centerline as particles pass through compression/shock and expansion waves in the plume. A series of numerical simulations were also performed to study the gas flow and particle agglomeration in a solid rocket motor with a radial slot. The D43 distribution over the entire domain showed an increase along the axial direction and a thin band of large agglomerates were created downstream of the slot exit along the axial direction. Parametric studies were performed with respect to Mach number, mass flow ratio, step heights of downstream propellant, and inlet mass fraction of particle phase. Studies reveal that a stable recirculation zone (vena-contracta) is created at very high mass flow ratios when Mach number is small and at lower mass flow ratios when Mach number is relatively large. The investigation of the effects of Mach number and mass flow ratio on agglomeration showed that the maximum averaged D43 is obtained at mid mass flow ratio with a constant Mach number at slot outlet and just after the vena contracta. All of above observations lead to conclude that the presence of large amount of metal oxide particles in rocket motors results in strong agglomeration of particles due to the shearing motion of flow and a significant inertia of particles and will have a significant influence on rocket performance.

Degree

Ph.D.

Advisors

Heister, Purdue University.

Subject Area

Aerospace engineering|Nanotechnology

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