Efficient Solution Methods for N-component Condensation

D.S. van Putten

Research output: ThesisPhD Thesis - Research external, graduation UT

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Abstract

This thesis describes efficient solution methods developed for N-component condensation processes. These methods are aimed at either the reduction of the numerical effort required for solving the equations describing the condensation process or the simplification of the physical description. The models and corresponding algorithms differ in their ability to describe the condensation phenomenon and the required computing times. The equilibrium thermodynamics of real gases is presented and a robust numerical procedure is constructed based on Newton-Raphson iteration. The Jacobian of the system of equations has been determined analytically. The initialization scheme for the iterative procedure for these equilibrium problems uses a pressure-extrapolation scheme. Results are given for a three-phase ternary real-gas mixture. A multigrid method has been developed to enhance the efficiency of implicit numerical methods for solving the N-component Becker-Döring (NBD) equations. The geometrical multigrid method for arbitrary number of grid levels is presented. The multigrid algorithm solves the full set of NBD equations 10 times faster than conventional iterative schemes. The method is restricted to the regime of small cluster sizes due to limited available computational resources. However, the time dependent solution of the NBD equations does provide useful insight in the physics of the initial stages of the nucleation process. For single component condensation the Stationary Diffusion Flux (SDF) model has been derived which is valid in the entire cluster size space. The diffusion flux in the Fokker-Planck equation for unsteady condensation contains an unknown distribution function. This distribution function is approximated by a closed-form expression based on the cluster size distribution function for steady condensation. The resulting Stationary Diffusion Flux model is valid for all cluster sizes, computationally efficient and applicable to various types of cluster formation processes. In the regime of supercritical cluster sizes the diffusion flux is given by an analytical expression. The Phase Path Analysis (PPA) algorithm has been extended to N-component mixtures. For this method the N-component General Dynamic Equation (NGDE) is constructed. This model introduces clusters at a source point in the N-component cluster size space. The model allows for a very fast solution of the approximate Ncomponent cluster size distribution. For validation of the method a nucleation pulse test case involving a binary mixture has been used. Comparison of the numerical results of the NBD equations and those from the NGDE shows excellent agreement for the cluster size, cluster composition and the integral properties of the cluster size distribution. The PPA algorithm applied to the NGDE reduces the computational effort by a factor 105 compared to the effort required for solving the full set of NBD equations.
Original languageUndefined
Awarding Institution
  • University of Twente
Supervisors/Advisors
  • Hoeijmakers, Hendrik Willem Marie, Supervisor
  • Hagmeijer, Rob , Advisor
Award date14 Oct 2011
Place of PublicationEnschede, the Netherlands
Publisher
Print ISBNs978-90-365-3265-5
DOIs
Publication statusPublished - 14 Oct 2011

Keywords

  • IR-78258
  • METIS-278675

Cite this

van Putten, D. S. (2011). Efficient Solution Methods for N-component Condensation. Enschede, the Netherlands: University of Twente. https://doi.org/10.3990/1.9789036532655