Efficient solution methods for Ncomponent condensation
Putten, Dennis Sebastian van (2011) Efficient solution methods for Ncomponent condensation. thesis.

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Abstract:  This thesis describes efficient solution methods developed for Ncomponent 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 NewtonRaphson 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 pressureextrapolation scheme. Results are given for a threephase ternary realgas mixture. A multigrid method has been developed to enhance the efficiency of implicit numerical methods for solving the Ncomponent BeckerDöring (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 FokkerPlanck equation for unsteady condensation contains an unknown distribution function. This distribution function is approximated by a closedform 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 Ncomponent mixtures. For this method the Ncomponent General Dynamic Equation (NGDE) is constructed. This model introduces clusters at a source point in the Ncomponent 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. 
Item Type:  Thesis 
Faculty:  Engineering Technology (CTW) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/78258 
Official URL:  http://dx.doi.org/10.3990/1.9789036532655 
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