Efficient solution methods for N-component condensation


Putten, Dennis Sebastian van (2011) Efficient solution methods for N-component condensation. thesis.

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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
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
Item Type:Thesis
Engineering Technology (CTW)
Research Group:
Link to this item:http://purl.utwente.nl/publications/78258
Official URL:https://doi.org/10.3990/1.9789036532655
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