Development of Constrained Equilibrium Codes and Their Applications in Nonequilibrium Thermodynamics

Abstract

Two constrained equilibrium codes, GNASA and GSTANJAN, have been developed which determine the composition of constrained equilibrium gas mixture. These codes use NASA and STANJAN equilibrium programs as the basis for generalized equilibrium routines. Gas mixture composition is determined by minimizing Gibbs free energy of the mixture subject to any specified constraints in addition to elemental constraints. Performances of these two codes have been compared to each other, and it has been found that GSTANJAN converges over a wider range of constraints, while the convergence of GNASA is limited. These codes have been applied in nonequilibrium evolution process of hydrogen-oxygen mixture. The nonequilibrium process has been modeled by using only two constraints in addition to elemental constraints. The results are in good agreement with detailed kinetic solution.

Quasi-equilibrium grid algorithm: Geometric construction for model reduction

“…In case 2, the parameter set is: reviewed by Keck (1990) and further developed in the recent literature [22,23], can be related to the quasi-equilibrium approximation. An interesting geometric viewpoint of RCCE is given by Tang and Pope [21].…”

Principle of Detailed Balance and the Second Law of Thermodynamics in Chemical Kinetics

“…Defining the "degree of departure from PDB" for each reaction Í as = In . t (13) and using relation (6), Eq. (12) takes the following form:…”

“…Such a state is independent 1.08 X 10-' 1.71 X 10-' 4.89 X 10-5 .45 X 10-1 .34 X 10-' 8.87 X .83 X 10-' 6.01 X 10-" 1.08 X 10-' 1.71 X 10-' 4.89 X .45 X 10-1 .34 X 10-' 8.87 X .83 X 10-' 6.01 X 10-" of the kinetic data and the kinetic path that bring the system to equilibrium [10]. General purpose equilibrium codes of NASA, [11], and STANJAN, [12], and extensions, [13], are standard tools to carry out such calculations. As shown in Table 1, it appears that the original rate constants in the mechanism do not satisfy PDB.…”

Development of Mutation++: Multicomponent Thermodynamic and Transport Properties for Ionized Plasmas written in C++

“…The efficient and robust computation of multiphase, constrained equilibrium compositions is an important topic in several fields, including combustion, aerospace and (bio)chemical engineering, metallurgy, paper processes, and the design of thermal protection systems for atmospheric entry vehicles (e.g., [23][24][25][26][27][28]). Several challenges associated with computing chemical equilibria make conventional methods hard to converge under some conditions [1,[29][30][31][32]. A new multiphase equilibrium solver, based on the single-phase Gibbs function continuation method [33,34], has been developed specifically for Mutation ++ .…”