Influence of reaction equilibrium on thermodynamic model calculations of quasi-static pressure for confined TNT explosions

The quasi-static pressure thermodynamic model for confined explosions provides an effective characterization of pressure evolution with mass-to-volume ratio m/V while enabling the derivation of critical parameters, including adiabatic index through moles of product and quasi-static temperature. However, the thermodynamic model based on detonation and combustion equations that neglects reaction equilibrium demonstrates growing deviations from the quasi-static pressure curve in UFC 3-340-02 blast-resistant design standard after carbon precipitates in detonation products, and existing research inadequately addresses the necessity of incorporating reaction equilibrium for various physical quantities in Trinitrotoluene (TNT) confined explosion thermodynamic models. To investigate the impact of reaction equilibrium on thermodynamic model results, the model neglecting reaction equilibrium was first modified based on the energy conservation equation of isochoric processes and the solid carbon precipitation phenomenon, which improves the model's consistency with the UFC curve when m/V≥0.371 kg/m3. Then, a comparative analysis was conducted on the results of thermodynamic models considering and not considering the reaction equilibrium based on the unified solution framework. The two thermodynamic models were solved within the range of 0.01 kg/m3≤m/V≤10 kg/m3 by using Newton's method and back propagation algorithm. The results indicate that while reaction equilibrium consideration induces less than 20% variation in quasi-static pressure predictions, it alters critical thresholds: the m/V for carbon precipitation shifts from 0.371 to 3.850 kg/m3, and peak temperature transitions from 0.371 to 0.680 kg/m3. Significant divergence in mole numbers of product composition emerges progressively when m/V exceeds 0.1 kg/m3. Therefore, the reaction equilibrium-based thermodynamic model is a more rational choice for calculating quantities related to components and temperature in TNT confined explosions with m/V>0.1 kg/m3. Finally, a simplified approach employing symbolic regression was developed for calculating moles of products, temperature, and pressure during the quasi-static phase of TNT confined explosions and shows high alignment with thermodynamic model results. The research contributes to a theoretical understanding of equilibrium effects on thermodynamic model results and the practical implementation of rapid parameter estimation in TNT confined explosion scenarios.