Ashwin Chinnayya

The use of complex equations of state (EOSs) in compressible flow solvers presents significant theoretical and numerical challenges. These EOSs often present a limited range of validity, leading to “loss-of-convexity” issues, affecting the computed thermodynamic state. Additionally, the complexity of these formulations increases computational cost, as iterative numerical procedures are required, thereby reducing robustness. A novel thermodynamic framework has recently been developed to address these issues. This method, known as the “thermodynamic relaxation method (TRM),” is relevant due to its simplicity, efficiency, and robustness. The method is based on two EOSs: a target equation of state, which represents the physical equation of state, and a predictor equation of state (PEOS), which is simple and convex over a wide range of thermodynamical states. The PEOS is used in the numerical method to close the corresponding hyperbolic system of equations, while thermodynamic parameters are relaxed after each time step to map the solution to the physical target equation. This approach results in faster and more efficient computations. However, the relaxation step, as developed in previous works, is based on heuristic relations, leaving opportunities to strengthen the mathematical foundation of the method. This paper aims to refine the theoretical basis of the TRM and to propose a novel and enhanced relaxation kernel. Additionally, the refinement of the PEOS is discussed. The method also yields a more accurate and consistent thermal equilibrium temperature.

A Lagrangian approach was proposed to analyze induction and reaction times in the cellular gaseous detonation. Two-dimensional simulations in an argon-diluted and non-diluted hydrogen-based mixtures were performed with detailed chemistry, along particle trajectories. The distribution of the induction and reaction times inside the cell was significantly different between the Eulerian and the Lagrangian perspectives, the latter showing non-monotonic behavior. Preferential thermodynamic paths laid along the Rankine–Hugoniot curve and behind transverse waves (TW). All particles were ignited within half and one cell cycle for the diluted and non-diluted mixture, respectively. The ignition mechanisms were not only one-dimensional, but also multi-dimensional, with ignition behind the TW being the most important, and collision of TW and triple points being secondary. A new topology inside the cell could be drawn, from the intersection of the ignition front with TW. TW appeared as phase waves in the (x,t) diagram. Comparison of H2O mass fraction between local and equilibrium values indicated that a local chemical disequilibrium remained (superequilibrium), due to TW. Equating the mean sonic plane with thermochemical equilibrium in the non-diluted case is not completely accurate. Furthermore, the characteristic time scales for chemical and hydrodynamic phenomena were compared. The diffusive phenomenon did not make any contribution in the mixtures tested. In comparison with the Zel'dovich–von Neumann–Döring model, a shorter average induction time was found in the non-diluted mixture, which is not in line with the results from previous Favre approaches. The average reaction time was also shorter in both mixtures.