[Paper Review] Simulations of detonation waves with smoothed dissipative particle dynamics

Gérôme Faure, Jean‐Bernard Maillet|arXiv (Cornell University)|Sep 11, 2017

Gas Dynamics and Kinetic Theory3 citations

TL;DR

This paper extends Smoothed Dissipative Particle Dynamics (SDPD) to model chemically reactive systems by introducing a progress variable per mesoparticle that evolves according to chemical kinetics. The method successfully simulates the shock-to-detonation transition and stationary detonation waves in nitromethane, recovering key physical properties such as detonation velocity and reactive zone width, with results consistent across varying reaction rate prefactors when resolution is sufficient.

ABSTRACT

Smoothed Dissipative Particle Dynamics (SDPD) is a mesoscopic method which allows to select the level of resolution at which a fluid is simulated. The aim of this work is to extend SDPD to chemically reactive systems.To this end, an additional progress variable is attached to each mesoparticle and evolves according to chemical kinetics. This reactive SDPD model is illustrated with numerical studies of the shock-to-detonation transition in nitromethane as well as the stationary behavior of the reactive wave.

Motivation & Objective

• To extend the SDPD method to simulate chemically reactive systems at mesoscopic scales.
• To enable simulation of detonation waves and the shock-to-detonation transition (STD) in reactive materials like nitromethane.
• To assess the influence of reaction rate prefactors on detonation wave structure and dynamics.
• To evaluate the impact of particle resolution on the accuracy of reactive SDPD simulations.
• To demonstrate that SDPD can capture key physical properties of detonation waves with coarser resolution than traditional MD or DPDE.

Proposed method

• Introduces a progress variable λ per mesoparticle to track chemical conversion in reactive systems.
• Adapts the reactive mechanism from DPDE (Maillet et al., 2007) to the SDPD framework.
• Uses the Arrhenius rate law with a temperature-dependent reaction rate to govern the evolution of λ.
• Applies a moving window technique to simulate long-time dynamics of detonation waves.
• Implements a thermodynamically consistent SDPD formulation with energy conservation and hydrodynamic forces.
• Performs simulations using a finite number of mesoparticles with smoothed particle interpolation to solve the Navier-Stokes equations.

Experimental results

Research questions

• RQ1 Can SDPD be effectively extended to model reactive systems with chemical kinetics at the mesoscale?
• RQ2 How does the Arrhenius prefactor affect the structure and dynamics of detonation waves in nitromethane?
• RQ3 To what extent does the particle resolution influence the accuracy of reactive SDPD simulations for fast reactions?
• RQ4 Does the reactive SDPD model correctly reproduce the shock-to-detonation transition and stationary detonation wave properties?
• RQ5 Can the method achieve scale-invariant behavior under changes in reaction rate, provided resolution is adequate?

Key findings

• The detonation velocity remains within 1% of theoretical predictions across all tested prefactors when resolution is sufficient.
• The width of the reactive zone scales approximately as the inverse of the prefactor, indicating a rescaling of time and length scales.
• For a prefactor of 4×10¹⁵ s⁻¹, the detonation velocity deviates by 15% when using coarse resolution, indicating insufficient resolution for fast kinetics.
• A higher-resolution simulation (K=10) with the same high prefactor yields a detonation velocity of 6777 m·s⁻¹, close to theoretical expectations.
• The pressure profiles for different prefactors collapse onto a single curve after rescaling, confirming scale invariance of the system.
• The reactive mechanism fails to accurately model fast reactions when mesoparticles are too large, highlighting the need for resolution-dependent tuning.