Direct simulation Monte Carlo modeling of relaxation processes in polyatomic gases

Abstract

Relaxation processes of polyatomic molecules are modeled and implemented in an in-house Direct Simulation Monte Carlo code in order to enable the simulation of atmospheric entry maneuvers at Mars and Saturn’s Titan. The description of rotational and vibrational relaxation processes is derived from basic quantum-mechanics using a rigid rotator and a simple harmonic oscillator, respectively. Strategies regarding the vibrational relaxation process are investigated, where good agreement for the relaxation time according to the Landau-Teller expression is found for both methods, the established prohibiting double relaxation method and the new proposed multi-mode relaxation. Differences and applications areas of these two methods are discussed. Consequently, two numerical methods used for sampling of energy values from multi-dimensional distribution functions are compared. The proposed random-walk Metropolis algorithm enables the efficient treatment of multiple vibrational modes within a time step with reasonable computational effort. The implemented model is verified and validated by means of simple reservoir simulations and the comparison to experimental measurements of a hypersonic, carbon-dioxide flow around a flat-faced cylinder.

An ES-BGK model for diatomic gases with correct relaxation rates for internal energies

“…The DSMC simulation was carried out with the identical VHS parameters. In addition, the prohibiting double relaxation method was used to reproduce the Landau-Teller equation as described in various studies Zhang & Schwartzentruber (2013); Pfeiffer et al (2016). The results are depicted in Fig.…”

Extending the Particle ESBGK Method to Diatomic Molecules including Quantized Vibrational Energies

“…If the translational-vibrational and translational-rotational relaxation is considered separately and an isothermal relaxation is assumed (T Eq,i (t) = T Eq,i (t = ∞)), it is possible to define an analytical solution of Eq. ( 12) 13,20 : The results are shown in Fig. 2.…”

“…Next to the translational energy also the relaxation of internal vibrational and rotational energies must be treated in flows including molecules. The relaxation of the rotational temperature T R and the vibrational temperature T V is typically described with the Landau-Teller equation [13][14][15]…”

“…In the second test case, a simultaneous relaxation of the translational, rotational and vibrational temperature is investigated. For this, the reservoir simulation with the conditions described before is used again, only the initial temperatures are changed to T tr = 16000 K, T R = 12000 K, and T V = 8000 K. The DSMC simulations are done using the prohibiting double relaxation method to reproduce the Landau-Teller equation as described in several works 13,20 . The results of the DSMC and the ESBGK simulation using the quantized vibrational model is shown in Fig.…”

Particle-based fluid dynamics: Comparison of different Bhatnagar-Gross-Krook models and the direct simulation Monte Carlo method for hypersonic flows

“…The third approach is the direct sampling from f ES by using a Metropolis-Hastings method which produces a Markov chain v 0 , v 1 , ..., v N M of samples from the target distribution [24][25][26][27] . The MH method has the advantage that the determination of the global maximum of the target distribution function, which can be computationally expensive (e.g.…”