4 Carlo direct simulation of rotational relaxation of diatomic molecules using classical trajectory calculations: Nitrogen shock wave

Koura, Katsuhisa

doi:10.1063/1.869462

Cited by 128 publications

(36 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This effect would only be observable in dense fluids. In dilute gas simulations 14,13 and experiments, 18 the rotational temperature rises in step with the density for low Mach numbers (M s ∼ 1.7) and lags the density for increased Mach numbers (M s ∼ 7). It has to be seen if the trend of T rot to lag the density occurs earlier or more pronounced for higher densities.…”

Section: Discussionmentioning

confidence: 99%

“…This likely results in quantitative discrepancies from the behavior of real nitrogen, but the qualitative behavior is captured and this case can more easily be accommodated by other numerical techniques and theoretical approaches. Previously, Koura 13 and Tokumasu & Matsumoto 14 have used MD to develop a binary collision model, which is subsequently used in a DSMC simulation of shock waves in nitrogen.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Molecular alignment in a shock wave

Schlamp

Hathorn

2006

Physics of Fluids

View full text Add to dashboard Cite

Molecular Dynamics simulations of dense nitrogen show that non-spherical molecules have a weak tendency to align their molecular axis such that it lies parallel to the plane of a shock wave front. As a consequence, there is also an even weaker tendency for the molecular rotation axis to align perpendicular to the shock front.The underlying mechanism is discussed and it is argued that this phenomenon can only be observed for dense fluids and only when considering realistic molecular interactions. A single relevant nondimensional parameter is proposed.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Molecular alignment in a shock wave

Schlamp

Hathorn

2006

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…In DSMC approach, one usually employs some empirical models [12], which very much resemble a BGK type relaxation model with a constant relaxation time. There are only a few attempts due to Koura [13] and Erofeev [14] for example, which employ the so called "trajectory calculations", where a realistic modeling of inelastic collisions with translational -rotational (T-R) transfer of energy is made. These computations require enormous CPU time.…”

Section: Introductionmentioning

confidence: 99%

Computation of Hypersonic Flow of a Diatomic Gas in Rotational Non-Equilibrium past a Blunt Body Using the Generalized Boltzmann Equation

Agarwal¹,

Chen²,

Cheremisin³

2008

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a monoatomic gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. The solution of GBE requires modeling of transition probabilities, elastic and inelastic cross-sections etc. of a diatomic gas molecule, needed for the solution of the collision integral. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

show abstract

“…Here, R nd is a uniform random number in the range [0,1], and b max is given by the following equation, which is based on the relation between the cutoff angle χ min in a monatomic molecule and the maximum impact parameter (b max ) e1 (5) :…”

Section: Monte Carlo Integration Of the Energy Gain Functionmentioning

confidence: 99%

“…For elastic molecular collisions, accurate and realistic calculation techniques based on scattering theory as well as simple scattering models (2) - (4) based on kinetic theory have been developed and applied to various rarefied gas flow problems. For a rotationally inelastic molecular collision, a simple model is more practicable for engineering because inelastic collision phenomena are quite complicated; enormous calculation time may be required for an accurate approach such as the classical trajectory calculation (CTC) (5) for diatomic molecules. Some attractive models have been developed, including: the dynamic molecular collision (DMC) (6) model, the phenomenological model formulated by Borgnakke-Larsen (BL) (7) model, and the statistical inelastic cross section (SICS) (8) model.…”

Section: Introductionmentioning

confidence: 99%

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method

Matsumoto

2006

JSME international journal. Ser. B, Fluids and thermal engineer

View full text Add to dashboard Cite

The rotational energy gain function for Monte Carlo simulation of an inelastic molecular collision in rarefied gas flow is revised by analysis using a combination of Monte Carlo integration and classical trajectory calculation (CTC) for diatomic molecules. The rotational energy gain function presented here is combined with the statistical inelastic cross-section (SICS) model and applied to evaluation of the transport coefficients of nitrogen gas using the Wang-Chang-Uhlenbeck (WCU) theory. The normal shock wave structures for nitrogen determined by the proposed energy gain function, Parker's energy gain function, and from experimental data are compared, and it is shown that the transport coefficients and shock wave structures given by the proposed function are in better agreement with the experimental results than Parker's energy gain function.

show abstract

4 Carlo direct simulation of rotational relaxation of diatomic molecules using classical trajectory calculations: Nitrogen shock wave

Cited by 128 publications

References 14 publications

Molecular alignment in a shock wave

Molecular alignment in a shock wave

Computation of Hypersonic Flow of a Diatomic Gas in Rotational Non-Equilibrium past a Blunt Body Using the Generalized Boltzmann Equation

Transport Coefficients of Inelastic Collision Model in the Direct Simulation Monte Carlo Method

Contact Info

Product

Resources

About