A few level approach for the electronic partition function of atomic systems

Colonna, G.; Capitelli, M.

doi:10.1016/j.sab.2009.07.002

Cited by 37 publications

(21 citation statements)

References 26 publications

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“…As discussed in Refs. [44,45], the behavior of the chemical reaction could change if the electronically metastable states of molecules and atoms are considered. In the present calculations, thermal equilibrium between the electron energy and electronic excitation energy modes is assumed, whereas this approximation may be insufficient for the freejet in the vacuum chamber.…”

Section: Number Densitymentioning

confidence: 99%

Advanced Validation of Nonequilibrium Plasma Flow Simulation for Arc-Heated Wind Tunnels

Takahashi

Abe

Takayanagi

et al. 2014

Journal of Thermophysics and Heat Transfer

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Turbulent plasma flows in arc heaters such as JAXA 750 kW, NASA 20 MW, and Kyushu University 20 kW facilities were investigated, and the distributions of the flowfield properties were successfully obtained. The arc discharge in the constrictor section and the expansion processes in the nozzle section play key roles in the formation of an arc-heated flow. Hence, for accurately predicting high-enthalpy flow properties, it is important to model correctly the complex phenomena observed in various-scale facilities. For this purpose, an integrated analysis model to simulate various-scale arc-heated flows with high accuracy was developed. The turbulent flow field was described using the Reynolds-averaged Navier-Stokes equations with a multitemperature model, which was tightly coupled with electric-field and radiation-field calculations. A sophisticated and low-cost radiation model and a low-Reynolds number two-equation turbulence model were introduced into the flow-field simulation. To validate the present integrated analysis model, the computed results were compared with the corresponding experimental data for the mass-averaged enthalpy, translational and rotational temperatures, and number density of nitrogen obtained through spectroscopic and laser-induced fluorescence techniques. Moreover, the mechanisms of energy input by discharge and energy loss are discussed with the distributions of the electronic excitation temperature and heat flux on the constrictor wall derived from the arc column. Although the results indicate that a relatively detailed discharge model is required to describe the arc discharge with relatively high accuracy, the present flow-field model was generally in good agreement with various operating conditions of the facilities.

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Section: Number Densitymentioning

confidence: 99%

Advanced Validation of Nonequilibrium Plasma Flow Simulation for Arc-Heated Wind Tunnels

Takahashi

Abe

Takayanagi

et al. 2014

Journal of Thermophysics and Heat Transfer

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“…[18]) or when the atomic states are grouped into a few virtual levels and the calculation of the partition function considering these virtual levels to follow Boltzmann distribution as recently suggested in Ref. [19].…”

Section: Ii-the Occupational Probability Formalismmentioning

confidence: 99%

On the ionization equilibrium of hot hydrogen plasma and thermodynamic consistency of formulating finite internal partition functions

Zaghloul

2010

Physics of Plasmas

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“…The calculation of the internal partition function of atomic species presents some problems since the number of levels is infinite for an infinite space containing a single atom [110]. Interactions with other particles limits the number of levels.…”

Section: Partition Function For Atomic Speciesmentioning

confidence: 99%

“…Interactions with other particles limits the number of levels. Colonna et al [110] developed a few-level approach for the electronic partition function of atomic systems. Their model groups the atomic states into a few virtual levels with suitable average energy and global statistical weight.…”

Section: Partition Function For Atomic Speciesmentioning

confidence: 99%

“…The cutoff energy in real systems is not constant but depends on some quantity such as particle density (Fermi criterion) or electron density Griem criterion [110]. The cutoff can be determined after the gas or plasma composition is known; however, this approach increases computational time, particularly for complex CFD codes that couple with kinetic or thermodynamic calculations.…”

Section: Partition Function For Atomic Speciesmentioning

confidence: 99%

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Tunable Diode Laser Absorption Spectroscopy of Aerospace Flows

Wheatley¹

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Direct and wavelength modulated methods of tunable diode laser absorption spectroscopy (TDLAS) techniques were applied to hypersonic and rarefied gas environments. Three experimental campaigns are discussed including direct absorption spectroscopy of a steam ejector flow, wavelength modulated TDLAS of scramjet combustion in an expansion tunnel, and temperature measurement of atomic oxygen in a plasma generator. The literature relevant to TDLAS is reviewed and the theoretical bases for the two techniques are presented. Each campaign required innovative solutions to experimental problems but, in the end, TDLAS was successfully applied on a proof-of-concept basis in each environment. The pressure and temperature in a 1 kms −1 steam ejector flow were measured using direct TDLAS.Three methods of analysing the data were compared for accuracy and ease of use. The best method was found to be using the Levenburg-Marquardt method to perform a non-linear least-squares minimisation of the residual between a Voigt fit of simulated and measured data. Absolute average residual errors of less than 0.1% were achieved together with pressure relative error of ±2% and temperature errors of ±10 K. Wavelength modulated TDLAS was investigated as a means to measure parameters in the combustor and nozzle of a scramjet in an expansion tunnel. The scramjet operated at an inlet Mach number of approximately 10 and a static pressure of 120 Pa simulating flight at approximately 30 km altitude. The test time was of the order of 1 ms. Hydrogen fuel was injected via five holes in the scramjet inlet ramp. Two laser diodes operating near 1392 nm were used to probe the scramjet nozzle flow. The lasers were simultaneously sinusoidally modulated in power and wavelength at a frequency near 1.0 MHz. Tests were conducted at various fuel injection pressures into both air and nitrogen test gas.Combustion was detected in the scramjet nozzle. Results are presented together with recommendations for future research. The atomic oxygen concentration in a microwave generated plasma generated by an Evenson cavity was measured using TDLAS to probe the oxygen triplet at 844.6 nm. The oxygen atoms in the plasma were highly excited and emitted radiation that could have overwhelmed the laser absorption. Any spectral features were expected to be narrow as the plasma pressure was between 80 Pa and 300 Pa. The measured intensity ratios were used to calculate the number density of oxygen atoms in the upper states with a relative error of approximately 5%. The calculated number density, mole fraction of atomic oxygen and intensity ratio were highly sensitive to the temperature as was expected given the exponential form of Boltzmann's equation. A brief analysis was also presented of a TDLAS system that could detect atomic oxygen in reflected shock or expansion tunnel experiments. Whilst the system was not implemented for this study, the information presented may assist future researchers to develop an atomic oxygen TDLAS system for free-piston hypersonic tunnels. Th...

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A few level approach for the electronic partition function of atomic systems

Cited by 37 publications

References 26 publications

Advanced Validation of Nonequilibrium Plasma Flow Simulation for Arc-Heated Wind Tunnels

Advanced Validation of Nonequilibrium Plasma Flow Simulation for Arc-Heated Wind Tunnels

On the ionization equilibrium of hot hydrogen plasma and thermodynamic consistency of formulating finite internal partition functions

Tunable Diode Laser Absorption Spectroscopy of Aerospace Flows

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