Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

Annis, B. K.; Malinauskas, A.P.

doi:10.1063/1.1674751

Cited by 31 publications

(12 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Presumably, in this manner, small inaccuracies in the theory would be of little importance. In fact, the results that have been obtained in this way by several investigators for the tranSlational Eucken factors and especially rotational relaxation numbers of polyatomic gases are in remarkably good agreement with.similar information gotten from other experimental techniques and from theory.l,4,15, [20][21][22] To use either Eqs. (3) or (4) for a relative rather than absolute determination of gas transport properties from thermal transpiration measurements, these equations are rearranged into a form so that experimental information only at the maximum pressure difference (AP max ) is used.…”

Section: Analysis Of the Datasupporting

confidence: 73%

Determination of thermal transport properties from thermal transpiration measurements. III. Polar gases

Tao

Revelt

Sandler

1974

The Journal of Chemical Physics

View full text Add to dashboard Cite

The results of capillary thermal transpiration measurements for nitrogen, oxygen, carbon monoxide, methane, methyl chloride, hydrogen sulfide, and sulfur dioxide over a (mean) temperature range of 408.6 to 501.3°K are reported. The problem that arises in interpreting the data to obtain thermal transport information is carefully considered. While this difficulty is not completely resolved, our data for the nonpolar gases are combined with our earlier results and used to compute smoothed values of the rotational relaxation numbers and Eucken factors for the temperature range l6S-S00'K.

show abstract

Section: Analysis Of the Datasupporting

confidence: 73%

Determination of thermal transport properties from thermal transpiration measurements. III. Polar gases

Tao

Revelt

Sandler

1974

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…The maximum temperature range for the reported Z~o t values is 160.3 to 1250 K for nitrogen. In the low temperature end of this range where many measurements are available, the agreement between the various sets of values is within a factor of about two [27,29]. Further, Tao et al [30] and others [25,26] have pointed out that the basic description of the phenomenon as well as the analysis procedure have not yet reached a stage of sophistication where unambiguous values of Zro t may be obtained from thermal transpiration experiments.…”

Section: Z= Zrotmentioning

confidence: 91%

“…This technique has been employed to measure rotational relaxation numbers for nitrogen by Malinauskas [22], Tip et al [23], Healy and Storvick [24], McConville et al [25] and Malinauskas et al [26]. In addition, Annis and Malinauskas [27], Ganzi and Sandier [28] and Butherus and Storvick [29] have measured Zro t as a function of temperature. The maximum temperature range for the reported Z~o t values is 160.3 to 1250 K for nitrogen.…”

Section: Z= Zrotmentioning

confidence: 98%

Thermal conductivity of nitrogen in the temperature range 350–2500 K

Saxena

Chen

1975

Molecular Physics

View full text Add to dashboard Cite

The thermal conductivity of nitrogen is determined in a conductivity column instrument in the temperature range of 338 to 2518 K with an estimated uncertainty of about _+1"5 per cent. The experimental data points are correlated by a cubic polynomial in temperature, viz. k(T)/(mW m -1 K -1) = 12.18 + 0"05224(T/K) -0"6482 x 10-6(T/K) 2 -0"2765 x 10-9(T/K) z. These conductivity values determined from heat transfer data taken in the continuum regime are found to be in fair agreement with the values obtained from similar data referring to low pressure range.The present results are compared with the conductivity determinations of other workers and with the predictions of various theories developed for polyatomic gases. It is pointed out that a reliable calculation of thermal conductivity over an extended temperature range is impossible at the present time due to the absence of a large variety of experimental molecular data needed for such an effort. Average values of the vibrational energy diffusion coefficient, Dvib, are computed from the present k(T) data.

show abstract

“…3, has been shown to depend on the gas temperature in previous theoretical, 15 computational, [16][17][18] and experimental studies. [19][20][21][22][23] In general, previous continuum and DSMC models successfully established the temperature dependence of Z rot . However, most of the models are constructed based upon some variant of the Parker model.…”

Section: Introductionmentioning

confidence: 96%

A Nonequilibrium-Direction-Dependent Rotational Energy Model for use in Continuum and Stochastic Molecular Simulation

Zhang

Valentini²,

Schwartzentruber³

2013

51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

View full text Add to dashboard Cite

A new rotational energy exchange model for direct simulation Monte Carlo (DSMC) and multi-temperature Navier-Stokes methods is presented. The DSMC model is based only on collision-quantities and reduces to a rotational collision number in the continuum limit, applicable for use with the Jeans relaxation equation. The model is formulated based on recent Molecular Dynamics (MD) simulations of rotational relaxation in nitrogen (Valentini et al, Phys. Fluids 24, 106101 (2012)) and accounts for the dependence of the relaxation rate on the direction to the equilibrium state. This enables a single parameterization of the model to accurately simulate rotational relaxation in both compressing and expanding flows, unlike the widely used Parker model. The DSMC model is simple to implement, numerically efficient, and accurately reproduces a range of pure MD solutions including isothermal relaxations, normal shock waves, and expansions. This demonstrates that the complexity of a state-resolved model is not required for translational-rotational relaxation. A general form for the energy distribution function that should be sampled for post-collision states (using the Borgnakke-Larsen approach) is presented. This general formulation ensures detailed balance and equipartition of energy at equilibrium for any collision-quantity based DSMC model and also explains the behavior of prior rotational models in the literature. The model formulation is also general to the inelastic collision selection procedure used, which is shown to be a crucial aspect in implementing a DSMC collision model. Finally, the increased accuracy of a collision-quantity based model compared to a cell-averaged model is demonstrated by comparing rotational energy distribution functions within a shock wave against a pure MD solution.Nomenclature ∆t DSMC simulation time step ∆x DSMC simulation cell size Γ(·) Gamma function ε r (t) average rotational energy at time t ε * r (t) instantaneous equilibrium rotational energy at time t λ molecular mean free path µ dynamic viscosity ω VHS collision model viscosity parameter ρ density τ c molecular mean collision time τ r characteristic rotational relaxation timẽ p rot intermediate rotational inelastic collision probability ε c total collision energy of a collision pair ε r molecular/particle rotational energy ε r molecular/particle rotational energy after collision ε t molecular/particle translational energy ε t molecular/particle translational energy after collision ζ r rotational degrees of freedom ζ t translational degrees of freedom a Parker model rotational collision number parameter b Parker model rotational collision number parameter C connection factor to link p rot andp rot in DSMC simulation d ref VHS collision model reference diameter k B Boltzmann constant n NDD model rotational collision number parameter p pressure p rot DSMC rotational inelastic collision probability T * NDD model/Parker model rotational collision number parameter T r (t) rotational temperature at time t T t (t) translational temperature at ...

show abstract

Temperature Dependence of Rotational Collision Numbers from Thermal Transpiration

Cited by 31 publications

References 29 publications

Determination of thermal transport properties from thermal transpiration measurements. III. Polar gases

Determination of thermal transport properties from thermal transpiration measurements. III. Polar gases

Thermal conductivity of nitrogen in the temperature range 350–2500 K

A Nonequilibrium-Direction-Dependent Rotational Energy Model for use in Continuum and Stochastic Molecular Simulation

Contact Info

Product

Resources

About