Dilute Gas Region Research Articles

Direct numerical simulation of fully-developed supersonic turbulent channel flows with dense vapors

This work aims to investigate the impact of the molecule-complexity effect and the non-ideal effect on wall-bounded turbulent flows by applying direct numerical simulation (DNS) to fully-developed channel flows of two typical organic vapors: R1233zd(E) and octamethyltrisiloxane (MDM). For each vapor, three thermodynamic states are analyzed: one in the dilute-gas region, one near the saturation line, and one in the supercritical region. For mean flow fields, it is found that, due to smaller Prandtl and Eckert numbers, both the molecule-complexity effect and the non-ideal effect reduce the mean temperature rise from the cold wall to the channel center. Meanwhile, the molecule-complexity effect weakens the mean density drop, while the non-ideal effect strengthens the drop. Furthermore, once the density and viscosity variations are considered, the mean streamwise velocity profiles of dense vapors are practically the same as the ideal gas. For turbulent fluctuations, it is found that the correlations between T′, p′, and ρ′ in dense vapors are more complicated than the ideal gas: for the ideal gas, fluctuations are dominated by “vorticity mode”; hence, ρ′ and T′ are strongly related to u′ but independent of p′; however, for dense vapors, “acoustic mode” can also play an important role. A newly derived equation illustrates that, through the “acoustic mode,” the molecule-complexity effect obviously enhances the positive correlation between ρ′ and p′, while the non-ideal effect can enhance the positive correlation between T′ and p′. Further analysis of instantaneous flow fields shows that p′ is isotropic. The isotropic character affects fluctuation magnitudes but has limited effect on the specified wall-direction turbulent transport. Consequently, Walz's equation and Reynolds analogy in terms of enthalpy are still valid. Finally, a comparison between the DNS energy budget and k equation of Reynolds-averaged Navier–Stokes (RANS) model has been carried out. Results show that obvious deviation happens on the production term in spite of the careful selection of eddy viscosity model.

Reference Correlation for the Thermal Conductivity of Ethane-1,2-diol (Ethylene Glycol) from the Triple Point to 475 K and Pressures up to 100 MPa.

We present a new wide-ranging correlation for the thermal conductivity of ethane-1,2-diol (ethylene glycol) based on critically evaluated experimental data. The correlation is designed to be used with an existing equation of state, and it is valid from the triple point to 475 K, at pressures up to 100 MPa. The estimated uncertainty is 2.2 % (at the 95 % confidence level), except in the dilute-gas region which is estimated to be 20 %, as there are no measurements in this region for comparison.

Reference Correlation for the Viscosity of Ethane-1,2-diol (Ethylene Glycol) from the Triple Point to 465 K and up to 100 MPa.

We present a new wide-ranging correlation for the viscosity of ethane-1,2-diol (ethylene glycol) based on critically evaluated experimental data. The correlation is designed to be used with an existing equation of state, and it is valid from the triple point to 465 K, at pressures up to 100 MPa. The estimated uncertainty is 4.9 % (at the 95 % confidence level), except in the dilute-gas region which is estimated to be 15 %, as there are no measurements in this region for comparison. The correlation behaves in a physically reasonable manner when extrapolated to 750 K and 250 MPa, however care should be taken when using the correlations outside of the validated range.

Reference Correlations of the Thermal Conductivity of o-Xylene, m-Xylene, p-Xylene, and Ethylbenzene from the Triple Point to 700 K and Moderate Pressures

This paper contains new, representative reference equations for the thermal conductivity of o-xylene, m-xylene, p-xylene, and ethylbenzene. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dilute-gas thermal conductivity, a theoretically based correlation was adopted in order to extend the temperature range of the experimental data. Moreover, in the critical region, the experimentally observed enhancement of the thermal conductivity is well represented by theoretically based equations containing just one adjustable parameter. All four correlations are applicable for the temperature range from the triple point of each fluid to 700 K, and an upper pressure limit determined by the maximum density limit for the equation of state used to provide density. At the upper temperature limit of 700 K, the maximum pressure was 200 MPa for m-xylene and p-xylene, but 60 and 70 MPa for ethylbenzene and o-xylene, respectively. At lower temperatures, the maximum pressure is lower. The overall uncertainty (at the 95% confidence level) of the correlations of the thermal conductivity of o-, m-, p-xylene, and ethylbenzene, over their range of applicability, varies for each fluid. For o-xylene, we estimate the uncertainty for liquid and supercritical densities for temperatures from the triple point to 400 K to be 2.6%, and 4% at higher temperatures, and in the dilute-gas region we estimate the uncertainty to be 2%. For m-xylene, the estimated uncertainty for liquid and supercritical densities at temperatures from the triple point to 375 K is 3.6%, and 5% at higher temperatures, and 6% for the dilute gas. For p-xylene, the estimated uncertainty for liquid and supercritical densities at temperatures from the triple point to 700 K is 3.6%, and 2.5% for the dilute gas. Finally, for ethylbenzene the estimated uncertainty for liquid and supercritical densities at temperatures from the triple point to 400 K is 2.8%, and 2.5% in the dilute-gas region. Uncertainties in the critical region for all four fluids are much larger, since the thermal conductivity approaches infinity at the critical point and is very sensitive to small changes in density.

Reference Correlation of the Viscosity of Cyclohexane from the Triple Point to 700 K and up to 110 MPa

A new correlation for the viscosity of cyclohexane is presented. The correlation is based upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory. It is applicable in the temperature range from the triple point to 700 K at pressures up to 110 MPa. In the dilute gas region, at pressures below 0.3 MPa, the correlation is valid up to 873 K. The overall uncertainty of the proposed correlation, estimated as the combined expanded uncertainty with a coverage factor of 2, varies from 0.5% for the viscosity of the dilute gas and of liquid at ambient pressure to 5% for the viscosity at high pressures and temperatures. Tables of the viscosity generated by the relevant equations, at selected temperatures and pressures and along the saturation line, are provided.

Reference Correlation of the Thermal Conductivity of Methanol from the Triple Point to 660 K and up to 245 MPa

This paper contains new, representative reference equations for the thermal conductivity of methanol. The equations are based in part upon a body of experimental data that has been critically assessed for internal consistency and for agreement with theory whenever possible. In the case of the dilute-gas thermal conductivity, a theoretically based correlation was adopted in order to extend the temperature range of the experimental data. Moreover, in the critical region, the experimentally observed enhancement of the thermal conductivity is well represented by theoretically based equations containing just one adjustable parameter. The correlation is applicable for the temperature range from the triple point to 660 K and pressures up to 245 MPa. The overall uncertainty (at the 95% confidence level) of the correlation over its range of applicability for the liquid and supercritical phases, excluding the critical region, is estimated to be less than 4.4%. The dilute gas region has an estimated uncertainty of 3%, and the liquid at atmospheric pressure is represented to 2%. Uncertainty in regions where data are unavailable for comparison, such as the dense gas region, may be larger.

Ideal Gas Heat Capacity Derived from Speed of Sound Measurements in the Gaseous Phase for trans-1,3,3,3-Tetrafluoropropene

trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze(E)) is considered as an alternative refrigerant in automobile air conditioning applications because of its low global warming potential. For the purpose of evaluation of thermophysical properties of HFO-1234ze(E), the speed of sound was measured in the dilute gas region in order to derive heat capacities in the ideal gas state. The speed of sound was obtained from measurements of acoustic resonance frequencies of radial modes in a spherical resonator filled with sample gas. Taking some perturbation effects into account, the speed of sound was determined with a relative uncertainty of 0.01 %. The speed of sound data were fitted to the acoustic virial equation. By extrapolating the speed of sound data on each isotherm to zero pressure, the ideal gas heat capacities at constant pressure were determined with a relative uncertainty of 0.1 %. The isobaric ideal gas heat capacities were represented by a third-order polynomial function in temperature.

Lennard-Jones Fluid and Diffusivity: Validity of the Hard-Sphere Model for Diffusion in Simple Fluids and Application to CO2

The validity of the hard-sphere (HS) model in determining the self-diffusion coefficient of simple fluids is studied using the Lennard-Jones (LJ) fluid as a test fluid. The latest simulation results on the LJ fluid are used along with the various perturbation theories to assess the HS model separately in the liquid, gas, and supercritical regions as a function of both density and temperature. Apart from the commonly used methods of estimating the effective hard-sphere diameter (EHSD), the Gibbs−Bogoliubov criterion, which provides an EHSD that is more representative of the intermolecular interactions, is used. This criterion gives a vastly different assessment of the HS model compared to other methods in the supercritical and liquid regions. All methods result in considerable errors in the low-density dilute gas region at lower temperatures. Next, the diffusivity of carbon dioxide is studied. Nine different sets of LJ potential parameters and three non-LJ potentials are considered. The LJ potential based ...

An Absolute Viscometer-Densimeter and Measurements of the Viscosity of Nitrogen, Methane, Helium, Neon, Argon, and Krypton over a Wide Range of Density and Temperature

An apparatus for the simultaneous measurement of viscosity and density of fluids is presented. The viscometer-densimeter covers a viscosity range up to 150 µPa⋅s and a density range up to 2000 kg⋅m−3 at temperatures from 233 to 523 K and pressures up to 30 MPa. Very accurate density measurements with uncertainties of ±0.02 to ±0.05% have always been carried out with this apparatus, although in its first version it was necessary to calibrate the viscosity measuring system on a reference fluid in order to achieve uncertainties of ±0.6 to ±1.0% in viscosity. After significant improvements, the apparatus now achieves uncertainties in viscosity of less than ±0.15% in the dilute gas region and less than ±0.4% for higher densities. Moreover, the viscosity measuring system can be described in an absolute way; calibration is no longer necessary. In order to test the advanced apparatus and to determine viscosity-density values of very high quality, comprehensive measurements on nitrogen, argon, and methane were carried out in the entire working range of the viscometer-densimeter. In addition, viscosity-density measurements on helium, neon, and krypton were made on two selected isotherms each. All measurements show that the estimated total uncertainty of ±0.15 to ±0.4% in viscosity and of ±0.02 to ±0.05% in density is clearly met. In order to verify the results of the combined viscometer-densimeter, a new apparatus for very accurate viscosity measurements was designed. While the working range of this apparatus is restricted to the dilute gas region, it yields uncertainties of less than ±0.07% in viscosity. Measurements carried out with this apparatus confirmed the previously measured values of the combined viscometer-densimeter within ±0.03%.

Measurement of thermal diffusivities with the photoacoustic effect

A non-resonant photoacoustic detector was used to determine thermal diffusivities of the refrigerants R134a and R32. The measurements were carried out at temperatures ranging from 294 K to 363 K at pressures close to the dilute gas region. The uncertainty for the experimental data of R134a and R32 is ±1.25%. With the aid of accurate equations of state for density and isochoric heat capacity, the measured thermal diffusivities were converted into thermal conductivities. Further improvements of the experimental setup were outlined leading to an uncertainty of ±0.65% with respect to thermal diffusivity.

Supergravity, the DBI action and black hole physics

The assumptions behind the recently conjectured relation between gauge theory and supergravity are elaborated on. It is pointed out that the scaling limit that preserves supergravity solutions, gives the entire DBI action on the gauge theory side, but in the low energy limit the relation between the conformal field theory and Anti-de Sitter supergravity emerges. We also argue that recent work on these issues may help in understanding the physics of five (four) dimensional black hole with three (four) charges in the so-called dilute gas region.

高圧流体物性 輸送性質の測定と問題点 非定常熱線法による熱伝導率の測定を中心に

In response to the earnest requirement in both science and industrial technology, several new devices for measurements of thermophysical properties have been developed. This article reviews briefly the experimental techniques for measurement of the viscosity and the thermal conductivity of fluids. A special topic focused on is the applicability of the transient hot-wire method to the measurement in dilute gas region. Some technical problems are discussed refering to the authors' experimental data as well as the recent theoretical discussions in the literature.

Transport properties of polydisperse fluids. I. Shear viscosity of polydisperse hard-sphere fluids

The shear viscosity expressions for a polydisperse hard-sphere fluid in both the dilute and dense fluid regions have been obtained as the solution of a set of linear integral equations in the Enskog transport theory. In the monodisperse limit we recover the known Enskog result. Explicit analytical solutions have been obtained for the special case of equal-mass particles. For general mass-size distributions, a simple numerical method has been proposed. Computations have been performed for a mass-size relation of power-law form. The two size distributions we have looked at are the Schulz distribution and the log-normal distribution. It is found that both distributions show similar effects on the shear viscosity. In the dilute-gas region, for each given fractal dimension, there exists a critical variance of the size distribution at which the shear viscosity attains a maximum. In the dense-gas region, the shear viscosity increases as the variance and the density increase except for the low density and the high fractal-dimension region where the shear viscosity attains a minimum at some particular variance. The shear viscosity diverges at a close-packing density that decreases with increasing variance.

The thermal conductivity surface for mixtures of methane and ethane

A correlation is presented for the extensive series of thermal conductivity measurements of binary methane-ethane mixtures. The composition dependences of the thermal conductivity in the dilute-gas region, dense-gas and liquid region, and critical region are discussed. The average absolute percentage deviation of the thermal conductivity surface as a function of temperature, density, and composition, from the experimental data, is 1.60%.

19F spin-lattice relaxation in WF6, MoF6, and UF6gases

Spin-lattice relaxation times have been measured for the fluorine nuclei in gaseous WF6, MoF6 and UF6 as a function of temperature in the dilute gas region. The measured temperature dependences are as predicted for relaxation resulting from a spin-rotation interaction. Effective cross sections for the transfer of angular momentum to molecular rotation during collisions are deduced.

Numerical Experiments on the Stochastic Behavior of a Lennard-Jones Gas System

It is known that the hard-sphere gas exhibits strongly stochastic properties. For it, most initially close phase-space-trajectory pairs separate exponentially with time, and Sinai has used this so-called $C$-system behavior to develop a rigorous proof of ergodicity and mixing in the hard-sphere gas. In this paper we numerically integrate the equations of motion for a Lennard-Jones gas, which has attractive as well as repulsive interparticle forces, and we demonstrate that this exponential separation of initially close trajectory pairs persists even in the presence of attractive forces over a fairly wide range of particle densities. In our calculations, this range extends from the dilute-gas region up to densities at which three-body and four-body collisions become significant. Moreover for this density range, we show that an expression for the trajectory-pair rate of exponential separation, rather crudely derived for a hard-sphere gas, fits the empirical Lennard-Jones data quite nicely. Our evidence thus indicates that a gas system with attractive forces can exhibit $C$-system behavior similar to that of the hard-sphere gas. Finally we point out that the exponential separation of trajectories as empirically observed here involves an unusual type of correlated collision sequence.

Spin–Lattice Relaxation in Dilute Gases. III. 1H Relaxation in NH3 and 19F Relaxation in BF3

Spin–lattice relaxation times have been measured for the protons in gaseous NH3 and for the fluorine nuclei in gaseous BF3 as a function of temperature and pressure in the dilute gas region. The measured temperature dependences are as predicted for relaxation resulting from a spin–rotation interaction. Cross sections for the relaxation are calculated and from them it is deduced that the long-range forces between the molecular electric dipole moments in NH3 contribute significantly to the randomization of the molecular rotational magnetic fields at the proton sites.

Spin-Lattice Relaxation in Dilute Gases. II. 19F Relaxation in CF4 and SiF4

Fluorine spin-lattice relaxation times have been measured in gaseous CF4 and SiF4 as a function of temperature and pressure in the dilute gas region. The observed temperature dependence is consistent with that expected for relaxation dominated by a spin-rotation interaction. Effective cross sections for the transfer of angular momentum to molecular rotation during collisions are deduced. It is found that between one and three binary collisions are sufficient to randomize the molecular rotational angular momentum of these molecules in the temperature range studied.

Spin—Lattice Relaxation in Dilute Gases. I. Proton Relaxation in HCl, HBr, and HI

Proton spin—lattice relaxation times have been measured in gaseous HCl, HBr, and HI as a function of temperature and pressure in the dilute-gas region. The observed temperature dependence is consistent with that expected for relaxation dominated by a spin—rotation interaction. Effective cross sections for the transfer of angular momentum to molecular rotation during collisions are deduced. The cross sections are large, indicating the importance of the long-range forces between the molecular dipole moments.