M. E. H. van Dongen

Self-sustained aero-acoustic pulsations in gas transport systems: Experimental study of the influence of closed side branches

Abstract A theoretical model is proposed for the aero-acoustic sources responsible for low-frequency self-sustained pulsations in pipes with closed side branches. The theory successfully explains the acoustic and hydrodynamic conditions for resonance in experiments with a single side branch. It also predicts the order of magnitude of the pulsation amplitude and the effect of losses due to friction and radiation. A high pulsation level, with acoustic velocities of the order of magnitude of the main flow, is observed in a double side branch set-up when the edges at the junctions are rounded. When in the double side branch set-up the rounded upstream edge of the second T-joint is replaced by a sharp edge, the pulsation amplitude is reduced by a factor of five. This effect, which can be explained with the theory of vortex sound, leads us to the design of spoilers. Various “spoilers” have been tested in scale model and full scale experiments. Some of these reduce the pulsation level by 40 dB.

Nucleation at high pressure II: Wave tube data and analysis.

Nucleation rate data, obtained from expansion wave tube experiments, are reported for several vapor–gas mixtures at high pressure. Results are given for water–vapor in the presence of helium and nitrogen gas, and for n-nonane in helium and methane. For all these mixtures, carrier gas pressures of 10, 25, and 40 bar have been applied, with temperatures ranging from 230 to 250 K. An extended form of the nucleation theorem (in terms of the derivative of the nucleation rate with respect to carrier gas pressure) is derived, which appears to be very helpful in the interpretation of high pressure data. It can be used to obtain the carrier gas content of the critical nucleus directly from the pressure dependence of experimental nucleation rates. Combining this method with the theoretical considerations of part I of this paper [J. Chem. Phys. 111, 8524 (1999), preceding paper]: the nucleation behavior of water at high pressures of both helium and nitrogen can quantitatively be understood. For n-nonane in helium ou...

Numerical simulation of the propagation of shock waves in compressible open-cell porous foams

Abstract A numerical model for the simulation of the interaction of weak shock waves with open-cell compressible porous foams is developed. It is assumed that the foam is infinitely weak and that its volume fraction, which was 0.05 in the cases studied herein, is relevant only when the interaction between the gaseous and the solid phases is considered. The gas is assumed to be inviscid and thermally nonconductive, except for the viscous drag interaction and the heat transfer between the two phases. It is also assumed that the heat transfer between the two phases is extremely efficient, i.e. that the heat transfer coefficient is infinitely large. The range of incident shock wave Mach numbers investigated herein is between 1.08 and 1.40, and the range of foam densities is between 14.8 and 57.4 kg/m 3 . The numerical results are in very good agreement with experimentally obtained pressure histories and foam particle paths when the incident shock wave Mach numbers are between 1.25 and 1.40 (weak shocks). The agreement between experimentally and numerically obtained pressure histories is poor when the incident shock wave Mach numbers are between 1.08 and 1.18 (very weak shocks). The results of the study indicate that when weak shocks interact with open-cell compressible foam, the transfer of momentum between the gaseous and the solid phases is of paramount importance. On the other hand, if the shocks are very weak , then the elasticity of the foam is an important parameter as well. It is therefore suggested that, while yielding very good results for weak shocks, the assumption of infinitely weak foam is inadequate for very weak shocks.

Shock wave structure in a mixture of gas, vapour and droplets

The structure of the relaxation zone behind a shock wave of moderate strength in a mixture of gas, vapour and droplets is analysed. A model is presented for shock induced evaporation, which is based on wet-bulb equilibrium and on the absence of relative motion between droplets and gas. Experimental and numerical data on heterogeneous condensation induced by an unsteady rarefaction wave and on re-evaporation due to shock wave passage are reported for a mixture of water vapour, nitrogen gas and condensation nuclei. Pressure, temperature, saturation ratio and droplet size are experimentally obtained and are very well predicted by a numerical simulation based on the non-linear quasisteady wet-bulb model for phase transition, as well for the expansion wave as for the shock wave. During expansion, droplet number density decays much faster than predicted, which is not yet satisfactorily explained. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5×10−3 to 0.2, corresponding to shock Mach numbers of 1.2 to 1.9. The evaporation times are well predicted by the theoretical model. No evidence is found for droplet break-up for Weber numbers up to 13, and droplet radii of the order of 1μm.

Waves in partially saturated porous media

The propagation of compressional waves in a porous medium is investigated in case the pore liquid contains a small volume fraction of gas. The effect of oscillating gas bubbles is taken into account by introducing a frequency-dependent fluid bulk modulus, which is incorporated in the Biot theory. Using a shock tube technique, new experimental data are obtained for a porous column subjected to a pressure step wave. An oscillatory behaviour is observed, consisting of two distinct frequency bands, which is predicted by the theoretical analysis.

Gradient theory computation of the radius-dependent surface tension and nucleation rate for n-nonane clusters

The Van der Waals-Cahn-Hilliard gradient theory (GT) is applied to determine the structure and the work of formation of clusters in supersaturated n-nonane vapor. The results are analyzed as functions of the difference of pressures of the liquid phase and vapor phase in chemical equilibrium, which is a measure for the supersaturation. The surface tension as a function of pressure difference shows first a weak maximum and then decreases monotonically. The computed Tolman length is in agreement with earlier results [L. Granasy, J. Chem. Phys. 109, 9660 (1998)] obtained with a different equation of state. A method based on the Gibbs adsorption equation is developed to check the consistency of GT results (or other simulation techniques providing the work of formation and excess number of molecules), and to enable an efficient interpolation. A cluster model is devised based on the density profile of the planar phase interface. Using this model we analyze the dependency of the surface tension on the pressure difference. We find three major contributions: (i) the effect of asymmetry of the density profile resulting into a linear increase of the surface tension, (ii) the effect of finite thickness of the phase interface resulting into a negative quadratic term, and (iii) the effect of buildup of a low-density tail of the density profile, also contributing as a negative quadratic term. Contributions (i)-(iii) fully explain the dependency of the surface tension on the pressure difference, including the range relevant to nucleation experiments. Contributions (i) and (ii) can be predicted from the planar density profile. The work of formation of noncritical clusters is derived and the nucleation rate is computed. The computed nucleation rates are closer to the experimental nucleation rate results than the classical Becker-Döring theory, and also the dependence on supersaturation is better predicted.

The random choice method applied to non-linear wave propagation in gas-vapour-droplets mixtures

Abstract The random choice method (RCM) has been used to calculate non-linear wave propagation in gas-vapour-droplets mixtures. The theoretical model of heterogeneous nucleation and droplet growth is discussed. The equations for wave propagation are formulated in such a way that only one source term due to condensation or evaporation remains. The specific source term properties are investigated and the implementation of the source term into the RCM by operator splitting is explained. Numerical calculations for an unsteady centred rarefaction wave and a shock wave are compared with experimental data. The formation of a condensation discontinuity is demonstrated.

On the effect of pressure and carrier gas on homogeneous water nucleation

Homogeneous nucleation rates of water droplets were measured at a nucleation temperature close to 240 K in a Pulse-Expansion Wave Tube (PEWT). Several measures were taken to improve the data obtained with the PEWT. For instance, the molar water vapor fraction was determined with three independent techniques. The resulting standard uncertainty of the supersaturation was within 1.8%. Results are given for water nucleation in helium at 100 kPa and at 1000 kPa and in nitrogen at 1000 kPa. Two trends were observed: (i) the values of the nucleation rate of water in helium at 1000 kPa are slightly but significantly higher (factor 3) than its values at 100 kPa and (ii) nucleation rates of water in nitrogen at 1000 kPa are clearly higher (factor 10) than in helium at the same pressure. It is argued that the explanation of the two observed trends is different. For case (i), it is the insufficient thermalization of the growing water clusters in helium at the lowest pressure that has a reducing effect on the nucleation rate, although a full quantitative agreement has not yet been reached. For case (ii), thermal effects being negligible, it is the pressure dependency of the surface tension, much stronger for nitrogen than for helium, that explains the trends observed, although also here a full quantitative agreement has not yet been achieved.

Spectral light extinction to characterize fast fog formation.

Two supplementary methods for time-dependent droplet sizing, both based on the spectral dependence of light extinction, are applied to an adiabatically expanding vapor in which droplets are formed as a result of heterogeneous condensation. First, by measuring the extinction coefficients at three different wavelengths, we obtain time-dependent values of the modal radius, the size variance, and the droplet number density, with a typical time resolution of 1 µs. The shape of the size-distribution function is investigated by a second method. Using a white-light source in combination with a spectrometer and a CCD array, we obtain the full visible light attenuation spectrum with a time resolution of 1.5 ms. By applying an inversion technique based on trial size distributions, we find that the zeroth-order log-normal distribution describes the fog adequately. Both methods yield the same droplet growth curves and droplet number densities.

Photophoresis of a sphere in a rarefied gas

Abstract The photophoresis of a sphere is studied on the basis of the linearized B—G—K equation. The photophoretic forces are calculated for both near continuum and near free molecular flows. The photophoretic velocity of a suspended sphere is also obtained.