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Metastable sound speed in gas-liquid mixtures
A new method of calculating speed of sound for two-phase flow is presented. The new equation assumes no phase change during the propagation of an acoustic disturbance and assumes that only the total entropy of the mixture remains constant during the process. The new equation predicts single-phase values for the speed of sound in the limit of all gas or all liquid and agrees with available two-phase, air-water sound speed data. Other expressions used in the two-phase flow literature for calculating two-phase, metastable sound speed are reviewed and discussed. Comparisons are made between the new expression and several of the previous expressions -- most notably a triply isentropic equation as used, a triply isentropic equation as used, among others, by Karplus and by Wallis. Appropriate differences are pointed out and a thermodynamic criterion is derived which must be satisfied in order for the triply isentropic expression to be thermodynamically consistent. This criterion is not satisfied for the cases examined, which included two-phase nitrogen, air-water, two-phase parahydrogen, and steam-water. Consequently, the new equation derived is found to be superior to the other equations reviewed.
Sound speed measurements in liquid oxygen-liquid nitrogen mixtures
The sound speed in liquid oxygen (LOX), liquid nitrogen (LN2), and five LOX-LN2 mixtures was measured by an ultrasonic pulse-echo technique at temperatures in the vicinity of -195.8C, the boiling point of N2 at a pressure of I atm. Under these conditions, the measurements yield the following relationship between sound speed in meters per second and LN2 content M in mole percent: c = 1009.05-1.8275M+0.0026507 M squared. The second speeds of 1009.05 m/sec plus or minus 0.25 percent for pure LOX and 852.8 m/sec plus or minus 0.32 percent for pure LN2 are compared with those reported by past investigators. Measurement of sound speed should prove an effective means for monitoring the contamination of LOX by Ln2.
Thermodynamic properties of nitrogen gas derived from measurements of sound speed
A virial equation of state for nitrogen was determined by use of newly measured speed-of-sound data and existing pressure-density-temperature data in a multiproperty-fitting technique. The experimental data taken were chosen to optimize the equation of state for a pressure range of 0 to 10 atm and for a temperature range of 60 to 350 K. Comparisons are made for thermodynamic properties calculated both from the new equation and from existing equations of state.
Measurement of hypersonic sound speeds in methane at moderate pressures
Measurement of hypersonic sound speeds in methane at moderate pressure and comparison with ultrasonic speed data
Profile types of sound speed in the lower atmosphere and their relationships to acoustic focusing
Profile types of sound speed in lower atmosphere and relations to acoustic focusing
Generalization of low pressure, gas-liquid, metastable sound speed to high pressures
A theory is developed for isentropic metastable sound propagation in high pressure gas-liquid mixtures. Without simplification, it also correctly predicts the minimum speed for low pressure air-water measurements where other authors are forced to postulate isothermal propagation. This is accomplished by a mixture heat capacity ratio which automatically adjusts from its single phase values to approximately the isothermal value of unity needed for the minimum speed. Computations are made for the pure components parahydrogen and nitrogen, with emphasis on the latter. With simplifying assumptions, the theory reduces to a well known approximate formula limited to low pressure.
Measurement of the speed of sound in ice
The data presented demonstrate the gathering of sound speed measurements in refrigerated ice, using both compressional and shear waves, on the basis of ice thickness and sound wave time-of-travel parameters. Clear and sharp echo reflections were obtained for both compressional and shear waves at the aluminum/ice and ice/aluminum interfaces for ice at -26 C; ice formed at various conditions can have different sound speeds, depending on the density and elastic constants.
Speed of sound in the solar interior
The sound speed of the solar interior is directly determinable on the basis of the frequencies of solar 5-min oscillations, irrespective of solar model, and relying only on a simple asymptotic description of the oscillations in terms of trapped acoustic waves. It is plausible that, by using this asymptotic determination as an initial trial in a more accurate inversion, and imposing constraints of smoothness on the solution resulting from the iteration, a good model representing the large scale structure of the sun which satisfies the observed frequencies may be determined.
Speed of sound along the vapor-liquid phase equilibrium curve. Speed of sound in saturated water vapor
Sound wave propagation in saturated and wet vapor, and sound speed measurements on vapor-liquid phase equilibrium curve
Numerical Speed of Sound and its Application to Schemes for all Speeds
The concept of "numerical speed of sound" is proposed in the construction of numerical flux. It is shown that this variable is responsible for the accurate resolution of' discontinuities, such as contacts and shocks. Moreover, this concept can he readily extended to deal with low speed and multiphase flows. As a results, the numerical dissipation for low speed flows is scaled with the local fluid speed, rather than the sound speed. Hence, the accuracy is enhanced the correct solution recovered, and the convergence rate improved. We also emphasize the role of mass flux and analyze the behavior of this flux. Study of mass flux is important because the numerical diffusivity introduced in it can be identified. In addition, it is the term common to all conservation equations. We show calculated results for a wide variety of flows to validate the effectiveness of using the numerical speed of sound concept in constructing the numerical flux. We especially aim at achieving these two goals: (1) improving accuracy and (2) gaining convergence rates for all speed ranges. We find that while the performance at high speed range is maintained, the flux now has the capability of performing well even with the low: speed flows. Thanks to the new numerical speed of sound, the convergence is even enhanced for the flows outside of the low speed range. To realize the usefulness of the proposed method in engineering problems, we have also performed calculations for complex 3D turbulent flows and the results are in excellent agreement with data.
Some applications of equilibrium thermodynamic properties to continuum gasdynamics
The speed of sound for the propagation of isentropic disturbances in a gas is developed, including corrections for chemical reaction. The term zero frequency is used to describe this isentropic limit sound speed; the term signifies that change in the gasdynamic variables are all very slow compared with the chemical rate changes in the gas. A faster, nonisentropic speed of propagation occurs for disturbances where the changes in gasdynamic variables are fast compared with the chemical rate changes. In the limit, this is known as the infinite frequency or frozen sound speed - the former term calling attention to the very high frequency of the disturbance, the latter term calling attention to the frozen character of the chemical reactions under such rapid changes of state. The true sound speed for a disturbance of finite frequency is shown to be between these two limits and is expressed in terms of the chemical relaxation time. The Riemann invariants that are useful in determining the changes in flow speed along characteristic directions in supersonic flow are derived in terms of integrations of acoustic impedance, and example results are given for air.
Speed of sound in fluid parahydrogen.
Speed of sound measured in compressed fluid para hydrogen for temperatures from 15 to 100 degrees K and pressures to 300 atmospheres
Speed of sound and temperature in the ocean by Brillouin scattering
A method is described to measure the speed of sound and the temperature in the sea as functions of depth. Backscattered laser light is analyzed with an interferometric spectrometer. The speed of sound at very short acoustic wavelengths is obtained directly from the wavelength shift of the Brillouin scattered light, and the temperature is deduced from the speed of sound together with auxiliary information on depth and salinity. Experiments are described.
Estimated wave speeds in coronal holes and streamers
In this paper, characteristic wave speeds in the solar corona are made based on published models of a coronal hole and streamer. It is found that the Alfven speed varies from over 4000 km/s at the center of the coronal hole at 2.0 solar radii down to about 100 km/s in the center of the streamer at 5.0 solar radii. Taking into account the bias in the streamer model, a more realistic estimate of the minimum Alfven speed is 800 km/s at the same location. The sound speed lies between 100 and 200 km/s everywhere between 2.0 and 5.0 solar radii while the flow speed is generally less than the sound speed at 2.0 solar radii and greater than the sound speed at 5.0 solar radii.
Bound oscillations on thin magnetic flux tubes - Convective instability and umbral oscillations
The possibility that 'tube waves' can be trapped on slender solar magnetic flux tubes is investigated. For rigid isothermal flux tubes, it is found that the flux tube geometry can by itself lead to waves which are trapped on the part of the tube that expands with height. Some geometries lead to trapped modes with eigenperiods near 180 s, if parameters appropriate to sunspot umbrae are chosen. It is possible that the umbral oscillations are a manifestation of such trapped waves, if sunspot umbrae consist of an assembly of slender flux tubes, as in the spaghetti model of Parker (1979). For flux tubes which have a constant ratio of Alfven speed to sound speed, it is found that it is primarily the variation of temperature with height which determines whether trapped waves can exist. Certain temperature profiles lead to disturbances for which omega squared is less than zero, corresponding to convective instability or Rayleigh-Taylor instability.
Solar structure inversion with LOWL data
Inversion results for the radial hydrostatic structure of the Sun, using six months of oscillation data obtained with the LOWL instrument, are presented. Both low and intermediate degree modes are used, thus avoiding the systematic errors that might have occurred in previous inversions by merging more than one data set. Using modes of between 0 deg and 90 deg and frequencies of between 1.5 mHz and 3.5 mHz, the variations with depth of the speed of sound, the density and the pressure were inferred for radii of between 0.05 and 0.85 stellar radius. It was found that in this region, the sound speed was within 0.15% of that of a model constructed using an equation of state that incorporated helium diffusion. The density difference between the Sun and the model was less than 0.8%. Given the small error bars on the inversion results, these differences are considered as being significant.
Turbulence Scales, Rise Times, Caustics, and the Simulation of Sonic Boom Propagation
The general topic of atmospheric turbulence effects on sonic boom propagation is addressed with especial emphasis on taking proper and efficient account of the contributions of the portion oi the turbulence that is associated with extremely high wavenumber components. The recent work reported by Bart Lipkens in his doctoral thesis is reexamined to determine whether the good agreement between his measured rise times with the 1971 theory of the author is fortuitous. It is argued that Lipken's estimate of the distance to the first caustic was a gross overestimate because of the use of a sound speed correlation function shaped like a gaussian curve. In particular, it is argued that the expected distance to the first caustic varies with the kinematic viscosity nu and the energy epsilon dissipated per unit mass per unit time, and the sound speed c as : d(sub first caustic) = nu(exp 7/12) c(exp 2/3)/ epsilon(exp 5/12)(nu x epsilon/c(exp 4))(exp a), where the exponent a is greater than -7/12 and can be argued to be either O or 1/24. In any event, the surprising aspect of the relationship is that it actually goes to zero as the viscosity goes to zero with s held constant. It is argued that the apparent overabundance of caustics can be grossly reduced by a general computational and analytical perspective that partitions the turbulence into two parts, divided by a wavenumber k(sub c). Wavenumbers higher than kc correspond to small-scale turbulence, and the associated turbulence can be taken into account by a renormalization of the ambient sound speed so that the result has a small frequency dependence that results from a spatial averaging over of the smaller-scale turbulent fluctuations. Selection of k(sub c). can be made so large that only a very small number of caustics are encountered if one adopts the premise that the frequency dispersion of pulses is caused by that part of the turbulence spectrum which lies in the inertial range originally predicted by Kolmogoroff. The acoustic propagating wave's dispersion relation has the acoustic wavenumber being of the form k = (omega/c) + F(omega), where c is a spatially averaged sound speed and where, for mechanical turbulence, the extra term F(omega) must depend on only the angular frequency omega, the sound speed c, and the turbulent energy dissipation epsilon per unit fluid mass and per unit time. If the turbulence is weak, then the quantity F(omega) has to be of second order in the portions of the turbulent fluid velocity in the inertial range, so, following Kolmogoroff's reasoning, it must vary with epsilon as epsilon(exp 2/3). Simple dimensional analysis then reveals that F(omega) is K epsilon(exp 2/3) c(exp -7/3) omega(exp l/3), K being a universal dimensionless complex constant.