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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 determination in copper shock compressed to 190 GPa
Sound speed measurements in shock compressed solids have long been valuable for the development of equations of state at extreme conditions, shock-induced phase transformations, and a comprehensive characterization of the thermophysical response of high-pressure standards. We present results from plate impact experiments to 190 GPa to determine the longitudinal sound speed in copper—an important high-pressure standard. Surprisingly, the sound speeds determined using the two most common experimental techniques—the front surface impact (FSI) approach and the release wave overtake (RWO) approach—diverge significantly for stresses greater than ~100 GPa. Further analyses, including numerical simulations, show that the FSI experiments provide the correct sound speeds and that fundamental assumptions underlying the RWO method are likely violated due to the complex release response of shock compressed copper. The sound speeds determined using the FSI approach provide for a more accurate high-pressure description of copper in dynamic compression experiments. The present findings are in contrast to the results for shock compressed silver [Wallace et al., Phys. Rev. B 104, 214106 (2021)], where both methods provided consistent sound speed results. Thus, the findings presented here demonstrate the need to experimentally verify the validity of the RWO method on a case-by-case basis. Finally, we note that even at the high stresses in the present work, the copper unloading response shows a time-dependent, quasielastic response often observed in metals at lower stresses.
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.
A semi-analytic estimate for the effective sound speed counterterm in the EFTofLSS
The Effective Field Theory of Large Scale Structure (EFTofLSS) has found tremendous success as a perturbative framework for the evolution of large scale structure, and it is now routinely used to compare theoretical predictions against cosmological observations. The model for the total matter field includes one nuisance parameter at 1-loop order, the effective sound speed, which can be extracted by matching the EFT to full N-body simulations. In this work we first leverage the Layzer-Irvine cosmic energy equation to show that the equation of state can be exactly computed with knowledge of the fully nonlinear power spectrum. When augmented with separate universe methods, we show one can estimate the effective sound speed. This estimate is in good agreement with simulation results, with errors at the few tens of percent level. Here, we apply our method to investigate the cosmology dependence of the effective sound speed and to shed light on what cosmic structures shape its value.
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
Sound speed measurements in shock-compressed cemented Tungsten carbides at pressures up to 100 GPa
To gain insights into thermodynamic states attained during shock compression of cemented tungsten carbide with 3.7 wt.% cobalt binder, we present results of longitudinal sound (release wave) speed measurements and their analysis at peak stresses up to 100 GPa (volumetric compression ratio ~ 15%). The sound speeds are determined using front-surface impact and release-wave overtake plate impact experimental configurations using laser interferometry. The measured sound speed data along with estimates for bulk sound speeds obtained using the fourth-order Birch-Murnaghan EoS and thermodynamics are used to determine the longitudinal moduli and shear moduli of shocked tungsten carbide at the various peak compression states attained in the experiments. Here, the longitudinal sound speeds were found to increase linearly with volume compression ratio from 6.97 ± 0.010 km/s at ambient conditions to 8.26 ± 0.156 km/s at a volume compression ratio of ~ 15%. The corresponding longitudinal elastic moduli also increase nearly linearly with the volume compression ratio but remain consistently lower than their theoretical predictions based on continuum models with no damage. Also, the sensitivity of shear moduli to pressure, as predicted by the Steinberg-Guinan model, is reduced substantially and the shear moduli of cemented WC with 3.7 wt.% Co remains nearly constant at ~ 310 GPa at the various peak compression stress states investigated in the present study.
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.
Speed of Sound Measurements of R-1130(E) and an Azeotropic Blend of R-1336mzz(Z)/1130(E)
Sound speed data measured using a dual-path pulse-echo instrument are reported for pure trans-1,2-dichloroethene (R-1130(E)) and an azeotropic blend of cis-1,1,1,4,4,4-hexafluorobutene (R-1336mzz(Z)) and R-1130(E) with a composition of 74.8 mass % R-1336mzz(Z) with the balance being R-1130(E). The azeotropic blend of R-1336mzz(Z)/1130(E) is classified as R-514A in ANSI/ASHRAE standard 34. Liquid phase speed of sound data are reported from just above the saturation pressure of pure R-1130(E) or the bubble point pressure of R-514A to a maximum pressure of 26.7 MPa. The relative combined expanded uncertainty in the speed of sound varies from 0.032 % to 0.148 % with the greatest deviations occurring at the lowest sound speeds. At present, no reference Helmholtz-energy-explicit equation of state (EOS) is available for R-1130(E). Therefore, the reported data for pure R-1130(E) are compared to an extended corresponding states (ECS) model. Deviations between the pure R-1130(E) sound speed data and the ECS model were found to be consistently negative ranging between − 4.1 % and − 3.5 %. The R-514A data are compared to a multifluid model inclusive of the established reference Helmholtz-energy-explicit EOS for R-1336mzz(Z) and ECS model for R-1130(E) with estimated binary interaction parameters. Deviations between the experimental speed of sound data and the multifluid model were also found to be consistently negative. However, deviations from the multifluid model were found to be as great as − 17.1 %. The large deviations from the ECS model and multifluid model underscore the need for a robust Helmholtz-energy-explicit EOS for R-1130(E).
Sound Speeds of Solids from Ultrasonic Pulse Receiver Measurements
A common method of determining elastic material properties is utilizing an ultrasonic pulse receiver. This is a non-destructive test (NDT) causing no plastic deformation of the material. It requires a pulse generator, oscilloscope, and two transducers to measure the sound velocity of a material. Both longitudinal and shear sound velocities may be obtained by utilizing the appropriate transducer. Acoustic nondestructive testing methods are often used in manufacturing certification processes and for material defect detection in industry. These methods can also be utilized to directly measure the elastic moduli of a material without damaging the material. Overall, it is a low-cost experiment with minimal preparation, and is easy to use.
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.
Exploring high-pressure tantalum sound speeds and strength using multi-sample shock release experiments
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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
Speed of Sound Measurements of Binary Mixtures of 1,1-Difluoroethylene (R-1132a) + Propane and Derived Speed of Sound of Pure R-1132a
Speed of sound data, measured using a dual-path pulse-echo instrument, are reported for three binary mixtures of 1,1-difluoroethylene (R-1132a) with propane at temperatures ranging from 230 to 345 K and pressures ranging from slightly above the bubble curve to a maximum pressure of 50 MPa. Significant attenuation of the pulse-echo signals was observed for measurements on pure R-1132a. Therefore, the R-1132a sample was doped with propane at mole fractions ranging from 0.0274 to 0.0887 and the propane + R-1132a mixture data was used to derive sound speeds for pure R-1132a. The data were compared to a preliminary equation of state for R-1132a, and deviations ranged from 2 % to 8 %. This demonstrates that the preliminary R-1132a EoS needs to be refit to better represent the speed of sound.
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.