The admissibility domain of rarefaction shock waves in the near-critical vapour–liquid equilibrium region of pure typical fluids

2016 ◽  
Vol 795 ◽  
pp. 241-261 ◽  
Author(s):  
Nawin R. Nannan ◽  
Corrado Sirianni ◽  
Tiemo Mathijssen ◽  
Alberto Guardone ◽  
Piero Colonna
Keyword(s):  
Shock Waves ◽  
Critical Point ◽  
Compressible Flows ◽  
Three Dimensional ◽  
Fundamental Equation ◽  
Phase Region ◽  
Liquid Equilibrium ◽  
Two Phase ◽  
Rarefaction Shock ◽  
Equilibrium Region

Application of the scaled fundamental equation of state of Balfour et al. (Phys. Lett. A, vol. 65, 1978, pp. 223–225) based upon universal critical exponents, demonstrates that there exists a bounded thermodynamic domain, located within the vapour–liquid equilibrium region and close to the critical point, featuring so-called negative nonlinearity. As a consequence, rarefaction shock waves with phase transition are physically admissible in a limited two-phase region in the close proximity of the liquid–vapour critical point. The boundaries of the admissibility region of rarefaction shock waves are identified from first-principle conservation laws governing compressible flows, complemented with the scaled fundamental equations. The exemplary substances considered here are methane, ethylene and carbon dioxide. Nonetheless, the results are arguably valid in the near-critical state of any common fluid, namely any fluid whose molecular interactions are governed by short-range forces conforming to three-dimensional Ising-like systems, including, e.g. water. Computed results yield experimentally feasible admissible rarefaction shock waves generating a drop in pressure from 1 to 6 bar and pre-shock Mach numbers exceeding 1.5.

Deposition of C60, C70 and C84 fullerene molecules, in benzene via a change of the fluid state, from a gas–liquid two phase region to the critical point

2011 ◽  
Vol 58 (3) ◽  
pp. 407-411 ◽  
Author(s):  
Takahiro Fukuda ◽  
Yoshihiro Katsube ◽  
Nami Watabe ◽  
Shunji Kurosu ◽  
Raymond L.D. Whitby ◽  
...  
Keyword(s):  
Critical Point ◽  
Phase Region ◽  
Two Phase ◽  
Fluid State

Modeling of the Onset of Gas Entrainment Through a Finite-Side Branch

2003 ◽  
Vol 125 (5) ◽  
pp. 902-909 ◽  
Author(s):  
M. Ahmed ◽  
I. Hassan ◽  
N. Esmail
Keyword(s):  
Froude Number ◽  
Three Dimensional ◽  
Phase Region ◽  
Side Branch ◽  
Critical Height ◽  
Two Phase ◽  
Gas Entrainment ◽  
Branch Model ◽  
Predicted Values ◽  
New Criterion

A theoretical investigation has been conducted for the prediction of the critical height at the onset of gas entrainment during single discharge from a stratified, two-phase region through a side branch with a finite diameter. Two different models have been developed, a simplified point-sink model and a three-dimensional finite-branch model. The two models are based on a new criterion for the onset of gas entrainment. The results of the predicted critical heights at the onset of gas entrainment showed that the finite-branch model approaches the physical limits at low Froude numbers. However, as the values of the Froude number increased, the predictions of both models eventually converged to the same value. Based on the results of the models, the critical height corresponding to the onset of gas entrainment was found to be a function of Froude number and fluid densities. The results of both models are compared with available experimental data. The comparisons illustrate a very good agreement between the measured and predicted values.

scholarly journals Method for constructing the fundamental equation of state that takes into account the peculiarities of the substance behaviour in a wide vicinity of the critical point

2021 ◽  
Vol 2057 (1) ◽  
pp. 012112
Author(s):  
S V Rykov ◽  
I V Kudryavtseva
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Equation Of State ◽  
Critical Point ◽  
Fundamental Equation ◽  
Virial Coefficients ◽  
Phenomenological Theory ◽  
Phase Region ◽  
Scale Functions ◽  
Fundamental Equation Of State

Abstract On the basis of the phenomenological theory of the critical point and the Benedek hypothesis, an expression for the Helmholtz free energy F with scale functions in the density-temperature variables has been developed. The proposed free energy equation has been tested on the example of constructing the fundamental equation of state of 2,3,3,3-tetrafluoropropene (R1234yf). By comparison with the known experimental data on the equilibrium properties of R1234yf – density and pressure on the phase equilibrium line, p-ρ-T-data in the single-phase region, the second and third virial coefficients, isochoric heat capacity, isobaric heat capacity and the sound velocity – the operating range of the equation of state of R1234yf has been established according to temperature from 220 K to 420 K and pressure up to 20 MPa.

Theoretical Analysis of the Onset of Gas Entrainment from a Stratified Two-Phase Region Through Two Side-Oriented Branches Mounted on a Vertical Wall

2005 ◽  
Vol 128 (1) ◽  
pp. 131-141 ◽  
Author(s):  
Mahmoud A. Ahmed
Keyword(s):  
Theoretical Analysis ◽  
Small Deviation ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Phase Region ◽  
Critical Height ◽  
Two Phase ◽  
Mass Rate ◽  
Gas Entrainment ◽  
Branch Model

A theoretical analysis has been developed to predict the critical height and the location of the onset of gas entrainment during discharge from a stratified two-phase region through two oriented-side branches mounted on a vertical wall. In this analysis, a point sink model was first developed, followed by a more accurate three-dimensional finite branch model. The models are based on a new modified criterion for the onset of gas entrainment. The theoretically predicted critical height and the location of the onset of gas entrainment are found to be a function of the mass rate of each branch (Fr1 and Fr2), the distance between the centerlines of the two branches (L∕d), and the inclination angle (θ). The effects of these variables on the predicted critical height and the onset location were investigated. Furthermore, comparison between the theoretically predicted results and the available experimental data was carried out to verify the developed models. The comparison shows that the predicted results are very close to the measured data within a deviation percentage of 12% at Fr1>10. This small deviation percentage reflects a good agreement between the measured and predicted results.

scholarly journals A study on phase equilibria in the CaO-Al2O3-SiO2-“Nb2O5”(5 mass pct) system in reducing atmosphere

2013 ◽  
Vol 49 (2) ◽  
pp. 145-151
Author(s):  
B. Yan ◽  
R. Guo ◽  
J. Zhang
Keyword(s):  
Phase Equilibria ◽  
Weight Ratio ◽  
Phase Relationship ◽  
Liquid Equilibrium ◽  
Two Phase ◽  
Sio2 System ◽  
Reducing Atmosphere ◽  
Isothermal Equilibration ◽  
Relationship Of ◽  
Equilibrium Region

Phase equilibria in 5 mass% ?Nb2O5? plane of CaO-Al2O3-SiO2-?Nb2O5? system at 1873 K in an oxygen partial pressure of 1.78?10-6 Pa have been investigated through isothermal equilibration and quenching followed by EPMA examinations. In order to characterize the effect of niobium oxide on the phase relationship of the CaO-Al2O3-SiO2 system, Nb2O5-containing and Nb2O5-free samples with the same CaO/Al2O3/SiO2 weight ratio were investigated simultaneously. The ratios of CaO/Al2O3/SiO2 were selected from the CaO?2Al2O3-liquid two-phase equilibrium region in the CaO-Al2O3- SiO2 system at1873 K. It was found that the adding of 5 mass% Nb2O5 to the CaO-Al2O3-SiO2 system caused the original CaO?2Al2O3-liquid equilibrium to become three different new equilibria. The three equilibria were single liquid phase, CaO?6Al2O3-liquid and gehlenite-CaO?2Al2O3-liquid equilibrium respectively. The gehlenite phase may be a new solid solution of 2CaO?Al2O3?SiO2 and NbOx with melting point higher than 1873 K.

Three-Dimensional Integrated Circuit With Embedded Microfluidic Cooling: Technology, Thermal Performance, and Electrical Implications

2016 ◽  
Vol 138 (1) ◽  
Author(s):  
Xuchen Zhang ◽  
Xuefei Han ◽  
Thomas E. Sarvey ◽  
Craig E. Green ◽  
Peter A. Kottke ◽  
...  
Keyword(s):  
Thermal Performance ◽  
Integrated Circuit ◽  
Single Phase ◽  
Three Dimensional ◽  
Phase Region ◽  
Heat Sinks ◽  
Thermal Testing ◽  
Two Phase ◽  
Maximum Heat ◽  
Maximum Heat Transfer

This paper reports on novel thermal testbeds with embedded micropin-fin heat sinks that were designed and microfabricated in silicon. Two micropin-fin arrays were presented, each with a nominal pin height of 200 μm and pin diameters of 90 μm and 30 μm. Single-phase and two-phase thermal testing of the micropin-fin array heat sinks were performed using de-ionized (DI) water as the coolant. The tested mass flow rate was 0.001 kg/s, and heat flux ranged from 30 W/cm2 to 470 W/cm2. The maximum heat transfer coefficient reached was 60 kW/m2 K. The results obtained from the two testbeds were compared and analyzed, showing that density of the micropin-fins has a significant impact on thermal performance. The convective thermal resistance in the single-phase region was calculated and fitted to an empirical model. The model was then used to explore the tradeoff between the electrical and thermal performance in heat sink design.

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