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Tommaso Ruggeri - One of the best experts on this subject based on the ideXlab platform.
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a 2 times 2 simple model in which the sub shock exists when the shock Velocity is slower than the maximum Characteristic Velocity
Ricerche Di Matematica, 2019Co-Authors: Shigeru Taniguchi, Tommaso RuggeriAbstract:For a generic hyperbolic system of balance laws, the shock-structure solution is not continuous and a discontinuous part (sub-shock) arises when the Velocity of the front s is greater than a critical value. In particular, for systems compatible with the entropy principle, continuous shock-structure solutions cannot exist when s is larger than the maximum Characteristic Velocity evaluated in the unperturbed state $$s >\lambda ^{\max }_0 $$ . This is the typical situation of systems of Rational Extended Thermodynamics (ET). Nevertheless, in principle, sub-shocks may exist also for s smaller than $$\lambda ^{\max }_0 $$ . This was proved with a simple example in a recent paper by Taniguchi and Ruggeri (Int J Non-Linear Mech 99:69, 2018). In the present paper, we offer another simple case that satisfies all requirements of ET, that is, the entropy inequality, convexity of the entropy, sub-Characteristic condition and Shizuta-Kawashima condition, however, there exists a sub-shock with s slower than $$\lambda ^{\max }_0 $$ . Therefore there still remains an open question which other property makes the systems coming from ET have this beautiful property that the sub-shock exists only for s greater than the unperturbed maximum Characteristic Velocity.
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shock structure and multiple sub shocks in binary mixtures of eulerian fluids
Ricerche Di Matematica, 2017Co-Authors: Fiammetta Conforto, Andrea Mentrelli, Tommaso RuggeriAbstract:The problem of sub-shock formation within a shock structure solution of hyperbolic systems of balance laws is investigated for a binary mixture of multi-temperature Eulerian fluids. The main purpose of this work is the analysis of the ranges of Mach numbers characterizing shock-structure solutions with different features, continuous or not, and to show the existence of ranges, below the maximum unperturbed Characteristic Velocity, for which each constituent of the mixture may develop a sub-shock within a smooth shock structure profile. The theoretical results are supported by numerical calculations.
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molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments
Annals of Physics, 2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Abstract Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The Characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium Characteristic Velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N ) by Boillat and Ruggeri (1997) λ ( N ) E , max c 0 ⩾ 6 5 ( N − 1 2 ) , ( c 0 = 5 3 k m T ) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule.
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Extended thermodynamics of rarefied polyatomic gases and Characteristic velocities
2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Extended Thermodynamics of rarefied polyatomic gases is characterized by two hi- erarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a particle is taken into account. To obtain the closed set of the field equations for the system with many moments and for an arbitrary entropy functional that includes degenerate gases, the entropy principle and maximum entropy principle are studied and the equivalence of these two methods is shown as in the well-established case of the monatomic gas. In addition the recent results of the present theory are summarized. On the basis of physical considerations, the truncation orders of the two hierarchies are seen to be not independent on each other. The equilibrium Characteristic velocities of the emerging hyperbolic system of partial di¤erential equations are analyzed and com- pared to those of monatomic gases. Inspection shows that the lower bound estimate of the maximum equilibrium Characteristic Velocity valid for monatomic gases, which increases as the truncation order increases, is valid for any rarefied polyatomic gas
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Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments
2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The Characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium Characteristic Velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N) by Boillat and Ruggeri (1997) $\frac{\lambda^{E, max}_{(N)}}{c_0} \geq \sqrt{\frac{6}{5}\left(N-\frac{1}{2}\right)}$, ($c_0 = \sqrt{\frac{5kT}{3m}}$) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule
Meisam Torabmostaedi - One of the best experts on this subject based on the ideXlab platform.
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new correlations for slip Velocity and Characteristic Velocity in a rotary liquid liquid extraction column
Chemical Engineering Research & Design, 2017Co-Authors: Mehdi Asadollahzadeh, Rezvan Torkaman, Meisam TorabmostaediAbstract:Abstract In this research work, the hydrodynamic behavior of a Kuhni extraction column has been investigated for determination of slip Velocity and Characteristic Velocity for three different liquid–liquid systems with and without mass transfer conditions and toluene–water system with the presence of silica nanoparticles. The effects of the agitation speed, dispersed as well as continuous phase Velocity, and interfacial tension were studied. The findings revealed that an increase in agitation speed and continuous phase Velocity led to the reduction of slip Velocity while it increased with increasing dispersed phase Velocity. More buoyancy and faster upward movement of larger drops accelerate the slip Velocity in the dispersed to continuous phase mass transfer condition as compared with the case of no mass transfer. In addition, the slip Velocity decreased in the experimental conditions with nanoparticles because of the decrease in Sauter mean drop diameter and the increase in the holdup. Empirical correlations for prediction of slip and Characteristic velocities are recommended. The results of the proposed correlations were compared with the experimental data obtained from the literature and the present investigation. Findings of this study demonstrated that the proposed correlations gave accurate predictions for slip Velocity and Characteristic Velocity.
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holdup Characteristic Velocity and slip Velocity between two phases in a multi impeller column for high medium low interfacial tension systems
Chemical Engineering and Processing, 2016Co-Authors: Mehdi Asadollahzadeh, Meisam Torabmostaedi, Shahrokh Shahhosseini, Ahad GhaemiAbstract:Abstract In this research work, liquid–liquid extraction via three different systems has been investigated for determination of holdup, slip Velocity and Characteristic Velocity in a multi-impeller column. The effects of the agitation speed, dispersed as well as continuous phase Velocity, direction of mass transfer, and interfacial tension were studied. The findings revealed that an increase in agitation speed and continuous phase Velocity led to the reduction of slip Velocity while it increased with increasing dispersed phase Velocity. More buoyancy and faster upward movement of larger drops accelerate the slip Velocity in the dispersed to continuous phase mass transfer condition as compared with the case of no mass transfer. Empirical correlations for prediction of holdup, and slip and Characteristic velocities are recommended. The results of the proposed correlations were compared with the experimental data obtained from the literature and the present investigation. Findings of this study demonstrated that the proposed correlations give accurate predictions for slip Velocity, Characteristic Velocity and holdup.
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dispersed phase hold up and Characteristic Velocity in a pulsed packed extraction column
Chemical Industry & Chemical Engineering Quarterly, 2012Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Ali Haghighiasl, Meisam TorabmostaediAbstract:Dispersed phase hold-up has been measured in a 76.2 mm diameter pulsed packed column for four different liquid-liquid systems. The effects of pulsation intensity, phase ratio, and packing Characteristic on the hold-up have been investigated under a variety of operating conditions. The dispersed phase axial hold-up shows a strong non-uniformity, depending on the operating conditions. The results indicated that the Characteristic Velocity approach is applicable to this type of extraction column for analysis of hold-up. An empirical correlation is derived for prediction of the hold-up in terms of operating variables, physical properties of the systems, and packing geometry. Good agreement between prediction and experiments was observed for all investigated operating conditions.
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holdup and Characteristic Velocity in a hanson mixer settler extraction column
Chemical Engineering Research & Design, 2010Co-Authors: M Napeida, Jaber Safdari, Haghighi A Asl, Meisam TorabmostaediAbstract:The hydrodynamic behavior of a pilot plant Hanson mixer–settler extraction column has been studied for three different liquid–liquid systems with and without mass transfer conditions. The dispersed phase axial holdup profile is investigated and an empirical correlation for prediction of dispersed phase holdup is recommended in terms of physical properties of liquid systems and operating conditions. A comparison between several correlations and experimental results shows that Pratt equation is more suitable for prediction of slip Velocity because of its simplicity. On this basis, an empirical correlation is derived for prediction of Characteristic Velocity in terms of physical properties of liquid systems and operating conditions.
Geoffrey W Stevens - One of the best experts on this subject based on the ideXlab platform.
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hydrodynamic performance of a pulsed solvent extraction column with novel ceramic internals holdup and drop size
Industrial & Engineering Chemistry Research, 2017Co-Authors: Yong Wang, Kathryn H Smith, Weiyang Fei, Geoffrey W StevensAbstract:Chloride in the extraction of lithium from brine in salt lakes and the separation of rare earth elements are both very corrosive to stainless steel extraction column internals, which is a significant problem in large scale production. The hydrodynamics of two types of novel anticorrosive ceramic internals, the hybrid ceramic internal and ceramic plate, are designed and tested under pilot plant conditions in order to be considered for application to these industries. The results show that holdup decreases first and then increases with an increase of pulsation intensity. Increasing dispersed phase Velocity also increases holdup. Sauter mean diameter, d32, decreases with an increase of pulsation intensity, while superficial velocities of both phases have little effect. A range of correlations for holdup and d32 from literature are compared to the data, and it is shown that new correlations are needed to accurately predict the performance of the two internal types. Characteristic Velocity, which is key parame...
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dispersed phase holdup and Characteristic Velocity in a pulsed and nonpulsed disk and doughnut solvent extraction column
Industrial & Engineering Chemistry Research, 2016Co-Authors: Kathryn A Mumford, Kathryn H Smith, Geoffrey W StevensAbstract:The dispersed-phase holdup and Characteristic Velocity, which are important hydrodynamic performance parameters for solvent extraction columns, were measured and compared to literature correlations under pulsing and nonpulsing conditions using a 75 mm diameter disk-and-doughnut column. The results show that the dispersed-phase holdup increased with increasing dispersed-phase flow rate, while there was no noticeable change in holdup with the continuous-phase flow rate. With increasing pulsation intensity from zero, the dispersed-phase holdup decreased at first and then increased. A minimum holdup was found in the transition from the mixer-settler to the emulsion regime, and it increased with increasing dispersed-phase Velocity. The experimental holdup and minimum holdup were correlated over a range of pulsation rates to within 13.3% and 8.8%, respectively. The Characteristic velocities under different pulsation conditions were calculated from the measured holdup for the pulsing conditions. The characterist...
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pulsed disc and doughnut column performance
Solvent Extraction and Ion Exchange, 2009Co-Authors: Ali B Jahya, Geoffrey W Stevens, H R C PrattAbstract:Abstract: A study of the hydrodynamic variables, drop size, continuous phase axial dispersion, and mass‐transfer coefficients of a pulsed annular disc‐and‐doughnut liquid extraction column are presented for three different systems. The results indicate that the Characteristic Velocity plot of Gayler et al. (1953) can be used to describe the variation of holdup with flow rate for a range of pulsation velocities. The existence of several different operating regimes, namely streamline, mixer‐settler, and emulsion regimes, was observed when the input energy was altered. Mass‐transfer data from 72.5 mm i.d. and 2.5 m i.d. columns were interpreted in terms of the differential axial‐dispersion model; the number of transfer units in a unit length of column is proposed as the basis for scale‐up of the mass‐transfer performance. By considering the free areas in the column, a method is proposed for the geometric scale‐up of pulsed disc‐and‐doughnut columns.
Takashi Arima - One of the best experts on this subject based on the ideXlab platform.
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Characteristic Velocity and dispersion relation of linear waves in extended thermodynamics of a van der Waals gas
Ricerche di Matematica, 2020Co-Authors: Takashi ArimaAbstract:We study the Characteristic velocities of the extended thermodynamics of molecular rotational- and vibrational- relaxation processes for a van der Waals gas. The lower and upper bounds of the Characteristic Velocity are, respectively, estimated by the one of rarefied gases and the one evaluated on the spinodal curve. We also study the dispersion relation of linear waves, in particular, the phase Velocity, attenuation factor and attenuation per wavelength in a low frequency region.
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molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments
Annals of Physics, 2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Abstract Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The Characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium Characteristic Velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N ) by Boillat and Ruggeri (1997) λ ( N ) E , max c 0 ⩾ 6 5 ( N − 1 2 ) , ( c 0 = 5 3 k m T ) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule.
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Extended thermodynamics of rarefied polyatomic gases and Characteristic velocities
2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Extended Thermodynamics of rarefied polyatomic gases is characterized by two hi- erarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a particle is taken into account. To obtain the closed set of the field equations for the system with many moments and for an arbitrary entropy functional that includes degenerate gases, the entropy principle and maximum entropy principle are studied and the equivalence of these two methods is shown as in the well-established case of the monatomic gas. In addition the recent results of the present theory are summarized. On the basis of physical considerations, the truncation orders of the two hierarchies are seen to be not independent on each other. The equilibrium Characteristic velocities of the emerging hyperbolic system of partial di¤erential equations are analyzed and com- pared to those of monatomic gases. Inspection shows that the lower bound estimate of the maximum equilibrium Characteristic Velocity valid for monatomic gases, which increases as the truncation order increases, is valid for any rarefied polyatomic gas
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Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments
2014Co-Authors: Takashi Arima, Andrea Mentrelli, Tommaso RuggeriAbstract:Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The Characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium Characteristic Velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N) by Boillat and Ruggeri (1997) $\frac{\lambda^{E, max}_{(N)}}{c_0} \geq \sqrt{\frac{6}{5}\left(N-\frac{1}{2}\right)}$, ($c_0 = \sqrt{\frac{5kT}{3m}}$) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule
Jaber Safdari - One of the best experts on this subject based on the ideXlab platform.
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experimental investigation on regime transition and Characteristic Velocity in a horizontal vertical pulsed sieve plate column
RSC Advances, 2017Co-Authors: Sahar Akhgar, Jaber Safdari, Jafar Towfighi, Pouria Amani, Mohammad H MallahAbstract:In this study, we attempted to evaluate the flow regime transitions in a novel type of extractor, called a horizontal–vertical pulsed sieve-plate column, for three liquid–liquid systems: toluene–water, butyl acetate–water, and n-butanol–water, with a 3% volumetric fraction of acetone in the dispersed phase as a mass transfer agent. Moreover, due to the importance of the Characteristic Velocity, the effects of operating parameters, such as the pulsation intensity and flow rate of the phases, have been investigated in each section of the column. The Characteristic Velocity shows different behaviors with the variation of the operating parameters in each section, which has been thoroughly discussed in this study. New correlations for the transitions from the mixer-settler regime to the dispersion regime in the vertical section and from the dispersion regime to the emulsion regime in the horizontal section have been proposed, which indicate the lower and upper limits of the proper pulsation intensity to identify the operational range of the dispersion regime. Furthermore, new correlations have been proposed for the prediction of the Characteristic Velocity in each section of the column, with average absolute relative errors (AAREs) ranging from 9.81% to 11.15%, which represent a satisfactory agreement between the experimental and calculated data.
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dispersed phase hold up and Characteristic Velocity in a pulsed packed extraction column
Chemical Industry & Chemical Engineering Quarterly, 2012Co-Authors: Mehdi Asadollahzadeh, Jaber Safdari, Ali Haghighiasl, Meisam TorabmostaediAbstract:Dispersed phase hold-up has been measured in a 76.2 mm diameter pulsed packed column for four different liquid-liquid systems. The effects of pulsation intensity, phase ratio, and packing Characteristic on the hold-up have been investigated under a variety of operating conditions. The dispersed phase axial hold-up shows a strong non-uniformity, depending on the operating conditions. The results indicated that the Characteristic Velocity approach is applicable to this type of extraction column for analysis of hold-up. An empirical correlation is derived for prediction of the hold-up in terms of operating variables, physical properties of the systems, and packing geometry. Good agreement between prediction and experiments was observed for all investigated operating conditions.
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holdup and Characteristic Velocity in a hanson mixer settler extraction column
Chemical Engineering Research & Design, 2010Co-Authors: M Napeida, Jaber Safdari, Haghighi A Asl, Meisam TorabmostaediAbstract:The hydrodynamic behavior of a pilot plant Hanson mixer–settler extraction column has been studied for three different liquid–liquid systems with and without mass transfer conditions. The dispersed phase axial holdup profile is investigated and an empirical correlation for prediction of dispersed phase holdup is recommended in terms of physical properties of liquid systems and operating conditions. A comparison between several correlations and experimental results shows that Pratt equation is more suitable for prediction of slip Velocity because of its simplicity. On this basis, an empirical correlation is derived for prediction of Characteristic Velocity in terms of physical properties of liquid systems and operating conditions.