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Fluids
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Bulk Viscosity and Relaxation Processes: Revisited
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Bulk Viscosity and Relaxation Processes: Revisited

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 11082

Special Issue Editors

Prof. Dr. Elena Kustova

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Guest Editor
Fluid Dynamics Department, Saint Petersburg State University, 199034 Saint Petersburg, Russia
Interests: nonequilibrium reacting flows; kinetic theory of transport processes; compressible flows
Dr. Rakesh Kumar

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Guest Editor
Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, Uttar Pradesh, India
Interests: nonequilibrium gas flows; micro/nano-fluidics; dusty-gas flows; heat transfer and thermal design of aerospace systems

Special Issue Information

Dear Colleagues,

Bulk viscosity is an interesting phenomenon in nonequilibrium gas and fluid flows. In dilute gases, it is related to the finite rate of energy redistribution between translational and internal degrees of freedom; in dense gases and fluids, it includes both the relaxation part and a configurational contribution due to elastic collisions determined by intermolecular interactions. Bulk viscosity was first discovered in the 1930s in sound-absorption experiments in molecular gases; it was shown that relaxation processes may violate the Stokes viscosity relation. Since that time, the problem of correct evaluation and interpretation of bulk viscosity remains one of the widely discussed topics in nonequilibrium fluid dynamics. The information related to the proposed theme is quite scattered (especially true for bulk viscosity). Large values of bulk viscosity coefficients found for polyatomic gases, when included in the Navier–Stokes equations, may yield incorrect physical solutions due to the wrong interpretation of various relaxation phenomena. Thus, a particular goal of this Special Issue is to gather the most recent developments in and around this area in a single Special Issue. This might provide readers with a coherent picture of the state-of-the-art in this interesting field of research.

Prof. Dr. Elena Kustova
Dr. Rakesh Kumar
Guest Editors

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Keywords

  • bulk viscosity
  • internal energy relaxation
  • nonequilibrium fluid dynamics

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Published Papers (5 papers)

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Research

23 pages, 1329 KiB  
Article
Continuum Models for Bulk Viscosity and Relaxation in Polyatomic Gases
by Elena Kustova, Mariia Mekhonoshina, Anna Bechina, Semen Lagutin and Yulia Voroshilova
Fluids 2023, 8(2), 48; https://doi.org/10.3390/fluids8020048 - 31 Jan 2023
Cited by 8 | Viewed by 2207
Abstract
Bulk viscosity and acoustic wave propagation in polyatomic gases and their mixtures are studied in the frame of one-temperature and multi-temperature continuum models developed using the generalized Chapman–Enskog method. Governing equations and constitutive relations for both models are written, and the dispersion equations [...] Read more.
Bulk viscosity and acoustic wave propagation in polyatomic gases and their mixtures are studied in the frame of one-temperature and multi-temperature continuum models developed using the generalized Chapman–Enskog method. Governing equations and constitutive relations for both models are written, and the dispersion equations are derived. In the vibrationally nonequilibrium multi-component gas mixture, wave attenuation mechanisms include viscosity, thermal conductivity, bulk viscosity, diffusion, thermal diffusion, and vibrational relaxation; in the proposed approach these mechanisms are fully coupled contrarily to commonly used models based on the separation of classical Stokes–Kirchhoff attenuation and relaxation. Contributions of rotational and vibrational modes to the bulk viscosity coefficient are evaluated. In the one-temperature approach, artificial separation of rotational and vibrational modes causes great overestimation of bulk viscosity whereas using the effective internal energy relaxation time yields good agreement with experimental data and molecular-dynamic simulations. In the multi-temperature approach, the bulk viscosity is specified only by rotational modes. The developed two-temperature model provides excellent agreement of theoretical and experimental attenuation coefficients in polyatomic gases; both the location and the value of its maximum are predicted correctly. One-temperature dispersion relations do not reproduce the non-monotonic behavior of the attenuation coefficient; large bulk viscosity improves its accuracy only in the very limited frequency range. It is emphasized that implementing large bulk viscosity in the one-temperature Navier–Stokes–Fourier equations may lead to unphysical results. Full article
(This article belongs to the Special Issue Bulk Viscosity and Relaxation Processes: Revisited)
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13 pages, 506 KiB  
Article
Bulk Viscosity of Dilute Gases and Their Mixtures
by Bhanuday Sharma, Rakesh Kumar and Savitha Pareek
Fluids 2023, 8(1), 28; https://doi.org/10.3390/fluids8010028 - 12 Jan 2023
Cited by 7 | Viewed by 2645
Abstract
In this work, we use the Green–Kubo method to study the bulk viscosity of various dilute gases and their mixtures. First, we study the effects of the atomic mass on the bulk viscosity of dilute diatomic gas by estimating the bulk viscosity of [...] Read more.
In this work, we use the Green–Kubo method to study the bulk viscosity of various dilute gases and their mixtures. First, we study the effects of the atomic mass on the bulk viscosity of dilute diatomic gas by estimating the bulk viscosity of four different isotopes of nitrogen gas. We then study the effects of addition of noble gas on the bulk viscosity of dilute nitrogen gas. We consider mixtures of nitrogen with three noble gases, viz., neon, argon, and krypton at eight different compositions between pure nitrogen to pure noble gas. It is followed by an estimation of bulk viscosity of pure oxygen and mixtures of nitrogen and oxygen for various compositions. In this case, three different composition are considered, viz., 25% N2 + 75% O2, 50% N2 + 50% O2, and 78% N2 + 22% O2. The last composition is aimed to represent the dry air. A brief review of works that study the effects of incorporation of bulk viscosity in analysis of various flow situations has also been provided. Full article
(This article belongs to the Special Issue Bulk Viscosity and Relaxation Processes: Revisited)
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22 pages, 2623 KiB  
Article
Navier–Stokes Equations and Bulk Viscosity for a Polyatomic Gas with Temperature-Dependent Specific Heats
by Shingo Kosuge and Kazuo Aoki
Fluids 2023, 8(1), 5; https://doi.org/10.3390/fluids8010005 - 22 Dec 2022
Cited by 5 | Viewed by 1827
Abstract
A system of Navier–Stokes-type equations with two temperatures is derived, for a polyatomic gas with temperature-dependent specific heats (thermally perfect gas), from the ellipsoidal statistical (ES) model of the Boltzmann equation extended to such a gas. Subsequently, the system is applied to the [...] Read more.
A system of Navier–Stokes-type equations with two temperatures is derived, for a polyatomic gas with temperature-dependent specific heats (thermally perfect gas), from the ellipsoidal statistical (ES) model of the Boltzmann equation extended to such a gas. Subsequently, the system is applied to the problem of shock-wave structure for a gas with large bulk viscosity (or, equivalently, with slow relaxation of the internal modes), and the numerical results are compared with those based on the ordinary Navier–Stokes equations. It is shown that the latter equations fail to describe the double-layer structure of shock profiles for a gas with large bulk viscosity. Full article
(This article belongs to the Special Issue Bulk Viscosity and Relaxation Processes: Revisited)
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38 pages, 485 KiB  
Article
Six-Field Theory for a Polyatomic Gas Mixture: Extended Thermodynamics and Kinetic Models
by Milana Pavić-Čolić and Srboljub Simić
Fluids 2022, 7(12), 381; https://doi.org/10.3390/fluids7120381 - 9 Dec 2022
Cited by 3 | Viewed by 1323
Abstract
Polyatomic gases may be characterized by internal molecular degrees of freedom. As a consequence, at a macroscopic level, dynamic pressure appears, which may be related to the bulk viscosity of the gas. Inspired by the models of a single polyatomic gas with six [...] Read more.
Polyatomic gases may be characterized by internal molecular degrees of freedom. As a consequence, at a macroscopic level, dynamic pressure appears, which may be related to the bulk viscosity of the gas. Inspired by the models of a single polyatomic gas with six fields, developed within rational extended thermodynamics (RET) and the kinetic theory of gases, this paper presents a six-field theory for the mixture of polyatomic gases. First, the macroscopic mixture model is developed within the framework of RET. Second, the mixture of gases with six fields is analyzed in the context of the kinetic theory of gases, and corresponding moment equations are derived. Finally, complete closure of the RET model, i.e., computation of the phenomenological coefficients, is achieved by means of a combined macroscopic/kinetic closure procedure. Full article
(This article belongs to the Special Issue Bulk Viscosity and Relaxation Processes: Revisited)
30 pages, 590 KiB  
Article
Internal Energy Relaxation Processes and Bulk Viscosities in Fluids
by Domenico Bruno and Vincent Giovangigli
Fluids 2022, 7(11), 356; https://doi.org/10.3390/fluids7110356 - 19 Nov 2022
Cited by 4 | Viewed by 1776
Abstract
Internal energy relaxation processes in fluid models derived from the kinetic theory are revisited, as are related bulk viscosity coefficients. The apparition of bulk viscosity coefficients in relaxation regimes and the links with equilibrium one-temperature bulk viscosity coefficients are discussed. First, a two-temperature [...] Read more.
Internal energy relaxation processes in fluid models derived from the kinetic theory are revisited, as are related bulk viscosity coefficients. The apparition of bulk viscosity coefficients in relaxation regimes and the links with equilibrium one-temperature bulk viscosity coefficients are discussed. First, a two-temperature model with a single internal energy mode is investigated, then a two-temperature model with two internal energy modes and finally a state-to-state model for mixtures of gases. All these models lead to a unique physical interpretation of the apparition of bulk viscosity effects when relaxation characteristic times are smaller than fluid times. Monte Carlo numerical simulations of internal energy relaxation processes in model gases are then performed, and power spectrums of density fluctuations are computed. When the energy relaxation time is smaller than the fluid time, both the two temperature and the single-temperature model including bulk viscosity yield a satisfactory description. When the energy relaxation time is larger than the fluid time, however, only the two-temperature model is in agreement with Boltzmann equation. The quantum population of a He-H2 mixture is also simulated with detailed He-H2 cross sections, and the resulting bulk viscosity evaluated from the Green–Kubo formula is in agreement with the theory. The impact of bulk viscosity in fluid mechanics is also addressed, as well as various mathematical aspects of internal energy relaxation and Chapman–Enskog asymptotic expansion for a two-temperature fluid model. Full article
(This article belongs to the Special Issue Bulk Viscosity and Relaxation Processes: Revisited)
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