1
|
Shakurova L, Kustova E. State-specific boundary conditions for nonequilibrium gas flows in slip regime. Phys Rev E 2022; 105:034126. [PMID: 35428104 DOI: 10.1103/physreve.105.034126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2022] [Accepted: 03/03/2022] [Indexed: 11/07/2022]
Abstract
Boundary conditions for fluid-dynamic variables of strongly nonequilibrium multicomponent gas mixture flows in slip regime are derived systematically by two different approaches. The flow is described in the framework of the state-to-state model for coupled detailed vibrational and chemical kinetics. The specular-diffusive model is applied for particles interaction with the solid wall, and the surface is assumed to be partially catalytic with possible state-specific chemical reactions and vibrational energy transitions described by a simple model based on the analogy with recombination coefficients. The first theoretical approach uses the technique proposed by Grad whereas the second one is based on the kinetic boundary condition. It is shown that for the Maxwell scattering kernel the two approaches are equivalent; at the same time, the approach based on the kinetic boundary condition provides more rigorous mathematical description of the problem and can be easily generalized for other scattering kernels and gas-surface interaction models accounting for surface inner geometry. The resulting boundary conditions are expressed in terms of state-specific transport coefficients: thermal conductivity, multicomponent diffusion of vibrational states, thermal diffusion, shear and bulk viscosity, and relaxation pressure. The dependence of the boundary conditions on the normal mean stress is obtained for the first time. Under thermal equilibrium conditions, the derived expressions reduce to known relations obtained earlier in the one-temperature approach.
Collapse
Affiliation(s)
- L Shakurova
- Saint-Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg 199034, Russia
| | - E Kustova
- Saint-Petersburg State University, Department of Mathematics and Mechanics, St. Petersburg 199034, Russia
| |
Collapse
|
2
|
Armenise I, Esposito F. N + O2(v) collisions: reactive, inelastic and dissociation rates for state-to-state vibrational kinetic models. Chem Phys 2021. [DOI: 10.1016/j.chemphys.2021.111325] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
3
|
Kustova E, Savelev A, Armenise I. State-Resolved Dissociation and Exchange Reactions in CO 2 Flows. J Phys Chem A 2019; 123:10529-10542. [PMID: 31714767 DOI: 10.1021/acs.jpca.9b08578] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
State-resolved chemical reactions in CO2 are studied by taking into account excitation of all vibrational modes and preferential reaction mechanisms. The effect of several parameters on the reaction rate coefficients is discussed; it is shown that the nonequilibrium factor in the expression for the rate coefficients of exchange reactions is much less sensitive to the number of accounted vibrational states and model parameters than that of dissociation. On the other hand, the choice of thermal equilibrium Arrhenius law parameters is crucial for the correct prediction of rate coefficients for both reactions. Developed models are implemented to the one-dimensional boundary layer code for coupled state-to-state simulations of nonequilibrium CO2 flows under Mars entry conditions. Vibrational distributions, mixture composition, flow variables, and heat flux are studied for several kinetic schemes and different models of chemical reactions. Whereas including the exchange reactions weakly affects the flow, switching between the Park and McKenzie sets of parameters results in significant modification of the kinetic mechanisms; for the McKenzie model, recombination near the wall is a dominating reaction, whereas for the Park model, chemical reactions are frozen. Different contributions to the heat flux are evaluated and a satisfactory agreement with experiments is shown.
Collapse
Affiliation(s)
- Elena Kustova
- Saint Petersburg State University , 7/9 Universitetskaya Nab. , Saint Petersburg 199034 , Russia
| | - Aleksei Savelev
- Saint Petersburg State University , 7/9 Universitetskaya Nab. , Saint Petersburg 199034 , Russia
| | | |
Collapse
|
4
|
Armenise I, Kustova E. Effect of Asymmetric Mode on CO 2 State-to-State Vibrational-Chemical Kinetics. J Phys Chem A 2018; 122:8709-8721. [PMID: 30351096 DOI: 10.1021/acs.jpca.8b07523] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Coupled state-to-state vibrational-chemical kinetics, gas dynamics, and heat transfer in the five-component mixture of dissociated CO2 are studied using the complete three-mode kinetic model and the reduced scheme involving mainly the vibrational states of the asymmetric mode. The emphasis is on the effect of asymmetric vibrations on the rate of dissociation, fluid dynamic variables, and heat flux. It is shown that intermode vibrational energy transitions between CO and CO2 asymmetric mode may considerably decrease the rate of dissociation; the presence of CO in the mixture quickly depletes high vibrational states and thus inhibits dissociation at low temperatures. The reduced model overpredicts populations of highly located states of the asymmetric mode, especially when intermode VV transitions are neglected; therefore, using the simplified model in flows with dominating dissociation may yield overestimated dissociation rate. In the hypersonic flow along the stagnation line, the influence of asymmetric vibrations on the fluid dynamics and heat transfer is weak; the main role belongs to chemical reactions and VT transitions in the bending mode. In this case, the computationally efficient simplified model can be used to predict macroscopic variables and heat flux without significant loss of accuracy.
Collapse
Affiliation(s)
- Iole Armenise
- CNR NANOTEC_PLASMI Lab , Via Amendola 122/D , 70126 , Bari , Italy
| | - Elena Kustova
- Saint Petersburg State University , 7/9 Universitetskaya nab. , St. Petersburg , 199034 , Russia
| |
Collapse
|
5
|
Armenise I, Kustova E. Mechanisms of Coupled Vibrational Relaxation and Dissociation in Carbon Dioxide. J Phys Chem A 2018; 122:5107-5120. [DOI: 10.1021/acs.jpca.8b03266] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Iole Armenise
- CNR NANOTEC_PLASMI Lab, Via Amendola 122/D, 70126, Bari, Italy
| | - Elena Kustova
- Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia
| |
Collapse
|
6
|
Arima T, Ruggeri T, Sugiyama M. Extended Thermodynamics of Rarefied Polyatomic Gases: 15-Field Theory Incorporating Relaxation Processes of Molecular Rotation and Vibration. ENTROPY (BASEL, SWITZERLAND) 2018; 20:E301. [PMID: 33265392 PMCID: PMC7512819 DOI: 10.3390/e20040301] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 04/03/2018] [Revised: 04/17/2018] [Accepted: 04/17/2018] [Indexed: 11/24/2022]
Abstract
After summarizing the present status of Rational Extended Thermodynamics (RET) of gases, which is an endeavor to generalize the Navier-Stokes and Fourier (NSF) theory of viscous heat-conducting fluids, we develop the molecular RET theory of rarefied polyatomic gases with 15 independent fields. The theory is justified, at mesoscopic level, by a generalized Boltzmann equation in which the distribution function depends on two internal variables that take into account the energy exchange among the different molecular modes of a gas, that is, translational, rotational, and vibrational modes. By adopting the generalized Bhatnagar, Gross and Krook (BGK)-type collision term, we derive explicitly the closed system of field equations with the use of the Maximum Entropy Principle (MEP). The NSF theory is derived from the RET theory as a limiting case of small relaxation times via the Maxwellian iteration. The relaxation times introduced in the theory are shown to be related to the shear and bulk viscosities and heat conductivity.
Collapse
Affiliation(s)
- Takashi Arima
- Department of Mechanical Engineering, Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan
| | - Tommaso Ruggeri
- Alma Mater Research Center on Applied Mathematics (AM), Department of Mathematics, University of Bologna, Bologna 40123-I, Italy
| | - Masaru Sugiyama
- Graduate School of Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan
| |
Collapse
|
7
|
Arima T, Ruggeri T, Sugiyama M. Rational extended thermodynamics of a rarefied polyatomic gas with molecular relaxation processes. Phys Rev E 2017; 96:042143. [PMID: 29347562 DOI: 10.1103/physreve.96.042143] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/12/2017] [Indexed: 11/07/2022]
Abstract
We present a more refined version of rational extended thermodynamics of rarefied polyatomic gases in which molecular rotational and vibrational relaxation processes are treated individually. In this case, we need a triple hierarchy of the moment system and the system of balance equations is closed via the maximum entropy principle. Three different types of the production terms in the system, which are suggested by a generalized BGK-type collision term in the Boltzmann equation, are adopted. In particular, the rational extended thermodynamic theory with seven independent fields (ET_{7}) is analyzed in detail. Finally, the dispersion relation of ultrasonic wave derived from the ET_{7} theory is confirmed by the experimental data for CO_{2}, Cl_{2}, and Br_{2} gases.
Collapse
Affiliation(s)
- Takashi Arima
- Department of Mechanical Engineering, Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan
| | - Tommaso Ruggeri
- Department of Mathematics, University of Bologna, Bologna, Italy
| | | |
Collapse
|
8
|
|
9
|
Armenise I. Excitation of the lowest CO 2 vibrational states by electrons in hypersonic boundary layers. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2017.04.011] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
10
|
Istomin V, Kustova E. State-specific transport properties of partially ionized flows of electronically excited atomic gases. Chem Phys 2017. [DOI: 10.1016/j.chemphys.2017.01.012] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
11
|
Kunova O, Kustova E, Savelev A. Generalized Treanor–Marrone model for state-specific dissociation rate coefficients. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2016.07.006] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
12
|
Kunova O, Kustova E, Mekhonoshina M, Nagnibeda E. Non-equilibrium kinetics, diffusion and heat transfer in shock heated flows of N2/N and O2/O mixtures. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2015.10.004] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
13
|
Kustova EV, Kremer GM. Effect of molecular diameters on state-to-state transport properties: The shear viscosity coefficient. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.07.012] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
14
|
N2, O2, NO state-to-state vibrational kinetics in hypersonic boundary layers: The problem of rescaling rate coefficients to uniform vibrational ladders. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2014.11.004] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
15
|
Kustova EV, Kremer GM. Chemical reaction rates and non-equilibrium pressure of reacting gas mixtures in the state-to-state approach. Chem Phys 2014. [DOI: 10.1016/j.chemphys.2014.10.019] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
16
|
Munafò A, Panesi M, Magin TE. Boltzmann rovibrational collisional coarse-grained model for internal energy excitation and dissociation in hypersonic flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:023001. [PMID: 25353565 DOI: 10.1103/physreve.89.023001] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2013] [Revised: 10/29/2013] [Indexed: 06/04/2023]
Abstract
A Boltzmann rovibrational collisional coarse-grained model is proposed to reduce a detailed kinetic mechanism database developed at NASA Ames Research Center for internal energy transfer and dissociation in N(2)-N interactions. The coarse-grained model is constructed by lumping the rovibrational energy levels of the N(2) molecule into energy bins. The population of the levels within each bin is assumed to follow a Boltzmann distribution at the local translational temperature. Excitation and dissociation rate coefficients for the energy bins are obtained by averaging the elementary rate coefficients. The energy bins are treated as separate species, thus allowing for non-Boltzmann distributions of their populations. The proposed coarse-grained model is applied to the study of nonequilibrium flows behind normal shock waves and within converging-diverging nozzles. In both cases, the flow is assumed inviscid and steady. Computational results are compared with those obtained by direct solution of the master equation for the rovibrational collisional model and a more conventional multitemperature model. It is found that the proposed coarse-grained model is able to accurately resolve the nonequilibrium dynamics of internal energy excitation and dissociation-recombination processes with only 20 energy bins. Furthermore, the proposed coarse-grained model provides a superior description of the nonequilibrium phenomena occurring in shock heated and nozzle flows when compared with the conventional multitemperature models.
Collapse
Affiliation(s)
- A Munafò
- Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640 Rhode-Saint-Genèse, Belgium
| | - M Panesi
- Department of Aerospace Engineering, Talbot Laboratory, University of Illinois at Urbana-Champaign, 104 South Wright Street, Urbana, Illinois 61801, USA
| | - T E Magin
- Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Chaussée de Waterloo 72, 1640 Rhode-Saint-Genèse, Belgium
| |
Collapse
|
17
|
|
18
|
Armenise I, Kustova E. State-to-state models for CO2 molecules: From the theory to an application to hypersonic boundary layers. Chem Phys 2013. [DOI: 10.1016/j.chemphys.2013.01.034] [Citation(s) in RCA: 76] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
19
|
|
20
|
Kustova E, Nagnibeda E, Alexandrova T, Chikhaoui A. On the non-equilibrium kinetics and heat transfer in nozzle flows. Chem Phys 2002. [DOI: 10.1016/s0301-0104(01)00578-x] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
21
|
|