The results for a set of vibrational nonequilibrium models with a range of fidelity are compared to experimental data for several post-normal shock test cases. The present work focuses solely on oxygen flows with an emphasis on the modeling of O2-O. The twotemperature (2T) model is the widely used approach for hypersonic analysis and is presented as the computationally efficient, lower fidelity modeling approach in this work. In contrast, the full state-to-state (STS), master equation approach is presented as the higher fidelity modeling approach. Both approaches have several available methods for obtaining rate data that are investigated. Specifically, the 2T model is driven by the rates from Millikan-White (MW) as well as recently available rates that are derived from a detailed quasi-classical trajectory (QCT) analysis for the O2-O system. The STS model uses transition rates from the forced harmonic oscillator (FHO) model and dissociation rates from previous work for O2 -O system. The O2-O system uses recently available QCT results for STS transitions and dissociation. The test case results show that capturing non-Boltzmann behavior in the vibrational population distribution is critical to accurate nonequilbirium modeling of hypersonic flows containing oxygen. Nomenclature A, B Millikan-White coefficients E v Vibrational eenergy [J] E * v Equilibrium vibrational energy [J] K Reaction rate [cm 3 /sec] µ Reduced mass [kg] P Pressure [atm] ρ Density [kg/m 3 ] T t Translational temperature [K] T v Vibrational temperature [K] τ v Vibrational relaxation time [sec] v Vibrational quantum state
The nonequilibrium modeling of reflected shock tube flows is investigated, motivated by hypersonic vehicle design. Oxygen nonequilibrium behavior is the focus of the work due to its contribution to modeling uncertainty, specifically the vibrational-translational energy transfer process of the O2-Ar system. Two levels of vibrational nonequilibrium modeling fidelity are evaluated. The lower fidelity model is the two-temperature model that uses Millikan-White vibration relaxation rates to capture the vibrational nonequilibrium process at the macroscopic level. The higher fidelity model is the state-resolved master equation method that uses vibrational state-to-state rates to explicitly calculate the vibrational state distribution throughout the analysis. The vibrational state-to-state rates are evaluated using the forced harmonic oscillator (FHO) model and a detailed quasi-classical trajectory (QCT) analysis. The nonequilibrium models are implemented in two flow solvers to analyze reflected shock tube experiments. First, a simple method is employed of chaining two post-normal shock analyses together to simulate the vibrational nonequilibrium behavior of a particular parcel of fluid in the reflected shock tube. Second, the nonequilibrium models are implemented in a 1-D unsteady flow solver to capture the entire behavior of the reflected shock tube. Comparisons are provided between results obtained with the two different flow solvers, and the three different physical models, for two different shock tube conditions.
The simulation results for a set of thermochemical nonequilibrium models with a range of fidelity is compared to experimental data for shock tube and double-cone flows. The present work focuses solely on oxygen flows. The two-temperature (2T) model is the widely used approach for hypersonic analysis and is presented as the computationally efficient, lower fidelity modeling approach in this work. In contrast, the full state-to-state (STS), master equation approach is presented as the higher fidelity modeling approach. Both approaches have several available methods for obtaining rate data that are investigated. The STS method introduces a large master equation system that has been prohibitive due to its computational expensive for design applications. The present paper aims to understand the deficiencies of the standard 2T model when compared to detailed STS analysis. Additionally, the STS rates allow for detailed investigation of the effects that nonequilibrium and non-Boltzmann behavior have on the macroscopic behavior. This present work suggests a modified 2T model, the 2T-NENB (nonequilibrium, non-Boltzmann) model, that aims to capture STS model behavior in a computationally inexpensive, 2T model form. The performance of this modified model is compared with standard 2T model results, full STS model results, and experimental data. Additionally, areas of future improvement and computational expense are discussed. Nomenclature A, B Millikan-White coefficients E v Vibrational energy [J] E * v Equilibrium vibrational energy [J] K d Total dissociation rate [cm 3 /sec] k d,i Dissociation rate from ith vibrational state [cm 3 /sec] k v,v Transition rate from vibrational state v to v' [cm 3 /sec] µ Reduced mass [kg] P Pressure [atm] ρ Density [kg/m 3 ] T t Translational temperature [K] T v Vibrational temperature [K] τ v Vibrational relaxation time [sec] v Vibrational quantum state
The results from a set of vibrational nonequilibrium models with a range of fidelity are compared to the recent experimental data for several postnormal shock test cases. The present work focuses solely on oxygen flows with an emphasis on implementing a new set of accurate state-specific rate coefficients for O 2-O collisions. The twotemperature model is presented as the computationally efficient, lower-fidelity approach in this work. The twotemperature model is driven by the relaxation parameters based on the Millikan-White empirical equation as well as on the parameters resulting from a master equation simulation that employs the database of state-resolved O 2-O rate coefficients. The full state-to-state master equation approach is presented as the higher-fidelity modeling approach. The O 2-O system uses recently available results of trajectory simulations for state-specific transition rate coefficients The O 2-O 2 system uses transition rates from the forced harmonic oscillator model. The test case comparison shows that the state-resolved modeling approach is more suitable for describing the vibrational temperature and chemically nonequilibrium zone behind the shock wave. It is shown that the capability of the state-resolved model to capture non-Boltzmann distribution is critical for accurately modeling the vibrational relaxation and dissociation phase.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.