Nonequilibrium Dissociation Research Articles

Two-Temperature Modeling of Nonequilibrium Relaxation and Dissociation in Shock-Heated Oxygen

Two-temperature models for coupled vibrational relaxation and dissociation in shock-heated oxygen are assessed using low-uncertainty measured data from reflected shock tube experiments. A computationally efficient multistep technique is developed to model the unsteady dynamics of shock reflection in a relaxing and dissociating gas. The developed technique is then benchmarked through comparison with unsteady computational fluid dynamic simulations. Results from the benchmarking effort demonstrate that the adopted multistep modeling procedure accurately captures the dominant gas dynamic effects influencing the state of the test gas at the measurement location. A parametric study is then performed to assess several combinations of possible two-temperature modeling approaches for nonequilibrium oxygen dissociation. The current assessment demonstrates that the widely adopted Park model is inconsistent with the measured data, while the recently developed modified Marrone and Treanor (MMT) model demonstrates promising agreement with the data. The results of the present study clearly indicate that the MMT model is more appropriate for two-temperature modeling of nonequilibrium oxygen dissociation than the legacy Park model. Patterns in the parametric comparison also suggest that the approximate treatment of non-Boltzmann vibrational state distributions within the MMT model may require improvement.

Application of Reflected Shock Wave Configuration to Validate Nonequilibrium Models of Reacting Air

The direct simulation Monte Carlo (DSMC) method is used to model transient thermal and chemical relaxation behind reflected shock waves in oxygen–argon and air mixtures under conditions reproducing earlier shock-tube experiments. Two vibration–translation and three popular DSMC chemical reaction models are tested. Where possible, model parameters are adjusted to match equilibrium and nonequilibrium relaxation times and reaction rates. A number of factors that impact relaxation and reaction model validation are examined, including gas–surface interactions, time-varying freestream properties, location of the observation point, electronic excitation, and nonequilibrium populations of vibrational states probed in the experiments. Comparison of numerical and experimental results has demonstrated that the reflected shock configuration is a platform very convenient for validation and analysis of high-temperature chemical reaction models. Computations have shown that the Bias reaction model is superior to the total collision energy and quantum kinetic models, providing reasonable agreement with measured absorbance time histories and vibrational temperatures in oxygen–argon mixtures and pure . There are some modeling-versus-experiment differences observed for air that may warrant additional studies focused on Zeldovich reaction rates and oxygen–nitrogen vibrational excitation and nonequilibrium dissociation rate.

On the Origin of Hemoglobin Cooperativity under Non-equilibrium Conditions.

Abnormal hemoglobins can have major consequences for tissue delivery of oxygen. Correct diagnosis of hemoglobinopathies with altered oxygen affinity requires a determination of hemoglobin oxygen dissociation curve, which relates the hemoglobin oxygen saturation to the partial pressure of oxygen in the blood. Determination of the oxygen dissociation curve of human hemoglobin is typically carried out under conditions in which hemoglobin is in equilibrium with O2 at each partial pressure. However, in the human body due to the fast transit of red blood cells through tissues hemoglobin oxygen exchanges occur under non-equilibrium conditions. We describe the determination of non-equilibrium oxygen dissociation curve and show that under these conditions the true nature of hemoglobin cooperativity is revealed as emerging solely from the consecutive binding of oxygen to each one of the four subunits of hemoglobin until the entire tetramer is saturated. We call this form of cooperativity the sequential cooperativity of hemoglobin and define the simplest model that includes it as the minimalist model of hemoglobin. A single instantiation of this model accounts for ~70% of hemoglobin cooperativity under non-equilibrium conditions. The total cooperativity of hemoglobin can be viewed more correctly as the summation of two instantiations of the minimalist model (each one corresponding to a tetramer of low and high affinity for O2, respectively) in equilibrium with each other, as in the Monod-Wyman-Changeux model of hemoglobin. In addition to offering new insights on the nature of hemoglobin reaction with oxygen, the methodology described here for the determination of hemoglobin non-equilibrium oxygen dissociation curve provides a simple, fast, low-cost alternative to complex spectrophotometric methods, which is expected to be particularly valuable in regions where hemoglobinopathies are a significant public health problem, but where highly specialized laboratories capable of determining a traditional oxygen dissociation curve are not easily accessible.

A non-equilibrium dissociation and vibrational relaxation model for computational fluid dynamics simulations of flows with shock waves

Gasdynamic equations describing a vibrationally non-equilibrium flow of a chemically reacting binary mixture A2/A are derived within the previously proposed general approach of solving the Boltzmann equation. The obtained equations differ from the traditional ones in their expressions for the reaction and relaxation rates. Aiming to obtain analytical expressions for these rates, a cutoff harmonic oscillator model for the vibrational spectrum of A2 molecules and dissociation from the highest vibrational level are assumed. The equation for the dissociation rate describes two different dissociation regimes, determined by the dissociation rate constant at “low” temperatures and by the vibrational energy exchange rate constants at “high” temperatures, since it is limited by the vibrational energy delivery to the highest vibrational levels. A parameter for determining the appropriate regime is proposed. The derived expressions for the reaction and relaxation rates are used in computations of O2/O and N2/N mixture flows. A comparison of our results with the numerical and experimental data of other authors shows that the model used for the reaction and relaxation rates calculation should be refined, at least by considering anharmonicity effects.

Rotation‐translation collision model for DSMC with restricted energy exchange

AbstractIn the standard implementation of Borgnakke–Larsen (BL) rotation and translation energy exchange in DSMC not every rotational mode of each molecule is active in every collision. In some collisions, the rotation mode of one molecule is “frozen” (cannot be changed by the collision); in other collisions the rotation mode of both molecules is frozen. Different relaxation rates are obtained by varying the proportion of frozen‐rotation collisions. In 1974 Larsen and Borgnakke proposed a “restricted exchange” version of BL in which a portion of the energy of each mode is frozen in each collision; the method seemed physically plausible but did not satisfy the detailed balance condition. In 1978 Pullin proposed a general restricted exchange of BL exchange which did satisfy the detailed balance condition; it was more CPU intensive than the original BL scheme. It was seen as “laborius” and “cumbersome” and it seemed to be incompatible with vibration energy‐exchange models. Here a simplified version, a special case, of Pullin's restricted exchange scheme is described. The new method is only 12%–17% more CPU‐intensive than standard BL methods and can be used with the standard DSMC quantum vibration exchange model. It is shown that the elimination of frozen‐rotation collisions changes the high energy distribution of vibration energy in nonequilibrium conditions which may slightly decrease the nonequilibrium dissociation rate when restricted exchange is used with the quantum‐kinetic method for dissociation reactions.

Non-equilibrium dissociation and relaxation behind the shock wave within two-temperature approach

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the equations for a dissociating diatomic gas have been derived assuming two-temperature (translational-rotational + vibrational) approximation. Corresponding expressions for the reaction and relaxation rates, determined by the quasi-stationary vibrational distributions, have been obtained under assumption of dissociation from the highest vibrational level. Cut-off harmonic oscillator approximation for the diatomic molecules is assumed. It is shown that all reaction rates are the complex functions of the species densities. Analysis of a flow behind a shock wave is performed in a wide range of the flow parameters. It is shown that under strong non-equilibrium condition the dissociation rate is determined not by the dissociation probability, but by the vibration probability, since the excitation of highest vibrational levels is the bottleneck of dissociation process. This means that the procedure of obtaining the data on dissociation rates needs the accurate revision.

Численное моделирование течения термически и химически неравновесного воздуха за фронтом ударной волны

We used the model of a five-component air mixture flow behind the front of a one-dimensional shock wave to compute the flow parameters for shock front temperatures of up to 7000 K, taking into account the variable composition, translational and vibrational temperatures and pressure in the relaxation zone. Vibrational level population in oxygen and nitrogen obeys the Boltzmann distribution with one common vibrational temperature. We consider the effect that temperature nonequilibrium has on the chemical reaction rate by introducing a nonequilibrium factor to the reaction rate constant, said factor depending on the vibrational and translational temperatures. We compared our calculation results for dissociation behind the shock front to the published data concerning temperature nonequilibrium in a pure oxygen flow behind a shock wave front for two different intensities of the latter. The comparison shows a good agreement between the vibrational temperature, experimental data and calculations based on the experimental values of vibrational temperature and molality. We computed the parameters of thermodynamically nonequilibrium dissociation in the air behind the shock wave front, comparing them to those of equilibrium dissociation and calculation results previously published by others. The study demonstrates that the molality values computed converge gradually with those found in published data as the distance from the shock front increases. We list the reasons for the discrepancy between our calculation results and previously published data

A general form of Macheret–Fridman classical impulsive dissociation model for nonequilibrium flows

The rate of dissociation behind a strong shock in thermochemical nonequilibrium depends on the vibrational excitation of the molecules, hence the rates become a function of translational-rotational and vibrational temperatures. The Macheret–Fridman (MF) model provides analytical expressions for nonequilibrium dissociation rates assuming the collision of molecules to be in the impulsive limit. However, the original form of the model was limited to the dissociation of homonuclear molecules. In this work, we present a general form of the Macheret–Fridman classical impulsive model by considering the dissociation of a heteronuclear molecule and present macroscopic rates applicable for modeling dissociation in computational fluid dynamics (CFD). The nonequilibrium dissociation rates from the MF-CFD model compared well with the available quasiclassical trajectory (QCT) data for some important reactions in the air. Additionally, we also present a comparison of the average vibrational energy removed in a dissociation reaction predicted by the MF-CFD model with QCT data for several reactions in air and propose some improvements to the model. The developed MF-CFD model was used to investigate various nonequilibrium flow problems and the results were compared with available experimental data. In general, the results from the MF-CFD model are promising and the model shows a possibility of becoming the standard tool for investigating nonequilibrium flows in CFD.

Data-Inspired and Physics-Driven Model Reduction for Dissociation: Application to the O2 + O System.

This work presents an in-depth discussion on the nonequilibrium dissociation of O2 molecules colliding with O atoms, combining quasi-classical trajectory calculations, master equation, and dimensionality reduction. A rovibrationally resolved database for all of the elementary collisional processes is constructed by including all nine adiabatic electronic states of O3 in the QCT calculations. A detailed analysis of the ab initio data set reveals that for a rovibrational level, the probability of dissociating is mostly dictated by its deficit in internal energy compared to the centrifugal barrier. Because of the assumption of rotational equilibrium, the conventional vibrational-specific calculations fail to characterize such a dependence. Based on this observation, a new physics-based grouping strategy for application to coarse-grained models is proposed. By relying on a hybrid technique made of rovibrationally resolved excitation coupled to coarse-grained dissociation, the new approach is compared to the vibrational-specific model and the direct solution of the rovibrational state-to-state master equation. Simulations are performed in a zero-dimensional isothermal and isochoric chemical reactor for a wide range of temperatures (1500-20,000 K). The study shows that the main contribution to the model inadequacy of vibrational-specific approaches originates from the incapability of characterizing dissociation, rather than the energy transfers. Even when constructed with only twenty groups, the new reduced-order model outperforms the vibrational-specific one in predicting all of the QoIs related to dissociation kinetics. At the highest temperature, the accuracy in the mole fraction is improved by 2000%.

Consistent kinetic-continuum dissociation model I. Kinetic formulation.

In this article, we propose a generalized non-equilibrium chemical kinetics model from ab initio simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross section model for dissociation that captures recent ab initio data accurately. The cross section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive a general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorporates key physics such as dependence on translational energy, rotational energy, vibrational energy, internal energy, centrifugal barrier, and non-Boltzmann effects such as overpopulation and depletion of high energy states. The model is shown to reproduce the rates from quasi-classical trajectory calculations for Boltzmann distributions of internal energy states. The reduced rates in a non-equilibrium steady state due to depletion of high internal energy states are also predicted well by the model. Furthermore, the model predicts the enhanced rates as observed due to significant overpopulation of high vibrational states relative to Boltzmann distributions while the gas is in non-equilibrium in the transient phase. The model provides a computationally inexpensive way of incorporating non-equilibrium chemistry without incurring additional cost in the existing computational tools. Further comparisons of the model are carried out in Paper II, where simplifications to the model are proposed based on the results.

Coarse-grain cross sections for rovibrational excitation and dissociation of the [formula omitted] system

We present a method to generate analytical coarse-grain cross sections for internal energy excitation and dissociation of nitrogen and apply it to the NASA Ames N2-Nab initio database. State-resolved cross sections from this database are reduced using the Uniform RoVibrational-Collisional bin model. With a 10-bin system as example we compare two sets of coarse-grain cross sections: one obtained by analytical inversion and another by direct binning. With analytical inversion we manage to compress the entire set of state-resolved data into a small set of parameters, sufficient to reconstruct the main features of the full database. This has the potential of massively reducing the computational cost in large-scale direct simulation Monte Carlo (DSMC) calculations, both concerning memory requirements and execution time. Combining this coarse-grain model with the N2-Nab initio database will enable much higher-fidelity DSMC simulation of nonequilibrium dissociation in shock-heated flows than is currently possible with conventional models.

Comparison of nonequilibrium dissociation models in the direct simulation Monte Carlo method

Various chemical dissociation reactions models (Total collision energy model – TCE, Quantum Kinetic model – QK and Extended vibrational bias model – EVB) were implemented in the direct simulation Monte Carlo code SMILE++. It was shown that the dissociation models considered predict the same reaction rate over a wide range of temperatures in thermal equilibrium case. The analysis for the nonequilibrium case was carried out on the basis of dissociating nitrogen gas flow modelling around the wedge for the Hornung and Smith experiments conditions. All dissociation models proposed predict various results both in the standoff distance of the bow shock wave and in the temperature values behind it. It was generally shown, that taking into account the vibrational favoring (during dissociation) results in decreasing the reaction rate, which can be manifested in increasing the shock wave standoff distance.

Vibrational Energy Transfer and Collision-Induced Dissociation in Collisions

This paper presents molecular dynamics calculations of vibrational energy transfer and nonequilibrium dissociation in collisions. The interactions are modeled using nine potential energy surfaces corresponding to the , , , , , , , , and states, which govern electronically adiabatic collisions of ground-electronic-state collisions of diatomic oxygen with atomic oxygen. Characteristic vibrational excitation times are calculated over a temperature range of to , and nonequilibrium dissociation rate coefficients are calculated over a temperature range of to . Vibrational relaxation rates, specific to each PES, are found to vary by over an order of magnitude, indicating that all spin couplings and spatial degeneracies must be considered for accurate predictions of collisions. It has been observed that the characteristic vibrational excitation time for interactions is weakly dependent on temperature and increases slightly with increasing temperature. Predicted nonequilibrium dissociation rates, during quasi-steady state. Agree well with available experimental data, and the coupling between vibrational energy and dissociation is characterized.

Construction of a coarse-grain quasi-classical trajectory method. II. Comparison against the direct molecular simulation method.

This work presents the analysis of non-equilibrium energy transfer and dissociation of nitrogen molecules (N2(Σg+1)) using two different approaches: the direct molecular simulation (DMS) method and the coarse-grain quasi-classical trajectory (CG-QCT) method. The two methods are used to study thermochemical relaxation in a zero-dimensional isochoric and isothermal reactor in which the nitrogen molecules are heated to several thousand degrees Kelvin, forcing the system into strong non-equilibrium. The analysis considers thermochemical relaxation for temperatures ranging from 10 000 to 25 000 K. Both methods make use of the same potential energy surface for the N2(Σg+1)-N2(Σg+1) system taken from the NASA Ames quantum chemistry database. Within the CG-QCT method, the rovibrational energy levels of the electronic ground state of the nitrogen molecule are lumped into a reduced number of bins. Two different grouping strategies are used: the more conventional vibrational-based grouping, widely used in the literature, and energy-based grouping. The analysis of both the internal state populations and concentration profiles show excellent agreement between the energy-based grouping and the DMS solutions. During the energy transfer process, discrepancies arise between the energy-based grouping and DMS solution due to the increased importance of mode separation for low energy states. By contrast, the vibrational grouping, traditionally considered state-of-the-art, captures well the behavior of the energy relaxation but fails to consistently predict the dissociation process. The deficiency of the vibrational grouping model is due to the assumption of strict mode separation and equilibrium of rotational energy states. These assumptions result in errors predicting the energy contribution to dissociation from the rotational and vibrational modes, with rotational energy actually contributing 30%-40% of the energy required to dissociate a molecule. This work confirms the findings discussed in Paper I [R. L. Macdonald et al., J. Chem. Phys. 148, 054309 (2018)], which underlines the importance of rotational energy to the dissociation process, and demonstrates that an accurate non-equilibrium chemistry model must accurately predict the deviation of rovibrational distribution from equilibrium.

Assessment of Classical Impulsive Models of Dissociation in Thermochemical Nonequilibrium

In strong shock waves in rarefied gases, chemical processes such as dissociation and exchange reactions occur in conditions of thermodynamic nonequilibrium, and the rate coefficients are functions of both translational–rotational and vibrational temperatures. In this work, we reexamine and validate the physical model for nonequilibrium dissociation rates proposed earlier by Macheret et al. The model is based on the classical impulsive approximation and enables analytical formulas for reaction thresholds, probabilities, and multitemperature rate coefficients. The recent quasi-classical trajectory calculations for , , , , and are used to evaluate the Macheret–Fridman dissociation model. The full version of the model that incorporates the reduction of dissociation energy due to rotation of the dissociating molecule as well as the appearance of the centrifugal barrier is found to be in good agreement with quasi-classical trajectory data, whereas the simplified version of the model that ignores the rotational effect significantly underpredicts the dissociation rates in vibrationally cold conditions. The good agreement with quasi-classical trajectory data validates the classical impulsive approximation and implies that details of the potential energy surface are not important for dissociation at high temperatures. Preliminary one-dimensional computational fluid dynamics calculations with the validated dissociation model were conducted for conditions of the shock-tube experiments in pure oxygen by Ibraguimova et al. Generally reasonable agreement was found between the calculations and the experimental data; however, some underprediction of the peak vibrational temperature suggests that some improvement in the model would be desirable.

Effect of nonequilibrium near-electrode layers on the structure of EHD flows in the three-ions model of a dielectric liquid

An electrohydrodynamic (EHD) flow is a spontaneous flow of a liquid in the electrode gap under the action of a strong electric field. Most experimental data from an investigation of the velocity field of EHD flows were obtained in the wire-over-plane electrode configuration. For this system, the flow can be treated as a 2D flow. We report on the results of a computer simulation of the complete system of electrohydrodynamics equations in the three-ion model of a dielectric liquid. The structure of nonequilibrium dissociation–recombination layers and their effect on the structure of EHD flows have been analyzed based on the results of the computer simulation of EHD flows in liquids with different low-voltage conductivities for the wireover- plane electrode system.

Assessment of vibration–dissociation coupling models for hypersonic nonequilibrium simulations

The fidelity of three widely-used two-temperature vibration–dissociation coupling models, including the Park model (1988), the Macheret–Fridman model (1994), and the coupled vibration–dissociation–vibration (CVDV) model (1963), is numerically investigated via a comparison with state-specific results and existing shock tube data for oxygen flows. Under the hypothetical condition where a Boltzmann distribution corresponding to a vibrational temperature is assumed, it is found that the CVDV model with a proper parameter is capable of providing the most accurate results, whereas the Park and Macheret–Fridman models present similar prediction accuracy for which the nonequilibrium dissociation rate coefficients could be as much as three orders of magnitude lower than state-specific values. However, for actual postshock flows with intensive vibrational excitation and dissociation processes, the CVDV model still shows significant discrepancies relative to state-specific results and experimental data, presenting a much lower vibrational temperature and a higher degree of dissociation. The essential cause for the disagreement lies in the existence of non-Boltzmann distributions observed when the incubation period is over and dissociation starts to dominate. Recommendations on further modification of two-temperature vibration–dissociation coupling models are presented.

Mapping and controlling ultrafast dynamics of highly excited H2 molecules by VUV-IR pump-probe schemes

We used ultrashort femtosecond vacuum ultraviolet (VUV) and infrared (IR) pulses in a pump-probe scheme to map the dynamics and nonequilibrium dissociation channels of excited neutral ${\text{H}}_{2}$ molecules. A nuclear wave packet is created in the $B\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$ state of the neutral ${\text{H}}_{2}$ molecule by absorption of the ninth harmonic of the driving infrared laser field. Due to the large stretching amplitude of the molecule excited in the $B\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$ electronic state, the effective ${\text{H}}_{2}{}^{+}$ ionization potential changes significantly as the nuclear wave packet vibrates in the bound, highly electronically and vibrationally excited $B$ potential-energy curve. We probed such dynamics by ionizing the excited neutral molecule using time-delayed VUV-or-IR radiation. We identified the nonequilibrium dissociation channels by utilizing three-dimensional momentum imaging of the ion fragments. We found that different dissociation channels can be controlled, to some extent, by changing the IR laser intensity and by choosing the wavelength of the probe laser light. Furthermore, we concluded that even in a benchmark molecular system such as ${\text{H}}_{2}$*, the interpretation of the nonequilibrium multiphoton and multicolor ionization processes is still a challenging task, requiring intricate theoretical analysis.

Nonequilibrium radiation and dissociation of CO molecules in shock-heated flows

Vehicles descending onto a planet's atmosphere create shocks and radiative heat transfer. A theoretical study on the behavior of the excited electronic states of CO molecules sheds light on the determination of the radiative heat loads generated while attempting to land on Mars.

Nonequilibrium mechanisms of weak electrolyte electrification under the action of constant voltage

The formation of space charge in weak electrolytes, specifically in liquid dielectrics, has been considered. An analytical solution is given to a simplified set of Nernst–Planck equations that describe the formation of nonequilibrium recombination layers in weak electrolytes. This approximate analytical solution is compared with computer simulation data for a complete set of Poisson–Nernst–Planck equations. It has been shown that the current passage in weak electrolytes can be described by a single dimensionless parameter that equals the length of a near-electrode recombination layer divided by the width of the interelectrode gap. The formation mechanism and the structure of charged nonequilibrium near-electrode layers in the nonstationary regime have been analyzed for different injection-to-conduction current ratios. It has been found that almost all charge structures encountered in weak dielectrics can be accounted for by the nonequilibrium dissociation–recombination mechanism of space charge formation.