J. Daniel Kelley

Vibrational Excitation, Thermal Nonuniformities, and Unsteady Effects on Supersonic Blunt Bodies

We have performed a computational study of the experiments performed by Lowry et al. at the Arnold Engineering Development Center. In these experiments, an rf discharge is used to weakly ionize a volume of air; then a projectileis e red through this plasma. Relativeto the conditionswithout the discharge, theshock standoff distance is observed to increase substantially, and the bow shock becomes e atter. We have modeled the rf discharge and the resulting thermochemical state of the air within the discharge region. Based on these conditions, the projectile e owe eld wassimulatedto determinewhethertherelaxation of thestored internalenergy causestheobservedshock movement. The results indicate that the stored internal energy does not relax fast enough to reproduce the experimental results, and, therefore, vibrational energy storage is not responsible for the observed shock movement. We considertwo additional mechanisms to explaintheexperiments: modie cationof theelectrice eld by thepresenceof the metallic projectile, and thermal nonuniformities in theplasma. The latter effect appears to provide the best explanation for the observations. We have also modeled experiments in which microwave-discharge excited air e ows over a model. Unsteady thermal effects in the pulsed discharge can account for most of the observed drag change.

Vibrational modeling of CO2 in high-enthalpy nozzle flows

A state-specific vibrational model for CO 2 , CO, O 2 , and O systems is devised by taking into account the first few vibrational states of each species. All vibrational states with energies at or below 1 eV are included in the present work. Of the three modes of vibration in CO 2 , the antisymmetric mode is considered separately from the symmetric stretching mode and the doubly degenerate bending modes. The symmetric and bending modes are grouped together because the energy transfer rates between the two modes are very large due to Fermi resonance. The symmetric and bending modes are assumed to be in equilibrium with the translational and rotational modes. The kinetic rates for the vibrational-translation energy exchange reactions and the intermolecular and intramolecular vibrational-vibrational energy exchange reactions are based on experimental data to the maximum extent possible. Extrapolation methods are employed when necessary. This vibrational model is then coupled with an axisymmetric computational fluid dynamics code to study the expansion of CO 2 in a nozzle.

Effect of internal energy excitation on supersonic blunt-body drag

The effect of upstream vibrational excitation on supersonic blunt-body drag is studied using computational fluid dynamics. The simulations model recent experiments in which a DC or microwave discharge excites the air upstream of a sphere. It is assumed that the discharge slightly dissociates the oxygen and excites the vibrational states of the diatomics. The computations show that the bow shock standoff distance increases, and the drag on the sphere decreases. Both of these effects depend on the degree of vibrational excitation in the flow. The results are in general agreement with the experimental observations. Preliminary calculations on a streamlined body do not show as large a drag reduction effect. Our plans for improvements to the simulation and for additional calculations will be discussed.

The Potential Role of Electronically-Excited States in Recombining Flows

Recent experimental measurements in the reflected shock tunnel CUBRC LENS-I facility raise questions about our ability to correctly model oxygen and carbon dioxide recombination. We consider two possible mechanisms involving the electronically excited states of these molecules that may help explain the experimental data. Oxygen has two low-lying electronically excited states, which have long radiative and collisional lifetimes. We postulate that recombination to these states may help explain the apparent errors in predicting the recombination of oxygen. Carbon dioxide has different behavior and has a single excited state just below the dissociation energy. A recent computational chemistry study shows that CO2 recombines to this state and then relaxes to the ground electronic state. We propose a simple model to represent the effect of this intermediate state in the recombination process. Preliminary simulations show that this model may help explain part of the puzzling data.

Analysis of Chemistry-Vibration Coupling in Diatomics for High Enthalpy Nozzle Flows

A state-specic model is developed to analyze the complex chemistry-vibration coupling present in high enthalpy nozzle o ws. A basic model is formulated assuming molecules are formed at a specic vibrational level and allowed to relax through a series of vibrationvibration and vibration-translation processes. This is carried out assuming that the molecules behave as either harmonic or anharmonic oscillators. The results are compared with the standard vibration-chemistry model for high enthalpy nozzle o ws. Next, a prior recombination model that accounts for the rotational - vibrational coupling is used to obtain prior recombination distribution. A distribution of recombining states is obtained as a function of the total energy available to the system. The results of this model are compared with recent experiments. I. Introduction In high enthalpy nozzle o ws, the expanding o w is often dominated by recombination reactions. Typically these recombining species form molecules that have substantial internal energy. One of the assumptions in non-equilibrium o ws is that the atoms recombine to form molecules at the local vibrational temperature. The vibration-vibration relaxation takes place at a much faster rate than other processes enabling the o w to be characterized by single vibrational temperature. The present work relaxes that assumption by analyzing the o w using a state-specic model. The state-specic model which deals with molecules in each vibrational state as a separate chemical species precludes the need to use a model for vibrational relaxation. The vibration-vibration and vibration-translation processes are treated as chemical reactions. The state-specic approach has been used before to analyze o ws in hypersonic nozzles 1, 2 and shock tunnels. 3 In this work, we focus on a simple diatomic molecule and consider its vibrational and dissociation/recombination behavior. In the rst part of this work, we force the recombining species to form a molecule at a pre-dened vibrational energy level. The molecule thereby has substantial internal energy, and then it relaxes through a series of vibration-vibration and vibration-translation processes. Both harmonic and anharmonic oscillator assumptions are used to describe the relaxation processes. The results are compared with a standard

Energy Bin Model for High-Enthalpy Flows Using Prior Recombination Distribution

An energy-bin-based coupling model for recombination is derived for high-enthalpy nozzle flows using oxygen as the test gas. The coupling between vibrational and rotationalmodes is taken into account by the use of energy bins. A prior recombination distribution of molecules, dependent on the total energy available to a recombining system, is obtained using information theory. The low-lying electronically excited states of oxygen are also considered. The energy levels are obtained assuming the oxygen molecules behave as Morse oscillators. The results from a statespecific model are used to compare with the energy-bin approach. The energy-bin approach using only the ground state of the oxygen molecule predicts similar conditions at the nozzle test section as the state-specific model. The inclusion of the excited electronic states in the energy-bin approach calculations produces test section conditionswith significant chemical nonequilibrium and also predicts nontrivial concentrations of the electronically excited states. The effect of energy bias in the initial recombination distribution and the sensitivity of the test section conditions to the interbin rate constants are also investigated.

Vibrational modeling of CO2 in high enthalpy nozzle flows

A state-specific vibrational model for CO 2 , CO, O 2 , and O systems is devised by taking into account the first few vibrational states of each species. All vibrational states with energies at or below 1 eV are included in the present work. Of the three modes of vibration in CO 2 , the antisymmetric mode is considered separately from the symmetric stretching mode and the doubly degenerate bending modes. The symmetric and bending modes are grouped together because the energy transfer rates between the two modes are very large due to Fermi resonance. The symmetric and bending modes are assumed to be in equilibrium with the translational and rotational modes. The kinetic rates for the vibrational-translation energy exchange reactions and the intermolecular and intramolecular vibrational-vibrational energy exchange reactions are based on experimental data to the maximum extent possible. Extrapolation methods are employed when necessary. This vibrational model is then coupled with an axisymmetric computational fluid dynamics code to study the expansion of CO 2 in a nozzle.

Energy Bin based Coupling Model for High Enthalpy Flows using Prior Recombination Distribution

An energy bin based coupling model for recombination is derived for high enthalpy nozzle flows using oxygen as the test gas. The inherent coupling between vibrational and rotational modes is taken into account by the use of energy bins. A prior recombination distribution of molecules dependent on total energy available to a recombining system is obtained using information theory. The low lying electronically excited states of oxygen are also considered. The results from a state-specific model (Doraiswamy, S., Kelley J. D. and Candler G. V., “Analysis of Chemistry-Vibrational Coupling in High Enthalpy Nozzle Flows”, AIAA-2010-1570, Jan. 2010) are used to compare against the results of the energy bin approach model. The energy bin approach using only the ground state of the oxygen molecule predicts similar conditions at the test section as the state-specific model. The inclusion of the excited electronic states in the energy bin approach calculations produces test section conditions with significant chemical nonequilibrium and also predicts non-trivial concentrations of the excited states. The effect of energy bias in the initial recombination distribution and the senstivity of the results to the rate constants are also investigated.

Calculating high-temperature thermodynamic properties of diatomics in air: Evaluation and accuracy assessment

Construction of a set of thermodynamic properties for air at high temperature is required for accurate modeling of hypersonic flow phenomena. Here we concentrate on the main diatomic species in air: N2, O2 and NO, and we use both state-sum and virial coefficient methods to calculate thermodynamic properties from 200K to 14,000K. We examine the results of these calculations and compare and contrast both methods, and also compare our results with those of other workers. Finally, we assess the accuracy one can realistically expect to obtain for these diatomic properties as the temperature increases to 14,000K and beyond, and the practical implications of these accuracy limitations.

Numerical investigation of double-cone flows using an energy-bin approach

An energy bin based coupling model for recombination is used to simulate flows over double-cones. The inherent coupling between rotational and vibrational modes is taken into account by the use of energy bins. A prior recombination distribution of molecules dependent on the total energy available to a recombining system is obtained using information theory. The low-lying electronic states of oxygen are also considered. The reservoir conditions of the shock tunnel are re-computed based on the energy bin approach to simulate the nozzle flowfield. The new test section conditions are used to compute the flow over the double-cone geometry. The results are compared with a previous study (“Numerical Comparison of Double-Cone Flow Experiments with High-Enthalpy Effects”, AIAA-20101283). The comparison shows that the energy-bin approach improves the prediction of the wall pressure and heat flux. Sensitivity to the model parameters in the energy bin approach is also investigated.