Sriram Doraiswamy

Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N4

Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with a review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N4. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.

Development of a Mach 5 Nonequilibrium-Flow Wind Tunnel

A small-scale Mach 5 blowdown wind tunnel has been developed to generate steady-state nonequilibrium flows. The wind tunnel uses transverse nanosecond pulse discharge, overlapped with transverse dc discharge, to load internal energymodes ofN2 andO2 in plenum. The stable discharge is operated at high plenum pressures, at energy loadings of up to 0:1 eV=molecule in nitrogen, generating nonequilibrium nitrogen and airflows with run time of 5–10 s, translational/rotational temperature of T0 300–400 K, and N2 vibrational temperature of up to TV

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.

Experimental and Numerical Investigation of Hypervelocity Carbon Dioxide Flow over Blunt Bodies

This paper represents ongoing efforts to study high-enthalpy carbon dioxide flows in anticipation of the upcoming Mars Science Laboratory and future missions. The work is motivated by observed anomalies between experimental and numerical studies in hypervelocity impulse facilities. In this study, experiments are conducted in the hypervelocity expansion tube that, by virtue of its flow acceleration process, exhibits minimal freestream dissociation in comparison with reflected shock tunnels, simplifying comparison with simulations. Shock shapes of the laboratory aeroshell at angles of attack of 0, 11, and 16 deg and spherical geometries are in very good agreement with simulations incorporating detailed thermochemical modeling. Laboratory shock shapes at a 0 deg of attack are also in good agreement with data from the LENS X expansion tunnel facility, confirming results are facility-independent for the same type of flow acceleration. The shock standoff distance is sensitive to the thermochemical state and is used as an experimental measurable for comparison with simulations and two different theoretical models. For low-density small-scale experiments, it is seen that models based upon assumptions of large binary scaling values do not match the experimental and numerical results. In an effort to address surface chemistry issues arising in high-enthalpy groundtest experiments, spherical stagnation point and aeroshell heat transfer distributions are also compared with the simulation. Heat transfer distributions over the aeroshell at the three angles of attack are in reasonable agreement with simulations, and the data fall within the noncatalytic and supercatalytic solutions.

Detached Eddy Simulations and Reynolds-Averaged Navier- Stokes Calculations of a Spinning Projectile

Reynolds-averaged Navier–Stokes and detached eddy simulations are performed on a 0.50 caliber spinning projectile for three yaw angles over the Mach number range of 0.6–2.7. The simulations are compared with the experimental data of McCoy (McCoy, R. L., “The Aerodynamic Characteristics of 0.50 Ball, M33, API, M8, and APIT, M20 Ammunition,” U.S. Army Ballistic Research Lab. BRL-MR-3810, Aberdeen Proving Ground, MD, Jan. 1990) and theReynolds-averagedNavier–Stokes results of Silton (Silton, S., “Navier-StokesComputations for a Spinning Projectile from Subsonic to Supersonic Speeds,” Journal of Spacecraft and Rockets, Vol. 42, No. 2, 2005, pp. 223–231). Unlike the Reynolds-averagedNavier–Stokes simulations, the detached eddy simulations are shown to predict unsteady base and wake flows, which affect the predicted aerodynamic behavior of the projectile. There are some notable differences between the predictions of the present Reynolds-averaged Navier–Stokes simulations and those of Silton; they are most likely a result of the different turbulence models used. This further illustrates the sensitivity of the results to the turbulence modeling approach, for both Reynolds-averaged Navier–Stokes and detached eddy simulations. The largest difference between Reynolds-averaged Navier–Stokes and detached eddy simulations is found for the Magnus moment coefficient at small yaw angles. Analysis shows that this moment is particularly sensitive to the unsteady wake and shock motion predicted by detached eddy simulations.

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.