Past Event: Oden Institute Seminar

Ab initio quantum-chemistry database for N2 (v,J) + N in a state-to-state implementation of the DSMC method

Erik Torres, Von Karman Institute for Fluid Dynamics, Belgium

Abstract

In this work, the implementation within DSMC of a coarse-grain model for nitrogen is presented. The main contribution of this thesis is the development of a methodology by which a detailed state-to-state reaction mechanism for internal energy exchange and molecular dissociation can be reduced to a manageable size and incorporated into a DSMC code. The feasibility of using this model to simulate problems with realistic 2D/3D geometries and conditions relevant for atmospheric entry applications is demonstrated. More specifically, the work performed consisted of several tasks. First, the detailed reaction-kinetic data for internal energy exchange and dissociation in N2 +N-collisions, which were extracted from an ab initio database developed at NASA Ames Research Center, had to be adapted to a form suitable for use by DSMC collision routines. It was found that the “raw” cross sections directly extracted from the database were affected by significant statistical noise, due to the relatively coarse sampling of impact parameters employed in the quasi-classical trajectory (QCT) method during their generation. As a consequence, the cross sections in their original form were considered unsuitable for direct use with DSMC. Instead, thermally averaged rate coefficients, obtained by integrating the original cross sections over all collision energies, were used as a starting point. This reduced the stochastic noise significantly, and in a subsequent step these temperature-dependent rate coefficients were converted back into collision energy-dependent cross sections. This inversion problem was tackled by an analytical technique, inspired by the cross section functional form used in Bird’s classical total collision energy method. Alternative inversion techniques for obtaining the cross sections numerically, such as Tikhonov regularization, or non-linear optimization via the downhill-simplex method were deemed too time-consuming to be practical. Second, in order to reduce the computational cost of the state-to-state model to reasonable levels, the number of discrete rovibrational states of N2 (and the associated mechanism for the internal energy exchange and dissociation reactions) had to be reduced considerably. For this purpose, an already existing coarse grain model known as the uniform rovibrational (URVC) bin model was adapted for its use with DSMC. In order to determine the most convenient distribution of rovibrational levels among a given number of bins, and to determine the minimum number of bins necessary to reproduce the behavior of the full system by means of the URVC model, a parametric study was conducted. This study helped determine the “binning strategy” to best approximate the thermodynamic behavior of the full set of levels. Using bins with fewer rovibrational levels at lower energies allows for a much better representation of the internal energy content in the gas at low temperatures. This is a desirable feature in atmospheric-entry flows, where the free stream is usually cold. The final choice used 10 variably-sized bins, which were able to reproduce the thermodynamic properties of the full set of levels over a wide range of temperatures. For purposes of model testing, a dedicated DSMC code capable of simulating the detailed chemical dynamics of the state-to-state mechanism in unsteady 0D- and steady 1D flows was written at VKI. With the help of this code, the DSMC implementation of the URVC bin model was verified against equivalent master equation calculations in adiabatic reservoir-type simulations. The sensitivity of the internal energy relaxation- and dissociation rates to the choice of bins was examined, and the 10 variably-sized bins were again found to produce results which closely approximate those of the full set of levels. Subsequently, the URVC bin model was used to study internal energy excitation and dissociation in nitrogen, as it is compressed across a normal shock. This test case revealed that the bin model based on the NASA Ames cross sections predicts extremely high kinetic temperatures in the shock, with relatively slow excitation of the rovibrational energy modes and a delay in the onset of dissociation. Finally, the bin model was adapted for use with an external production-level DSMC tool. In this case, the RGDAS code developed at the Institute for Theoretical and Applied Mechanics (ITAM) in Novosibirsk, Russia was used. This integration was done in order to demonstrate the feasibility of using the state-to-state model two large-scale 2D and 3D DSMC simulations. As examples, two test cases roughly representative of Earth atmospheric entry of blunt bodies were used. The behavior of the bin model was studied by comparing it to calculations, with the conventional Larsen-Borgnakke and total collision energy models. It was found that the bin model predicts a much lower degree of internal energy excitation and slower dissociation across the bow shock than the conventional models. There are several ways in which continued research into such high-fidelity models will still provide beneficial for future applications. One of its main uses will be to verify, or challenge some of the core assumptions inherent to the much less costly models currently in general use (i.e. Larsen-Borgnakke+TCE models in DSMC, or multi-temperature models in CFD), and help to propose improvements, or alternatives to these conventional models. Furthermore, since the QCT-derived chemistry data are essentially parameter-free, they are of special use to study the detailed chemical behavior of the gas in situations where experimental data is scarce, or nonexistent.