Paolo Valentini

An improved potential energy surface and multi-temperature quasiclassical trajectory calculations of N2 + N2 dissociation reactions

Accurate modeling of high-temperature hypersonic flows in the atmosphere requires consideration of collision-induced dissociation of molecular species and energy transfer between the translational and internal modes of the gas molecules. Here, we describe a study of the N2 + N2⟶N2 + 2N and N2 + N2⟶4N nitrogen dissociation reactions using the quasiclassical trajectory (QCT) method. The simulations used a new potential energy surface for the N4 system; the surface is an improved version of one that was presented previously. In the QCT calculations, initial conditions were determined based on a two-temperature model that approximately separates the translational-rotational temperature from the vibrational temperature of the N2 diatoms. Five values from 8000 K to 30,000 K were considered for each of the two temperatures. Over 2.4 × 10(9) trajectories were calculated. We present results for ensemble-averaged dissociation rate constants as functions of the translational-rotational temperature T and the vibrational temperature T(v). The rate constant depends more strongly on T when T(v) is low, and it depends more strongly on T(v) when T is low. Quasibound reactant states contribute significantly to the rate constants, as do exchange processes at higher temperatures. We discuss two sets of runs in detail: an equilibrium test set in which T = T(v) and a nonequilibrium test set in which T(v) < T. In the equilibrium test set, high-v and moderately-low-j molecules contribute most significantly to the overall dissociation rate, and this state specificity becomes stronger as the temperature decreases. Dissociating trajectories tend to result in a major loss of vibrational energy and a minor loss of rotational energy. In the nonequilibrium test set, as T(v) decreases while T is fixed, higher-j molecules contribute more significantly to the dissociation rate, dissociating trajectories tend to result in a greater rotational energy loss, and the dissociation probabilitys dependence on v weakens. In this way, as T(v) decreases, rotational energy appears to compensate for the decline in average vibrational energy in promoting dissociation. In both the equilibrium and nonequilibrium test sets, in every case, the average total internal energy loss in the dissociating trajectories is between 10.2 and 11.0 eV, slightly larger than the equilibrium potential energy change of N2 dissociation.

GPU-accelerated Classical Trajectory Calculation Direct Simulation Monte Carlo applied to shock waves

Abstract In this work we outline a Classical Trajectory Calculation Direct Simulation Monte Carlo (CTC-DSMC) implementation that uses the no-time-counter scheme with a cross-section determined by the interatomic potential energy surface (PES). CTC-DSMC solutions for translational and rotational relaxation in one-dimensional shock waves are compared directly to pure Molecular Dynamics simulations employing an identical PES, where exact agreement is demonstrated for all cases. For the flows considered, long-lived collisions occur within the simulations and their implications for multi-body collisions as well as algorithm implications for the CTC-DSMC method are discussed. A parallelization technique for CTC-DSMC simulations using a heterogeneous multicore CPU/GPU system is demonstrated. Our approach shows good scaling as long as a sufficiently large number of collisions are calculated simultaneously per GPU (∼100,000) at each DSMC iteration. We achieve a maximum speedup of 140× on a 4 GPU/CPU system vs. the performance on one CPU core in serial for a diatomic nitrogen shock. The parallelization approach presented here significantly reduces the cost of CTC-DSMC simulations and has the potential to scale to large CPU/GPU clusters, which could enable future application to 3D flows in strong thermochemical nonequilibrium.

Molecular dynamics simulation of O2 sticking on Pt(111) using the ab initio based ReaxFF reactive force field

The molecular dynamics technique with the ab initio based classical reactive force field ReaxFF is used to study the adsorption dynamics of O(2) on Pt(111) for both normal and oblique impacts. Overall, good quantitative agreement with the experimental data is found at low incident energies. Specifically, our simulations reproduce the characteristic minimum of the trapping probability at kinetic incident energies around 0.1 eV. This feature is determined by the presence of a physisorption well in the ReaxFF potential energy surface (PES) and the progressive suppression of a steering mechanism when increasing the translational kinetic energy (or the molecules rotational energy) because of steric hindrance. In the energy range between 0.1 and 0.4 eV, the sticking probability increases, similar to molecular beam sticking data. For very energetic impacts (above 0.4 eV), ReaxFF predicts sticking probabilities lower than experimental sticking data by almost a factor of 3 due to an overall less attractive ReaxFF PES compared to experiments and density functional theory. For oblique impacts, the trapping probability is reduced by the nonzero parallel momentum because of the PES corrugation and does not scale with the total incident kinetic energy. Furthermore, our simulations predict quasispecular (slightly supraspecular) distributions of angles of reflection, in accordance with molecular beam experiments. Increasing the beam energy (between 1.2 and 1.7 eV) causes the angular distributions to broaden and to exhibit a tail toward the surface normal because molecules have enough momentum to get very near the surface and thus probe more corrugated repulsive regions of the PES.

Large-scale molecular dynamics simulations of normal shock waves in dilute argon

Large-scale molecular dynamics (MD) simulations using the Lennard-Jones potential are performed to study the structure of normal shock waves in dilute argon. Nonperiodic boundary conditions in the flow direction are applied by coupling the MD domain with a two-dimensional finite-volume computational fluid dynamics (CFD) solver to correctly generate the inflow and outflow particle reservoirs. Detailed comparisons are made with direct simulation Monte Carlo (DSMC) solutions using the variable-hard-sphere (VHS) collision model. By performing realistic MD simulations of full shock waves, this article presents a more sensitive evaluation of the VHS model parameters (via temperature and velocity distribution functions) than is possible using available experimental density measurements. In the high temperature range (300–8000 K), where the Chapman–Enskog theory supports the VHS model assumptions, near-perfect agreement between MD and DSMC solutions is demonstrated and inverse shock thickness predictions reproduc...

Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface

The direct molecular simulation (DMS) approach is used to predict the internal energy relaxation and dissociation dynamics of high-temperature nitrogen. An ab initio potential energy surface (PES) is used to calculate the dynamics of two interacting nitrogen molecules by providing forces between the four atoms. In the near-equilibrium limit, it is shown that DMS reproduces the results obtained from well-established quasiclassical trajectory (QCT) analysis, verifying the validity of the approach. DMS is used to predict the vibrational relaxation time constant for N2–N2 collisions and its temperature dependence, which are in close agreement with existing experiments and theory. Using both QCT and DMS with the same PES, we find that dissociation significantly depletes the upper vibrational energy levels. As a result, across a wide temperature range, the dissociation rate is found to be approximately 4–5 times lower compared to the rates computed using QCT with Boltzmann energy distributions. DMS calculations predict a quasi-steady-state distribution of rotational and vibrational energies in which the rate of depletion of high-energy states due to dissociation is balanced by their rate of repopulation due to collisional processes. The DMS approach simulates the evolution of internal energy distributions and their coupling to dissociation without the need to precompute rates or cross sections for all possible energy transitions. These benchmark results could be used to develop new computational fluid dynamics models for high-enthalpy flow applications.

Rovibrational coupling in molecular nitrogen at high temperature: An atomic-level study

This article contains an atomic-level numerical investigation of rovibrational relaxation in molecular nitrogen at high temperature (>4000 K), neglecting dissociation. We conduct our study with the use of pure Molecular Dynamics (MD) and Classical Trajectory Calculations (CTC) Direct Simulation Monte Carlo (DSMC), verified to produce statistically identical results at the conditions of interest here. MD and CTC DSMC solely rely on the specification of a potential energy surface: in this work, the site-site Ling-Rigby potential. Additionally, dissociation is prevented by modeling the N–N bond either as a harmonic or an anharmonic spring. The selected molecular model was shown to (i) recover the shear viscosity (obtained from equilibrium pure MD Green-Kubo calculations) of molecular nitrogen over a wide range of temperatures, up to dissociation; (ii) predict well the near-equilibrium rotational relaxation behavior of N2; (iii) reproduce vibrational relaxation times in excellent accordance with the Millikan-...

Molecular dynamics simulation of rotational relaxation in nitrogen: Implications for rotational collision number models

We study the rotational relaxation process in nitrogen using all-atom molecular dynamics (MD) simulations and direct simulation Monte Carlo (DSMC). The intermolecular model used in the MD simulations is shown to (i) reproduce very well the shear viscosity of nitrogen over a wide range of temperatures, (ii) predict the near-equilibrium rotational collision number in good agreement with published trajectory calculations done on ab initio potential energy surfaces, and (iii) produce shock wave profiles in excellent accordance with the experimental measurements. We find that the rotational relaxation process is dependent not only on the near-equilibrium temperature (i.e., when systems relax to equilibrium after a small perturbation), but more importantly on both the magnitude and direction of the initial deviation from the equilibrium state. The comparison between MD and DSMC, based on the Borgnakke-Larsen model, for shock waves (both at low and high temperatures) and one-dimensional expansions shows that a j...

A combined Event-Driven/Time-Driven molecular dynamics algorithm for the simulation of shock waves in rarefied gases

A novel combined Event-Driven/Time-Driven (ED/TD) algorithm to speed-up the Molecular Dynamics simulation of rarefied gases using realistic spherically symmetric soft potentials is presented. Due to the low density regime, the proposed method correctly identifies the time that must elapse before the next interaction occurs, similarly to Event-Driven Molecular Dynamics. However, each interaction is treated using Time-Driven Molecular Dynamics, thereby integrating Newtons Second Law using the sufficiently small time step needed to correctly resolve the atomic motion. Although infrequent, many-body interactions are also accounted for with a small approximation. The combined ED/TD method is shown to correctly reproduce translational relaxation in argon, described using the Lennard-Jones potential. For densities between @r=10^-^4kg/m^3 and @r=10^-^1kg/m^3, comparisons with kinetic theory, Direct Simulation Monte Carlo, and pure Time-Driven Molecular Dynamics demonstrate that the ED/TD algorithm correctly reproduces the proper collision rates and the evolution toward thermal equilibrium. Finally, the combined ED/TD algorithm is applied to the simulation of a Mach 9 shock wave in rarefied argon. Density and temperature profiles as well as molecular velocity distributions accurately match DSMC results, and the shock thickness is within the experimental uncertainty. For the problems considered, the ED/TD algorithm ranged from several hundred to several thousand times faster than conventional Time-Driven MD. Moreover, the force calculation to integrate the molecular trajectories is found to contribute a negligible amount to the overall ED/TD simulation time. Therefore, this method could pave the way for the application of much more refined and expensive interatomic potentials, either classical or first-principles, to Molecular Dynamics simulations of shock waves in rarefied gases, involving vibrational nonequilibrium and chemical reactivity.

Uncertainty Analysis of Reaction Rates in a Finite-Rate Surface-Catalysis Model

The implementation of a nite-rate-catalytic wall boundary condition easily incorporated into generic hypersonic ow solvers is described in detail. Simulations of hypersonic ow over a cylinder are presented using the nite-rate-catalytic model parameterized with a test air-silica chemical model comprising the gas-surface reaction mechanisms and their associated rates. It is demonstrated that backwards recombination rates should not be arbitrarily set but must be consistent with the gas-phase thermodynamics, otherwise a drift from the equilibrium state may occur. The heat ux predicted by the nite rate model lies between non-catalytic and super-catalytic limits depending on the surface temperature. It is found that even for a constant surface temperature, the oxygen recombination eciencies determined by the model are not only a function of temperature, but also a function of the surface coverage, where recombination eciencies are seen to rise as coverage decreases. Monte Carlo uncertainty analysis is performed to correlate the inuence of individual mechanisms to the stagnation point heat ux. The expected progression of dominant mechanisms is found as the surface temperature is raised, and the uncertainty in heat ux is highly correlated to the reaction rate of the dominant mechanism at a specied surface temperature. It is found that increased surface reactivity increases the chemical heat ux while also altering the boundary layer in a manner that decreases the convective heat heat ux.

Direct simulation of rovibrational excitation and dissociation in molecular nitrogen using an ab initio potential energy surface

We present an atomic-level study of vibrational excitation and chemical dissociation in molecular nitrogen at high temperature. The computational techniques, quasiclassical trajectory calculations (QCT) and classical trajectory calculation direct simulation Monte Carlo (CTC DSMC), solely rely on the specification of a highly accurate ab initio surface for N2-N2 interactions. We show that the simulations accurately reproduce the vibrational relaxation times obtained from the Millikan-White correlation and further support existing high-temperature corrections. Using both QCT and CTC DSMC methods with the same PES, we show that dissociation proceeds 4 to 5 times faster under equilibrium conditions compared to quasi-steady-state nonequilibrium conditions. At high translational energies (20,000 K and 30,000 K), the overall vibrational energy ladder is depleted, and dissociation proceeds at a rate approximately corresponding to a lower vibrational temperature. Conversely, at lower energies (10,000 K), almost no dissociation occurs from low-lying vibrational energy states. In this case, even a slight depletion of the upper-level vibrational energy states, which preferentially dissociate and are not rapidly re-populated due to slow bound-bound energy transfer mechanisms, causes a remarkable reduction of the dissociation rate. The ab initio CTC DSMC method is able to directly simulate rovibrational excitation and dissociation processes without computing the large number of cross-sections required by a state-resolved approach, and can be used directly to form new CFD models.