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In this work, an artificial neural network (ANN) aided vapor–liquid equilibrium (VLE) model is developed and coupled with a fully compressible computational fluid dynamics (CFD) solver to simulate the transcritical processes occurring in high-pressure liquid-fueled propulsion systems. The ANN is trained in Python using TensorFlow, optimized for inference using Open Neural Network Exchange Runtime, and coupled with a C++ based CFD solver. This plug-and-play model/methodology can be used to convert any multi-component CFD solver to simulate transcritical processes using only open-source packages, without the need of in-house VLE model development. The solver is then used to study high-pressure transcritical shock-droplet interaction in both two- and four-component systems and a turbulent temporal mixing layer (TML), where both qualitative and quantitative agreement (maximum relative error less than 5%) is shown with respect to results based on both direct evaluation and the state-of-the-art in situ adaptive tabulation (ISAT) method. The ANN method showed a 6 times speed-up over the direct evaluation and a 2.2-time speed-up over the ISAT method for the two-component shock-droplet interaction case. The ANN method is faster than the ISAT method by 12 times for the four-component shock-droplet interaction. A 7 times speed-up is observed for the TML case for the ANN method compared to the ISAT method while achieving a data compression factor of 2881. The ANN method also shows intrinsic load balancing, unlike traditional VLE solvers. A strong parallel scalability of this ANN method with the number of processors was observed for all the three test cases. Code repository for 0D VLE solvers, and C++ ANN interface—https://github.com/UMN-CRFEL/ANN_VLE.git. 

Abstract Self-consistent 1D modeling of streamers in ammonia-oxygen-nitrogen-water mixtures has been performed in this work. A fluid model that includes species transport, electrostatic potential, and detailed chemistry was developed and verified. This model is then used to simulate the avalanche, streamer formation and propagation phases, driven by a nanosecond voltage pulse, at different thermochemical conditions derived from a 1D laminar premixed ammonia-air flame. The applicability of the Meek’s criterion in predicting the streamer inception location was successfully confirmed. Streamer formation and propagation duration were found to vary significantly with different thermochemical conditions, due to the difference in ionization rates. The thermochemical state also affected the breakdown characteristics which was tested by maintaining the background reduced electric field constant. Detailed kinetic analyses revealed the importance of $\mathrm{O}{(}^1\mathrm{D})$in the production of key radicals, such as O, OH, and NH₂. Furthermore, the contributions of the dissociative electronic excitation of NH₃towards the production of H and NH₂radicals have also been reported. Spatial and temporal evolution of the electron energy loss fractions for various inelastic collision processes at different thermochemical states uncovered the input plasma energy spent of fuel dissociation and the large variability in the dominant processes during the avalanche and streamer propagation phases. The methodology and analyses reported in this work are key towards developing effective strategies for controlled nanosecond-pulsed non-equilibrium plasma sources used for ammonia ignition and flame stabilization. 

The impacts of the pulse repetition frequency (PRF), number of pulses, and energy per pulse in a train of nanosecond discharge pulses on the ignition of a flowing lean premixed methane–air mixture are investigated using numerical simulations. A phenomenological plasma model coupled with a compressible reacting flow solver is used for these simulations. The simulation strategy has been well validated by comparing the experimental schlieren and OH planar laser induced fluorescence (PLIF) results with the numerical schlieren (i.e., density gradient) and OH density profiles, respectively. The characteristics of the ignition kernels produced by each discharge pulse and their interaction with each other as functions of the PRF are investigated. Three regimes were defined in the literature based on this interaction of the ignition kernels — fully coupled, partially coupled, and decoupled. This study uses numerical simulations to probe into the constructive and destructive effects, that ultimately determine ignition success, in these different regimes. The complete overlap of kernels and the complete lack of synergy between kernels produced by consecutive pulses are attributed to the success and failure of ignition and flame propagation in the fully coupled and decoupled regimes, respectively. In the partially coupled regime, the convection heat loss driven by the shock-turned-acoustic wave of the next discharge pulse, on the kernel produced by the previous discharge pulse, in addition to diffusion losses, contribute to ignition failure. However, the expansion of the next kernel in a region of higher average temperature and radical concentration created by the previous kernel could help to bridge the gap between the two kernels and result in successful ignition. The important parameters of energy per pulse, number of pulses, and equivalence ratio affect the competition between these constructive and destructive effects, which eventually determines the ignition success in this regime. Finally, the change in the nature of interaction between consecutive kernels from decoupled to partially coupled, at the same frequency but with different energies per pulse, is also shown. 

Abstract The present work improves a phenomenological plasma-assisted combustion model by integrating the spatiotemporal distribution of plasma power density, thereby considering the evolution of plasma streamers in the modeling, and subsequently, better predicting the ignition kernel evolution. The improved phenomenological model is validated against experiments representing the plasma discharge and post-discharge ignition kernel evolution. Specifically, the new model demonstrates a more accurate prediction of ultrafast gas heating and O₂dissociation during the plasma discharge, compared to the original model. In addition, the new model is found to closely match the experimental pressure wave and heated channel profiles post-discharge without the need for tuning the energy deposition (unlike the original model), highlighting its accuracy of post-discharge ignition kernel dynamics. The improved phenomenological model is then employed to investigate ignition kernel evolution for a stoichiometric methane-air discharge across various discharge gap configurations. Simulations reveal a non-uniform temperature and streamer distribution progressing from the electrode tips toward the center, contrasting uniform cylindrical discharges previously described in the original model. Streamer propagation is observed to be faster for larger gaps when maintained at the same average electric field for different discharge gaps. The tendency of smaller gaps to produce detached toroidal ignition kernels is observed, while larger gaps promote cylindrical and attached ignition kernels. Interactions between successive ignition kernels from consecutive discharges varied significantly, with the smallest gap (1 mm) promoting the quenching of the preceding ignition kernel due to the initial kernel–kernel separation. The intermediate gap (2 mm) promotes detached kernel growth. In contrast, in the largest gap (4 mm), kernels consistently combine and expand attached to electrodes. The impact of homogeneous isotropic turbulence is also explored, showing the persistence of ignition kernels early on but eventually quenching due to enhanced radical and heat losses with pronounced turbulence intensity. 

Vapor-liquid equilibrium (VLE) is a family of first-principled thermodynamic models for transcritical multiphase flows, which can accurately capture the phase transitions at high-pressure conditions that are difficult to deal with using other models. However, VLE-based computational fluid dynamics (CFD) simulation is computationally very expensive for multi-component systems, which severely limits its applications to real-world systems. In this work, we developed a new ISAT-VLE method based on the in situ adaptive tabulation (ISAT) method to improve the computational efficiency of VLE-based CFD simulation with reduced memory usage. We developed several ISAT-VLE solvers for both fully conservative (FC) and double flux (DF) schemes. New methods are proposed to delete redundant records in the ISAT-VLE table and the ISAT-VLE method performance is further improved. To improve the convergence of the VLE solvers, a modified initial guess for equilibrium constant is also introduced. Simulations of high-pressure transcritical two-phase temporal mixing layers and shock-droplet interaction were conducted using the ISAT-VLE CFD solvers. The simulation results show that the new method obtains a speed-up factor approximately from 10 to 60 and the ISAT errors can be controlled within 1%. The shock-droplet interaction results show that the DF scheme can achieve a higher speed-up factor than the FC scheme. The two sets of simulations exhibit the phase separation at high-pressure conditions. It was found that even at supercritical pressures with respect to each component, the droplet surface could still be in a subcritical two-phase state, because the mixture critical pressure is often significantly higher than each component and hence triggers phase separation. In addition, a shock wave could partially or completely convert the droplet surface from a subcritical two-phase state to a single-phase state by raising temperature and pressure. 

The requirement of high power outputs and high efficiencies of combustion engines such as rocket engines, diesel engines, and gas turbines has resulted in the incremented of the system pressure close to the thermodynamically critical point. This increase in pressure often leads to the fluids becoming either transcritical or supercritical in state. This has led to increased interest in both the multi-component phase change phenomena as well as their chemical reactions. In this work, an artificial neural network (ANN) aided VLE model is coupled with a fully compressible computational fluid dynamics (CFD) solver to simulate the transcritical processes occurring in high-pressure liquid-fueled propulsion systems. The ANN is trained on Python using the TensorFlow library, optimized for inference (i.e., prediction) using ONNX Run-time (a cross-platform inference and training machine-learning accelerator), and coupled with a C++ based fully compressible CFD solver. This plug-and-play model/methodology can be used to convert any fully compressible and conservative CFD solver to simulate transcritical processes using only open-source packages, without the need of in-house VLE-based CFD development. The solver is then used to study high-pressure shock-droplet interaction in both two- and four-component systems where qualitative and quantitative agreement is shown with results based on both direct evaluation and the state-of-the-art in-situ adaptive tabulation (ISAT) method. The ANN model is faster than the direct evaluation method and the ISAT model by 4 times for the four-component shock-droplet interaction. The ANN model also shows implicit load balancing as long as the MPI decomposition is performed uniformly amongst the number of cores chosen, as the inference time for ANN predict does not change with the change in thermodynamic state, unlike traditional VLE solvers. Regarding the parallel scalability of this model, good strong scaling characteristics with number of processors is also observed. 

Supercritical fluids, often present in modern high-performance propulsion systems, result from elevated operating pressures. When these systems utilize fluid mixtures as fuel or oxidizers, a transcritical effect often occurs. This effect can lead to misjudgments, as mixture critical points exceed those of individual components. Fluid mixing may induce phase separation, creating liquid and vapor phases due to the transcritical multi-component effect. Consequently, two-phase modeling is essential for transcritical and supercritical fluids. Traditional interface capturing methods, like Volume of Fluid (VOF) and Level Set (LS), present challenges such as computational expense and lack of conservatism. The Phase Field (PF) method, or the Diffuse Interface (DI) method which uses a phase fraction transport equation, emerges as a conservative alternative. Despite the absence of an initial interface in transcritical fluids, phase separation from mixing may form liquid droplets, necessitating multiphase modeling. To address these complexities, a Vapor-Liquid Equilibrium (VLE) model, coupled with the PR equation of state, is introduced. This model estimates phase fractions, liquid and vapor compositions, densities, and enthalpies through a flash problem solution. The conventional PF model is enhanced by replacing the phase fraction transport equation with VLE-derived values. The resulting VLE-based PF method is implemented into an OpenFOAM compressible solver, ensuring numerical stability with explicit phase field terms and a new CFL criterion. Test cases involve 1D interface convection and 2D droplet convection. In the 1D test, the VLE-based PF model adeptly captures interfaces, adjusting thickness as needed. The 2D droplet case, challenging due to a non-aligned Cartesian grid, exhibits uniform interface thickness and preserves droplet shape. The VLE-based PF model demonstrates versatility and reliability in capturing complex fluid behaviors, offering promising prospects for future research. 

The backward problem of plasma assisted combustion emphasizes evaluating the effect of the evolving thermochemical state on the plasma discharge. This paper investigates the dependence of avalanche to streamer to spark formation dynamics and kinetics on the gas composition and temperature at different points in an ammonia-air premixed laminar flame using a self-consistent multigrid-based 1D plasma solver. Different values of alpha, the coefficient for effective ionization events per unit length, have been reported for electron avalanches in air and stoichiometric NH3-air mixtures. The streamer inception has been shown to obey the Meek’s criterion. An exponential reduction in streamer and spark formation time has been observed from plasma simulations at different points in the unburnt, pre-heat zone, reaction zone and the fully burnt regions of the premixed flame. While the enhancement of the reduced electric field with increasing temperature affects effective ionization, there exists a minimum breakdown field for streamer formation, which does not vary proportionally with the changing number density of the gas. The change in the mixture from reactants (NH3, O2, N2) to products of complete combustion of ammonia in air (N2, H2O) has also been shown to affect the streamer and spark formation. Finally, the major pathways during the streamer and spark phases which are responsible for producing important radicals used in combustion of NH3 are also discussed. 

Natural gas contains a significant fraction of methane, a strong greenhouse gas besides being a potent hydrogen carrier. Thus, reforming methane to a more reactive gas mixture could potentially abate the associated greenhouse heating by depleting methane and provide a pathway to generate hydrogen. The present study investigates the non-equilibrium plasma-assisted reforming of methane to produce hydrogen and reactive alkenes using repetitive nanosecond pulse discharges. A detailed gas-phase chemical kinetics mechanism along with plasma reforming kinetics derived from our previous work are used to perform 0D calculations to obtain the energy fractions for various plasma processes. A phenomenological model for the plasma-assisted reforming of methane/nitrogen mixtures is developed by considering the vibrational energy transport equations of both methane and nitrogen separately. The energy fractions involved in various plasma processes, such as ultra-fast gas heating and ultra-fast gas dissociation due to the electron excitation reactions, and slow gas heating due to the relaxation of vibrational excitation modes of methane and nitrogen, are accounted for in our new phenomenological model using energy fractions derived earlier. The newly developed phenomenological model is then used to perform 3D direct numerical simulation (DNS) of methane reforming diluted with 60% nitrogen in a pin-to-pin electrode configuration with a discharge gap of 1 mm. The effect of pulsing on the evolution of reformed mixture kernels is investigated by comparing two cases: a single-pulsed case with a pulse energy of 0.8 mJ, and another case using 4 pulses at 200 kHz, with a per pulse energy of 0.2 mJ. The single-pulsed case was observed to promote kernel separation and higher fractions of reformed products, while the multiple-pulsed case resulted in a more diffused kernel.