Accurate Nitrogen Plasma Modelling Improves Predictions of Electron Temperature.

A new thermodynamically consistent model accurately predicts electron temperature in non-equilibrium flows, resolving limitations of prior approaches. By applying detailed balance and a Boltzmann vibrational distribution, the model achieves convergence at equilibrium and predicts electron temperatures that are up to six times lower than those in existing simulations, thereby improving plasma modelling for aerospace applications.

The accurate determination of electron temperature within hypersonic flows presents a significant challenge to plasma modelling, impacting applications ranging from spacecraft design to radio frequency communication. Existing models frequently struggle to reconcile theoretical predictions with experimental data, often failing to converge towards thermodynamic equilibrium. Researchers at the University of Arizona, Felipe Martin Rodriguez Fuentes and Bernard Parent, address this issue in their paper, ‘Electron Heating in Hypersonic Flows: A New Thermodynamically Consistent Model’, by presenting a revised approach to calculating electron heating derived from the principle of detailed balance. Their work introduces a simplified heating-to-cooling ratio utilising an effective activation energy and a characteristic vibrational temperature of nitrogen, offering improved accuracy, particularly at lower electron temperatures, and better alignment with flight-test results. This refined model promises to enhance the reliability of simulations for technologies reliant on plasma behaviour, including mitigation of radio-frequency blackout, magnetohydrodynamic aerocapture, and advanced cooling systems.

Hypersonic flight and atmospheric entry generate non-equilibrium plasmas, presenting considerable challenges for accurate modelling of critical aerospace technologies. These plasmas, formed by the intense heating of air at extreme velocities, deviate significantly from thermal equilibrium, meaning electron temperatures differ markedly from those of the surrounding gas. Existing plasma models frequently struggle to predict electron temperatures accurately, largely due to limitations in representing electron heating derived from vibrationally excited nitrogen molecules. Nitrogen, comprising approximately 78% of the atmosphere, becomes vibrationally excited at these high temperatures, and this excitation plays a crucial role in energy transfer within the plasma.

The team has developed a novel, thermodynamically consistent model for electron heating, addressing these limitations and improving the fidelity of plasma simulations for high-speed flight applications. The model rigorously applies the principle of detailed balance, a fundamental concept in thermodynamics stating that, in equilibrium, the rates of forward and reverse processes are equal. Assuming a Boltzmann vibrational distribution – a statistical description of how energy is distributed among vibrational energy levels – the researchers introduced an effective activation energy to derive a simplified heating-to-cooling ratio. Activation energy represents the minimum energy required for a process to occur. This formulation ensures convergence of electron and vibrational temperatures at thermal equilibrium, a crucial validation absent in many prior models, and allows for a more accurate representation of energy transfer processes within the plasma. A key advantage of this approach is its ability to utilise total cooling rates obtained from experiments, providing a direct link between simulation and real-world observations.

The researchers demonstrate that the model accurately predicts electron temperatures in non-equilibrium plasmas, offering a substantial improvement over existing methodologies. The model’s ability to accurately represent plasma behaviour under flight conditions is critical for advancing technologies such as mitigation of radio-frequency blackout – a phenomenon where plasma interferes with radio communications – optimisation of electron transpiration cooling techniques, where electrons are used to dissipate heat, and enhancement of electromagnetic shielding effectiveness.

Validation against flight-test data reveals a substantial improvement in predictive capability, with the new model predicting electron temperatures up to six times lower than those obtained using previous methodologies. This enhanced accuracy stems from a more realistic representation of energy transfer processes within the plasma, and provides a more reliable basis for designing and optimising high-speed vehicles. The discrepancy between previous models and experimental data highlights the importance of accurately capturing the complex energy exchange mechanisms within these plasmas.

The team plans to extend the model to incorporate the effects of other molecular species present in atmospheric plasmas, such as oxygen and their excited states. Investigating the influence of non-Maxwellian velocity distributions on the electron heating rate also represents a valuable area for further research. A Maxwellian distribution describes the statistical distribution of speeds of particles in a gas at thermal equilibrium; deviations from this distribution can significantly affect plasma behaviour. Exploring the model’s performance under a wider range of plasma conditions, including varying pressures and altitudes, will be essential to fully characterise its capabilities and limitations.

Coupling this improved electron heating model with computational fluid dynamics solvers will enable more comprehensive simulations of plasma-flow interactions, providing a more complete understanding of the complex phenomena occurring during high-speed flight. This will allow engineers to design more efficient and reliable high-speed vehicles, and to develop new technologies that exploit the unique properties of non-equilibrium plasmas. The researchers believe that this work represents a significant step forward in our ability to model and predict the behaviour of non-equilibrium plasmas, and that it will have a lasting impact on the field of aerospace engineering.