One of the most persistent, and often overlooked, challenges in hypersonic vehicle design lies in the transitional flow regimes encountered at high altitudes, typically between 70 and 120 kilometers. In this range, the mean free path of air molecules becomes comparable to the characteristic size of some parts of the vehicle (e.g. curvature radius of edges and corners), and the continuum assumptions of classical fluid dynamics begin to break down. Yet, neither is the flow fully in the free-molecular regime. This intermediate zone, often referred to as the “transitional regime,” is where many physical models lose their predictive power.

This regime is particularly relevant for air-breathing hypersonic platforms, reentry vehicles, and upper-atmosphere maneuvering systems, which must operate across a wide range of altitudes. In these flows, plasma-based flow control, particularly via electric discharges or body-mounted actuators, has been proposed as a way to dynamically modulate aerodynamic forces, heat transfer, and boundary layer characteristics.

However, applying plasma actuators in transitional flow introduces a unique set of challenges.

What Makes the Transitional Regime Difficult?

At sea level and at altitudes where airliners fly, the assumptions behind Navier-Stokes equations are generally valid: local thermodynamic equilibrium, negligible mean free path compared to system dimensions, and isotropic stress and heat flux tensors. But at altitudes above ~60 km, the Knudsen number (defined as the ratio of the molecular mean free path to a characteristic length scale) rises above 0.01, signaling a breakdown in continuum assumptions.

Standard CFD solvers that rely on conventional boundary-layer models, turbulence closures, and Fourier-based heat conduction begin to fail. On the other hand, full kinetic solvers such as Direct Simulation Monte Carlo (DSMC) become increasingly computationally expensive at higher densities. This leaves a gap in modeling fidelity, just where many hypersonic vehicles spend a significant fraction of their flight.

Now consider plasma: an inherently non-equilibrium medium, with distinct distributions for ions, electrons, and neutrals, often far from thermodynamic equilibrium. Superimposing such a plasma into a rarefied, high-altitude flow only magnifies the modeling difficulty. But it also presents a unique opportunity.

Electric Discharges in Rarefied Environments

The physics of gas discharges in rarefied conditions differs markedly from those at atmospheric pressure. First, the electron mean free path becomes long (on the order of centimeters or even tens of centimeters). Even more importantly, since the average fraction of energy the electron loses in a collision with molecules is small due to the huge difference in masses of electrons and molecules, the electron mean free path with respect to energy relaxation is at least one or two orders of magnitude longer than just the mean free path and thus becomes comparable with geometric sizes even at air densities and altitudes where Navier-Stokes fluid dynamics is still valid. This results in a highly non-local relationship between the electric field and ionization processes and, therefore, plasma density. Second, the thickness of electrically charged sheaths near cathodes grows to centimeters of even meters, taking up the regions that would have been occupied by quasineutral plasma at higher gas densities. Third, transport processes such as diffusion and heat conduction become so fast that localized discharges such as constricted arcs become impossible and plasmas are diffuse in nearly all regimes.

In rarefied flows, the electron energy distribution function (EEDF) becomes not only non-local, i.e. dependent on the electric field in a wide area around the given point, but also much more anisotropic and can more readily develop high-energy tails, enhancing the rates of some key reactions such as vibrational excitation and stepwise ionization.

These and many other features of low-pressure plasmas and electric discharges make high-altitude plasma technologies quite interesting.

Plasma-Flow Coupling in the Transitional Regime

The presence of plasma in transitional hypersonic flow modifies several key parameters:

1. Viscosity and Thermal Conductivity
    At high levels of ionization, the effective transport properties of the gas are altered. Ion-neutral and electron-neutral collisions contribute significantly to energy exchange, while Coulomb (electron-electron and electron-ion) collisions affect internal energy transfer and momentum coupling. Electron heat transfer is the fastest transport process, and due to it, the electron temperature is equilibrated throughout the low-pressure plasma almost instantaneously.
   
   
2. Boundary Layer Structure
    In high-altitude hypersonic flow, boundary layers are often tenuous or nonexistent. However, applying localized plasma can initiate pseudo-boundary layers, where the density and conductivity gradients create virtual shear regions. These may be used to suppress flow separation or generate surface-normal forces.
   
   
3. Electromagnetic Body Forces
    In rarefied flow, the traditional Lorentz force becomes spatially extended. That is, the current paths and magnetic field penetration depths can be on the order of system size. This means the plasma actuator is no longer localized but can instead exert distributed body forces across the vehicle forebody or control surfaces.
   
   
4. Ionization-Induced Drag Reduction
    A curious effect in rarefied flows is that localized heating and subsequent expansion due to ionization actually decreases the density and dynamic pressure on the vehicle surface. In very high Knudsen number regimes, this may be used to reduce heat loads or modify vehicle trim without mechanical actuation.