Comment on “Jet propulsion by microwave air plasma in the atmosphere” [AIP Adv. 10, 055002 (2020)]

In a recent article, Ye et al.¹ demonstrated microwave ionization of air in a quartz tube. The authors attempted to estimate the thrust produced by the device by blocking the exhaust with a ball of variable weight. The authors assumed that the “threshold weight at which the steel ball started to rattle” corresponded to the thrust produced by the device. Unfortunately, this method falsely relates the internal pressure of a blocked exit to the propulsive thrust that would be experienced in the absence of the blockage. In this Comment, we show that, due to this inaccurate estimation method, the thrust reported by the authors is up to 9 times the theoretical thrust levels possible for a microwave-driven thrust device, i.e., where 100% of the input microwave power is converted to thrust. To describe the source of this overestimate, we use a control volume analysis of the experimental conditions described by Ye et al.,¹ which captures the effect of blocking the chamber exhaust. This analysis demonstrates that the measured pressure using this method is internal stagnation pressure and cannot be used to estimate thrust. The results of the model are consistent with the reported experimental data. Therefore, through the combination of the efficiency analysis and the control volume analysis, we show that the authors’ proposed thrust estimation technique leads to a significant overestimation of thrust.

To evaluate the reported measurements, it is instructive to perform a simple calculation of the total efficiency of the device. Ye et al.¹ presented a set of data for the purported thrust of the microwave device for a range of operating conditions with flows between 0.7 m³/h and 1.45 m³/h, and input microwave powers between 400 W and 800 W. Forces measured using the ball method were between 3 N and 10 N, which when scaled to account for the net thrust at zero input power resulted in a net propulsion pressure between 2 kPa and 16 kPa.

The efficiency of an electrically powered thruster, η_T, is the ratio of jet power to input electrical power,^2,3 which can be calculated using

where F is thrust, ṁ is the mass flow rate, and Ẇ_in is the input electrical power. Equation (1) is developed through conservation of energy, so it is applicable regardless of mechanisms specific to the investigated device. The total efficiency of the device has been calculated using the given values of pressure, flow rate, and input power in Fig. 5 of Ye et al.¹ assuming an inlet with standard temperature and pressure conditions. The “net propulsive pressure” has been converted to the estimated thrust by multiplying by the area of the tube. These values are presented in Figs. 1 and 2 and reach up to nearly 80 times unity, i.e., there is 8000% as much jet power leaving the system as electrical power entering it. The calculated efficiency is above the maximum allowable efficiency of 100%, suggesting that the steel ball method is unreasonable for approximating thrust. If we constrain the thruster efficiency to the theoretical maximum of 100%, with standard temperature and pressure air at the inlet and 600 W input power and 1.15 m³/h of flow, the anticipated thrust generated would only be 0.7 N, which is an order of magnitude less than the authors’ reported results.

By using the method of placing a weighted ball on the exhaust of the device, the authors are creating a partially sealed chamber out of the quartz tube and measuring the internal pressure rather than the thrust produced by the device. Modeling of this case can be performed with a control volume analysis, with the inside of the tube considered as the control volume. A diagram of the experimental configuration is shown in Fig. 3. The inlet flow rate must be equal to the outlet flow rate; both can be designated as ṁ. In lieu of any described acceleration mechanism associated with the plasma, the microwave source can be assumed to act only as a heating mechanism. By conservation of energy, the energy leaving the cylinder by transport and heat loss due to convection must be equal to the heat entering due to transport and as microwave power,

where T_atm is the ambient temperature, c_p is the specific heat, T is the temperature inside the tube, Q_g is the heat generated by microwave irradiation, h is the convection coefficient, and A_s is the exposed surface area of the cylinder. For the sake of simplicity, conductive heat loss through the ball and structure and radiative heat transfer are ignored. The compressed air is also assumed to enter the quartz tube at atmospheric temperature. Because the quartz walls of this device are thin, the temperature drop associated with conduction through this medium can be ignored. Equation (2) can then be simplified as

The ball on the exhaust of the tube blocks flow from exiting the tube. When the ball is not vibrating as described in the paper, flow can only exit through a thin channel formed at the interface between the ball and the cylinder or through grooves caused by the surface roughness of the ball and tube. This channel has a high hydraulic resistance that is assumed to be constant throughout all tests. An Ohm’s law analogy for fluid flow (ΔP = QR_hyd) can be used to determine the pressure drop through this channel. The ideal gas law is used as an equation of state for determining the density of the gas in the tube, ρ,

where P_atm is the ambient pressure, R_hyd is the hydraulic resistance of the thin flow channel between the tube and the weighted ball, and R is the ideal gas constant. At this point, Eq. (3) can be substituted into Eq. (4) and simplified for P,

The required weight of the steel ball, F_w, can then be calculated with a force balance,

where A_e is the exhaust area of the tube. With Eqs. (3), (5), and (6), the force required to hold the ball steady can be calculated. The results from this analysis are plotted with experimental data in Figs. 4 and 5 with the following values assumed: c_p = 1 kJ/kg K, R_hyd = 1.2 × 10⁹ Pa s/m³, and h = 15 W/m² K. Experimental data are taken from Fig. 4 of Ye et al.¹ This analysis shows that the increase in pressure is likely due to heating from the microwave source and the flow restriction caused by the ball blocking the exhaust of the tube. The microwave ionization simply acts as a heat source in this scenario. The flow reaching the weighted ball is nearly stagnated, so this approach is measuring stagnation pressure, not thrust. The control volume model can be extended to the normal operating conditions of the device (i.e., where the weighted ball is removed) by drastically reducing the value of R_hyd. Equation (4) shows that as R_hyd goes to zero, P approaches P_atm; in this case, by the same analysis as used by Ye et al. [i.e., Eq. (6)],¹ the propulsive thrust of the device goes to zero. By comparing these two scenarios, it is clear that the presence of blockage at the exhaust of the device has a drastic effect on the pressure in the quartz tube; experimental conditions are not comparable with and without the steel ball.

Predicting the performance of the device in application as an air-breathing thruster without the steel ball restriction requires knowledge of the future device configuration and operating conditions. If the stagnation pressure measured using the ball method were to be expanded through a nozzle, then there would be thrust produced, albeit at a significantly lower level than reported. The microwave heating element may be integrated into a turbojet as a replacement for the combustion chamber, although it is unclear that this would be more efficient than an electric motor directly driving a propeller. If the thruster employed a gas reservoir instead of a compressor, then the presented device embodies a warm-gas thruster commonly used for space applications with no nozzle.⁴ There are several in-space propulsion technologies that rely on microwave or RF power to ionize gas and produce thrust,^5–8 although such devices typically employ additional electrostatic or electromagnetic acceleration mechanisms, rather than only thermal heating of neutral gas. Direct plasma acceleration of air has also been performed using dielectric-barrier discharges⁹ and magneto-plasma compressors.¹⁰ 

We suggest that future efforts to estimate thrust use proven and verified techniques. Additionally, the reported thrust values should be compared to theoretically achievable values.