Optimal voltage slope range for enhancing thrust-to-power ratio of dielectric barrier discharge plasma actuator: experimental and phenomenological investigations

Dielectric barrier discharge plasma actuators generate flow by inducing ion motion through the Coulomb force. The voltage slope of the driving waveform directly affects the discharge behavior and the resulting Coulomb force, making it a critical parameter for actuator performance. To provide a design guideline for driving waveforms, this study investigates the voltage slope range that provides a high thrust-to-power ratio and clarifies the underlying mechanism through combined experimental and phenomenological approaches. Both sinusoidal and trapezoidal waveforms were examined by thrust measurements, induced flow analysis via particle image velocimetry, and electrical circuit measurements. We develop a phenomenological model to describe the temporal variation of the Coulomb force based on fundamental barrier discharge characteristics. The experimental results show that a higher voltage slope reduces the thrust-to-power ratio for trapezoidal waveforms. This trend is explained by our phenomenological model: a higher voltage slope shortens the interval between successive discharge pulses relative to the characteristic deposition time of volume charges onto the dielectric, causing the next discharge to occur before the generated volume charges are fully transferred to the dielectric and thereby reducing the Coulomb-force impulse per pulse. In the sinusoidal case, increasing the frequency—which corresponds to a higher averaged voltage slope—leads to thrust saturation due to the same mechanism: the thrust increment due to increasing pulse numbers per unit time is offset by the decrease in impulse per pulse. Conversely, at lower voltage slopes, the impulse per cycle approaches saturation, and the practical optimum is determined by the balance between thrust generation and efficiency. Evaluating this balance using a composite performance index identifies a high-performance voltage-slope range of 170–200 V μ s −1 under the present experimental conditions. These observations suggest that, under the investigated conditions, waveforms should be designed to maintain this specific slope range, rather than simply increasing the applied voltage or frequency.