**3. Differences in the working mechanisms of the plasma-based approach from conventional resistive electric heating methods for aircraft inflight icing mitigation**

Since the impingement of supercooled water droplets onto an airframe surface is the precursor for the ice accretion over the airframe surface, a better understanding about the heat transfer mechanisms during the impinging process of the water droplets onto the surface of a plasma actuator against that of a conventional electrical film heater is very helpful to elucidate the underlying physics to reveal the significant differences in the working mechanisms of DBD plasma-based approaches from those of conventional resistive electric heating methods for aircraft icing mitigation.

**Figure 4** shows the schematics to reveal the great differences in the heating mechanisms as a water droplet impinging onto airfoil surfaces protected by using two different anti−/de-icing systems (*i.e.*, conventional electrical heating method *vs.* DBD plasma-based approach). For the case with a conventional electrical film heater, the thermal energy is generated on the heater surface through resistive electric heating as supplied from the electrical power source. While a portion of the thermal energy may be dissipated to the airflow above the heater surface due to the development of thermal boundary layer via convective heat transfer, which could warm up the impinging water droplet before it is in contact with the heater surface, the dominating mechanism for heating the water droplet would be through heat conduction after the dynamic impinging process (*i.e.*, droplet impacting, splashing, and receding), as

### **Figure 4.**

*Comparison of different heating mechanisms as water droplet impinging onto the surface of an electrical film heater against that of a DBD plasma-based actuator.*

*An Experimental Investigation on the Thermodynamic Characteristics of DBD Plasma… DOI: http://dx.doi.org/10.5772/intechopen.100100*

shown schematically in **Figure 4(a)**. Due to the significant temperature differences between the impinging supercooled water droplet and the heater surface, the thermal energy would be transferred from the heater surface to the water droplet, which can keep the droplet warm up (*i.e.*, above the freezing point) or even being evaporated after the water droplet impacted onto the surface of the electric film heater.

However, as shown schematically in **Figure 4(b)**, the situation would become much different for the case as the water droplet impinging onto the airfoil surface protected by a DBD plasma actuator. As described in Tirumala et al. [32], the primary heating mechanism for plasma discharges is through heat transfer from the plasma to the ambient gas, which then heats up the dielectric surface through direct injection, convection and radiation. This is a reverse thermal path in comparison with that of the scenario of the conventional electrical heating method. Therefore, as the water droplet impinging onto the airfoil surface protected by the DBD plasma actuator, the water droplets would not only be heated up through heat conduction after impacted onto the hot dielectric surface, more importantly, but also be effectively heated up through forced convective heat transfer as the droplet traveling through the hot air in the plasma region even before becoming in contacting with the surface of the plasma actuator, as shown clearly in **Figure 4(b)**.

As described in Li *et al*. [46], the transient temperature of an in-flight droplet can be calculated by using equation of

$$T = \left[T\_i - T\_\epsilon + T\_\epsilon \exp\left[\left(\mathfrak{G}t\_f h\right) / \left(\rho \mathfrak{c}\_p D\right)\right]\right] / \exp\left[\left(\mathfrak{G}t\_f h\right) / \left(\rho \mathfrak{c}\_p D\right)\right] \tag{1}$$

where *T* is the transient temperature of the in-flight droplet, *h* is the convection coefficient of air around the surface of the in-flight droplet, *T*i is the initial temperature of the droplet, *T*e is the air temperature surrounding the droplet, *ρ* is the density of the droplet, *c*p is the specific heat of the droplet; *t*f is the time of flight of the droplet in the convective air flow, and *D* is the diameter of the flying droplet. It is obvious that, with the same flight time, a higher temperature of the surrounding air would imply a higher transient temperature of the inflight water droplet. Since DBD plasma actuation would induce a significant gas heating above the surface of the plasma actuator, the temperature of the water droplet before impacting on the surface of the plasma actuator would become much higher than that of the case above the electrical film heater.
