# Effect of NS-DBD Actuator Parameters on the Aerodynamic Performance of a Flap Lifting Device
## 3 Discharge Position and Parameter Setting of the Plasma Actuator  
In this paper, the plasma actuators are placed at three different positions near the flap, and the effect on the aerodynamic performance of the high lift device is analysed by adjusting the parameters of the actuators. The three discharge positions are: (1) The upper surface of the main wing near the trailing edge (abbreviated as the upper surface); (2) the upper surface of the main wing close to the trailing edge (abbreviated as the upper trailing edge); and (3) the lower surface of the main wing close to the trailing edge (abbreviated as the lower trailing edge). The specific locations are shown in Figure 3.  
The numerical simulation for the plasma actuator based on the UDF programme approximates the pulse generated by the nanosecond discharge to the square wave signal, and the process of DBD discharge is simulated by adding a joule heat source in the discharge position. The influence of different parameters on the aerodynamic performance of the high lift device can be studied by changing the discharge frequency, pulse width, and number of heat sources in UDF. The value of joule heat applied to each grid cell requires a change of the heating file, which is read separately in the programme. In this paper, the three parameters of discharge frequency, pulse width, and energy density are selected to study the different effects of the NS-DBD plasma actuator applied to the flow control in the flap.  
Since the dominant effect of the NS-DBD actuator is known to be the thermal effect (namely, Joule heating) ([PERSON] et al., 2016; [PERSON] et al., 2016; [PERSON] et al., 2016), in the numerical simulation the effect of the discharge of the NS-DBD actuator is represented as instantaneous gas heating ([PERSON] et al., 2016). In this paper, the NS-DBD numerical simulation is based on phenomenological theory. During the NS-DBD discharge process, due to the short discharge time (on the order of ns), the body-force effect on the flow field is ignorable when compared to bulk-heating-induced effect. As a result, Joule heat is added as a source term to the energy equation by writing a UDF in Fluent. The two-dimensional unsteady, compressible Reynolds Average Navier-Stokes governing equations are as follows:  
Figure 3: Discharge positions of DBD (dielectric barrier discharge) plasma actuators.  
\[\frac{\partial\rho}{\partial t}+\
abla\cdot(\rho\mathbf{u})=0 \tag{1}\]  
\[\frac{\partial(\rho u)}{\partial t}+\
abla\cdot(\rho\mathbf{u}.\mathbf{u}+p\mathbf{I}-\mathbf{ \tau})=F \tag{2}\]  
\[\frac{\partial\Big{(}\rho C_{p}T\Big{)}}{\partial t}+\
abla\Big{(}\rho\mathbf{u}C_ {p}T-\
abla(k\
abla T)\Big{)}=Q \tag{3}\]  
where \(\tau=\mu[\
abla u+(\
abla u)^{\mathrm{T}}-\frac{2}{3}(\
abla.u)^{\mathrm{I}}]\).  
In the equations above, \(\rho\) is the density, \(\mathrm{p}\) is the pressure, \(\mathrm{T}\) is the temperature, \(\mathrm{Cp}\) is the specific heat capacity at constant pressure, \(\mathrm{I}\), \(\mu\), and \(\mathrm{k}\) are the tensor unit, viscosity coefficient, and thermal conductivity, respectively. \(\mathrm{Q}\) is the power density produced by the plasma discharge process. Body force \(\mathrm{F}\) is set to 0 due to its little effect on the flow field. The flow field is set as the ideal gas. The standard \(\mathrm{k}\)-\(\varepsilon\) model is adopted in all simulations.  
The intensity of the source representing the discharge of the NS-DBD actuator (\(\mathrm{Q}\)) is based on the result from the work by [PERSON] [33] regarding a 15 kV voltage pulse, so the value of discharge voltage is 15 kV. The governing equation is solved with the density-based solver of the ANSYS 17.1 (FLUENT 17.1) software. The gas is assumed to be a perfect gas, and the coefficient of viscosity is calculated according to Sutherland's law.