Data regarding the computational fluid dynamics simulations of an airfoil with plasma actuator in unsteady flow

The data regard the analysis reported in the research article “Influence of actuation parameters of multi-DBD plasma actuators on the static and dynamic behavior of an airfoil in unsteady flow” [1]. The data are related to the study focused on the evaluation of the effects of an active flow control system on the performance of an airfoil in an unsteady flow, with particular focus on the influence of actuation parameters on the global performances.

The evaluated parameters for the C L involve the phase shift, the mean value and the standard deviation in a cycle of fluctuations. About the C M , instead, calculation have included to the parameters already calculated for the C L , also the imaginary part of the first coefficient of Fourier series, the hysteresis area, the static and the dynamic pitching coefficients.
For all the reduced frequencies end the actuation law phases, the following data are provided: Specifications The influence of the actuation law has been analyzed through changing the force phase q that regulates turning ON and turning OFF timing of the actuators. "Influence of actuation parameters of multi-DBD plasma actuators on the static and dynamic behavior of an airfoil in unsteady flow" [1].

Value of the Data
Simulations allow to evaluate the effect of the application of an active flow control technique based on Dielectric Barrier Discharge Plasma Actuator to control loads on an airfoil in an unsteady flow; data can be used to evaluate the best actuation switching frequency for different unsteadiness reduced frequencies; the numerical data about the temporal evolution of lift and moment coefficients could be used to verify modeling predictions of unsteady flow over an airfoil; the role of actuation switching law for flow control in pitching airfoil has been highlighted; the data can be used for comparing with the results of the application of other active flow control techniques for load alleviation of an airfoil under unsteady flow; the data can serve as a benchmark for future research on active flow control on unsteady flow over an airfoil.
4. Performance comparison between the different actuation conditions analyzed in synthetic tables (section "summary tables").

Experimental design, materials, and methods
An unsteady flow around a NACA23012 airfoil has been analyzed. The flow is directed with an average relative angle with respect to the airfoil of 7.7 deg, and a velocity magnitude of 31.16 m/s. The horizontal and vertical components of the flow free-stream velocity, change during time with a sinusoidal law, bringing to an unsteadiness in the real angle of attack.
The fluid flow is considered as incompressible, due to the Mach <0.3 and the absence of heating source or regions with strongly different pressure. Temperature has been assumed constant in all the domain, with a value of 288.15K. Pressure is set at 1 atm, so the density has been taken equal to 1.1835 kg/m 3 . The airfoil chord is 0.30 m and the Reynolds number is 600 0 000.
Simulation have been carried out by using the software Ansys Fluent Release 19.2. Turbulence has been modelled by using the Spalart-Allmaras RANS, while the pressure-velocity coupling equations have been solved through a Semi-Implicit Method for Pressure Linked Equations (SIMPLE) scheme. Time step have been fixed as 1/200 of the pitching period of the highest reduced frequency simulated, which corresponds to a time step of 3.14 Â 10 À4 s.
Computational domain consists of a 99,604 quadrangular elements C-Mesh, which reproduces a single NACA23012 airfoil in a free-stream flow. External domain boundaries are located more than 30 chords away from the airfoil.
Load response, evaluated in terms of lift and moment coefficients have been analyzed. Moment coefficient is considered positive when induces a nose-down torsion on the airfoil.
Based on the lift and moment coefficient temporal evolution, the phase lag between loads and instantaneous angle of attack, the mean value and the signal standard deviation have been calculated. Moreover, the moment coefficient imaginary part of the first Fourier series coefficient and hysteresis area have been computed for analysis. At the end, airfoil stability is evaluated through the static and dynamic pitch stability coefficients.
The phase lag, reported in degrees, represents the difference between the pulses at which correspond respectively the maximum peak of the instantaneous angle of attack and the maximum peak of the lift or moment signal.
The signal standard deviation is calculated for both the lift and the moment coefficients with the formula: Signals are approximated through a Fourier series with complex-valued coefficients, obtaining a filtered sinusoidal signal of the load coefficients. The imaginary part of the first coefficient of Fourier series Imða 1;CM Þ can suggest if the blade is aerolastically stable or unstable. In particular Imða 1;CM Þ <0 represents a stable behavior. 8 > > > > < > > > > : The hysteresis area represents the energy exchanged between flow and airfoil. A positive value for hysteresis area means that the profile works on the flow, having a damping effect on profile oscillation and movements. Aerodynamic performance parameters for an external flow with a pulse of 60 rad/s for clean case (baseline case without actuation) and the cases with actuation and different force phase values. Bold characters indicate a parameter of actuated case better than the clean case. For stability coefficients, a green is used when the coefficient suggests a stable behavior, while orange is used for unstable behavior. Table 1 Aerodynamic performance parameters for an external flow with a pulse of 20 rad/s for clean case (baseline case without actuation) and the cases with actuation and different force phase values. Bold characters indicate a parameter of actuated case better than the clean case. For stability coefficients, a green is used when the coefficient suggests a stable behavior, while orange is used for unstable behavior.
The static pitch stability coefficient is defined as the slope of the line that connects the two extremes angle of attack in a C M -a plot. The relevance of this coefficient is that shows the tendency of airfoil to move back to equilibrium position after small disturbances.
The dynamic pitch stability coefficient, instead, evaluates the damping behavior of the airfoil. It is obtained as half of the difference of the C M signal during the pitch up and pitch down phases, divided by the reduced frequency multiplied for the pitching amplitude. Dynamic Pitch Stability coeff: ¼ C M; pitch up À C M; pitch down 2,k q (5)

Summary tables
The value of the analyzed parameters for all the reduced frequencies and force phases tested (27 cases) are summarized by the following tables (see Tables 1e3).  Table 3 Aerodynamic performance parameters for an external flow with a pulse of 100 rad/s for clean case (baseline case without actuation) and the cases with actuation and different force phase values. Bold characters indicate a parameter of actuated case better than the clean case. For stability coefficients, a green is used when the coefficient suggests a stable behavior, while orange is used for unstable behavior.