Addendum to 'velocity-information based force-term estimation of dielectric barrier discharge plasma actuators'

In a recent publication [1] we contrasted the variety of published strategies to estimate magnitude and distribution of the body force produced by dielectric barrier discharge plasma actuators on the basis of identical PIV data. Particularly, the determined force distributions of the above paper turned out to be beneficial for subsequent efforts to simulate discharge-based flow control and/or derive empirical plasma-actuator models. First efforts based on the data already demonstrate considerable success for either branch of application [2–7].

The purpose of this addendum, therefore, is to make the underlying data of the original publication [1] publicly available. Only the most important information is repeated here for brevity. All experimental details can be found in the original publication [1] together with discussions on assumptions and simplifications for the data (post-)processing. However, the finally implemented equations are repeated here for clarity, such that straight-forward processing of the velocity fields is possible from this addendum. Note that case labels and equation numbers were kept identical to the original publication [1] to avoid confusion.

Wilke [8] proposed the application of the Navier–Stokes equation (NSE), labeled as Case 5:

$$\begin{eqnarray}&&{{f}_{x}}(x,y)=\rho \left(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}\right)-\mu \left(\frac{{{\partial}^{2}}u}{\partial {{x}^{2}}}+\frac{{{\partial}^{2}}u}{\partial {{y}^{2}}}\right),\end{eqnarray} \tag{ 16a }$$

$$\begin{eqnarray}&&{{f}_{y}}(x,y)=\rho \left(u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}\right)-\mu \left(\frac{{{\partial}^{2}}v}{\partial {{x}^{2}}}+\frac{{{\partial}^{2}}v}{\partial {{y}^{2}}}\right).\end{eqnarray} \tag{ 16b }$$

Complementary, Albrecht et al [9] proposed the application of the vorticity equation (VE), i.e. the curl of NSE, which is labeled Case 6:

$$\begin{eqnarray}&&{{f}_{x}}(x,y)=-\rho {\int}_{\infty}^{0}\left[u\frac{\partial \omega}{\partial x}+v\frac{\partial \omega}{\partial y}-\frac{\mu}{\rho}\left(\frac{{{\partial}^{2}}\omega}{\partial {{x}^{2}}}+\frac{{{\partial}^{2}}\omega}{\partial {{y}^{2}}}\right)\right]\text{d}y.\end{eqnarray} \tag{ 22 }$$

The force distributions as determined by means of the NSE (16a) and (16b) and VE (22) appear as fxNSE, fyNSE and fxVE in the supplemental material stacks.iop.org/JPhysD/48/329401/mmedia, respectively. Furthermore, the coordinates (x, y) and velocities (u, v) are contained in the files. Further relevant quantities are listed in table 1, which contains the plotted values of the original paper. Finally, these quantities are provided alongside with useful information on chosen parameters and settings during experimentation in the headers of each file.

Table 1. Electrical and fluid-mechanical quantities; constant values: $f=11.0$ kHz, ${{C}_{0}}\approx 83.3$ pF m$^{-1}$.

File name:		08 kV	09 kV	10 kV	11 kV	12 kV
V [kV]		7.76	8.82	9.83	10.81	11.81
${{P}_{\text{A}}}/L$ [W m$^{-1}$]		19.22	30.35	45.71	67.97	93.35
${{C}_{\text{eff}}}/L$ [pF m$^{-1}$]		213.3	260.0	306.7	346.6	373.4
${{u}_{\text{max}}}$ [m s$^{-1}$]		1.74	3.04	4.04	5.43	5.81
$F/L$ [mN m$^{-1}$]	Case 5	1.93	6.75	12.06	22.07	25.45
	Case 6	2.11	6.76	12.87	22.75	27.76