Turbulence and entrainment in an atmospheric pressure dielectric barrier plasma jet

Particle Image Velocimetry, Laser-Induced Fluorescence, and computational modeling are used to quantify the impact of plasma generation on air entrainment into a helium plasma jet. It is demonstrated that discharge generation yields a minor increase in the exit velocity of the gas. In contrast, the laminar to turbulent transition point is strongly affected, attributed to an increase in plasma-induced perturbations within the jet shear layer. The temporal decay of laser-induced fluorescence from OH is used as an indicator for humid air within the plasma. The results show that plasma-induced perturbations increase the quenching rate of the OH fluorescent state; indicating shear layer instabilities play a major role in determining the physicochemical characteristics of the plasma.

and a repetition rate of 10 Hz. A number of LIF excitation schemes have been proposed for the 106 measurement of OH radicals in atmospheric pressure plasmas. [25][26][27] In this work, the dye laser was The 282.58 nm beam emitted from the dye laser was measured to have a pulse energy in excess of 114 17 mJ, a value several orders of magnitude above the range linear LIF measurements are typically 115 made (1 -10 µJ). [29] Operation beyond the linear region greatly complicates the interpretation of the 116 results, as the ground rotational level is significantly depleted by light absorption and partially 117 refilled by fast rotational redistribution, altering the LIF outcome dependent on the unknown gas 118 composition and temperature. To attenuate the laser energy to a suitable range an optical 119 arrangement similar to that employed by Ries et al. was adopted, [21] two quartz plates were angled 120 to split the beam as shown in Figure 2, with a small fraction being reflected towards the plasma jet and the majority of the beam passing through to beam dumps mounted behind each plate. Following 122 attenuation, the beam was directed through an uncoated quartz plano-convex lens with a focal 123 length of 1 m, and a pinhole of 1 mm was positioned to act as a spatial filter, further attenuating the 124 beam. Using this approach, the maximum laser pulse energy was found to be approximately 15 µJ; 125 small changes to the Q-switch delay of the pump laser were subsequently used to vary the pulse 126 energy between 1 and 15 µJ. Laser power was measured using a Thorlabs PM100D optical power 127 and energy meter equipped with a thermal volume absorber power sensor.  highlights optical arrangement used to achieve a three-order reduction in laser intensity.

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Absolute calibration of the LIF signal to determine the density of ground-state OH can be achieved 147 via several methods, including UV absorption, chemical modeling, and Rayleigh scattering. [28,30] In 148 this investigation, the Rayleigh scattering approach was adopted due to its high degree of accuracy, 149 and a similar methodology to that described by Verreycken et al. was adopted. position by applying a time delay to the iCCD camera from 6 ns (i.e., immediately after the laser interrogation area on the jet centreline was determined and plotted as a function of delay time, an 160 exponential fit was applied to determine the decay rate at each spatial position.

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In addition to the gas composition, the gas temperature can also affect the interpretation of the LIF 162 data. To investigate the influence of plasma generation on gas temperature, an Omega FOB100 163 fiber-optic thermometer was used, the dielectric temperature probe was positioned in the plasma at 164 various points downstream of the jet orifice and the temperature recorded. The temperature was 165 found to vary little with spatial position, with a maximum of 10 K above ambient located close to 166 the capillary orifice, such observations are in-line with previous studies. [8] 167 The remainder of the calibration process closely followed that reported previously by Verreycken et 168 al. and will only be summarized in brief here. [28] To obtain Rayleigh scattering data for calibration, Where η is the calibration constant (#counts sr J −1 ), Nn is the density of scattering particles (m -3 ), 178 ∂ β=0 σ0 /∂Ω is the differential cross-section for Rayleigh scattering (m 2 sr −1 ), VRay is the volume from 179 which Rayleigh scattering is collected (m 3 ), IL is the laser irradiance (W m -2 ) and tL is the temporal 180 length of the laser pulse (s), which was measured by replacing the power meter shown in Figure 2 Table 1, the gas composition determined by the 208 flow model described in section 2.3, and an estimated ground state OH density. Solving the 4-level 209 model provides a prediction of the LIF signal intensity, which by comparison to the measured LIF 210 signal intensity is used to determine the actual ground-state OH density. Full details of the implementation can be found in the works of Verreycken and colleagues. [28]

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To account for the varying composition of gas downstream of the jet orifice, a computational model p is the gas mixture's pressure (Pa), is the gas mixture's viscosity (Pa s), I is the identity matrix, 232 is the density of air (kg m -3 ), and g is the gravitational constant (m s -2 ), i is the mass fraction of 233 the i th species, and i is the diffusive flux of the i th species, which is calculated according to 234 Maxwell-Stefan theory for diffusion as given by Equation (8 -10). [31,32] 235 Where ⃑ is the diffusion velocity of the i th species (m s -1 ), xi is the mole fraction of the i th species 239 (dimensionless), which is related to the mass fraction by Equation (8), and is the binary 240 diffusion coefficients between the i th and the j th species (m 2 s -1 ). A list of the binary diffusion 241 coefficients used in the model is given in Table 2. It should be noted that Equation (9)

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As stated in the introduction section, it is hypothesized that plasma-induced turbulence affects the 250 flow's velocity field and thus the gas composition. To account for such effects in the computational followed, where a turbulent viscosity (also known as eddy viscosity) was added to the viscosity 253 of the gas mixture. The eddy viscosity is a mathematical means to describe the loss of momentum 254 of the flow as a result of turbulence as an "effective" viscosity that is added to the physical viscosity 255 of the fluid. Similarly, a turbulent diffusivity is added to the binary diffusion coefficients. [32] The 256 computation of the eddy viscosity is typically done using one of the conventional RANS turbulence 257 models, such as the − model. Considering that such models were calibrated for flows without 258 plasma, their use for plasma modified flows will yield results with unknown accuracy. To overcome 259 this challenge, statistical analysis of the PIV data was conducted to obtain the necessary parameters 260 to calculate the eddy viscosity resulting from the plasma generation. Following the − modeling 261 approach, the turbulent kinetic energy k (m 2 s -2 ) and the turbulent kinetic energy dissipation rate 

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(m 2 s -3 ) are defined by Equation (11) and (12). [36] 263 = 1 2 ( ′ 2 + ′ 2 ) (11) 264 = 2 ′ • ′ (12) 265 Where ′ and ′ are the time fluctuating velocity field components with respect to the average 266 velocity field, which were calculated from PIV data by subtracting the time-averaged velocity field 267 from each of the 400 instantaneous velocity maps captured during a measurement, then averaging 268 the square of these fluctuations. In Equation (12), is the kinematic viscosity (m 2 s -1 ), and ′ is the 269 fluctuating deformation rate of the fluid (s -1 ), which was calculated from the PIV data as outlined by 270 Xu and colleagues. [37] After calculating k and  the eddy viscosity was calculated according to 271 Equation (13). [36] 272 = 2 (13) 273 Where C is a constant equal to 0.0016 and is the self-consistent gas mixture density calculated by 274 the model. The turbulent diffusivity is related to the eddy viscosity by Equation (14). [28] 275 = Where is the turbulent Schmidt number, obtaining an accurate value for this in a plasma- In absolute terms, the generation of plasma with an applied voltage of 14 kV was found to increase that turbulence initiates due to instabilities within the shear layers at the jet exit that become 325 amplified as they travel downstream. [13][14][15][16][17] As the instabilities grow, they cause velocity fluctuations,

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Reynolds shear stresses, and thus the production of turbulence. [8] Many previous studies have 327 explored 'excited' jets that employ alternative means to perturb the jet flow in order to investigate 328 the mechanisms of turbulence generation. [40][41][42][43][44][45] For example, the impact of sonic excitation on the 329 jet velocity profile shows a remarkable similarity to those observed in this study [41] ; hence it is 330 posited that plasma generation is an alternative means to excite an axisymmetric round jet, resulting 331 in the rapid onset of turbulence through increased shear layer instability with little change to 332 velocity.

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While the growth of small-scale instabilities within the jet shear layer has a significant impact on 335 the laminar to turbulent transition, they also provide a mechanism to enhance entrainment of 336 quiescent air into the laminar region of the plasma jet. [45] To investigate the influence of plasma 337 generation on instabilities in the jet shear layer, the eddy viscosity T was calculated. The eddy 338 viscosity profiles for the two plasma cases investigated in this work are shown in Figure 4 (a-b).

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Three characteristic zones can be observed within the profiles, the first is close to the jet orifice, 340 where a region of low T exists, which can be explained by the fact that this is the laminar region 341 where the amplitude of velocity fluctuations is small, leading to low turbulent kinetic energy k, and 342 consequently, a low T as Equation (13) shows. The second zone (e.g., 4 -10 x/D in Figure 4(b)) coincides with the transition region, as inferred from Figure 3(d), where the value of T peaks. This 344 is attributed to the large scale fluctuations/eddies starting to appear in the transition region, leading 345 to high turbulent kinetic energy k, considering that such large fluctuations live long enough to be 346 transported downstream, the dissipation rate of the turbulent energy  is relatively low in this 347 region, thus leading to a peak of T as follows from Equation (13). The third zone (e.g. > 10 x/D in 348 Figure 4(b)) coincides with the turbulent region, as inferred from Figure 3(d), which has a moderate 349 value of T. As known from the energy cascade theory of turbulence, [46] the large eddies generated 350 in the transition region break into smaller eddies in the fully turbulent region, the small eddies are 351 dissipated into heat due to the physical viscosity of the fluid. [46] In this sense, the turbulent kinetic 352 energy k is high, while the turbulent dissipation rate is also high, leading to a moderate value of T.

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From Figure 4(a-b), it is clear that the eddy viscosity for the 14 kV case has a larger magnitude 354 compared to the 10 kV case, which is consistent with the PIV results presented in Figure 3(b-c).

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When comparing the average value of T in zone one (x/D < 4) for both cases it is found that T for 356 the 10 kV case is approximately 70%-80% of that for the 14 kV case, indicating that the plasma's   experimentally and found to be in good agreement. Finally, the computational model was used to 459 convert the measured LIF intensity into an absolute OH density from which it was concluded that 460 OH production is strongly influenced by the interplay between the propagating plasma and the 461 background air. At high applied voltages, it was found that OH density increases close to the exit 462 but is rapidly reduced downstream as a result of the elevated air content quenching the discharge.