Identification of Coherent Flow Structures in Nonequilibrium Plasmas

Nonequilibrium atmospheric-pressure plasmas are at the core of a broad range of energy, medical, environmental, and manufacturing applications. The analysis of coherent flow structures is used in diverse areas of fluids engineering for the study of complex flows, and can lead to greater understanding of nonequilibrium plasma flows, particularly of the dynamics of their degree of thermodynamic nonequilibrium. Three different coherent structure identification criteria are used to analyze simulation results of the flow dynamics from an arc plasma torch obtained with a thermodynamic nonequilibrium model. The results reveal some of the possibilities and challenges of the studied criteria for the study of nonequilibrium discharges. Nonequilibrium (non-thermal) atmospheric-pressure plasmas sources are at the core of a wide range of medical, environmental, energy, and manufacturing applications. These sources are traditionally limited to processes with small aspect ratios (i.e. volume/area) of processing medium (e.g. microdischarges, thin slits, channels). The devising of sources for large aspect ratio processing would require deeper understanding of the interactions between energy transport by electrons and heavy-species, e.g. from kinetic equilibration due to collisions, to molecular dissipation and advective transport. The identification of coherent flow structures long-lived flow features such as vortices, vortex tubes and ribbons is used in diverse areas of fluids engineering for the understanding of complex flows, particularly unsteady and turbulent flows [1]. The analysis of coherent structures in thermal plasmas has been reported in [2] and elsewhere for fusion and space plasmas. The long-lived nature of coherent structures makes them enticing for the investigation of their role in the maintenance of thermodynamic nonequilibrium. Figure 1 shows the identification of coherent structures from simulations of the flow of argon from a plasma torch (Praxair’s SG-100) using a thermodynamic nonequilibrium model [3]. The two columns of Fig. 1 show different aspects of the flow at two different time instants spaced by 50 μs. The first row shows the distribution of heavy-species temperature Th, and the second row, the distribution of the nonequilibrium parameter θ = Te/Th, i.e. the ratio between electron and heavy-species temperatures. The largest values of θ are found in the regions where the plasma interacts with the cold surrounding gas. Rows three to five show coherent structures identified using three different criteria. These criteria are given by isosurfaces of vorticity modulus ||ω ||, helicity H, and of Q, the second invariant of ∇u ; these quantities are defined by: ω =∇×u , (1) H = u ⋅ω , and (2) Q = 2 ((Ω :Ω)− (S :S)) , (3) where u is the flow velocity, and Ω = 2 (∇u−∇u T ) the antisymmetric and S = 2 (∇u+∇u T ) the symmetric parts of the tensor ∇u (i.e., ∇u =Ω+S ). The quantities ||ω ||, H, and Q are normalized using ω0 = (uref/Lref), H0 = (uref 2 / Lref ) , and Q0 = (uref/Lref), respectively, where uref = 500 [m-s] (~ 1⁄2 the maximum velocity of the jet) and Lref = 5 [mm] (comparable to the 4 [mm] nozzle radius) are reference values of velocity and length, respectively. The ω-criterion inherently emphasizes the role of solid boundaries, where vorticity is highest. The H-criterion identifies regions with positive/negative rotating vortex chains, but excludes the effect of solid no-slip boundaries (i.e., u = 0). In regions where Q > 0, the strength of rotation overcomes strain, a necessary condition for the occurrence of vortex envelopes. Q-criterion structures provide a balanced view of the effect of the walls; e.g. the results show the persistence of vortex rings along the ends of the nozzle walls. The distribution of θ over the structures arguably suggests that no clear correlation exists between the degree of thermodynamic nonequilibrium and the evolution of the structures; nevertheless, this may be caused by the inherent limitations of the criteria used, originally devised for the analysis of incompressible flows.