2D numerical modeling for plasma-assisted CO₂ pooling in supersonic nozzles: importance of a proper nozzle contour design

Abstract

Plasma assisted CO 2 dissociation has recently been the topic of many studies. The production of chemical fuels from environmentally unfriendly CO 2 through supersonic nozzles is one of the most prominent approaches under investigation. However, the experiments show that the theoretical conversion rates are far away from being achieved. In this study, two-dimensional fully coupled cases are investigated. This brings insights about how the CO 2 dissociation can be improved; mainly by a correct design of nozzles. The proper shape of a nozzle is a fundamental aspect to be taken into account numerically and in experiments to avoid undesirable phenomena such as the occurrence of shocks. The proper design of the nozzle shape leads to a shock-free flow being uniform at the nozzle outlet. A high degree of cooling can be achieved in a shock-free nozzle. Moreover it is shown that there is no optimal value for Mach number provided that the nozzles are sized properly. If the sizing is done correctly, it is found that higher Mach numbers lead to higher degree of non-equilibrium and thereby to higher dissociation rate. The sizing of the nozzle to maximize the departure from equilibrium in the nozzle is the final key of an efficient CO 2 dissociation. Finally, the results are compared with those of a semi-analytical method to conclude that if the nozzle is conceived in a proper way, simpler approaches can also give satisfactory results.

Boosting the dissociation of by employing shock‐free supersonic expansion

“…F I G U R E 1 Sketches of two different types of nozzle, in both cases, showing the separation of the subsonic and supersonic zone by a throat where the Mach number equals M* = 1; the left structure is based on a cosine form as used in studies Peerenboom et al [13] and Khaji et al [14] ; the right is a design based on a MOC design. [16] The dashed line at the bottom in 2D planar and axisymmetry nozzles refer to, respectively, a symmetry plane and a line of rotation Apart from the quantities, ρ p , , and u introduced above, we find the mass-related energy density E (in J/kg) and the power density ∕ ω ˙(W m ) H 3 associated with the change in chemical composition. The former can be expressed via:…”

“…The models presented in Peerenboom et al [13] and Khaji et al [14] are based on one-dimensional (1D) configurations. However, it was found in Khaji et al [16] that a 2D description of the flow in the cosine-like configuration used in Peerenboom et al and Khaji et al [13,14] reveals the presence of shock waves, a phenomenon that was also found in other CO 2 valorization studies. [5,17] That shocks must be avoided is evident if we realize that they generate heat, that this facilitates VT transitions and thus frustrates the push-up of the VDF-tail.…”

“…[15] And indeed, performing 2D simulations in properly designed nozzles leads to shock-free supersonic expansions. [16] The negative news is that 2D simulations are very time-consuming but positive is the message that if the MOC is performed and the resulting nozzle shape applied correctly, we get in the end the same results as what 1D simulations predict. This means that the search to the best conditions for CO 2 dissociation can be done using 1D models (software) but that the result of the MOC design must be applied in the workshop where the nozzle is physically constructed (hardware).…”

“…The left structure is based on a cosine form as used in studies Peerenboom et al [13] and Khaji et al [14] ; the right is a design based on a MOC design for the supersonic divergent part of the nozzle. [16] The subsonic convergent part is the same in both sketches. In contrast to the left configuration, the right sketch supports shock-free expansion.…”

“…The aim of the 1D and 2D model calculations in Peerenboom et al and Khaji et al [13,14,16] was to study the effect of supersonic expansion on the VDF change as created by the VV-VT competition under expansion created cooling conditions. The emphasis was put on finding the nozzle that gives the highest push-up of the VDF tail, as higher push-ups will lead to higher dissociation degrees.…”