Aerodynamics of axisymmetric counterflowing jets

Abstract

The laminar flow resulting from impingement of two steadily fed low-Mach-number gaseous jets issuing into a stagnant atmosphere from coaxial cylindrical ducts at moderately large Reynolds numbers, often used in combustion experiments, is studied through numerical integrations of the Navier-Stokes equations. In the Reynolds-number range addressed, 50-1000, the flow of the approaching jets is nearly inviscid, with viscous effects and mixing being restricted to the thin mixing layers surrounding the jets and to a thin layer located at the separating stream surface. The analysis of the main inviscid flow shows that only two parameters, based on the scales associated with the radius and the velocity profiles of the two feed streams, are needed to characterize the flow, namely, the ratio of the inter-jet separation distance to the duct radius and the ratio of momentum fluxes of the jets. The numerical results for uniform and Poiseuille velocity profiles provide, in particular, the value of the strain rate at the stagnation point for use in the analysis of experimental studies of counterflow premixed and diffusion flames.

Aerodynamics of planar counterflowing jets

“…As indicated in the insets of figure 1, one of the mixing layers is localized at the fluid surface separating the two jets, which departs from the central stagnation point, and the others at the fluid surfaces originating at the rims of the nozzles, separating the jets from the outer stagnant gas. For the moderately large values of the Reynolds number found in applications, the shear-driven instabilities affecting the mixing layers develop at a sufficiently slow rate for the central near-stagnation point region to remain virtually steady, as verified in recent direct numerical simulations (Carpio et al 2017).…”

“…2 can be determined, with small relative errors of order Re −1/2 1, from the analysis of the inviscid collision of two jets of different density, as done earlier in connection with axisymmetric counterflows (Carpio et al 2017). The corresponding analysis for the case of planar jets, of direct interest for slot-jet counterflow burners, is to be presented below.…”

“…The specific conditions addressed here, namely, low-Mach-number jets with moderately large Reynolds numbers and nozzle separation distances of the order of the nozzle transverse size, are of interest in laminar counterflow burners, schematically represented in figure 1, which are used in combustion experiments to characterize the response to strain of nonpremixed and premixed flames (Peters 2000). Both axisymmetric and planar configurations are of interest in applications, with the former geometry analyzed in recent studies (Scribano & Bisetti 2016;Carpio et al 2017) and the latter being investigated in the present paper by a combination of analytical and numerical methods.…”

Aerodynamics of Tsuji Burners with Augmented Fuel Injection

“…Consideration of the limit Re 1 will be seen to reduce the problem to that of inviscid flow, with the solution depending in general on two parameters, namely, the fuel-to-air density ratio ρ F /ρ A and the fuel-to-air velocity ratio U i /U c . Use of a densityweighted vorticity-streamfunction formulation [4,5] further reduces the problem to the constant-density case, with Λ = (ρ F /ρ A ) 1/2 U i /U c entering as the only governing parameter.…”

“…The free-boundary problem defined in (2.12)-(2.15) determines ψ(r, θ) along with the vorticity distribution ω w (θ) and the separating surface r s (θ) for given values of U i /U ∞ and ρ F /ρ A . As shown in [4,5], the solution can be simplified by incorporating a renormalization factor (ρ F /ρ A ) 1/2 in the definition of new kinematic variables…”