Large-eddy simulation of a plane reacting jet transversely injected into supersonic turbulent channel flow

Abstract

A plane, chemically reacting jet of fuel injected through a narrow spanwise slot into supersonic and fully turbulent air flow in a channel with isothermal, parallel walls is investigated using a semi-implicit large-eddy simulation technique. It is based on a variant of the approximate deconvolution method (ADM) proposed by Mathew et al. (2003; An explicit filtering method for LES of compressible flows. Physics of Fluids, 15 (8), 2279–2289) and on explicit modelling of the filtered heat release term. The fuel jet consists of a mixture of H₂ and N₂, the mass fractions being Y_H2 = 0.016875 and Y_N2 = 0.983125, respectively. Chemical reaction of H₂ and O₂ to water is modelled as an infinitely fast, irreversible one-step reaction. The composition is described by a mixture fraction ξ evolving according to a transport equation for a passive scalar, which is solved along with the compressible Navier–Stokes equations. A ratio of slot width to channel height of h₂/h₁ = 1/32 characterises the geometric configuration. Spatial derivatives are computed using a tridiagonal finite-difference scheme of sixth order of accuracy given by Lele (1992; Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics, 103, 16–42), while an explicit five-step Runge–Kutta algorithm by Kennedy et al. (1999; Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Technical report 99–22, ICASE.) is used for time integration. Turbulent inflow conditions are generated by a separate LES of fully developed supersonic channel flow at a bulk Mach number of M = 3.1 and a friction Reynolds number of Re_τ ≈ 456 and introduced well upstream of the injection station using characteristic boundary conditions. The complex transport processes of mass, momentum and energy in the neighbourhood of the injection region are documented by snapshots of instantaneous flow variables and by profiles and contour plots of statistically averaged quantities.

Keywords:

• large-eddy simulation
• plane jet in crossflow
• supersonic turbulent channel flow
• infinitely fast chemistry
• high-order numerical schemes

Acknowledgements

The work presented in this article has been supported by Deutsche Forschungsgemeinschaft (DFG) within the framework of the research group GRK 1095/1 on aero-thermodynamic design of a scramjet-propulsion system for future space transportation. Numerical simulations have been carried out using the national supercomputer SGI Altix 4700 (HLRB II) at the Leibniz Computing Centre of the Bavarian Academy of Sciences.

Notes

1. We are aware of the fact that the diffusion coefficient of hydrogen differs remarkably from that of the other species and that the use of constant Schmidt numbers prevents us from predicting extinction and ignition processes. However, proper prediction of these processes would lead to complex chemical kinetics and diffusion mechanisms. It has been shown in Mahle et al. (2008) that the use of multicomponent diffusion and the inclusion of Soret and Dufour effects in LES predictions of temporal mixing layers at low subsonic Mach numbers leads to mean species mass fractions of water vapour and hydrogen and their variances which differ from those computed with simple Hirschfelder–Curtiss models for the diffusion coefficients by 10 percent or more. At the same time, temperature variances are nearly unaffected. This means that not all variables are sensitive to the diffusion model used. A detailed analysis of these effects is beyond the scope of this work.