Application of the sparse-Lagrangian multiple mapping conditioning approach to a model supersonic combustor

Abstract

The Multiple Mapping Conditioning/Large Eddy Simulation (MMC-LES) model is extended for the first time to high-speed, compressible flow conditions and validated against non-reacting and reacting experimental data from a model supersonic combustor. The MMC-LES method solves the subgrid joint composition filtered density function through a Monte Carlo approach, and it permits a low-cost numerical implementation using a sparse distribution of stochastic Lagrangian particles. The sensitivity of results to the particle resolution is examined, and similar to past low-speed applications of MMC-LES, that sensitivity is found to be low. In comparison to the model equations for subsonic turbulent combustion conditions, the pressure work and viscous heating effects have been incorporated here to account for the effects of compressibility. As expected, the viscous heating effects are small for this flow case and can be ignored, while the pressure work is not negligible and makes a significant contribution at expansion fans and shock fronts where the magnitude of the pressure derivative term in non-reacting/reacting cases is as much as 23.8%/24.5% and 19.2%/18.6% of the stochastic particle standardized enthalpy, respectively. The MMC-LES predictions show good quantitative agreement with the available experimental data for the mean and root-mean-square of axial velocity, mean temperature, and wall pressure. Good qualitative comparison to the data is also observed for major flow characteristics, including location and size of shocks, expansion fans, and recirculation zone, and combustion characteristics such as flame lift-off distance. Although the effects of the pressure work on the mean flame lift-off distance are negligible, they have a significant influence on the predicted spatial fluctuations of the flame base.

Numerical simulation of two-dimensional detonation propagation in partially pre-vaporized n-heptane sprays

“…The second-order central differencing scheme is applied for the diffusion terms. It has been validated and successfully used for gaseous supersonic flows and detonative combustion problems [16][17][18][19]. For the liquid phase, they are solved using first-order implicit Euler method, which is sufficiently accurate with the time step used in this work (about 10 -9 s).…”

Large eddy simulation of a supersonic lifted hydrogen flame with sparse-Lagrangian multiple mapping conditioning approach

“…The equivalent set of Stochastic Differential Equations (SDEs) for the evolution of the joint FDF of species mass fractions and standardised enthalpy are solved on an ensemble of Lagrangian notional particles [21,29]. They read…”

“…Different from the previous MMC model for low-Mach flows [21,35], the pressure work, 𝑊 𝑃 𝑞 = ( , are incorporated in Eq. ( 11) and their roles in predicting supersonic flames are preliminarily discussed in our recent work [29].…”

“…The numerical implementation of the hybrid Eulerian/Lagrangian compressible MMC-LES model into the mmcFoam suite of solvers [35] was recently presented in [29]. The Eulerian scheme is based on the RYrhoCentralFoam solver [39][40][41] which has been validated previously for a range of benchmark problems, including Sod's shock tube, a forward-facing step, a supersonic jet and shockvortex interaction [39,40].…”

“…piloted methane / air jet diffusion flames [25], methane / air swirl flames [26], Sandia DME flame series [27] and turbulent spray flames [28]. In our recent work, sparse MMC-LES was extended to highly-compressible conditions for the first time [29] and demonstrated good accuracy against experimental data [30] for velocity, pressure and temperature data in a model supersonic combustor. The roles of pressure work and viscous heating in flame stabilization were preliminarily analyzed and it was found that the pressure work played a significant role in the unsteady behavior of the flame base whereas the viscous heating was negligibly small.…”