Description Of Turbulent Mixing Research Articles

Lagrangian Intermittent Modelling of a Turbulent Lifted Methane-Air Jet Flame Stabilized in a Vitiated Air Coflow

The present manuscript reports results of numerical simulations of turbulent lifted jet flames of methane with special emphasis placed on the autoignition effects. The impact of dilution with burned gases on the flame stabilization is analyzed under the conditions of a laboratory jet flame surrounded by a vitiated air coflow. In this geometry, mass flow rates, temperature levels and exact chemical composition of hot products mixed with air are fully determined. The effects of both finite rate chemistry and partially premixed combustion are taken into account within a Lagrangian intermittent framework. Detailed chemistry effects are incorporated through the use of chemical time scales, which are tabulated as functions of the mixture fraction. The concept of residence time (or particle age) and the transport equation for the mean scalar dissipation rate of the mixture fraction fluctuations, i.e., \(\widetilde{\varepsilon}_Z=\overline{\rho \mathcal{D} (\partial Z'' / \partial x_i) (\partial Z'' / \partial x_i) }/\overline{\rho}\), are also considered. This allows to improve the description of turbulent mixing including both the large scales engulfment processes through the consideration of the residence time scale, as well as the small scales molecular mixing processes the intensity of which is set by the integral scalar (mixing) time scale \(\tau_Z=\widetilde{Z''^2}/\widetilde{\varepsilon}_Z\). Numerical simulations of the turbulent diluted jet flame of methane studied by Cabra and his co-workers are performed. The flame liftoff height is reasonably well-captured and the computational results display a fairly satisfactory level of agreement with experimental data. They also confirm that the consideration of an additional transport equation for the mean scalar dissipation rate may significantly improve the computational results. The investigation is supplemented by a sensitivity analysis of the scalar to turbulence time scale ratio Cmix = τZ/τt often referred to as the mixing constant. Finally, the manuscript ends with the application of the proposed closure to experimental conditions which are characterized by variations of (i) the jet exit velocity, (ii) coflow velocity and (ii) coflow temperature.

Measurement and Simulation of Turbulent Mixing in a Jet in Crossflow

Computational fluid dynamics (CFD) has an important role in current research. While large eddy simulations (LES) are now common practice in academia, Reynolds-averaged Navier–Stokes (RANS) simulations are still very common in the industry. Using RANS allows faster simulations, however, the choice of the turbulence model has a bigger impact on the results. An important influence of the turbulence modeling is the description of turbulent mixing. Experience has shown that often inaccurate simulations of combustion processes originate from an inadequate description of the mixing field. A simple turbulent flow and mixing configuration of major theoretical and practical importance is the jet in crossflow (JIC). Due to its good fuel-air mixing capability over a small distance, JIC is favored by gas turbine manufacturers. As the design of the mixing process is the key to creating stable low NOx combustion systems, reliable predictive tools and detailed understanding of this basic system are still demanded. Therefore, the current study has re-investigated the JIC configuration under engine relevant conditions both experimentally and numerically using the most sophisticated tools available today. The combination of planar particle image velocimetry and laser induced fluorescence was used to measure the turbulent velocity and concentration fields as well as to determine the correlations of the Reynolds stress tensor ui′uj′¯ and the Reynolds flux vector ui′c′¯. Boundary conditions were determined using laser Doppler velocimetry. The comparisons between the measurements and simulation using RANS and LES showed that the mean velocity field was well described using the SST turbulence model. However, the Reynolds stresses and more so, the Reynolds fluxes deviate substantially from the measured data. The systematic variation of the turbulent Schmidt number reveals the limited influence of this parameter indicating that the basic modeling is amiss. The results of the LES simulation using the standard Smagorinsky model were found to provide much better agreement with the experiments also in the description of turbulent mixing.

Time scales of stratified turbulent flows and relations between second-order closure parameters and flow numbers

The description of turbulent mixing and chemical reactions by Lagrangian probability density function methods offers some significant advantages over other methods, mainly due to the simulation of mixing processes and the exact treatment of chemical transformations. A key problem of such methods is the information on the time scales of processes, because they determine the dynamics and intensity of mixing. This question is considered for stratified flow. Different models are presented for the development of these time scales in time and their stationary spatial patterns in dependence on shear and stratification. The model predictions are shown to be in agreement with large-eddy simulations of stratified homogeneous shear flow. Two further applications of these models are considered: the description of transitions between flow regimes (characterized by different scaling quantities) in the stationary atmospheric surface layer and, second, the simulation of buoyant plume rise. It is shown that the predictions of the stationary frequency model agree with measured data. The consideration of limit cases of this model leads to connections between second-order closure parameters and (critical) flow numbers that characterize these transitions. These relationships are shown to be very advantageous for the application of closure models. A new flow number that characterizes the transition to free convective flow under unstable stratification is introduced here in analogy to the critical gradient Richardson number, which characterizes the onset of turbulence in stably stratified flow. The second application provides a new theory for buoyant plume rise. Two parameters that describe the turbulent mixing in the entrainment and extrainment stages of plume rise are explained as ratios of the relevant time scales. The two-thirds power law of buoyant plume rise, which is observed for nonturbulent and neutrally stratified flow, is obtained without having to make ad hoc assumptions. For turbulent flow, the plume’s leveling-off is calculated in accord with measurements.