Mode-stirred reverberation chambers: A paradigm for spatio-temporal complexity in dynamic electromagnetic environments

We investigate probability distributions in dynamic multi-mode electromagnetic cavities, commonly referred to as mode-stirred reverberation chambers. We show that Bessel K$K$ and Bessel I$I$ distributions play a prominent role when a large but finite number of excited modes, loss of energy (through aperture leakage or dissipation), or nonstationary transient fields are involved. With the aim at reducing the number of simultaneously excited cavity modes as much as possible while maintaining a well-characterizable quasi-random field, measurement results indicate that single-mode stirring is feasible at certain frequencies well below the usual ‘lowest usable frequency’ of the cavity. Distributions for nonstationary fields are shown to allow for improved estimation of the maximum-to-mean ratio of the received power during stepwise rotation of the mode stirrer.     

A DNS evaluation of mixing and evaporation models for TPDF modelling of nonpremixed spray flames

In the present work, nonpremixed temporally evolving planar spray jet flames are simulated using both direct numerical simulation (DNS) and the composition transported probability density function (TPDF) method. The objective is to assess the performance of various mixing and evaporation source term distribution models which are required to close the PDF transport equation in spray flames. Quantities which would normally be provided to the TPDF solver by spray models and turbulence models are provided from the DNS: the mean flow velocity, turbulent diffusivity, mixing frequency, and cell-mean evaporation source term. Two cases with different Damköhler numbers (Da) are considered. The low Da case (Da-) features extinction followed by reignition while extinction in the high Da case (Da+) is insignificant. The TPDF modelling considers two mixing models: interaction by exchange with the mean (IEM) and Euclidean minimum spanning trees (EMST). Three models for distribution of the evaporation source terms are considered: EQUAL which distributes them in proportion to notional particles’ mass weight, NEW which creates new particles of pure fuel, and SAT which distributes the sources preferentially to notional particles close to saturation. It is found that the IEM model overpredicts the extinction when used with any evaporation model for both Da- and Da+ cases. The EMST model captures well the trend for extinction and reignition for the Da- case when it is coupled with the EQUAL evaporation model, but it overpredicts the extinction when coupled with the NEW or SAT evaporation model. For the Da+ case, all evaporation models reasonably capture the flame dynamics when coupled with EMST. The flame temperature in the mixture fraction space was examined to further assess the model performance. In general the EMST model results in narrow PDFs with little conditional fluctuation, while the IEM model produces bimodal PDFs with burning and partial extinction branches.     

Application of a multiple mapping conditioning mixing model to ECN Spray A

The engine combustion network (ECN) Spray A is modelled using the Reynolds-averaged Navier–Stokes-transported probability density function (RANS-TPDF) approach to validate the application of a new multiple mapping conditioning (MMC) mixing model to multiphase reactive flows. The composition TPDF equations are solved using a Lagrangian stochastic approach and the spray is modelled with a discrete particle approach. The model is first validated under non-reacting conditions (at 900 K) using experimental mixture-fraction data. Reactive simulations are then performed for three different ambient temperatures (800, 900, 1100 K) and oxygen concentrations (13, 15, 21%) at an ambient density of 22.8 kg/m³. The MMC mixing model is compared with the interaction by exchange with the mean (IEM) mixing model. The ignition delay predictions are not sensitive to the mixing model and are predicted well by both the mixing models under all the tested ambient conditions. The IEM model overpredicts the flame lift-off length (FLOL) at high temperature and high oxygen conditions with a mixing constant $C_{?}=2$. The MMC model with $C_{?}=2$ and a target correlation coefficient $r_t=0.935$ between the mixture fraction and a reference variable used to condition mixing predicts good FLOL under all the conditions except 800 K. It is demonstrated that the lift-off length is controllable by changing the target correlation coefficient, while C_? and therefore the mixing fields are held fixed. In comparison to the MMC model, the IEM model predicts a higher variance of temperature conditioned on mixture fraction near the flame base owing to its lacking the property of localness. The mixing distance between the notional TPDF particles in the composition space is also higher with the IEM model and it is demonstrated that by changing r_t, different levels of mixing locality can be achieved.