Statistics of the scalar dissipation rate using direct numerical simulations and planar laser-induced fluorescence data

Abstract: The statistics of the scalar dissipation rate (SDR) in gaseous flows with Schmidt numbers close to unity were examined in a joint numerical and experimental effort, in a shearless mixing layer in the presence of decaying turbulence using three-dimensional Direct Numerical Simulations (DNS), and in an axisymmetric plume formed by the continuous low-momentum release of an acetone-laden stream (used as a tracer to measure the passive scalar) along the centreline of a turbulent pipe flow of air downstream of a turbulence generating grid using Planar Laser-Induced Fluorescence (PLIF). For the flows examined good agreement was found between the DNS and the experiment, both of which indicate that: (i) the probability density functions of the unconditional and conditional SDR show small departures from lognormality; (ii) the ratio of the standard deviation of the unconditional SDR to its respective Reynolds-averaged mean, as well as the ratio of the standard deviation of the conditional SDR to its conditional mean (these ratios do not vary strongly with the value of the mixture fraction at which it is evaluated), both increase over a few Kolmogorov time scales from zero (at the injector nozzle in the experiment and initially in the DNS) to some value downstream and at later times; (iii) the long-time values of the ratios of the standard deviation to the mean of the conditional and unconditional SDR increase with the turbulent Reynolds number; (iv) for the same turbulent Reynolds number, the DNS and the experiment showed that the ratio related to the unconditional SDR increases to a long-time value of approximately 2.3 (±20%), while the ratio related to the conditional SDR increases quickly to a value that stays within the range 1.0–1.4 (or, 1.2±0.2) and reaches a maximum value of 1.3–1.4 by the end of the DNS run and at the downstream edge of the experimental domain. The development of the conditional SDR fluctuations is discussed by comparing the early and late stages of mixing. The agreement between the PLIF measurements, which can only resolve two-dimensional fields, and the DNS, which provides access to the fully resolved three-dimensional field, suggests that the present conclusions are not limited by resolution or the lack of measurement in the third dimension. The results are useful for the development and validation of turbulent reacting flow models such as advanced flamelet, Conditional Moment Closure (CMC), and transported Probability Density Function (PDF) closures. [Copyright &y& Elsevier]