The influence of probe resolution on the measurement of a passive scalar and its derivatives

The influence of probe resolution on the statistical measurement of a passive scalar is reported. A spectral method is employed to simulate degradation of the spatial resolution of a probe on the measured variances of a fluctuating scalar and its streamwise derivative by low-pass filtering a time-series of data at different cutoff frequencies. Direct measurements are also employed by varying probe sensor separation. The far field of a circular jet and the near wake of a circular cylinder are both investigated using air as the working fluid. The use of this low-Schmidt number working fluid and relatively low turbulence Reynolds numbers allows for good resolution of small scales of scalar fluctuations. By comparison, the same level of resolution is much more difficult to achieve when utilising a high-Schmidt number working fluid. A small temperature differential above ambient is used to mark the passive scalar, which is measured using a cold-wire anemometer. Taylor's hypothesis is employed to determine length scales. The present results are in good agreement with previous direct measurements using both optical techniques and cold-wire probes. It is found that the spatial resolution required for accurate measurement of the scalar dissipation rate is well described by the characteristic smallest scale of the scalar fluctuation, i.e. 'the Batchelor scale'. However, an order of magnitude less resolution is required for the scalar variance. The effect of degrading resolution on the variance measurements is more significant in the near wake than the far-field jet, suggesting that these requirements may be flow-dependent.