On the high contraction ratio anomaly of axisymmetric contraction of grid-generated turbulence

Abstract

The present paper deals with the anomalous increase in second-order moments of longitudinal velocity fluctuations reported in experiments carried out to measure properties of axisymmetric strained turbulence when the strain is provided by axisymmetric contractions (nozzles). Experimental evidence is provided that the increase is due to inaccuracies in the measurements. It is shown that the imperfect spatial resolution of X-wire probes, the mass flow rate fluctuations in the flow facility, and the electronic noise contaminate the hot-wire measurements of not only the longitudinal but also the transverse velocity fluctuation components. These kinds of contaminations start to dominate the measurements, especially when the contraction ratio of the nozzle is high and/or the turbulence level is low and turbulence length scales are small. A series of measurement and correction methods is proposed employing two single normal wires and one inclined wire to detect and eliminate all three types of contaminations of longitudinal and transverse velocity fluctuation measurements. These methods are subsequently employed to carry out turbulence measurements of grid turbulence strained in a converging nozzle with a high contraction ratio. The resulting Reynolds stress developments along the nozzle do not involve an erroneous increase in longitudinal turbulent velocity fluctuations and are consistent with theoretical expectations such as the direct numerical simulations and the rapid distortion theory. The corrected results revealed that turbulence along the nozzle reaches the two-component axisymmetric state when looked at through the anisotropy of Reynolds stresses. Furthermore, the anisotropy of Reynolds stresses exhibits zero gradient at that state. For the first time in the literature, experimental confirmation of rapid distortion theory is supplied for the axisymmetric contraction of turbulence within nozzles having a contraction ratio higher than 9. Finally, a set of experimental data is provided for the validation of turbulence models.