Joint statistics between velocity-gradient and fluctuating pressure in a turbulent planar jet

Abstract

Joint statistics between velocity gradient and fluctuating static pressure in a turbulent planar jet are experimentally investigated. The experimental data was acquired by simultaneous measurements of velocity gradient ( ∂u’2/∂x1 and ∂u’1/∂x2, where u’1, u’2, x1 and x2 are fluctuating stereamwise velocity, fluctuating cross-streamwise velocity, streamwise coordinate, and cross-streamwise coordinate, respectively) and fluctuating pressure p′ using two combined probes. One of the combined probe consists of an X-type hot-wire probe and a pressure probe and the other combined probe consists of two I-type hot-wire probes arranged in vertical direction and a pressure probe. In the time-series, it is shown that the events in which the instantaneous Reynolds stress, squared cross-stramwise velocity, and product of velocity gradient and pressure shows significantly large value (so-called “significant events”) occur intermittently with negative pressure fluctuation, this implies that the Reynolds stress transport phenomena are locally active with the large-scale vortex structures observed in a turbulent planar jet. It was also found that the standard deviation of (p’/ρ)(∂u’2/∂x1) conditioned by the negative pressure fluctuation is 21% larger than the unconditioned standard deviation. The cospectra show that the correlation (p’/ρ)(∂u’2/∂x1) greatly contributes the local isotropy of the flow field. On the other hand, we confirmed that ∂u’1/∂x2 is almost unrelated to the pressure fluctuation in the present turbulent planar jet. The results show that there is little contribution on the Reynolds stress transport by the correlation (p’/ρ)(∂u’1/∂x2).

Keywords

• turbulent jet
• hot-wire
• pressure measurement
• reynolds stress
• joint statistics