Experimental study of a turbulent stratified jet

Duo Xu, Purdue University

Abstract

Stratified flows with small density difference commonly exist in geophysical and engineering applications, which often involve interaction of turbulence and buoyancy effect. A combined particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF) system is developed to measure the velocity and density fields in a dense jet discharged horizontally into a tank filled with light fluid. The refractive indices of both liquids are matched. The flow structures and mixing dynamics are studied by examining the averaged parameters, turbulent kinetic energy budget, as well as modeling of momentum flux and buoyancy flux. At downstream of the jet, profiles of velocity and density display strong asymmetry with respect to its center. This is attributed to the fact that stable stratification reduces mixing and unstable stratification enhances mixing. Experimental data also indicate that at downstream locations mixing length model performs better in mixing zone of stable-stratification regions, whereas in other regions eddy viscosity/diffusivity models with static model coefficients represent effectively momentum and buoyancy flux terms. The measured turbulent Prandtl number displays strong spatial variations in the stratified jet. Quantifying the turbulent dissipation rate provides insights into the physics of the turbulent flows. However, the accuracy of estimating turbulent dissipation rate using velocity data measured by planar PIV is affected by the way of modeling the unresolved velocity gradient terms and the PIV spatial resolution. The synthetic PIV data are generated from a turbulence DNS dataset for validating the effectiveness of different methods. Direct estimate of turbulent dissipation rate from its definition using velocity gradients, with the assumption of isotropy, local axisymmetry, or local isotropy, shows significant decrease as interrogation window size increases. On the other hand, the indirect estimates of turbulent dissipation rate from energy spectra and structure function demonstrate less severe decrease as interrogation window size increases. We further propose two modified methods. The Modified Structure Function Method relies on an empirical relationship established by analyzing the synthetic PIV data. For a given measured value turbulent dissipation rate under a given interrogation window size, the true value can be determined from this relationship. The Modified Spectra Curvefit Method accounts the averaging effect introduced by the interrogation window in PIV processing algorithm and thus gives a better calculation of the energy spectra. When the new spectra data are used to curve fit the −5/3 slope, an improved estimate of turbulent dissipation rate is expected. Both modified methods are applied to experimental PIV data acquired from the turbulent jet experiment. They give nearly converged estimates of turbulent dissipation rate and Kolmogorov scale at different interrogation window sizes. The measured velocity and scalar data are used to test Refined Similarity Hypotheses and its extension to passive scalar without adopting Taylor's hypothesis. In the previous studies, Taylor's hypothesis is widely applied to hot/cold wire data acquired in wind tunnels, and it is believed to introduce the artificial effect to the test results. In our study, the test results show that the stochastic variable υ is independent of r and &epsis; r in the inertial subrange. Investigating P(υ: Rer) strongly supports the statement that P(υ) is independent on Rer when Rer > 100. We also observe Rer dependence of P(υ) when Rer ∼ 1. For RSH-P, P(υ&thetas;) depends on Rer when r << L and is universal when Rer >> 1. However, the independence of υ&thetas; on r, &epsis;r and χ r is not fully supported by the present experimental results. (Abstract shortened by UMI.)

Degree

Ph.D.

Advisors

Chen, Purdue University.

Subject Area

Mechanical engineering

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