Decomposition of the scalar field in a turbulent jet flow

In the present work, a detailed experimental analysis of geometries called dissipation elements and of the turbulent/non-turbulent interface of a scalar field is conducted. To this end, three-dimensional measurements of the mass fractionof propane discharging into coflowing CO2 from a turbulent round jet using a high-speed Rayleigh scattering technique have been performed. This procedure allows to acquire highly resolved twodimensional data at nozzle based Reynolds numbers Re0 between 3,000-18,440 and in combination with Taylor’s hypothesis three-dimensional data up to Re0 = 8,600, see chapter two for details. In chapter three, the distribution of extremal points in the scalar fields and its scalar dissipation rate are examined. It is shown that the mean linear distance lm between a maximum and a minimum is of the order of the Taylor microscale. Afterwards, the experimental results for the normalized marginal probability density function (pdf) ˜P(˜l) of the length of dissipation elements are compared to a theoretical model and a good agreement is found. Furthermore, the conditional mean already scales with Kolmogorov’s 1/3 for separation distances of O(lambda). In a next step, the statistics of the scalar increment conditioned on the instantaneous value of the scalar dissipation rate are examined. Extending the works of Kholmyansky & Tsinober (2009) and Wang & Peters (2006), we have conditioned on strong dissipative events based on the dissipation rate maximum points and their local size and observe similar results as the above authors. The exponential tails observed for the pdf of the scalar increment are thus concluded to be due to diffusivity and dissipation dominated parts of the field. In chapter four, dissipation elements in the instantaneous kinetic energy field of various DNS cases are studied. The universal validity of ˜P(˜l) is confirmed, as no dependence on the Reynolds number, the scalar field or the type of turbulent flow has been observed. Furthermore, we have examined the first-order velocity structure function along gradient trajectories. The latter is negative for small separation distances, followed by a linear increase with a zero-crossing at around lambda. Scaling the first-order velocity structure function with the asymptotic strain rate of dissipation elements and the Taylor microscale allows to collapse the curves for all DNS cases. In chapter five, the scalar turbulent/non-turbulent interface and its impact on the scalar pdf are examined. Based on the experimental data, in a first step the composite model of Effelsberg & Peters (1983) is used to construct the mixture fraction pdfs. A very good overall agreement of the composite pdfs with the experimental data at different radial and axial location as well as at varying Reynolds numbers and intermittency factors is obtained. Non-negligible contributions of the turbulent/non-turbulent interface are present together with a close to constant mean value of the pdf of the fully turbulent part. Based on these findings, it is concluded that the turbulent/non-turbulent interface and its contributions to the mixture fraction pdf are of major importance in the early part of the jet where the measurements are performed. In addition, we analyze the scaling of the thickness delta of the scalar turbulent/non-turbulent interface. In agreement with da Silva & Pereira (2008), delta ~ lambda is observed. This scaling also supports the modeling of the stoichiometric scalar dissipation rate as a Reynolds number independent quantity. Then, the local structure of the turbulent scalar field as well as the scalar pdf using scalar gradient trajectories are investigated. The latter are calculated for every grid point and scalar profiles along the latter are parameterized by the arithmetic mean Zm of minimum and maximum value of the extremal points that bound the gradient trajectory and the scalar difference DeltaZ between them. Using these parameters, the turbulent scalar field is partitioned into three regions – a fully turbulent one, the outer flow and in between a scalar turbulent/non-turbulent interface. In a next step, the joint pdf P(Zm,DeltaZ) as well as P(Zm) and P(DeltaZ) are investigated in the different zones. Small fluctuations together with a large mean scalar value are typical for the fully turbulent region, while the regularly observed large jump of the scalar value across the interface is caught by the gradient trajectory statistics in the scalar turbulent/non-turbulent interface. Finally, a method to reconstruct the overall scalar pdf P(Z) based on gradient trajectories using the joint pdf P(Zm,DeltaZ) in the different zones of the scalar field is presented. We observe a good agreement between the experimentally obtained pdf with the reconstructed one.