Spectral Analysis of the Flow in an Intermediate Turbine Duct

Abstract

The meaning of integral length scale is discussed in the context of inlet boundary conditions for an intermediate turbine duct located downstream a high-pressure turbine stage. Contrary to popular belief, the integral scale determined from spectral or correlation data is not the same as that commonly used in turbulence models, even when the periodic components are removed from consideration. In particular, the “pseudo-integral-scale”, Lε = q3/ε, defined from the turbulence intensity and dissipation, can differ by an order of magnitude or more from the true integral scale, no matter how the latter is determined. And even though the ratio may be asymptotically constant with increasing Reynolds number, it depends on the nature of the turbulence present. It is the pseudo-integral scale that is mostly wanted (at least by turbulence modelers), but it is the dissipation that complicates its determination experimentally. This paper outlines a procedure for obtaining the dissipation using the measured one-dimensional energy spectrum, and lays out criteria for when the procedure can be legitimately used. The theoretical arguments, based on the postulated existence of k−5/3 range, are illustrated with spectral measurements immediately downstream a single-stage turbine using the Chalmers large-scale turbine facility. The spectra are obtained from area traverses with a 2-component hot-wire.