Average Passage Flow Field and Deterministic Stresses in the Tip and Hub Regions of a Multistage Turbomachine

Abstract

This paper continues our effort to study the dynamics of deterministic stresses in a multistage turbomachine using experimental data. Here we focus on the tip and hub regions and compare them to midspan data obtained in previous studies. The analysis is based on data obtained in particle image velocimetry (PIV) measurements performed in the second stage of a two-stage turbomachine. A complete data set is obtained using blades and fluid with matched optical index of refraction. Previous measurements at midspan have shown that at midspan and close to design conditions, the deterministic kinetic energy is smaller than the turbulent kinetic energy. The primary contributor to the deterministic stresses at midspan is the interaction of a blade with the upstream wakes. Conversely, we find that the tip vortex is the dominant source of phase-dependent unsteadiness and deterministic stresses in the tip region. Along the trajectory of the tip vortex, the deterministic kinetic energy levels are more than one order of magnitude higher than the levels measured in the hub and midspan, and are of the same order of magnitude as the turbulent kinetic energy levels. Reasons for this trend are explained using a sample distribution of phase-averaged flow variables. Outside of the region affected by tip-vortex transport, within the rotor-stator gap and within the stator passages, the turbulent kinetic energy is still 3–4 times higher than the deterministic kinetic energy. The deterministic and turbulent shear stress levels are comparable in all spanwise locations, except for the wakes of the stator blades, where the turbulent stresses are higher. However, along the direction of tip-vortex transport, the deterministic shear stresses are about an order of magnitude higher than the turbulent shear stresses. The decay rates of deterministic kinetic energy in the hub and midspan regions are comparable to each other, whereas at the tip the decay rate is higher. The decay rates of turbulent kinetic energy are much smaller than those of the deterministic kinetic energy. The paper also examines terms in the deterministic kinetic energy transport equation. The data indicate that “deterministic production” and a new term, here called “dissipation due to turbulence,” are the dominant source/sink terms. Regions with alternating signs of deterministic production indicate that the energy transfer between the phase-averaged and average-passage flow fields can occur in both directions. The divergence of the pressure-velocity correlation, obtained from a balance of all the other terms, is dominant and appears to be much larger than the deterministic production (source/sink) term. This trend indicates that there are substantial deterministic pressure fluctuations in the flow field, especially within the rotor-stator gap and within the stator passage.