For a single-stage transonic compressor rig at the TU Darmstadt, three-dimensional viscous simulations are compared to L2F measurements and data from the EGV leading edge instrumentation to demonstrate the predictive capability of the Navier–Stokes code TRACE_S. In a second step the separated regions at the blade tip are investigated in detail to gain insight into the mechanisms of tip leakage vortex-shock interaction at operating points close to stall, peak efficiency, and choke. At the casing the simulations reveal a region with axially reversed flow, leading to a rotationally asymmetric displacement of the outermost stream surface and a localized additional pitch-averaged blockage of approximately 2 percent. Loss mechanisms and streamline patterns deduced from the simulation are also discussed. Although the flow is essentially three-dimensional, a simple model for local blockage from tip leakage is demonstrated to significantly improve two-dimensional simulations on S1-surfaces.
The objective of this paper is to establish, in a rigorous mathematical manner, a link between the dissipation of unsteadiness in a 2D compressible flow and the resulting mixing loss. A novel asymptotic approach and a control-volume argument are central to the analysis. It represents the first work clearly identifying the separate contributions to the mixing loss from simultaneous linear disturbances, i.e. from unsteady entropy, vorticity, and pressure waves. The results of the analysis have important implications for numerical simulations of turbomachinery flows; the mixing loss at the stator/rotor interface in steady simulations and numerical smoothing are discussed in depth. For a transonic turbine, the entropy rise through the stage is compared for a steady and an unsteady viscous simulation. The large interface mixing loss in the steady simulation is pointed out and its physical significance is discussed. The asymptotic approach is then applied to the first detailed analysis of interface mixing loss. Contributions from different wave types and wavelengths are quantified and discussed.
A 2D, linearized approach is used to investigate second-order effects of unsteadiness on the time-mean efficiency of turbomachinery. The objective is to quantify unsteady losses with a nonzero time-mean and to examine numerical simulations with respect to the modeling of unsteady flow fields and loss mechanisms. Results of simulations constitute the input to the analytical models employed. Two unsteady loss mechanisms, one of inviscid and the other of viscous nature, are considered. The unsteady circulation losses, i.e., the transfer of kinetic energy into the unsteady part of the flow field through vorticity shed at the trailing edge of a blade, was first considered by Keller (1935) and later by Kemp and Sears (1956). The vorticity is shed in response to an unsteady blade circulation and determined from Kelvin’s circulation theorem which is valid in compressible homentropic flow. Use of a numerical simulation to obtain circulation amplitudes avoids the limitations of thin-airfoil theory and yields results more realistic for modern turbomachinery. For the unsteady viscous loss mechanism, i.e., the dissipation in an unsteady boundary layer on the blade surface, Lighthill’s high-reduced-frequency limit (1955) is used to obtain the local velocity distribution in the laminar sublayer and the corresponding time-mean unsteady dissipation. The input to the model is the time-harmonics of the pressure gradient along a blade surface obtained from a simulation. A numerical study of the errors introduced by a departure from the high-reduced-frequency limit is presented. Losses from both sources are found to be small.
For a single-stage transonic compressor rig at the TU Darmstadt 3D viscous simulations are compared to L2F-measurements and data from the EGV leading edge instrumentation to demonstrate the predictive capability of the Navier-Stokes code TRACE_S. In a second step the separated regions at the blade tip are investigated in detail to gain insight into the mechanisms of tip leakage vortex-shock interaction at operating points close to stall, peak efficiency and choke. At the casing the simulations reveal a region with axially reversed flow, leading to a rotationally asymmetric displacement of the outermost stream surface and a localized additional pitch-average blockage of app. 2%. Loss mechanisms and streamline patterns deduced from the simulation are also discussed. Although the flow is essentially 3D, a simple model for local blockage from tip leakage is demonstrated to significantly improve 2D-simulations on S1-surfaces.
Three-dimensional multistage Navier–Stokes simulations for compressor components, rigs, and cascades have been analyzed to gain insight into the tip leakage blockage evolution. From pitch-averaged flow quantities the local displacement caused by tip leakage is determined by means of a novel technique. Close to the throat an additional displacement of about 1–4 percent axial chord is observed for unchoked flow conditions. With tip gap height, stagger, and inlet Mach number as governing variables, a correlation for the tip leakage blockage transition function in blade passages is established, which may be used to improve the predictive capability of S1/S2 compressor aerodesign systems. [S0889-504X(00)00903-X]
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