Second-Order Effects of Unsteadiness on the Performance of Turbomachines

Abstract

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.

Effect of Upstream Rotor Vortical Disturbances on the Time-Average Performance of Axial Compressor Stators: Part 2 — Rotor Tip Vortex/Streamwise Vortex-Stator Blade Interactions

“…This is in agreement with the result of Denton (1993). While unsteady vortex shedding might not be important in a 2D flow (Fritsch 1992), this is not the case for the present 3D flow. In the ID/SW flow situation, shedding of streamwise vorticity from the TE of the blades is a noticeable source of loss.…”

“…Therefore, the kinetic energy in the shed streamwise vortices is about one-fourth to one-third that of the incoming SW vortices. Thus, the contribution of 3D trailing vortices to loss is substantially larger than that of 2D shed vortices investigated by Fritsch (1992).…”

“…The resulting redistribution of vorticity leads to an increase in passage loss. For tip vortex interaction, the loss increase occurs in the tip region of the stator (Howard, et al, 1994). • Both mechanisms are associated with the relative total pressure /velocity defect of the disturbances in the relative frame.…”

An Asymptotic Analysis of Mixing Loss

“…Due to restrictive conditions on the rectification of energy associated with the part of the flow field unsteady in the relative frame [Fri92], it is important to know the mixing loss resulting from the dissipation of this energy. This approach, i.e.…”

Direct Numerical Simulations of Compressible Vortex Flow Problems

“…In case of high Re-number flows, the disparity of the scales becomes overwhelming and instead of Direct Numerical Simulations (DNS) less drastically expensive Large Eddy Simulations (LES) are used in which large flow scales are explicitly resolved on the grid and the small scales are modelled. For engineering applications, examples of unsteady vortical flows include the interaction of wakes and shocks with the boundary layer in a transonic turbine and vorticity dissipation shed due to the temporal variations in blade circulation that can have a profound loss influence and affect the overall performance of a turbomachine (e.g., Fritsch and Giles, 1992;Michelassi et al, 2003). Another example is dynamics and acoustics of high-speed jet flows that is affected by the jet inflow conditions such as the state of the boundary layer at the nozzle exit (e.g., Bogey and Bailly, 2010).…”