Trailing edge loss is one of the main sources of loss for transonic turbine blades, contributing typically 1/3 of their total loss. Transonic trailing edge flow is extremely complex, the basic flow pattern is understood but methods of predicting the loss are currently based on empirical correlations for the base pressure. These correlations are of limited accuracy. Recent findings that the base pressure and loss can be reasonably well predicted by inviscid Euler calculations are justified and explained in this paper. For unstaggered choked blading, it is shown that there is a unique relationship between the back pressure and the base pressure and any calculation that conserves mass, energy and momentum should predict this relationship and the associated loss exactly. For realistic staggered blading, which operates choked but with subsonic axial velocity, there is also a unique relationship between the back pressure and the base pressure (and hence loss) but the relationship cannot be quantified without knowing a further relationship between the base pressure and the average suction surface pressure downstream of the throat. Any calculation that conserves mass, energy and momentum and also predicts this average suction surface pressure correctly will again predict the base pressure and loss. Two-dimensional Euler solutions do not predict the suction surface pressure exactly because of shock smearing but nevertheless seem to give reasonably accurate results. The effects of boundary layer thickness and trailing edge coolant ejection are considered briefly. Coolant ejection acts to reduce the mainstream loss. It is shown that suction surface curvature downstream of the throat may be highly beneficial in reducing the loss of blades with thick trailing edges operating at high subsonic or low supersonic outlet Mach numbers.

Trailing edge loss is one of the main sources of loss for transonic turbine blades, contributing typically 1/3 of their total loss. Transonic trailing edge flow is extremely complex, the basic flow pattern is understood but methods of predicting the loss are currently based on empirical correlations for the base pressure. These correlations are of limited accuracy. Recent findings that the base pressure and loss can be reasonably well predicted by inviscid Euler calculations are justified and explained in this paper. For unstaggered choked blading it is shown that there is is a unique relationship between the back pressure and the base pressure and any calculation that conserves mass, energy and momentum should predict this relationship and the associated loss exactly. For realistic staggered blading which operates choked but with subsonic axial velocity there is also a unique relationship between the back pressure and the base pressure (and hence loss) but the relationship cannot be quantified without knowing a further relationship between the base pressure and the average suction surface pressure downstream of the throat. Any calculation that conserves mass, energy and momentum and also predicts this average suction surface pressure correctly will again predict the base pressure and loss. Two dimensional Euler solutions do not predict the suction surface pressure exactly because of shock smearing but nevertheless seem to give reasonably accurate results.

In the present study, numerical simulation of the flow field of the tubercled NACA0021 (National Advisory Committee for Aeronautics) wing has been conducted with the large eddy simulation model. Then, proper orthogonal decomposition (POD) analysis has been carried out at trough and peak sections. According to the spatial distributions and temporal coefficients in the case of αA=5°, the physical backgrounds of corresponding POD modes could be identified, including flow attachment, separation, and the dynamic stall vortex (DSV). The onsets of local dynamic stall could be indicated with the extremum values of the DSV mode coefficients, which stay almost synchronized at trough and peak. Actually, the DSV is originally generated at trough and then moves to peak due to the spanwise convection induced by streamwise vorticity. The generation of the secondary vortex at trough is triggered with the streamwise pressure gradient, the development of which pinches off the feeding vorticity of the DSV and results in the detachment of the DSV. Eventually, the influence of pitching amplitude has also been discussed. The strength of the DSV at peak is increased with a larger pitching amplitude, which could be interpreted with the feeding sheet connected with the leading edge.

In consideration of the turbulent inflow condition of engineering applications, the flow mechanisms of dynamic stall of a tubercled airfoil have been comprehensively analyzed with an upstream cylinder. Numerical simulation of the flowfield of a tubercled wing with NACA0021 (National Advisory Committee for Aeronautics) airfoil has been conducted with the large eddy simulation (LES) model. Then, flow mechanisms have been analyzed based on the aerodynamic performances and flow structure descriptions. Meanwhile, proper orthogonal decomposition (POD) analysis has been carried out at both trough and peak sections to reveal the flow dynamics. It turns out that the dynamic stall process vanishes and performances would be obviously impacted by the incoming cylinder wake in the case of alphaA=5deg due to the enforced resistance of adverse pressure gradient. Furthermore, the first leading POD mode corresponds to the pitching movement at both trough and peak sections, while the high-order modes represent the influence of cylinder wake. Eventually, the influence of pitching amplitude has also been discussed in the case of alphaA=15deg. Different from the case of alphaA=5deg, dynamic stall phenomenon emerges, and the influence of wake impingement could be barely detected from the mode information except for the third mode at the trough section. The detachment of the dynamic stall vortex (DSV) takes place corresponding to the dynamic stall onset, which is driven by the streamwise pressure gradient near the trough leading-edge.

A simple numerical method for predicting the profile loss of turbine blades in subsonic and transonic flows is presented. A time marching Euler solver is used to obtain the main flow through the blade passages, the loss due to the surface friction is calculated using an integral boundary layer method, the total mixed out loss is evaluated from the mass flow and momentum balances between the trailing edge plane and an imaginary downstream plane where the flow is uniform. The base pressure acting on the trailing edge of the blade is calculated directly from the inviscid calculation without empirical correlations. The spurious numerical loss in the Euler calculation is separated from the real loss. The rationality of the approach is justified by the agreement of the prediction with a wide range of experimental measurements.