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Blade Pressure Distribution
The blade pressure distribution, given as isentropic Mach number (Fig. 4) in the NGV at 50% span compares the results of the steady and unsteady results of both the source term approach and the fully discretized cooling holes as well as experiments.
Quite interestingly, although the unsteady results are fhctuating within a hardly visible range, the time average deviates significantly from the steady calculation performed by using a mixing plane approach. The differences occur mainly in three areas.
First, all the pressure peaks around the emerging cooling jets are by far more dominant in the unsteady calculation than in the steady results. Here, any in – flience from the downstream rotor can be excluded since the location of the cooling holes is upstream of the sonic throat. The pressure peaks are particularly significant in case of the fully meshed cooling holes, and less obvious in the source term results. These pressure over – and undershoots originate in a quasi stagnation of the main ft>w immediately in front of the cooling jet. After a severe deceleration, the main flow is forced around the cooling jet resulting in a strong acceleration. In such a case the cooling jet behaves very much like a solid obstacle in the flow, characteristic for cylindrical cooling holes (Hildebrandt, Ganzert, Fottner (2000)). Strong interactions between the emerging cooling jets and the main flow occur. These interactions lead to a complicated system of vortices (Vogel (1997)), which are prone to self-excited unsteadiness.
The second region of interest is around the exits of the second row of cooling holes located at the pressure side at around (x/lax = 0.5). The cooling holes on the pressure side are arranged in two double rows. In the steady calculation, a strong peak occurs, which corresponds to the first set of holes of the second rows, while the effects from the second part of the double row is barely visible. In contrast, the time accurate solution produces the dominant velocity peak
Normalized Axial Distance
Figure 5. Blade Pressure Distribution Rotor 50% Span
around the position of the second set of cooling holes in the double row. The unsteadily computed jets of the first row are apparently by far stronger than their counterparts from the steady solution. The strong peak visible for the first cooling hole row on the suction side gives also evidence to this. Consequently, the stronger unsteady jet of the first line of holes forces the main fbw away from the blade surface, which results in a much less severe interaction between the main ft>w and the jets emerging from the second line of holes. Again this effect is by far less pronounced, but still detectable in case of the source term approach. Here, the cooling jets are always weaker than in case of the fully discretized holes. The steady source term calculation hardly shows any sign of the cooling jets in the isentropic Mach number distribution.
Third, the second row of cooling holes on the suction side have the most visible effect on the main ft>w, recognizable by a strong pressure under – and overshoot. The location (x/lax = 0.7) is close to the peak Mach-Number of the main flow. Hence, the jets are emerging into a region of low pressure, resulting in a high local blowing rate. The succeeding shock (x/lax = 0.75) is less pronounced in the unsteady time-averaged calculation. The unsteady shock fluctuations are smeared out by the time-averaging. Since there are hardly any differences between source term approach and the discretized cooling holes, it is obvious that this phenomena is not connected to any film cooling effects.
The blade pressure on the rotor surface is given for all the unsteady time steps, the unsteady time average and the steady computation (Fig. 5). Naturally, the time dependent flictuations inside the rotor are by far more dominant, forced by the impinging wakes from the upstream NGV. The differences between the time averaged and the steady results is largest at the rotor leading edge. It is this region, which suffers most from the numerical simplifications necessary for a mixing plane approach. The range of the time dependent flic – tuations is large throughout nearly the complete blade. However, approaching the trailing edge, the fluctuations are damped out, showing hardly any influence on the rotor exit Mach number.
