Three dimensional flow structures

Figures 108 to 110 below show the vortex structure in the flow at varying incidence, with and without contouring. The different tubes, ribbons and lines are identified by colour as follows:

 Red stream tubes – pressure side horseshoe vortex

 Blue stream tubes – suction side horseshoe vortex

 Grey ribbons – endwall crossflow and passage vortex

 Yellow ribbons – tip endwall horseshoe vortices

 Orange ribbons – tip clearance vortex

 Purple stream lines – blade suction surface flow.

(b)

Angular Displacement from Suction Surface/wake (°)

(b)

Angular Displacement from Suction Surface/wake (°)

Annular 2300 RPM 2820 RPM

Contoured 2300 RPM 2820 RPM

(b)

Angular Displacement from Suction Surface/wake (°)

1907 RPM 2300 RPM 2820 RPM

1907 RPM 2300 RPM 2820 RPM

(b)

Angular Displacement from Suction Surface/wake (°)

Annular 2300 RPM 2820 RPM

Contoured 2300 RPM 2820 RPM

(b)

Angular Displacement from Suction Surface/wake (°)

1907 RPM 2300 RPM 2820 RPM

1907 RPM 2300 RPM 2820 RPM

The starting positions for streamlines were chosen to highlight the vortex structures, but is entirely consistent between cases with the exception of the following:

 The tangential start and end locations for the different legs of the horseshoe vortex which was altered both for the different speed cases and for the change in endwall

 The chordwise location of the initiation points of tip clearance vortices which were varied between the speed cases only to capture the breakpoint between the tip endwall horseshoe vortex the pressure leg of which is pulled through the tip gap, and the pure tip gap leakage flow downstream.

The combination of suction and pressure legs of the horseshoe vortex are quite different between endwalls, with the annular cases generally reflecting close wrapping of the two systems, while the contouring appears to hold the suction leg closer to the endwall and only entraining into the pressure leg as it leaves the passage. Roughly one rotation of the suction leg of the horseshoe vortex occurs through the length of the passage in the profiled case at design while the equivalent annular case exhibits 1½ to 2 turns. This results in a widely spread vortex system at the exit to the row in the profiled case; compared to an intense and localised one for the annular case.

The grey cross passage flow streamlines changes angle with increasing load, becoming more tangential. This occurs in both annular and profiled cases, however the profiled cases exhibit more axial flow in the front of the passage for all cases which is entirely consistent with the endwall pressure contour results. The cross passage flow then interacts quite differently with the combined horseshoe vortices between the different endwall cases in a way which becomes more noticeable with increasing incidence. In the annular case the cross passage flow is immediately wrapped up in the horseshoe vortices. While in the profiled case the flow crosses the passage and is swept up the suction surface before wrapping around the pressure leg of the horseshoe vortex.

In all cases the blade surface flows, are also entrained into the vortex system in the latter half of the passage and as they are loosely wrapped form pools of highly turned flow as filaments are spun out of the vortex core.

The exception to this is the lightly loaded case where the passage cross flow and pressure side leg of the horseshoe vortex appear to interact in such a way as to cause the breakup of the horseshoe vortex in the annular case.

The hub endwall flows consistently climb into the passage earlier and higher and exit the passage at marginally higher spans in the presence of endwall profiling.

The tip clearance flows are almost identical between cases with one almost imperceptible difference in that the yellow ribbons exhibit slightly more turning in the annular case, particularly at the highest incidence.

(a) Annular

(b) Contoured

Figure 108: Secondary flow streamlines for the lightly loaded -5° incidence case with rotor relative exit flow angle contours shown on the exit plane

(a) Annular

(b) Contoured

Figure 109: Secondary flow streamlines for the design case with rotor relative exit flow angle contours shown on the exit plane

(a) Annular

(b) Contoured

Figure 110: Secondary flow streamlines for the highly loaded +5° incidence case with rotor relative exit flow angle contours shown on the exit plane

Figures 111 to 113 provide greater insight into the initiation of the endwall vortex structures by providing a zoomed in view of the front of the passage for each case and for clarity the horseshoe vortex streamtubes have been limited to just 2 streamtubes per leg.

Pressure coefficient contours and isolines (the same as those found in Figure 91) are also plotted for reference.

Probably the most striking feature of these three sets of figures is the lack of clear trends in the development of the vortex structures as the load varies for either endwall. The following statements are however consistently true for the contoured versus annular endwalls:

 The pressure gradient across the passage is slightly reduced (3 isolines) by the introduction of the endwall profiling and the shape and distribution of the isolines clearly altered.

 The introduction of the contoured endwalls sees a clear shift in the cross passage streamlines towards the rear of the passage and as a result the reinforcement of what appears to be the corner vortex. In the front of the passage the contoured endwalls are extremely sparsely populated with streamlines despite the consistent location of their initiation points.

The corner vortex in the junction between the pressure surface and the endwall appears to emanate from the peak pressure point in this junction and is clearly much stronger and separated from the pressure surface in the profiled endwall case. In the lightly loaded case however there are distinct differences in the endwall cross flow. Firstly the annular case exhibits a strong cross passage flow just behind the horseshoe vortices which appears to join the two horseshoe vortices at the same point at which they themselves met. In the profiled endwall case however this is delayed until much later in the passage and it appears as if the corner vortex bifurcates with the first component crossing the passage tangentially. The other significant difference is in the lightly loaded cases is the lack of a rotational component to the streamtubes used to indicate horseshoe vortices in the annular case, while rotation is clearly present in the profiled case.

At design and increased incidence there is a strong component of low momentum fluid from the cross passage streamlines which actually moves around the leading edge from pressure to suction side joining the suction side leg of the horseshoe vortex.

Looking at the rotational component of the horseshoe vortices there is a strongly increasing trend in those for the annular case, while those for the contoured case exhibit a clear increase (0 versus 1 rotation across the width of the passage) between the lightly loaded and design case, but the characteristic of the pressure leg of the vortex changes as load is increased further rather than there being an increase in the vortex diameter.

The angle at which the pressure side leg of the vortex crosses the passage is almost constant with increasing load, and endwall geometry.

(a) Annular

(b) Contoured

Figure 111: Endwall streamlines and oil flow for the lightly loaded -5° incidence case (pressure contours are identical to those of Figure 91)

(a) Annular

(b) Contoured

Figure 112: Endwall streamlines and oil flow for the design case (pressure contours are identical to those of Figure 91)

(a) Annular

(b) Contoured

Figure 113: Endwall streamlines and oil flow for the highly loaded +5° incidence case (pressure contours are identical to those of Figure 91)

6.3 Overview

Pressure data extracted from the CFD as well as the streamline plots show the generic endwalls to affect the flow in line with the original design intent. That is that the cross passage pressure gradient is reduced and the low momentum flow in the boundary layer crosses the passage in a more axial direction. The crossing angle of the pressure leg of the horseshoe vortex is however unaffected, but its size, strength and even characteristic is affected. The combining of the two legs of the horseshoe vortices are also clearly affected as is the inclusion of the cross passage flow into the vortex system and lead to a wider spread, less intense vortex system at exit to the row in the profiled passages.

The composition of the corner vortices on the pressure side of the blade are also clearly affected and exhibit radically different structures at low incidence. This in combination with the effect of contouring on the strength of the horseshoe vortex probably account for the decreased performance of the profiled blading at reduced load.

Tip secondary flows are only slightly affected in the streamline plots but the pressure plots reveal a clear effect of the hub endwall geometry which extends up to the tip region and is evident throughout the length of the passage.

7 Discussion