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Research Papers

# Velocity Distributions for Low Pressure Turbines

[+] Author and Article Information
J. D. Coull, R. L. Thomas, H. P. Hodson

Whittle Laboratory, University of Cambridge, Cambridge CB3 0DY, UK

The ninth design ($DF=40%$, $Speak/S0=62%$) was found to exhibit high levels of secondary flow so has not been measured.

Although the flow is not laminar during reattachment, the mixing loss is dependant on the maximum displacement thickness of the bubble (see Ref. 28), which will be governed by the laminar portion of the bubble.

The shortening of the separation bubble with increasing diffusion rate may at first seem nonintuitive. However, bubbles in highly decelerating flow will grow in height more quickly, promoting earlier breakdown into turbulence. Thus, transition and reattachment will tend to move upstream. It should also be noted that the loss produced by a separation bubble is not dependant on its length; rather it is the maximum height of the bubble which is important (see Ref. 28).

Not all of the designs were tested at the highest reduced frequency; hence there is no optimum line for the 40% diffusion factor designs in Fig. 1.

J. Turbomach 132(4), 041006 (Apr 27, 2010) (13 pages) doi:10.1115/1.3192149 History: Received July 14, 2008; Revised March 26, 2009; Published April 27, 2010; Online April 27, 2010

## Abstract

A parametric set of velocity distributions has been investigated using a flat-plate experiment. Three different diffusion factors and peak velocity locations were tested. These were designed to mimic the suction surfaces of low pressure (LP) turbine blades. Unsteady wakes, inherent in real turbomachinery flows, were generated using a moving bar mechanism. A turbulence grid generated a freestream turbulence level that is believed to be typical of LP turbines. Measurements were taken across a Reynolds number range 50,000–220,000 at three reduced frequencies (0.314, 0.628, and 0.942). Boundary layer traverses were performed at the nominal trailing edge using a laser Doppler anemometry system and hot films were used to examine the boundary layer behavior along the surface. For every velocity distribution tested, the boundary layer separated in the diffusing flow downstream of the peak velocity. The loss production is dominated by the mixing in the reattachment process, mixing in the turbulent boundary layer downstream of reattachment, and the effects of the unsteady interaction between the wakes and the boundary layer. A sensitive balance governs the optimal location of peak velocity on the surface. Moving the velocity peak forward on the blade was found to be increasingly beneficial when bubble-generated losses are high, i.e. at low Reynolds number, at low reduced frequency, and at high diffusion factors.

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## Figures

Figure 1

Schematic of the flat-plate experiment

Figure 2

Measured surface velocity for T106A (14) and T106C (15). Rec≈210,000, fr≈0.6, and Tu≈4%.

Figure 3

Measured surface velocity for all velocity distributions tested (Rec=200,000 and fr=0.628) with assumed pressure-side distributions for each

Figure 4

LHS: Space-time plot for design D for Rec=127,000 and fr=0.628. Flood contours of quasi-wall shear stress, line contours of intermittency (in steps of 0.1). RHS: Trailing edge momentum thickness variation.

Figure 5

Loss variation for design D at fr=0.628 with error bars and curves of Rec−0.5 and Rec−0.2

Figure 6

Time variation of trailing edge momentum thickness for design D at fr=0.314 for three Reynolds numbers, with estimated steady flow values

Figure 7

Variation of loss coefficient with Reynolds number at three reduced frequencies for design D

Figure 8

Time variation of trailing edge momentum thickness for design D at Rec≈210,000 and three reduced frequencies

Figure 9

Loss coefficient variation against Reynolds number at three diffusion factors. Speak/S0=52%, and fr=0.628.

Figure 10

Comparison of measured loss coefficients for fr=0.628 against non-separated NGTE boundary layer calculations.

Figure 11

Relative loss versus diffusion factor for current measurements and those of Curtis (3) at Rec=200,000.

Figure 12

Influence of varying peak velocity location. Loss for designs C–E (DF=28%) at fr=0.314.

Figure 13

Flood contours of quasi-wall shear stress and line contours of intermittency (in steps of 0.1) for design C (DF=28%, Speak/S0=42%, Rec=130,000, and fr=0.628)

Figure 14

Flood contours of quasi-wall shear stress and line contours of intermittency (in steps of 0.1) for design E (DF=28%, Speak/S0=62%, Rec=138,000, and fr=0.628)

Figure 15

Influence of varying peak velocity location. Loss coefficients for designs A and B (DF=40%) at fr=0.628 with optimum line. Approximate optimum peak velocity locations have been added.

Figure 16

Optimum lines and approximate optimum peak suction locations for each diffusion factor. (a) fr=0.314, (b) fr=0.628, and (c) fr=0.942.

## Errata

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