Abstract
In a high Reynolds number axial-flow pump, laser velocimeter (LV) measurements were made to study the size and structure of the end-wall vortex. The time mean measurements show that the core size of the end-wall vortex increased with decreasing tip clearance, which is contrary to existing theory. Observations of cavitation in the vortex showed that the flow was unsteady. The vortices emanating from the smaller clearances were observed to wander or meander spatially and to develop kinks more than the vortices emanating from the larger tip clearances. This observed unsteadiness has a significant effect on the time mean size and velocity distribution of the vortex as measured with the LV employing the field point measurement technique. In order to obtain an estimate of the true size and velocity distribution, computational experiments were conducted which modelled a periodically wandering vortex and the LV measurement process. The computational and experimental results show good agreement, including a broadened and reduced tangential velocity distribution. In this paper, the end-wall vortex LV measurements are presented, and the method of analyzing the vortex wandering is described.
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Abbreviations
- c :
-
tip chord, 206 mm
- f :
-
frequency
- h :
-
tip clearance
- H :
-
blade span, 267 mm
- N :
-
number of LV data points
- P :
-
probability function
- q :
-
data acquisition rate
- r :
-
radial distance from mean position of vortex axis
- r c :
-
vortex core radius
- t m :
-
maximum tip thickness
- T :
-
time period for integration
- u :
-
axial velocity of vortex (along vortex axis)
- U ∞ :
-
freestream velocity
- v θ :
-
tangential velocity of vortex (about vortex axis)
- x :
-
axial position downstream
- y :
-
distance from end-wall
- Y :
-
displacement of vortex axis from mean position
- Γ :
-
circulation
- ζ :
-
coordinate for vortex motion
- η :
-
coordinate for vortex motion
- λ :
-
tip clearance to maximum tip thickness ratio
- λ s :
-
scaled wavelength of tunnel turbulence spectrum. The turbulent energy is divided equally between wavelengths longer and shorter than λ s
- κ :
-
eddy diffusivity
- σ :
-
root-mean-squared value
- τ :
-
duration of LV data collection
- ω :
-
radian frequency at half power point of turbulent spectrum
- -:
-
average value
- max:
-
maximum value
- app:
-
apparent, not true value
- cav:
-
quantity evaluated under cavitating conditions
References
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Farrell, K. J. 1989: An investigation of end-wall vortex cavitation in a high Reynolds number axial-flow pump. M. S. Thesis, Dept. of Mechanical Engineering, The Pennsylvania State University, University Park, PA
Farrell, K. J.; McBride, M. W.; Billet, M. L. 1987: High Reynolds number pump facility for cavitation research. ASME Int. Symp. on Cavitation Research Facilities and Techniques. FED-57, 61–68.
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Straka, W.A., Farrell, K.J. The effect of spatial wandering on experimental laser velocimeter measurements of the end-wall vortices in an axial-flow pump. Experiments in Fluids 13, 163–170 (1992). https://doi.org/10.1007/BF00218163
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DOI: https://doi.org/10.1007/BF00218163