Abstract
To clarify the influences of the tip clearance flows on the unsteady cavitating flow, the three-dimensional unsteady cavitating flows through both the two-dimensional cascades and the three-dimensional inducer with and without tip clearance are performed numerically. The governing equations for the compressible fluid flow with the DES turbulence model are employed with the assumption of the isentropic process of liquid phase. The evolution of cavities is represented as the source/sink of vapor phase. The basic equations in the curve linear coordinate are solved by the finite difference method. As the results of the three-dimensional cavitating flows through the two-dimensional cascades, the tip clearance flows from the pressure side to the suction side of the blade produces the tip vortex cavitation, which affects the sheet cavitation on the leading edge of the next blade and enhances the blockage effect near the casing than the flows without tip clearance. On the other hand, in the case of the three-dimensional inducer, the large backflow cavitation is observed around the inlet of the inducer, where the cavities are developed on the casing by the tip clearance flows. The large pressure gradient between the non-cavitating pressure side and the cavitating suction side enhances the tip clearance flows. The calculation considering the tip clearance reproduces the developed cavitation region similar to that of experimental visualizations. Additionally, the backflow cavitation rotates with the speed slower than the rotation speed of the inducer. Then, the rotation of backflow cavitation causes the periodic fluctuation of the outlet pressure greater than that of the inlet pressure.
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Abbreviations
- C:
-
Cord length, constant of cavitation model
- d:
-
Distance function
- d̃:
-
Length scale
- fL:
-
Volume fraction of liquid
- F:
-
External force
- g:
-
Metric tensor gmn = β m j β n j
- J:
-
Jacobian (J=|∂x i /∂ξj])
- k:
-
Turbulence kinematic energy
- M:
-
Mach number
- p:
-
Pressure
- Re:
-
Reynolds number
- S:
-
Magnitude of vorticity
- S̃:
-
Production
- u:
-
Velocity component on Cartesian coordinate
- U:
-
Contravariant velocity component on curvilinear coordinate
- t:
-
Time
- x:
-
Cartesian coordinate
- β:
-
Metric (β i j=∂ξj/∂x i )
- δ:
-
Dirac delta
- Δ:
-
Grid scale
- μ:
-
Viscosity
- ν:
-
Kinematic viscosity
- ρ:
-
Density
- σ:
-
Cavitation number
- τ:
-
Stress
- ω:
-
Vorticity
- Ω:
-
Cangular velocity
- ξ:
-
Curvilinear coordinate
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Biography: OKITA K. (1974-), Male, Ph. D., Senior Scientist
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Okita, K., Ugajin, H. & Matsumoto, Y. Numerical Analysis of the Influence of the Tip Clearance Flows on the Unsteady Cavitating Flows in a Three-Dimensional Inducer. J Hydrodyn 21, 34–40 (2009). https://doi.org/10.1016/S1001-6058(08)60116-X
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DOI: https://doi.org/10.1016/S1001-6058(08)60116-X