In a previous study, vane-rotor shock interactions and heat transfer on the rotor blade of a highly loaded transonic turbine stage were simulated. The geometry consists of a high pressure turbine vane and a downstream rotor blade. This study focuses on the physics of flow and heat transfer in the rotor tip, casing, and hub regions. The simulation was performed using the unsteady Reynolds-averaged Navier–Stokes code MSU-TURBO. A low Reynolds number $k-ε$ model was utilized to model turbulence. The rotor blade in question has a tip gap height of 2.1% of the blade height. The Reynolds number of the flow is approximately $3×106/m$. Unsteadiness was observed at the tip surface that results in intermittent “hot spots.” It is demonstrated that unsteadiness in the tip gap is governed by inviscid effects due to high speed flow and is not strongly dependent on pressure ratio across the tip gap contrary to published observations that have primarily dealt with subsonic tip flows. The high relative Mach numbers in the tip gap lead to a choking of the leakage flow that translates to a relative attenuation of losses at higher loading. The efficacy of new tip geometry is discussed to minimize heat flux at the tip while maintaining choked conditions. In addition, an explanation is provided that shows the mechanism behind the rise in stagnation temperature on the casing to values above the absolute total temperature at the inlet. It is concluded that even in steady (in a computational sense) mode, work transfer to the near tip fluid occurs due to relative shearing by the casing. This is believed to be the first such explanation of the work transfer phenomenon in the open literature. The difference in pattern between steady and time-averaged heat fluxes at the hub is also explained.

1.
Cumpsty
,
N.
, 2003,
Jet Propulsion
,
Cambridge University Press
,
Cambridge
.
2.
Shyam
,
V.
, 2009, “
3-D Unsteady Simulation of a Modern High Pressure Turbine Stage: Analysis of Heat Transfer and Flow
,” Ph.D. thesis, Ohio State University, Columbus, OH.
3.
Bunker
,
R. S.
, 2001, “
A Review of Turbine Blade Tip Heat Transfer
,”
0077-8923,
934
, pp.
64
79
.
4.
Ameri
,
A. A.
, 2004, “
Turbine Blade Tip Design and Tip Clearance Treatment
,” notes from von Karman Lecture Series 2004.
5.
Zhou
,
C.
, and
Hodson
,
H.
, 2009, “
The Tip Leakage Flow of an Unshrouded High Pressure Turbine Blade With Tip Cooling
,”
ASME
Paper No. GT2009-59637.
6.
Ameri
,
A. A.
,
,
E.
, and
Rigby
,
D. L.
, 1998, “
Effect of Squealer Tip on Rotor Heat Transfer and Efficiency
,”
ASME J. Turbomach.
0889-504X,
120
, pp.
753
759
.
7.
Ameri
,
A. A.
,
,
E.
, and
Rigby
,
D. L.
, 1999, “
Effects of Tip Clearance and Casing Recess on Heat Transfer and Stage Efficiency in Axial Turbines
,”
ASME J. Turbomach.
0889-504X,
121
, pp.
683
693
.
8.
O’Dowd
,
D.
,
Zhang
,
Q.
,
Ligrani
,
P.
,
He
,
L.
, and
Friedrichs
,
S.
, 2009, “
Comparison of Heat Transfer Measurement Techniques on a Transonic Turbine Blade Tip
,”
ASME
Paper No. GT2009-59376.
9.
Hofer
,
T.
, and
Arts
,
T.
, 2009, “
Aerodynamic Investigation of the Tip Leakage Flow for Blades With Different Tip Squealer Geometries at Transonic Conditions
,”
ASME
Paper No. GT2009-59909.
10.
Krishnababu
,
S. K.
,
Dawes
,
W. N.
,
Hodson
,
H. P.
,
Lock
,
G. D.
,
Hannis
,
J.
,
Whitney
,
C.
, 2007, “
Aero-Thermal Investigations of Tip Leakage Flow in Axial Flow Turbines, Part II—Effect of Relative Casing Motion
,”
ASME
Paper No. 2007-GT-27957.
11.
Wheeler
,
A. P. S.
,
Atkins
,
R.
, and
He
,
L.
, 2009, “
Turbine Blade Tip Heat Transfer in Low and High Speed Flows
,”
ASME
Paper No. GT2009-59404.
12.
Shyam
,
V.
,
Ameri
,
A.
,
Luk
,
D. F.
, and
Chen
,
J. P.
, “
3-D Unsteady Simulation of a Modern High Pressure Turbine Stage Using Phase Lag Periodicity: Analysis of Flow and Heat Transfer
,”
ASME
Paper No. GT2009-60322.
13.
Chen
,
J. P.
, and
Whitfield
,
D. L.
, 1993, “
Navier-Stokes Calculations for the Unsteady Flowfield of Turbomachinery
,” Paper No. AIAA-93-0676.
14.
Chen
,
J. P.
, and
Barter
,
J.
, 1998, “
Comparison of Time-Accurate Calculations for the Unsteady Interaction in Turbomachinery Stage
,” Paper No. AIAA-98-3292.
15.
Chen
,
J. P.
, and
Briley
,
W. R.
, 2001, “
,”
ASME
Paper No. 2001-GT-0348.
16.
Luk
,
D. F.
, 2008, “
Steady Heat Transfer predictions for a Highly Loaded Single Stage Turbine With a Flat Tip
,” MS thesis, Ohio State University, Columbus, OH.
17.
Tallman
,
J. A.
,
Haldeman
,
C. W.
,
Dunn
,
M. G.
,
,
A. K.
, and
Bergholz
,
R. F.
, 2006, “
Heat Transfer Measurements and Predictions for a Modern, High-Pressure, Transonic Turbine, Including Endwalls
,”
ASME
Paper No. GT2006-90927.
18.
Green
,
B. R.
,
Barter
,
J. W.
,
Haldeman
,
C. W.
, and
Dunn
,
M. G.
, 2005, “
Averaged and Time-Dependent Aerodynamics of a High Pressure Turbine Blade Tip Cavity and Stationary Shroud: Comparison of Computational and Experimental Results
,”
ASME
Paper No. 2004-GT-53443.
19.
Zhu
,
J.
, and
Shih
,
T. H.
, 1995, “
A Turbulence Module for the NPARC Code
,”
NASA
, Report No. CR-198358.
20.
Shapiro
,
A. H.
, 1954,
The Dynamics and Thermodynamics of Compressible Fluid Flows
,
Ronald Press Company
,
New York
.
21.
Ameri
,
A. A.
,
Rigby
,
D. L.
,
,
E.
,
Heidmann
,
J.
, and
Fabian
,
J. C.
, 2007. “
Unsteady Analysis of Blade and Tip Heat Transfer as Influenced by the Upstream Momentum and Thermal Wakes
,”
ASME
Paper No. GT2008-51242.
22.
Thorpe
,
S. J.
, and
Ainsworth
,
R.
, 2006, “
The Effects of Blade Passing on the Heat Transfer Coefficient of the Over-Tip Casing in a Transonic Turbine Stage
,” ASME Paper No. GT2006-90534.
23.
Thorpe
,
S. J.
,
Miller
,
R. J.
,
Yoshino
,
S.
,
Ainsworth
,
R. W.
, and
Harvey
,
N. W.
, 2005, “
The Effect of Work Processes on the Casing Heat Transfer of a Transonic Turbine
,” ASME Paper No. GT2005-68437.