The mainstream flow past the stationary nozzle guide vanes and rotating turbine blades in a gas turbine creates an unsteady nonaxisymmetric variation in pressure in the annulus, radially outward of the rim seal. The ingress and egress occur through those parts of the seal clearance where the external pressure is higher and lower, respectively, than that in the wheel-space; this nonaxisymmetric type of ingestion is referred to here as externally induced (EI) ingress. Another cause of ingress is that the rotating air inside the wheel-space creates a radial gradient of pressure so that the pressure inside the wheel-space can be less than that outside; this creates rotationally induced (RI) ingress, which—unlike EI ingress—can occur, even if the flow in the annulus is axisymmetric. Although the EI ingress is usually dominant in a turbine, there are conditions under which both EI and RI ingress are significant, these cases are referred to as combined ingress. In Part I of this two-part paper, the so-called orifice equations are derived for compressible and incompressible swirling flows, and the incompressible equations are solved analytically for the RI ingress. The resulting algebraic expressions show how the nondimensional ingress and egress vary with $Θ0$, which is the ratio of the flow rate of sealing air to the flow rate necessary to prevent ingress. It is shown that $ε$, the sealing effectiveness, depends principally on $Θ0$, and the predicted values of $ε$ are in mainly in good agreement with the available experimental data.

1.
Bayley
,
F. J.
, and
Owen
,
J.
, 1970, “
The Fluid Dynamics of a Shrouded Disk System With a Radial Outflow of Coolant
,”
ASME J. Eng. Power
0022-0825,
92
, pp.
335
341
.
2.
,
U. P.
, and
Owen
,
J. M.
, 1983, “
An Investigation of Ingress for an ‘Air Cooled’ Shrouded Rotating Disk System With Radial Clearance Seals
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
105
, pp.
178
183
.
3.
,
U. P.
, and
Owen
,
J. M.
, 1988, “
Aerodynamic Aspects of the Sealing of Gas-Turbine Rotor-Stator Systems, Part 1: The Behaviour of Simple Shrouded Rotating-Disk Systems in a Quiescent Environment
,”
Int. J. Heat Fluid Flow
0142-727X,
9
, pp.
98
105
.
4.
,
U. P.
, and
Owen
,
J. M.
, 1988, “
Aerodynamic Aspects of the Sealing of Gas-Turbine Rotor-Stator Systems, Part 2: The Performance of Simple Seals in a Quasi-Axisymmetric External Flow
,”
Int. J. Heat Fluid Flow
0142-727X,
9
, pp.
106
112
.
5.
,
U. P.
, and
Owen
,
J. M.
, 1988, “
Aerodynamic Aspects of the Sealing of Gas-Turbine Rotor-Stator Systems, Part 3: The Effect of Non-Axisymmetric External Flow on Seal Performance
,”
Int. J. Heat Fluid Flow
0142-727X,
9
, pp.
113
117
.
6.
Chew
,
J. W.
, 1991, “
A Theoretical Study of Ingress for Shrouded Rotating Disc Systems With Radial Outflow
,”
ASME J. Turbomach.
0889-504X,
113
, pp.
91
97
.
7.
Chew
,
J. W.
,
,
S.
, and
Turner
,
A. B.
, 1992, “
Rim Sealing of Rotor-Stator Wheelspaces in the Absence of External Flow
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
433
438
.
8.
,
S.
,
Turner
,
A. B.
, and
Chew
,
J. W.
, 1992, “
Performance of Radial Clearance Rim Seals in Upstream Rotor-Stator Wheelspaces
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
439
445
.
9.
Graber
,
D. J.
,
Daniels
,
W. A.
, and
Johnson
,
B. V.
, 1987, “
Disk Pumping Test, Final Report
,” Air Force Wright Aeronautical Laboratories, Report No. AFWAL-TR-87-2050.
10.
Daniels
,
W. A.
,
Johnson
,
B. V.
,
Graber
,
D. J.
, and
Martin
,
R. J.
, 1992, “
Rim Seal Experiments and Analysis for Turbine Applications
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
426
432
.
11.
Owen
,
J. M.
, and
Rogers
,
R. H.
, 1989,
Flow and Heat Transfer in Rotating Disc Systems, Volume 1 - Rotor-Stator Systems
,
Research Studies Press
,
Taunton, UK
;
John Wiley
,
New York
.
12.
White
,
F. M.
, 1988,
Heat and Mass Transfer
,
,
.
13.
Owen
,
J. M.
, and
Rogers
,
R. H.
, 1995,
Flow and Heat Transfer in Rotating Disc Systems, Volume 2 - Rotating Cavities
,
Research Studies Press
,
Taunton, UK
;
John Wiley
,
New York
.
14.
Schlichting
,
H.
, 1968,
Boundary-Layer Theory
,
McGraw-Hill
,
New York
.