In Part I of this two-part paper, the orifice equations were solved for the case of externally induced (EI) ingress, where the effects of rotational speed are negligible. In Part II, the equations are solved, analytically and numerically, for combined ingress (CI), where the effects of both rotational speed and external flow are significant. For the CI case, the orifice model requires the calculation of three empirical constants, including $Cd,e,RI$ and $Cd,e,EI$, the discharge coefficients for rotationally induced (RI) and EI ingress. For the analytical solutions, the external distribution of pressure is approximated by a linear saw-tooth model; for the numerical solutions, a fit to the measured pressures is used. It is shown that although the values of the empirical constants depend on the shape of the pressure distribution used in the model, the theoretical variation of $Cw,min$ (the minimum nondimensional sealing flow rate needed to prevent ingress) depends principally on the magnitude of the peak-to-trough pressure difference in the external annulus. The solutions of the orifice model for $Cw,min$ are compared with published measurements, which were made over a wide range of rotational speeds and external flow rates. As predicted by the model, the experimental values of $Cw,min$ could be collapsed onto a single curve, which connects the asymptotes for RI and EI ingress at the respective smaller and larger external flow rates. At the smaller flow rates, the experimental data exhibit a minimum value of $Cw,min$, which undershoots the RI asymptote. Using an empirical correlation for $Cd,e$, the model is able to predict this undershoot, albeit smaller in magnitude than the one exhibited by the experimental data. The limit of the EI asymptote is quantified, and it is suggested how the orifice model could be used to extrapolate the effectiveness data obtained from an experimental rig to engine-operating conditions.

1.
Owen
,
J. M.
, 2011, “
Prediction of Ingestion Through Turbine Rim Seals. Part I: Rotationally-Induced Ingress
,”
ASME J. Turbomach.
0889-504X,
133
, p.
031005
.
2.
Owen
,
J. M.
, 2011, “
Prediction of Ingestion Through Turbine Rim Seals. Part II: Externally-Induced and Combined Ingress
,”
ASME J. Turbomach.
0889-504X,
133
, p.
031006
.
3.
Owen
,
J. M.
,
Kunyuan
,
Z.
,
Pountney
,
O.
,
Wilson
,
M.
, and
Lock
,
G. D.
, 2012, “
Theoretical Prediction of Ingress Through Turbine Rim Seals—Part I: Externally Induced Ingress
,”
ASME J. Turbomach.
,
134
, p.
031012
.
4.
,
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
.
5.
,
A. V.
,
Heitland
,
G.
, and
Hosseini
,
K. M.
, 2009, “
The Effect of Annulus Reynolds Number on Rotor-Stator Cavity Sealing Flow
,”
ASME
Paper No. GT2009-59380.
6.
Vaughan
,
C.
, 1986, “
A Numerical Investigation Into the Effect of an External Flow Field on the Sealing of a Rotor-Stator Cavity
,” Ph.D. thesis, University of Sussex, UK.
7.
Owen
,
J. M.
, and
Rogers
,
R. H.
, 1989,
Flow and Heat Transfer in Rotating Disc Systems, Volume 1—Rotor-Stator Systems
,
Wiley
,
New York
.
8.
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
.
9.
Bohn
,
D.
, and
Wolff
,
M.
, 2003, “
Improved Formulation to Determine Minimum Sealing Flow—Cw, min—For Different Sealing Configuration
,”
ASME
Paper No. GT2003-38465.
10.
Johnson
,
B. V.
,
Jakoby
,
R.
,
Bohn
,
D. E.
, and
Cunat
,
D.
, 2006, “
A Method for Estimating the Influence of Time-Dependent Vane and Blade Pressure Fields on Turbine Rim Seal Ingestion
,”
ASME
Paper No. GT2006-90853.
11.
Hamabe
,
K.
, and
Ishida
,
K.
, 1992, “
Rim Seal Experiments and Analysis of a Rotor-Stator System With Nonaxisymmetric Main Flow
,”
ASME
Paper No. 92-GT-160.
12.
Chew
,
J. W.
,
Green
,
T.
, and
Turner
,
A. B.
, 1994, “
Rim Sealing of Rotor-Stator Wheelspaces in the Presence of External Flow
,”
ASME
Paper No. 94-GT-126.
13.
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.
14.
Owen
,
J. M.
, and
Rogers
,
R. H.
, 1995,
Flow and Heat Transfer in Rotating Disc Systems, Volume 2—Rotating Cavities
,
Wiley
,
New York
.