Abstract

This paper introduces a bulk-flow model for prediction of the static and dynamic force coefficients of angled injection Lomakin bearings. The analysis accounts for the flow interaction between the injection orifices, the supply circumferential groove, and the thin film lands. A one control-volume model in the groove is coupled to a bulk-flow model within the film lands of the bearing. Bernoulli-type relationships provide closure at the flow interfaces. Flow turbulence is accounted for with shear stress parameters and Moody’s friction factors. The flow equations are solved numerically using a robust computational method. Comparisons between predictions and experimental results for a tangential-against-rotation injection water Lomakin bearing show that novel model well predicts the leakage and direct stiffness and damping coefficients. Computed cross-coupled stiffness coefficients follow the experimental trends for increasing rotor speeds and supply pressures, but quantitative agreement remains poor. A parameter investigation shows evidence of the effects of the groove and land geometries on the Lomakin bearing flowrate and force coefficients. The orifice injection angle does not influence the bearing static performance, although it largely affects its stability characteristics through the evolution of the cross-coupled stiffnesses. The predictions confirm the promising stabilizing effect of the tangential-against-rotation injection configuration. Two design parameters, comprised of the feed orifices area and groove geometry, define the static and dynamic performance of Lomakin bearing. The analysis also shows that the film land clearance and length have a larger impact on the Lomakin bearing rotordynamic behavior than its groove depth and length.

1.
San Andrés
,
L.
, 1995, “
Thermodynamic Analysis of Fluid Film Bearings for Cryogenic Applications
,”
AIAA J.
0001-1452,
11
(
5
), pp.
964
972
.
2.
Fayolle
,
P. G.
,
Phillips
,
S. G.
, and
Childs
,
D. W.
, 1997, “
Experimental Rotordynamic Coefficient Results for a 0.100‐mm Clearance Tangential-Against-Rotation Injection Lomakin Bearing
,” Technical Report No. TAMU 0710,
Texas A&M University
, College Station, TX.
3.
Lomakin
,
A.
, 1958, “
Calculation of Critical Speed and Securing of the Dynamic Stability of Rotors in High-Pressure Hydraulic Machines With Reference to Forces Arising in Seal Gaps
,”
Energomashinostroenie
0131-1336,
4
(
4
), pp.
1
5
.
4.
Childs
,
D. W.
, 1983, “
Finite-Length Solutions for Rotordynamic Coefficients of Turbulent Annular Seals
,”
ASME J. Lubr. Technol.
0022-2305,
105
, pp.
437
445
.
5.
Von Pragenau
,
G. L.
, 1992, “
From Labyrinth Seals to Damping Seals∕Bearings
,”
Fourth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
, Honolulu, HI, Vol.
A
, pp.
277
285
.
6.
Childs
,
D.
, and
Vance
,
J.
, 1994, “
Annular Seals as Tools to Control Rotordynamic Response of Future Gas Turbine Engines
,”
30th AIAA∕ASME∕SAE∕ASEE Joint Propulsion Conference
, Indianapolis, IN, Vol.
AIAA 94–2804
, pp.
1
9
.
7.
Martzinkovsky
,
V. A.
, 1993, “
The Lomakin Effect and Its Applications in Pumps and Sealings
,” in
Proceedings of the Rotating Machinery Conference and Exposition
, Somerset, NJ, Vol.
2
, pp.
1
59
.
8.
Black
,
H. F.
,
Allaire
,
P. E.
, and
Barrett
,
L. E.
, 1981, “
Inlet Flow Swirl in Short Turbulent Annular Seal Dynamics
,”
Ninth International Conference on Fluid Sealing
, BHRA Fluid Engineering, Leeuwenhorst, Netherlands, pp.
1
14
.
9.
San Andrés
,
L.
, and
Childs
,
D.
, 1997, “
Angled Injection—Hydrostatic Bearings, Analysis and Comparison to Test Results
,”
ASME J. Tribol.
0742-4787,
119
(
1
), pp.
179
187
.
10.
Franchek
,
N.
, and
Childs
,
D.
, 1994, “
Experimental Test Results for Four High-Speed, High Pressure, Orifice-Compensated Hybrid Bearings
,”
ASME J. Tribol.
0742-4787,
116
(
2
), pp.
285
290
.
11.
Kim
,
C. H.
, and
Lee
,
Y. B.
, 1994, “
Test Results for Rotordynamic Coefficients of Anti-Swirl Self-Injection Seals
,”
ASME J. Tribol.
0742-4787,
116
, pp.
508
513
.
12.
Arauz
,
G. L.
, and
San Andrés
,
L.
, 1996, “
Experimental Study on the Effect of a Circumferential Feeding Groove on the Dynamic Force Response of a Sealed Squeeze Film Damper
,”
ASME J. Tribol.
0742-4787,
118
, pp.
900
905
.
13.
San Andrés
,
L. A.
, 1991, “
Analysis of Variable Fluid Properties, Turbulent Annular Seals
,”
ASME J. Tribol.
0742-4787,
113
, pp.
694
702
.
14.
Hirs
,
G. G.
, 1973, “
A Bulk-Flow Theory for Turbulence in Lubricant Films
,”
ASME J. Lubr. Technol.
0022-2305,
95
(
2
), pp.
137
146
.
15.
Childs
,
D. W.
, 1983, “
Dynamic Analysis of Turbulent Annular Seals Based On Hirs’ Lubrication Equation
,”
ASME J. Lubr. Technol.
0022-2305,
105
, pp.
429
436
.
16.
Nelson
,
C. C.
, 1985, “
Rotordynamic Coefficients for Compressible Flow in Tapered Annular Seals
,”
ASME J. Tribol.
0742-4787,
107
, pp.
318
325
.
17.
San Andrés
,
L.
, 1993, “
Dynamic Force and Moment Coefficients for Short Length Annular Seals
,”
ASME J. Tribol.
0742-4787,
115
, pp.
61
70
.
18.
Childs
,
D. W.
, 1993,
Turbomachinery Rotordynamics
,
Wiley
,
New York
, Chap. 5.
19.
Soulas
,
T.
, 2001, “
A Bulk-Flow Model of Angled Injection Lomakin Bearings
,” M.S. thesis, Texas A&M University, College Station, TX.
20.
Li
,
J.
,
San Andrés
,
L.
, and
Vance
,
J.
, 1999, “
Bulk Flow Analysis of Multiple-Pocket Gas Damper Seals
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
121
(
2
), pp.
355
362
.
21.
Childs
,
D.
, 1989, “
Fluid Structure Interaction Forces at Pump-Impeller-Shroud Surfaces for Rotordynamic Calculations
,”
ASME J. Vib., Acoust., Stress, Reliab. Des.
0739-3717,
111
, pp.
216
225
.
22.
Launder
,
B. E.
, and
Leschziner
,
M.
, 1978, “
Flow in Finite Width Thrust Bearings Including Inertial Effects, I-Laminar Flow, II-Turbulent Flow
,”
ASME J. Lubr. Technol.
0022-2305,
100
, pp.
330
345
.
23.
Van Doormal
,
J. P.
, and
Raithby
,
G. D.
, 1984, “
Enhancements of the Simple Method for Predicting Incompressible Fluid Flows
,”
Numer. Heat Transfer
0149-5720,
7
, pp.
147
163
.
You do not currently have access to this content.