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GAS LABYRINTH SEALS: ON THE EFFECT OF
GEOMETRY AND OPERATING CONDITIONS ON FLOW
FRICTION FACTORS – A CFD INVESTIGATION
Luis San Andrés
Mast-Childs Chair Professor
Tingcheng Wu
Research Assistant
TEES Project # 400124-00099PRESSING NEEDS FOR SEALS /BEARING SOFTWARE DEVELOPMENT
TRC-SEAL-02-18
May 2018
Year II
2
Introduction
(1) TOS: all teeth on stator
(2) TOR: all teeth on rotor
(3) ILS : teeth on both rotor and stator
The capability to accurately predict LS leakage and rotordynamic force
coefficients is a must for efficient and rotordynamic stable operation of
turbomachinery.
TOS TOR ILS
Restrict secondary flow;
Affect rotor system
dynamic stability.
Labyrinth seals (LS)
3
Labyrinth Seals
Core Flow: jet flow along leakage path plays dominant role.
Vortex Flow: Vortices (recirculation zones) in a cavity contribute to
mechanical energy dissipation.
TOS TOR
ILS STEPPED
4
Bulk-flow Model (BFM) for Labyrinth Seal
1
( ) ( )0
i i i i ii i
s
A U Am m
t R
Continuity Equation
/ ( )i i g gP Z R T
Ui (across film average) circumferential velocity in cavity
with
Ai Cross-section area Ai= (B+ Cr)Li
Mass flow rate (per unit circumference length) = f(Pi, Pi−1)
m i = m i+1
m
5
Neumann’s Leakage Model
2
1 1 16.6 /
r iC L
1
2
11
i
NT
NT
Mass Flow through a tooth
2 2
11 2
i i
i i r
g
P Pm DC
R T
2 22 5 2i
i i
1
11
ii
i
P
P
Kinetic Energy Carry-over Coefficient μ1i
Flow Discharge Coefficient μ2i
Note*: for ILS, μ1i =1 for all teeth.
* Childs, D. W., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, Chap.5, “Rotordynamic
Models for Annular Gas Seals", John Wiley & Sons.
Pi-1 Pi
m
Pi-1 Upstream pressure
Pi Downstream pressure
6
BFM circumferential momentum in a LS
Shear stresses on rotor & stator surfaces( ),r s
Blasius friction factor mf nRe
212, , ,r s r s r sf U
1( ) ( )
i i i i
i i i ii i i i i i i i r r s s i
s s
U U A PA U A m U U a a L
t R R
CFD investigation to quantify effects of seal clearance and
operating conditions on friction factors (frθ, fsθ) of a LS.
Objective
Radial clearance: ±20%Cr
Rotor speed: 5 krpm to 15 krpm
Inlet pre-swirl ratio: 0.42 to 0.72
Supply pressure: 6 to 10 MPa
Pressure ratio: 0.40 to 0.85
Cr
Ω
α
Pin
PR
Integrate into BFM for
better predictions:
Circumferential
flow velocity
Seal rotordynamic
force coefficients
New f
8
TOS Labyrinth Seal 1 Geometry & operating conditions
(1) Vannini, G., et al., 2014, "Labyrinth Seal and Pocket Damper
Seal High Pressure Rotordynamic Test Data," ASME J Eng Gas
Turb Power, 136(2).
Mesh ~8M nodes
9
CFD Predicted Velocity and Density Fields
Pin = 7.3 MPa, Pout = 5.1 MPa, rotor speed 12 krpm
Velocity (U) and density (ρ) evenly
distributed in a cavity:
Operating
Conditions
TYP Blasius friction factor
model under estimates frθ , fsθ
CFD vs. BFM Predicted Friction Factor (frθ, fsθ)
22
r
2 2
s
U = W + U - R
U = W +U
,, 2
,
2 r sr s
i r s
fU
, Remr sf n
CFD derived
Blasius Friction
ROTOR
surface
STATOR
surface
TYP n = 0.079, m = -0.25
NEW: n = 0.14, m = -0.25
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Increase in Cr has no effect on frθ
Friction factors (frθ, fsθ) vs. radial clearance (Cr):±20% change
fsθ increases with Cr
frθ≪ fsθ
Radial clearance Cr varies ±20%. A
larger change, up to 2Cr, is needed for
practical use.
Cr nr mr ns ms
0.8 0.14
-0.25
0.23
-0.251 0.14 0.28
1.2 0.14 0.35
New n,m coeffs.
From CFD cavity averaged f’s.
12
Friction factors (frθ, fsθ) vs. rotor speed (Ω): 5k-15 krpm
frθ , fsθ decrease as shaft
speed increases
frθ≪ fsθ
Ω (krpm) nr mr ns ms
5 0.25
-0.25
0.70
-0.257 0.20 0.48
12 0.14 0.28
15 0.13 0.23
New n,m coeffs.
13
Friction factors (frθ, fsθ) vs. pressure ratio (PR): 0.40-0.85
frθ , fsθ decrease as PR increases
frθ≪ fsθfrθ , fsθ sensitive to PR, but not to
magnitude of supply pressure
(Pin) or discharge pressure (Pout).
PR nr mr ns ms
0.40 0.20
-0.25
0.43
-0.250.51 0.18 0.38
0.70 0.14 0.28
0.85 0.12 0.17
New n,m coeffs.
14
Friction Factor (frθ, fsθ) vs. Inlet Pre-Swirl Ratio(α):0.42 – 0.72
α ↑ frθ constant.
α ↑ fsθ ↓
Increase in inlet pre-swirl
decreases fsθ towards frθ.
α nr mr ns ms
0.42 0.14
-0.25
0.20
-0.250.53 0.14 0.19
0.64 0.14 0.17
0.72 0.14 0.16
New n,m coeffs.
Findings
frθ fsθRadial Clearance Cr↑ cons. ↑
Rotor Speed Ω↑ ↓ ↓
Pressure Pin↑
Pressure Ratio PR↑ ↓ ↓
Inlet Pre-Swirl α↑ cons. ↓
Note:
↑ Positive correlation; ↓Negative correlation; cons. Constant
CFD investigation quantifies effects of seal clearance and operating
conditions on friction factors (frθ, fsθ).
Radial clearance: 0.8 Cr to 1.2 Cr;
Rotor speed: 5 krpm to 15 krpm; Pressure ratio: 0.40 to 0.85;
Supply pressure: 6 to 10 MPa;
Inlet pre-swirl ratio: 0.42 to 0.72;
The new coefficients (n, m) produce higher friction factors than classical ones (n =
0.79, m = -0.25) do. The BFM with new friction factors delivers less stiffness (KXX,
KXY) and larger damping (CXX) than with the original friction factor model.
16
2018 continuation proposal to TRC
CFD-BULK FLOW MODEL:
ANALYSIS OF KINETIC ENERGY
CARRY-OVER COEFFICIENTS FOR
IMPROVED PREDICTION OF LEAKAGE
IN GAS LABYRINTH SEALS
Project Pressing Needs for Seals /Bearing Software Development
17
Background
BFM program (XLLaby©) utilizes Neumann’s Equation to calculate mass
flow rate through a tooth, and to obtain the cavity pressures (Pi).
2
1 1 16.6 /
r iC L
1
2
11
i
NT
NT
Neumann’s Equation
2 2
11 2
i i
i i r
g
P Pm DC
R T
Kinetic Energy Carry-over Coefficient μ1i
For a LS having a large Cr/Li ratio, BFM predictions produce an overly
large pressure drop across the first tooth over-predicted mass flow
rate. There is a significant difference in kinetic energy carry-over
coefficients between first tooth and other teeth. This pressure is not
realistic, as observed and discussed by a concerned XLTRC2 LABYseal
code user.
∆P1
∆P2
∆P1 >>∆P2
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2018 Proposal (Continuation )
CFD-BULK Flow Model: Analysis of Kinetic Energy Carry-over
Coefficients for Improved Prediction of Leakage in Gas Labyrinth Seals
Aim
and Tasks:
3. Integrate found (numerical) kinetic energy carry-over coefficient
relations into BFM program (XLLaby©).
4. Produce predictions and quantify improvement.
To better predict seal leakage and rotordynamic force
coefficients in labyrinth seals:
1. CFD : LS (14 teeth) with increasing Cr/Li ratio and operating at
various inlet supply pressure (Pin), exit pressure (Pout), and rotor
speed (Ω).
2. Obtain CFD mass flow rates and compare against those from BFM.
Modify/update kinetic energy carry-over coefficient model.
19
TRC Budget
Support for graduate student (20 h/week) x $ 2,200 x 12
months
$ 26,400
Fringe benefits (2.5%) and medical insurance ($422/month) $ 5,697
Tuition three semesters (24 credit hours) $ 13,275
HPRC fees and PC upgrade $ 1,800
Travel & registration to technical conference $ 1,800
2018-2019
Year III
$ 48,972Total Cost:
XLLaby© integrated with CFD-derived kinetic energy carry-over
coefficients will deliver more accurate mass flow rate and cavity pressure
predictions.
Learn more at http://rotorlab.tamu.edu
Questions (?)
Acknowledgements
Turbomachinery Research Consortium