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

11

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

18

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