Stator

Stator Land

Rotor

Seal Teeth (“Knife Edges”)

High Pressure Region

Low Pressure Region

Leakage Flow

t

w

h

crb

θh/2f1

f2

rs

tL

rL,1 rL,2

L1

L2

L3

tL

Stator

Stator Land

Rotor

Seal Teeth Ups

trea

m A

nnul

s

Dow

nstr

eam

Ann

uls

Parameter Value Units

t 0.275 inches

h 0.25 inches

w 0.11 inches

cr 5-15 mils

b 0.010 inches

θ 70 degrees

f1 0.030 inches

f2 0.020 inches

rs 8.0 inches

Parameter Value Units

rL,1 8.4 inches

rL,2 8.1 inches

tL 0.15 inches

L1 2.2 inches

L2 3.25 inches

L3 5.0 inches

Boundary Condition Value Units

Pup 500 psia

Tup 1000 F

RPMF,up 0

Turbulent Intensity Up 5 %Length Scale Up 0.01 inches

Pdown 250 psiaTurbulent Intensity Down 5 %

Length Scale Down 0.01 inchesω 18000 rpmcr 5 mils

ω

Pup

Tup

RPMFup

Pdown

cr

Grid Density

# Cells Cell Size Region A (mils)

Cell Size Region B (mils)

# Cells in clearance gap

Very Coarse 6,500 10 20 6

Coarse 2,300 5 10 6

Medium 91,000 2.5 5 7Fine 260,000 1.25 2.5 7

AB

B

Grid Density # Cells Flow Rate YY (lbm/s)

Total Temperature at XX (F)

Total Temperature at ZZ (F)

Very Coarse 6,500 0.898 1116.8 1249.0

Coarse 2,300 0.954 1111.9 1230.4

Medium 91,000 0.917 1106.0 1217.9Fine 260,000 0.902 1103.0 1210.0

Very Coarse Coarse

Medium Fine

Fluent CFD Setting Value

Solver Type Pressure

Velocity Formulation Absolute

Turbulence Model k-omega SSTw/Viscous Heatingw/Compressibility Effects

Air Density Ideal GasAir Specific Heat / Conductivity / Viscosity Property Curves- See AppendixSolution Scheme SimpleSpatial Discretization: Density, Momentum, Swirl Velocity, Energy

Second Order Upwind

Spatial Discretization: Turbulent Kinetic Energy, Specific Dissipation Rate

First Order

Spatial Discretization: Gradient Least Squares Cell BasedSpatial Discretization: Pressure Standard

XXYY ZZ

T = T = =

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 5 mils

Total Temperature (F)

Stream Function (lbm/s)

Pressure (psia)

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 5 mils

Swirl Velocity (ft/s)

RPMF

% Swirl Velocity

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 5 mils

Total Relative Temperature (F)

Total Temperature (F)

Total Temperature no viscous work (F)

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 5 mils

Convergence

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 5 mils

Axial=5.136” Axial=6.309”

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 5 mils

Result Value UnitsLeakage 0.9173 lbm/s

Tt,abs,xx 1107 F

Tt,abs,zz 1218 F

111 F

27.27 BTU/s

σmethod1 0.91 -

25.63 BTU/s

105 F

σmethod2 0.87 -

XXYY ZZ

10 Mil Clearance

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 10 mils

Total Temperature (F)

Stream Function (lbm/s)

Pressure (psia)

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 10 mils

Swirl Velocity (ft/s)

RPMF

% Swirl Velocity

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 10 mils

Total Relative Temperature (F)

Total Temperature (F)

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 10 mils

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 10 mils

Axial=5.136” Axial=6.309”

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 10 mils

Result Value UnitsLeakage 2.07 lbm/s

Tt,abs,xx 1066 F

Tt,abs,zz 1138 F

71 F

39.45 BTU/s

σmethod1 0.58 -

32.75 BTU/s

60 F

σmethod2 0.49 -

XXYY ZZ

15 Mil Clearance

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 15 mils

Total Temperature (F)

Stream Function (lbm/s)

Pressure (psia)

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 15 mils

Swirl Velocity (ft/s)

RPMF

% Swirl Velocity

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 15 mils

Total Relative Temperature (F)

Total Temperature (F)

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 15 mils

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 15 mils

Axial=5.136” Axial=6.309”

Boundary Condition

Value Units

Pup 500 psia

Tup 1000 F

Pdown 250 psia

ω 18000 rpm

Cr 15 mils

Result Value UnitsLeakage 3.40 lbm/s

Tt,abs,xx 1044 F

Tt,abs,zz 1100 F

56 F

50.98 BTU/s

σmethod1 0.46 -

38.76 BTU/s

42.7 F

σmethod2 0.35 -

XXYY ZZ

5 mil

10 mil

15 mil

Fixed Pressure

Cr (mil) (lbm/s) (Btu/s) ΔTt (F) σ RPMFup

5 0.92 27.3 111 0.91 0.322

10 2.07 39.5 71 0.58 0.255

15 3.4 51.0 56 0.46 0.173

Fixed Pressure

Fixed Flow

15 mil

10 mil

5 mil

Cr (mil) (lbm/s) (Btu/s) ΔTt (F) σ RPMFup

5 0.91 27.27 111 0.91 0.32

10 0.9 21.46 89 0.73 0.33

15 0.9 19.33 81 0.67 0.31

Fixed Flow

15 mil

10 mil

5 milFixed Flow

Case # Inlet Total Temperature (F)

Rotor Temperature (F)

Stator Temperature (F)

1 1000 500 Adiabatic2 1000 Adiabatic 500

3 1000 1500 Adiabatic4 1000 Adiabatic 1500

Tstator=500F

Trotor=500F

Trotor=1500F

Tstator=1500F

Trotor=500F; Tt,rel Contours

Case # Rotor Temperature (F)

Stator Temperature (F)

Average Rotor HTC (BTU/hr-ft2-F)

Average Stator HTC (BTU/hr-ft2-F)

1 500 Adiabatic 658 ---

2 Adiabatic 500 --- 1269

3 1500 Adiabatic 618 ---

4 Adiabatic 1500 --- 1275

Trotor=500F No Viscous Heating

Tstator=500F No Viscous Heating

Case # Rotor Temperature (F)

Stator Temperature (F)

Average Rotor HTC (BTU/hr-ft2-F)

Average Stator HTC (BTU/hr-ft2-F)

1a 500 Adiabatic 594 ---

2a Adiabatic 500 --- 1097

|𝑉 𝑎𝑥𝑖𝑎𝑙

𝑉 𝑠𝑤𝑖𝑟𝑙|

tfoil

Cell Size

3D Model # Cells # Nodes

1/8” Honeycomb 5.3 million 1.1 million

1/32” Honeycomb 8.4 million 1.8 million

Pressure (psia)

Total Temperature (F)

Velocity Magnitude (ft/s)

Swirl Velocity (ft/s)

RPMF

Cr (mil) Cell Size (in) (lbm/s) (Btu/s) σ ΔTt (F)

5 None; Solid 0.92 25.6 0.91 111

10 None; Solid 2.07 32.7 0.58 71

15 None; Solid 3.4 38.8 0.46 56

5 1/8” 2.25 28.1 0.38 47

5 1/32” 0.54 21.0 1.2 144

Pressure (psia)

Total Temperature (F)

Velocity Magnitude (ft/s)

Swirl Velocity (ft/s)

RPMF

Low pressure compressor stator shrouds

High pressure compressor stator shrouds

Bearing compartment buffer seals

Low turbine inter-stage seals and blade tips

High pressure turbine inter-stage seals and blade tips