Flow Simulator is an integrated flow, heat transfer, and combustion design software that enables multidisciplinary engineering simulations
to optimize machine design.
The Labyrinth Seal Tooth by Tooth (TbT) element is typically used to model leakage
flow through labyrinth seals found in rotating machinery (gas turbines). The flow
rate, swirl, and fluid temperature rise, due to windage, are calculated based on the
seal geometry and fluid conditions at the inlet and exit of the seal.
This element's main feature is that it performs a tooth by tooth marching along the
flow direction to calculate the pressure distribution inside the seal. It also takes
into account local (in-pocket) changes in fluid properties due to changes in
pressure and temperature, thus providing a more detailed modeling of the labyrinth
seals.
The seal clearance is the main dimension that controls the flow rate passing through
the seal. It is the distance between the tip of the seal tooth and the opposite
surface, which is usually honeycomb. The seal clearance changes during gas turbine
operations since the parts move due to temperature and rotation. With the labyrinth
seal TbT element, you can input individual seal clearances for every tooth in the
seal and study their impact on leakage.
The element is typically used for compressible flow, but Flow Simulatoralso uses this element with incompressible or
compressible fluid.
Create a Lab Seal TbT
Go to Compressible Gas Elements > Seals to select the Lab Seal Tooth by Tooth element. Figure 1.
The figure below shows the geometric inputs. The seal clearance and seal geometry are
the major inputs. Besides this, you must enter honeycomb information. Figure 2.
A labyrinth seal typically has the seal teeth rotating. This requires you to enter an
RPM reference condition in the Solution Panel. Figure 3.
Labyrinth TbT Seal Inputs
The inputs for the labyrinth TbT seal are listed below. See the image in the user
interface to understand the geometric variables.
Labyrinth Seal TbT Element Input
Variables
Index
UIName (*.flo label)
Description
1
Seal Clearance (CL)
Seal clearance.
This can be averaged or tooth by
tooth).
2
Nominal Seal Radius or Inlet Radius (RAD)
Nominal seal radius for a straight seal or the inlet radius for a
stepped seal.
It can be a constant for the entire seal or vary
tooth by tooth.
The constant value provided is assigned to
every tooth in the seal.
Tooth by tooth radius values can
be provided in a table. The application writes the flag "-999"
to the *.flo file if table entries exist.
Every pocket is identified as either straight or stepped based
on the individual tooth radius.
3
Number of Teeth (NT)
Number of teeth in the seal.
4
Seal Axial Pitch (PT)
Seal axial pitch.
It can be a constant for the entire seal or
vary pocket by pocket.
The constant value provided is
assigned to every tooth in the seal.
Pocket by pocket
pitch values can be provided in a table. The application writes
the flag "-999" to the *.flo file if table
entries are present.
5
Tooth Tip Width (WT)
Axial width of seal tooth tip.
It can be a constant for the
entire seal or vary tooth by tooth.
The constant value
provided is assigned to every tooth in the seal.
Tooth by
tooth width values can be provided in a table. The application
writes the flag "-999" to the *.flo file if
table entries exist.
6
Seal Tooth Height (HT)
Seal tooth height.
This variable influence only the windage
calculated for a rotating seal.
It can be a constant for
the entire seal or vary tooth by tooth.
The constant value
provided is assigned to every tooth in the seal.
Tooth by
tooth height values can be provided in a table. The application
writes the flag "-999" to the *.flo file if
table entries exist.
7
Wedge Angle (AN)
Angle between sides of a seal tooth.
It can be a constant for
the entire seal or vary tooth by tooth.
The constant value
provided is assigned to every tooth in the seal.
Tooth by
tooth wedge angle values can be provided in a table. The
application writes the flag "-999" to *.flo
file if table entries exist.
8
Rotor Surf. Rot. Speed (RPMSELR)
Rotational speed pointer of seal rotor surface.
0.0: Specifies
a stationary element.
1.0: Points to general data
ELERPM(1).
2.0: Points to general data
ELERPM(2).
3.0: Points to general data
ELERPM(3).
Index
UIName (*.flo label)
Description
9
Slant Angle (SL)
Angle the tooth centerline makes with the radial
direction.
Positive angle if tooth is angled into the flow and
negative angle if slanted away from the flow.
It can be a
constant for the entire seal or vary tooth by tooth.
The
constant value provided is assigned to every tooth in the seal.
Tooth by tooth slant angle values can be provided in a
table. The application writes the flag "-999" to the
*.flo file if table entries
exist.
10
Land Surf. Rot. Speed (RPMSELL)
Rotational speed pointer of seal land surface. 0.0: Specifies a
stationary element.
1.0: Points to general data
ELERPM(1).
2.0: Points to general data
ELERPM(2).
3.0: Points to general data
ELERPM(3).
11
BASE_EQUATION
BASE EQUATION is the user dependent choice for pressure
calculation formula in tooth by tooth marching:
0:
Saikishan-Morrison Base Equation.
1: Neumann Base
Equation.
2: Compressible Flow Function.
The details
of these base equations are provided in the Theory
Section.
12
Portion of Ustrm Cham. Dyn. Head Lost (DQ_IN)
Inlet dynamic head loss.
If DQIN ≥ 0 and the upstream chamber
has a positive component of relative velocity aligned with the
axis of the tube, the driving pressure is reduced by the
equation.
The default value of -1.0 is interpreted by
Flow Simulator as a flag to use
only static pressure if the upstream chamber is an inertial
chamber and a DQ_IN of 0 if the upstream chamber is a momentum
chamber.
13
Element Alignment (AXIS_DIR)
Direction of positive flow through the seal.
If AXIS_DIR ≥ 0,
the axial direction for positive flow is assumed to be the
direction defined by THETA = 0, PHI = 0.
If AXIS_DIR <
0, the axial direction for positive flow is assumed to be the
direction defined by THETA = 180, PHI = 0.
14
Laminar-Transitional Reynolds Number (RE_LAM)
Reynolds number below which pocket swirl flow is assumed to be
laminar. Flow at Reynolds numbers between RE_LAM and RE_TURB are
assumed to be in the transition region. Defaults to 2070 for
Labyrinth Seal.
15
Turbulent-Transitional Reynolds Number (RE_TURB)
Reynolds number above which pocket swirl flow is assumed to be
turbulent. Flow at Reynolds numbers between RE_LAM and RE_TURB are
assumed to be in the transition region. Defaults to 2530 for
Labyrinth Seal.
16
Clearance Factor Method (KFAC_METHOD)
0: Bell-Bergelin curve for CD of annular orifice.
1:
Bell-Bergelin Advanced, Table Lookup for multiple Re
(Default).
-1: User supplies their own KFAC, either
constant value or calculated using controllers. See KFAC details
below.
17
Kinetic Energy Carryover Method (KE_METHOD)
0: Vermes 1961 Kinetic Energy Carryover curve.
1: Morrison
Kinetic Energy Carryover curve.
2: Minimum of Vermes and
Morrison curves (default, matches NASA Tipton data
best).
3: Saikishan-Morrison.
4: Neumann Kinetic
Energy Carryover curve.
5: Stepped Kinetic Energy
Carryover.
6: Auto.
-1: User-supplied KEMULT, either
constant value or calculated using controllers. See KEMULT
details below.
Index
UIName (*.flo label)
Description
18
Honeycomb Method (HC_METHOD)
1: Auto, Tipton/Schramm Method (Default) – Tipton for Straight
Seals, Schramm for Stepped Seals.
2: Stocker curve for straight
seals.
3: Schramm curve for stepped seals.
4: Tipton
table lookup for straight seals.
-1: User-supplied HCMULT,
either constant value or calculated using controllers. See
HCMULT details below.
19
Slanted Teeth Method (SL_METHOD)
1:Curve fitted to NASA Tipton data.
-1:User supplies their own
SLMULT, either constant value or calculated using controllers.
See SLMULT details below.
2: Auto.
3: Stepped
slanted tooth factor.
20
Honeycomb Size (HCSIZE)
Honeycomb Size – Standard choices are 1/32”, 1/16”, and 1/8”.
However, it is possible to input a custom honeycomb size. Solver
units are inches.
21
Clearance Factor(KFAC)
Clearance factor is the Discharge Coefficient of a single annular
orifice or tooth gap. The value is between 0 and 1, usually between
0.6 and 0.9. See Vermes 1961 or Bell-Bergelin.
22
Kinetic Energy Carryover Factor (KEMULT)
Kinetic Energy Carryover Factor is a value from 1 to about 2.4.
It accounts for axial momentum and energy that is retained as flow
goes around a tooth. A value of 1 means the tooth blocked all
kinetic energy. A value higher than 1 implies some kinetic energy
was carried over. Please see Vermes 1961, Morrison, and Alexiou for
details.
23
Honeycomb Flow Multiplier (HCMULT)
Honeycomb Flow Knockdown Factor is a multiplier that is applied
to non-honeycomb leakage flow to calculate the corrected leakage
flow with a honeycomb stator. Typical values are from 0.8 to 1.2.
Values less than one imply the honeycomb is supplying an additional
source of resistance, which is often true for straight seals. Values
greater than one imply that the honeycomb is creating a new path for
leakage flow, which is often true for stepped seals. Please see
Stocker and Schramm for additional details.
24
Slant Flow Multiplier (SLMULT)
Slanted Teeth Flow Knockdown Factor is a multiplier that is
applied to straight-tooth leakage flow to calculate the corrected
leakage flow with slanted teeth. Typical values are from 0.85 to
1.1. Three-dimension flows in seal pockets are complex, and it is
difficult to explain why the factor is sometimes less than one and
sometimes greater.
25
Swirl Carryover Factor per Tooth (ETATOOTH)
Swirl Carryover per Tooth is the fraction of tangential fluid
velocity(relative to the stator) that passes each tooth and enters
the next pocket. This is a calibration parameter that helps to match
the correct swirl and windage heating. It is especially useful for
stepped honeycomb seals where the air passes over the tooth and
immediately impinges on the honeycomb step.
It can be a constant
for the entire seal or vary tooth by tooth.
The constant
value provided is assigned to every tooth in the seal.
Tooth by tooth swirl carryover values can be provided in
a table. The application writes tbe flag "-999" to the
*.flo file if table entries
exist.
Index
UIName (*.flo label)
Description
26
Friction and Windage – Rotor:
Friction Relation
(FRIC_REL_R)
0: Swamee-Jain Approximation to Colebrook-White-Moody Friction
(Default).
1: MacGreehan-Ko Rotating Cavity/Pocket
Friction.
5: Sultanian.
-1: User-supplied
FRICF_STATOR, either constant value or calculated using
controllers. See FRICF_STATOR details below.
27
Rotor Sandgrain Roughness (ROUGH_ROTOR)
Roughness of the rotor surface. It is assumed to be a sand-grain
type roughness, which is consistent with
Colebrook-White-Moody.
28
Friction and Windage – Rotor:
Friction Multiplier
(F_MULT_ROTOR)
Friction multiplier on Rotor is used if you want the friction
curve to follow that same basic trend as Swamee-Jain or
MacGreehan-Ko but your custom friction curve differs by a
multiplication factor.
29
Friction and Windage – Rotor:
Friction Coefficient
(FRICF_ROTOR)
Fanning Friction Coefficient on Rotor can be supplied as a
constant value, or it can be calculated using a controller.
30
Friction and Windage – Rotor:
Total Rotor Surface Area
(ASR)
Generally, ASR=0 and the rotor friction area is calculated from
other geometric inputs such as tooth height, spacing, wedge angle,
slant angle, etc. If you enter a non-zero value, your input
overrides the calculated area. Solver units are sq. in.
31
Friction and Windage – Stator:
Friction Relation
(FRIC_REL_S)
0: Swamee-Jain Approximation to Colebrook-White-Moody Friction
(Default).
1: MacGreehan-Ko Rotating Cavity/Pocket
Friction.
5: Sultanian.
-1: User-supplied
FRICF_STATOR, either constant value or calculated using
controllers. See FRICF_STATOR details below.
32
Stator Sandgrain Roughness (ROUGH_STATOR)
Roughness of the stator surface. It is assumed to be a sand-grain
type roughness, which is consistent with Colebrook-White-Moody.
Estimating a suitable roughness for a honeycomb surface is one
challenge, but no advice can be given here.
33
Friction and Windage – Stator:
Friction Multiplier
(F_MULT_STATOR)
Friction multiplier on Stator is used if you want the friction
curve to follow that same basic trend as Swamee-Jain or
MacGreehan-Ko but your custom friction curve differs by a
multiplication factor.
Index
UIName (*.flo label)
Description
34
Friction and Windage – Stator:
Friction Coefficient
(FRICF_STATOR)
Fanning Friction Coefficient on Stator can be supplied as a
constant value, or it can be calculated using a controller.
35
Friction and Windage – Stator:
Total Land Surface Area
(ASS)
Generally, ASR=0 and the rotor friction area is calculated from
other geometric inputs such as tooth height, spacing, wedge angle,
slant angle, etc. If you enter a non-zero value, your input will
override the calculated area. This is especially useful for stepped
seals, since the current lab Seal element does not have a step
height input. However, it could be better to ignore the step height
and rely on ETATOOTH – please see above. Solver units are sq.
in.
36
(CL_TABLE)
Number of entries in the CL_VALUES table.
37
Groove Depth (GRV_DEPTH)
Depth of the groove (GD) in the honeycomb (or other land
material).
38
Groove Width (GRV_WIDTH)
Width of the groove (GW) in the honeycomb (or other land
material).
39
Groove Tooth Axial Position (GRV_AX)
Location of the tooth in the groove. 0 = tooth in the center of
the groove.
-1 = tooth hitting left edge of groove1 = tooth
hitting right edge of groove.
Not used in built-in methods
yet but can be useful for controller or custom groove loss
correlations.
40
Groove Multiplier (GRV_MULT)
Groove Flow Knockdown Factor is a multiplier that is applied to a
no-groove leakage flow to calculate the leakage flow with a groove.
Can be greater or less than 1. If the tooth is outside the groove,
GRV_MULT should be > 1 indicating more flow through the
seal.
41
Groove Method (GRV_METHOD)
Method to use to calculate the groove effect.
-1= User
Specified GRV_MULT 1 = Zimmerman Method.
42
User Multiplier (USRMULT)
A user supplied flow knockdown factor. Can be used with a
controller for general purpose effects if needed.
Index
UIName (*.flo label)
Description
43
Exit Radius (RAD_EX)
The exit radius for a stepped seal.
44
Pocket Heat Transfer Option – Rotor (HTOPT_ROTOR)
The heat transfer option to use on the rotor surface in each
pocket.
0: No Heat Transfer (default)
1: Heat Transfer
ON with a constant HTC
2: Heat Transfer ON with a
constant Q
>1000: Heat Transfer ON with a custom HTC
correlation (ROTATING_CAVITY_NU)
45
Pocket Heat Transfer Option – Stator (HTOPT_STATOR)
The heat transfer option to use on the stator surface in each
pocket. Same options as rotor surface of pocket.
Table1
Individual Tooth Clearances (CL_VALUES)
There is an option to provide an array of individual clearance
values, one for each seal tooth.
HTC or Q Tables
(ROTOR_PKT_HTC_OR_Q), (STATOR_PKT_HTC_OR_Q)
A constant Heat Transfer Coefficient (HTC), BTU/(hr ft^2 F) or
constant heat addition (Btu/sec).
Separate tables for Rotor and
Stator. One entry for each pocket.
The table only exists
when needed for the heat transfer option. No table if there is
no heat transfer.
Wall Temperature Tables
(ROTOR_PKT_TWALL), (STATOR_PKT TWALL)
The wall temperature to us pocket heat transfer (deg
F).
Separate tables for Rotor and Stator. One entry for each
pocket.
The table only exists when needed for the heat
transfer option. No table if there is no heat
transfer.
Table 2
Individual Tooth Swirl Carryover
An array of the individual tooth swirl carryover, one for each
seal tooth.
Table 3
Individual Tooth Radius
An array of the individual tooth radius, one for each
tooth.
Table 4
Individual Tooth Width
An array of the individual tooth width, one for each
tooth.
Table 5
Individual Pocket Pitch
An array of the individual pocket pitch, one for each
pocket.
Table 6
Individual Tooth Height
An array of the individual tooth height, one for each
tooth.
Table 7
Individual Tooth Slant Angle
An array of the individual tooth slant angle, one for each
tooth.
Table 8
Individual Tooth Wedge Angle
An array of the individual tooth wedge angle, one for each
tooth.
Labyrinth Seal TbT Element Theory
Flow Rate Calculation Base Equations.
0. The Saikishan Morrison Base Equation:
The Saikishan Morrison equation
(Ref 2) used to calculate the flow rate across the nth tooth
is defined as:(1)
Where,
= Mass flow rate across the
nth tooth.
= Discharge coefficient across the
nth tooth.
= Geometrical flow area through the
clearance.
= Expansion factor accounting for fluid
expansion after coming out of the tooth gap.
= Density of the fluid at the upstream
pocket of the tooth.
= Pressure at the upstream pocket of the
tooth.
= Pressure at the downstream pocket of
the tooth.
is the geometrical flow
area:(2)
The expansion factor as per Saikishan Morrison
is given as:
For compressible flow:(3)
For incompressible flow:(4)
The discharge coefficient for , for the nth tooth, is
written as:(5)
These factors are described in the section Leakage
Flow Factors. Calculating these factors for any nth tooth
incorporates the corresponding tooth geometry.
1. The Neumann Base Equation:
The Neumann Base equation (Ref 10) used to
calculate the flow rate across the nth tooth is defined
as:(6)
Where,
= Mass flow rate across the
nth tooth.
= Discharge coefficient across the
nth tooth.
= Geometrical flow area through the
clearance.
= Temperature of fluid at the upstream
pocket of the tooth.
= Gas constant of fluid at the upstream
pocket of the tooth.
= Pressure at the upstream pocket of the
tooth.
= Pressure at the downstream pocket of
the tooth.
2. The Compressible Flow Function:
The Compressible Flow function used to
calculate the flow rate across the nth tooth is defined
as:(7)
Where, is the total flow parameter,
and,(8)
(9)
Where,
= Temperature of the fluid at the
upstream pocket of the tooth.
= Discharge coefficient across the
nth tooth.
= Geometrical Flow area through the
clearance.
= Gas constant of the fluid at the
upstream pocket of the tooth.
= Specific heat ratio of the fluid at
the upstream pocket of the tooth.
= Total pressure at the upstream pocket
of the tooth.
= Gravitational constant.
Leakage Flow Factors
KEMULT
KEMULT is the kinetic energy carryover factor. There are eight options
for the kinetic energy carryover.
0. Vermes
(10)
1. Morrison (Ref 2, eq 5)
(11)
2. Vermes-Morrison
Use the minimum alpha from 1 and
2.
3. SAIKISHAN_MORRISON (Ref 2, eq 7).
This method uses the flow
Re to calculate the KEMULT. Since the flow Re depends on the
flow through the seal, this method uses the flow from the
previous iteration.(12)
4. Neumann (Ref 10)
(13)
(14)
5. Stepped Kinetic Energy Carryover
KEMULT = 1.0
6. Auto
The Auto method uses the recommended Neumann Kinetic
Energy carryover for straight pockets, and Stepped Kinetic
Energy Carryover for stepped pockets. This is the default
option.
Note: For the first tooth
of a stepped seal, there is no pocket upstream, hence
the Auto method applies the recommended straight
correlation for the first tooth.
7. User-specified KEMULT
You can enter your own Kinetic Energy
Carryover. The application writes a flag (-1) when you input
a Kinetic Energy Carryover.
KFAC
KFAC, or clearance factor, is equivalent to the Vermes K variable that
accounts for the effect of the ratio of seal tooth tip width to the seal
clearance. There are five options:
0. Bell-Bergelin (Ref 3)
The value used approximates the data
shown in Figure 2 of the Vermes paper (also from
Bell-Bergelin, ref. 3) and is given by the
equation:(15)
1. Bell-Bergelin Advanced. Uses a table of KFAC vs WT/CL for
several Reynolds numbers from Ref. 3. Bilinear interpolation
used to find KFAC. The Bell-Bergelin equation shown above
matches the Re = 10,000 curve. The Advanced option is more
accurate for Re < 10,000. Re is the annular orifice (tooth
gap) Reynolds number and can be found in the
*.res file. Figure 4.
2. Saikishan Morrison KFAC
It uses the Clearance factor from
the Saikishan Morrison paper (Ref 2). The factor described
as the CD for first tooth is treated as KFAC here. Since the
Saikishan Morrison formulation corresponds to straight and
smooth seals, the CD for the first tooth has only two
components, KEMULT and KFAC. KEMULT = 1.0 for the first
tooth. As per Saikishan Morrison, the KFAC is written
as:
For the first tooth,(16)
For subsequent
teeth,(17)
3. Neumann KFAC
Neumann KFAC is the clearance factor as
described in the Ref 10. It takes into account the pressure
ratio at upstream and downstream of the tooth. Neumann KFAC
is given by following equation:(18)
(19)
Where,
is the specific heat ratio
at the upstream pockets.
SLMULT
Auto.
The Auto method uses the recommended NASA Tipton Fitted
Curve for straight teeth pockets, and the Stepped Slanted
Tooth Factor for stepped teeth pockets. This is the default
option.
Note: For the first tooth
of a stepped seal, there is no pocket upstream, hence
the Auto method applies the recommended straight
correlation for the first tooth.
Stepped Slanted Tooth Factor.
SLMULT = 1.0.
User Specified.
You can enter your own Slanted Tooth Factor.
The application writes a flag (-1) when you input a Slanted
Tooth Factor.
HCMULT
The honeycomb flow multiplier has five options.
Auto.
The Auto method uses the recommended Tipton Straight HC
curve for straight teeth pockets, and the Schramm Stepped
for stepped teeth pockets. This is the default.
Note: For the first tooth of a stepped
seal, there is no pocket upstream, hence the Auto method
applies the recommended straight correlation for the
first tooth.
Schramm Stepped Seal (Ref 4, Fig 12).
(20)
Stocker Straight (Ref 4, Fig 12).
(21)
Tipton Straight (Ref 7, Fig 26).
An HCMULT is calculated using
a bilinear interpolation of the curves shown here. Figure 5.
User Specified.
GVRMULT
The flow knockdown factor due to a groove in the honeycomb.
There are two options:
-1: User Specified
1: Based on Zimmerman (Fig. 7 in Ref 8).
Figure 6.
The groove width/groove depth (GW/GD) is limited in the
solver to between 1 and 10. The (groove depth +
clearance)/clearance ((GD+CL)/CL) is limited in the solver
to between 1 and 3. Valid for Re>5000, GW/GD>2.5, but
correlation uses GW/GD=1 curve also.
Choked Flow Calculation
For compressible gases, the calculated seal mass flow is compared to the mass flow
for choked flow through the last tooth. If the choked flow through the last tooth is
less than the calculated seal mass flow, the choked flow is used. The equations for
the choked flow calculation are:(22)
(23)
Where,
This accounts for the additional flow area if the honeycomb cell allows the seal to
flow more than a smooth surface (HCMULT > 1 if clearance is small and HC size is
large).
Calculating Seal Pocket Pressure
Use Saikishan Morrison Base Equation, rearranging Equation 1:(24)
Use Neumann base equation, rearranging Equation 6:(25)
Use Compressible Flow Function
For the Compressible Flow function, the
mass flow rate across the first tooth is used to calculate the pressure
ratio across the subsequent teeth (using Equation 7). At the last tooth, however, the pressure ratio is known after the
tooth by tooth marching is complete for that iteration, therefore the
pressure ratio is used in Equation 7 and the mass flow across last tooth is determined. At convergence,
the relative difference between the mass flow across the first tooth and
last tooth becomes smaller and smaller.
Tooth by Tooth Marching Algorithm Figure 7.
Calculation of Seal Pocket Swirl
Lab Seal Geometry Calculations Figure 8.
Seal with Individual Tooth Characteristics Figure 9.
Where,(26) (27)
(28)
(29)
Use the following to calculate the seal “rotor” surface area:(30)
(31)
(32)
(33)
(34)
Surface area per pocket: (35)
Surface area for all pockets: (36)
The labyrinth seal “stator” surface area is calculated using the
following:(37)
Surface area per pocket: (38)
Where,(39)
Surface area for all pockets: (40)
Sultanian Friction (ref 9)
Rotor Surface: (41)
Stator Surface: (42)
Calculation of Seal Windage Temperature Rise
Seal Pocket Heat Transfer
In addition to the fluid temperature change due to windage, the fluid temperature can
also change due to the fluid convection to the pocket surface. The convection Q is
applied at each pocket. The typical convection heat transfer equation is
used:(43)
HTC = heat transfer coefficient that is
user-defined or calculated by the correlation.
Area = pocket surface area.
Tsurf = the surface temperature
(user-defined).
Tfluid rel = the relative fluid total
temperature, adjusted for fluid and surface rotation.
Labyrinth Seal TbT Element Output
Output is saved to the *.res file. Use the Output
Control panel to control the output units. Figure 10.
Name
Description
Units ENG,SI
SEAL_POSITIVE_FLOW_DIRECTION
The positive flow direction through the seal.
1: Axial
direction for the positive flow is assumed to be the direction
defined by THETA = 0, PHI = 0.
-1: Axial direction for
positive flow is assumed to be the direction defined by THETA =
180, PHI = 0.
PRESSURE
Static pressure in every pocket in the seal is output in the form
of a table in a *.res file.
Psi, MPa
TEMPERATURE
Total temperature in every pocket in the seal is output in the
form of a table in a *.resfile.
0F, K
RHO
Density in every pocket in the seal is output in the form of a
table in a *.res file.
lbm/ft3, kg/m3
TOOTH
Seal tooth type (STRAIGHT or SLANT).
None
CL
Seal clearance for every tooth is provided in the form of a table
in a *.res file.
Inch,mm
AREA
Seal geometric flow area for every tooth is provided in the form
of a table in a *.res file.
Inch2, mm2
RAD
Nominal seal radius. Distance from engine centerline to the seal
tooth tip.
Inch,m
WT
Axial width of seal tooth tip.
Inch,mm
PT
Seal axial pitch.
Inch,mm
NO_TEETH
Number of seal teeth.
(number)
HT
Seal tooth height.
This variable influences only the windage
calculated for a rotating seal.
Inch,mm
TYPE
Pocket type, either STRAIGHT or STEPPED as identified by the
solver.
-
K/E_RPM
Rotational speed of the rotor surface.
rev/min
LAND_RPM
Rotational speed of the land surface. Also referred to as
“stator”.
rev/min
DT
Absolute total temperature rise across the seal.
degF,k
TEX
Absolute total temperature at the exit of the seal.
degF,k
XKABS_IN
Swirl ratio entering the seal. Swirl in the absolute frame of
reference.
None
XKABS_OUT
Swirl ratio exiting the seal. Swirl in the absolute frame of
reference.
None
ASR_TOTAL
Rotor surface area.
In^2,m^2
ASS_TOTAL
Stator(aka Land) surface area.
In^2,m^2
DH_POCKET
Hydraulic diameter of the seal pockets. Assume each pocket is
same.
Inch,mm
KFAC
Calculated clearance factor.
None
KEMULT
Calculated kinetic energy carryover factor.
None
HCMULT
Calculated Honeycomb Flow knockdown factor.
None
SLMULT
Calculated slanted tooth flow knockdown factor.
None
Name
Description
Units ENG,SI
Expansion Factor
Expansion factor across every tooth for compressible
flows.
-
XKrel
Swirl ratio in each pocket. Swirl relative to the land, which is
usually stationary. If the land is stationary XKrel is in the
absolute frame of reference.
None
WIND.
Windage in each pocket.
BTU/s,W
ReynR
Reynolds number relative to the rotor surface.
None
FricFannR
Fanning Friction factor on the rotor surface.
None
ReynS
Reynolds number relative to the stator surface.
None
FricFannS
Fanning Friction factor on the stator surface.
None
MACH NO.
The Mach number of the flow in every tooth gap. Based on physical
area times HCMULT if greater than 1.0.
None
Re
Reynolds number of the flow in the tooth gap.
None
Labyrinth Seal TbT Validation
The labyrinth seal tooth by tooth results were compared to results from Tipton et al.
(ref 7).
There are 705 labyrinth seal cases with a wide range of geometries and operating
conditions.
Tooth Tip Radius (in): 2.0, 2.26, 3.0, 3.36,
5.0, 7.63
Clearance (in): 0.004, to 0.061
Geometry Ratios
Pitch/Clearance: 4 to 156
Width/Clearance: 0.25 to
62.75
Width/Pitch: 0.031 to 0.67
Width/Honeycomb Size:
0.08 to 0.48
Clearance/Honeycomb Size: 0.04 to 0.65
Operating Conditions
Pressure Ratio: 1.04 to 6.8
Rotor Speed (RPM): 0, 13000, 20000, 30000
Element Leakage Flow Factor Settings
Figure 11.
Figure 12.
Statistics of the comparison based on:(44)
Avg
Mean
Max
Min
Std_dev
Count
Within +/10%
Within +/20%
10%
6%
59%
-30%
14%
705
459
632
459 out of 705 test cases match within 10%.
Labyrinth Seal Tooth by Tooth References
Vermes, Geza, “A Fluid Mechanics Approach to the Labyrinth Seal Leakage
Problem,” Transactions of the ASME, Journal of Engineering for Power, April
1961, pp161-169.
Suryanarayanan, S & Morrison G.L “Labyrinth Seal Discharge Coefficient
for Rectangular Cavities”, ASME 2009.
K.J. Bell & O.P. Bergelin, "Flow Through Annular Orifices", ASME
1957.
Schramm V., Willenborg K., Kim S., Wittig S., “Influence of a Honeycomb
Facing on the Flow Through a Stepped Labyrinth Seal” ASME 2002.
Stocker,H. L., 1978, ‘‘Determining and Improving Labyrinth Seal Performance
in Current and Advanced High Performance Gas Turbines,’’ AGARD CP273.
McGreehan W.F., & Ko S.H.,1989, “Power Dissipation in Smooth and
Honeycomb Labyrinth Seals” ASME Paper No 89-FT-220.
Tipton D.L., Scott T.E, Vogel R.E., 1986, “Labyrinth Seal Analysis. Volume
3. Analytical and Experimental Development of a Design Model for Labyrinth
Seals” AFWAL-TR-85-2103.
Zimmermann H., Wolff K. H., “Air System Correlations Part 1: Labyrinth
Seals” ASME 98-GT-206.
Bijay K. Sultanian, “Gas Turbines – Internal Flow Systems Modeling”,
Cambridge Aerospace series, 2018, ISBN 978-1-107-17009-4.
Eldin, A. M. G., “Leakage and Rotordynamic Effects of Pocket Damper Seals
and See-Through Labyrinth Seals”, Texas A&M Dissertation, 2007.