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1ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Czestochowa University of Technology
Częstochowa University of Technology
Institute of Thermal Machinery
Witold Elsner , Piotr Warzecha
TRANSITION MODELING IN TURBOMACHINERY FLOWS
Papers:1. PIOTROWSKI W., ELSNER W., DROBNIAK S., Transitio n Prediction on Turbine Blade Profile with
Intermittency Transport Equation, 2010, Trans.ASME J. Turbomach. Vol.132 nr 12. ELSNER W., WARZECHA P., Modeling of rough wall bo undary layers with an intermittency transport
model, 2010, TASK QUARTERLY 14 No 33. PIOTROWSKI W., KUBACKI S., LODEFIER K., ELSNER W. , DICK E., Comparison of Two Unsteady
Intermittency Models for Bypass Transition Prediction on a Turbine Blade Profile, Flow TurbulenceCombust, 2008
2ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
1. Motivation
2. Intermittency Transport model (ITM) – basic assumptio n
3. Intermittency Transport model (ITM) – modifications t o account for a wall roughness >> (ITM R)
4. Calculations of simple flows with rough walls
5. Verification of ITM R procedure for turbine blade with wall roughness
6. Some examples of steady and unsteady calculations
7. Concluding remarks
Scope of the presentation
3ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Influence of artificial roughness
High-loaded
T106 bladeWake influence
roughness influence
Zhang, Hodson, 2004
Motivation
It is useful for the designer to have an estimate of the effects of upstream wakes and surface roughness on both heat transfer and aer odynamic performance
The study suggests that such a blade with as-cast surface roughness has a lower loss than a polished one !
VKI, 2004
4ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Motivation
(Ellering, 2001)
The blade surfaces varied significantly with time. The types of surfaces could becategorized as:
• erosion (due to prolonged use or hostile operating environments – the surface istypically characterized as having peaks above and v alleys below the mean surface level),
• deposits (deposits were typically raised above the me an surface level of the blade),
• corrosion/pitting (small canyons of measuring depths of 250 µm and widths of 5 cm).
Rough surfaces are characterized by statistical par ameters such as average centerline roughness Ra, which are correlated to the well-defin ed equivalent sandgrainroughness, k s
The other measure is nondimensional sandgrain height ντ s
s
kuK =+
5ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Transition Model based on the local formulations γ-Reθ (Menter’04)
Intermittency Transport Model (ITM) - γ-Reθ extended by inhouse correlations(Piotrowski at al., 2007)
require empirical input for transition onset detection are based on non local formulations not compatible with modern CFD approaches
An alternative
Motivation
As the roughness height progressively increases l-t t ransition moves forward on !
There are many various approaches to model transiti onal flows, but generally Transition Models
6ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Modified SSTturbulence model
Intermittency factor ( γ) transportequation
Local transition onset momentum thickness Reynolds number (Reθθθθt)
transport equation
Intermittency Transport Model - basic assumptions
Solver => Fluent => 4 User’s Defined Scalars
k transport equation
+ωωωω transport equation
+
7ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Intermittency Transport Model - basic assumptions
c
VonsetF
θRe193.2
Re1_ ⋅
=
( ) ( )
∂∂
+
∂∂+−+−=
∂∂
+∂
∂jf
t
jj
j
xxEPEP
x
U
t
γσµµ
γρργγγγγ 2211
Transport Equation for Intermittency Factor ( γγγγ)
Transition Sources[ ] 5.0
1 2 onsetlength FSFP ⋅⋅⋅⋅⋅= γργ γγγ ⋅⋅= 111 PcE e
Destruction/Relaminarization Sources
turbFP ⋅⋅Ω⋅⋅= γργ 06.02 γγγ ⋅⋅= 22 50 PE
The main difference to other intermittency models lies in the formulation of Fonset
used to trigger the intermittency production
Reθθθθc and Flength could be correlated to the local transition momentum thickness Reynolds number Reθθθθt obtained from the additional transport equation
( )1_onsetonset FfF =
where tPc F θθ eR~
Re ⋅=( )tc eR~
fRe θθ =
(Piotrowski at al., 2007)
8ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Intermittency Transport Model - missing correlations
tPc F θθ eR~
Re ⋅=( )tc eR~
fRe θθ =Flow direction
The key element of the methodology is a relation between Reθθθθc and Flength
and local momentum thickness Reynolds number Reθθθθt ?
Those relations were obtained based on numerical experiment!
0 200 400 600 800 1000 1200
525
FP
Reθθθθt max wall
T3A T3C3 T3B T3C4 T3C1 N3-60 4.0 T3C2 N3-60 0.4 T3C5
0 100 200 300 400 500 600
250
T3C1 T3C2 T3C3 T3C4 T3C5
T3A T3B
Fle
ngth
Reθθθθt max wall
9ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Introduced modifications: For turbulent boundary layer: modification of wall boundary condition for ω and for
turbulent eddy viscosity (Hellstein&Laine,1997)
Intermittency Transport Model - modifications to account for wall roughness (ITM R)
Rw Su
νω τ
2
=
[ ]25/100
25;max(/502
min
≥=
<=++
+++
SSR
SSSR
KdlaKS
KdlaKKS
);( 321
1
FFAMAX
kaT Ω
=ρµ
)regionwallnearin01F(
d
150tanh1F
3
4
23
→=
−=
ωνν
τ ss
kuK =+
10ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Introduced modifications: For turbulent boundary layer: modification of wall boundary condition for ω and for
turbulent eddy viscosity (Hellstein&Laine,1997)
For transitional boundary layer: combination of Reθt transport equation with the onset correlation of Stripf at al. (2008).
The correlation accounts for the effects of roughness height and density as well as turbulence intensity.
Rw Su
νω τ
2
=
[ ]25/100
25;max(/502
min
≥=
<=++
+++
SSR
SSSR
KdlaKS
KdlaKKS
);( 321
1
FFAMAX
kaT Ω
=ρµ
)regionwallnearin01F(
d
150tanh1F
3
4
23
→=
−=
ων
for kr/δ* > 0.01
−+=−1
Tuf
*r
twallt 01.0
kf0061.0
Re
1MINRe
δΛΘ
Θ
ƒTu= ƒ(Tu) ƒΛ= ƒ(ΛR)
-0.5 0.0 0.5 1.00
80
160
240
Re θC
s/c
smooth HP_01_20a HP_01_40b HP_01_70
Roughness height
ντ s
s
kuK =+
Intermittency Transport Model - modifications to account for wall roughness (ITM R)
11ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Calculations of simple flows with rough walls
Flat plate flow with zero gradient (Halzer,1974)
copper balls with a diameter of d0 = 1.27 mmequivalent sand roughness ks=0.62⋅⋅⋅⋅d0=0.79 mmTu=0.4%; U∞∞∞∞=27, 42, 58 m/s
0,0 0,5 1,0 1,5 2,0 2,50,003
0,004
0,005
0,006
0,007
0,008
0,009
0,010
Cf
x [m]
Exp DEM-TLV Mills&Hang ITM
0,0 0,5 1,0 1,5 2,0 2,50,003
0,004
0,005
0,006
0,007
0,008
0,009
0,010
Cf
x [m]
Exp DEM-TLV Mills&Hang ITM
R
46.2))/ln(707.0476.3( −+= sf kxc
Calculations verified against DEM-TLV (Stripf, 2007) andcorrelation by Mills and Hang (1983)
U∞∞∞∞=27m/s U∞∞∞∞=42m/s
12ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Verification of ITM procedure for turbine blade with wall roughness
High pressure turbine vane (Stripf, 2007). Type of surface roughness
Tu=3.5 %; U∞∞∞∞=29.8 m/s
][Paτ ]/[ smuτ*δks/
Test caseks [mm] [mm] Tueff [%] ΛR
HP_01_20a 22.05 0.072 39 6.21 0.157 0.98 5.7 0.46
HP_01_40b 48.13 0.129 57.9 7.57 0.102 1.0 5.4 1.26
HP_01_70 99.03 0.238 72 8.44 0.073 1.19 5.2 3.26
][−+SK
Condition to induce the response of b.l. (acc. to Zhang, Hodson’04): ks> 0.15% chord >> HP_01_40b
*δ
13ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Verification of ITM procedure for turbine blade with wall roughness
Symbols – experimental dataLines - num. results (Stripf’08)Parameter –Nusselt Number Nu c
14ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Verification of ITM procedure for turbine blade with wall roughness
Symbols – experimental dataLines - num. results (Stripf’08)Parameter –Nusselt Number Nu c
][Paτ
Symbols – experimental dataLines - own num. resultsParameter –shear stresses
-0.5 0.0 0.5 1.00
20
40
60
80
100
120
140
160
τ [P
a]
s/c
ITMR - τ
ITMR - τ
ITMR - τ
0
500
1000
1500
2000
2500
3000
3500
4000
Exp. - Nu Exp. - Nu Exp. - Nu
Nu
15ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Calculations for flat plate with pressure gradient (Lou, Hourmouziadis, 2000)
Ks+=10-50;
Tu=0.6%; U∞=9 m/s
incoming flow
separation bubble
Steady and unsteady calculations of simple flows with rough walls
16ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Ks+=10-50;
Tu=0.6%; U∞=9 m/s
incoming flow
separation bubble
Unsteady results: oscillating inflow conditions
[[[[ ]]]])ft2sin(A1U)t(U in ππππ++++====∞∞∞∞
A=13%, f=7Hz
Steady and unsteady calculations of simple flows with rough walls
Calculations for flat plate with pressure gradient (Lou, Hourmouziadis, 2000)
17ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Ks+=10-50;
Tu=0.6%; U∞=9 m/s
Influence of surface roughness
Steady and unsteady calculations of simple flows with rough walls
Calculations for flat plate with pressure gradient (Lou, Hourmouziadis, 2000)
18ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
U/U∝
Steady and unsteady calculations of simple flows with rough walls
Calculations for flat plate with pressure gradient ( Lou, Hourmouziadis, 2000)
Velocity distributions for chosen surface roughness
19ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
A
B
C
A
B
C A
B
C
ττττ/T≈≈≈≈0.20 ττττ/T≈≈≈≈0.49 ττττ/T≈≈≈≈0.61
Wake deformation and displacement towards the sucti on side
Difficult task for transition modelling
Unsteady results: instantaneous solutions Tu in=0.4% and d=4mm
Unsteady calculations of N3-60 blade
20ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
PUIM
TUCz ExperimentITM
The time traces of Hat the location SS=0.65
The same start of transition under the wake
Some differences in the extend of the turbulent wedge
The model indicates transitionin separated boundary layer
0,0 0,4 0,8 1,2 1,6 2,01,2
1,6
2,0
2,4
2,8
3,2
H
ττττ/T
exp. PUIM ITM
Unsteady results: instantaneous solutions Tu in=0.4% and d=4mm
Unsteady calculations of N3-60 blade
21ERCOFTAC Spring Festival, Gdansk, 12-13 May 2011
Concluding remarks
• the ITM procedure with proposed correlations for transit ion onset and transition length is able to predict the boundary layer development for simply as well as turbine blade test cases
• An approach to calculating roughness effect in the fr amework of transition model has been presented
• The results of simulations are consistent with experim ental data, at least qualitatively
• The methodology needs further tests and evaluations
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