Cz ęstochowa University of Technology Institute of …...4. Calculations of simple flows with rough...

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


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


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


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 =+


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


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

+


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)


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


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 =+


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)


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


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



Symbols – experimental dataLines - num. results (Stripf’08)Parameter –Nusselt Number Nu c



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


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


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




Ks+=10-50;

Tu=0.6%; U∞=9 m/s

Influence of surface roughness




U/U∝


Calculations for flat plate with pressure gradient ( Lou, Hourmouziadis, 2000)

Velocity distributions for chosen surface roughness


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


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


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

Cz ęstochowa University of Technology Institute of …...4. Calculations of simple flows with rough...

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