Częstochowa University of Technology Institute of Thermal Machinery TRANSITION MODELING IN TURBOMACHINERY FLOWS

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1 Czestochowa University of Technology Częstochowa University of Technology Institute of Thermal Machinery Witold Elsner, Piotr Warzecha TRANITION MODELING IN TURBOMACHINERY FLOW Papers: 1. PIOTROWKI W., ELNER W., DROBNIAK., Transition Prediction on Turbine Blade Profile with Intermittency Transport Equation, 2010, Trans.AME J.Turbomach. Vol.132 nr 1 2. ELNER W., WARZECHA P., Modeling of rough wall boundary layers with an intermittency transport model, 2010, TAK QUARTERLY 14 No 3 3. PIOTROWKI W., KUBACKI., LODEFIER K., ELNER W., DICK E., Comparison of Two Unsteady Intermittency Models for Bypass Transition Prediction on a Turbine Blade Profile, Flow Turbulence Combust,

2 cope of the presentation 1. Motivation 2. Intermittency Transport model (ITM) basic assumption 3. Intermittency Transport model (ITM) modifications to 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. ome examples of steady and unsteady calculations 7. Concluding remarks 2

3 Motivation Influence of artificial roughness Wake influence roughness influence High-loaded T106 blade VKI, 2004 Zhang, Hodson, 2004 The study suggests that such a blade with as-cast surface roughness has a lower loss than a polished one! It is useful for the designer to have an estimate of the effects of upstream wakes and surface roughness on both heat transfer and aerodynamic performance 3

4 Motivation The blade surfaces varied significantly with time. The types of surfaces could be categorized as: erosion (due to prolonged use or hostile operating environments the surface is typically characterized as having peaks above and valleys below the mean surface level), deposits (deposits were typically raised above the mean surface level of the blade), corrosion/pitting (small canyons of measuring depths of 250 µm and widths of 5 cm). (Ellering, 2001) Rough surfaces are characterized by statistical parameters such as average centerline roughness Ra, which are correlated to the well-defined equivalent sandgrain roughness, k s The other measure is nondimensional sandgrain height K = s uτ k ν s 4

5 Motivation As the roughness height progressively increases l-t transition moves forward on! There are many various approaches to model transitional flows, but generally Transition Models require empirical input for transition onset detection are based on non local formulations not compatible with modern CFD approaches An alternative Transition Model based on the local formulations γ-re θ (Menter 04) Intermittency Transport Model (ITM) -γ-re θ extended by inhouse correlations (Piotrowski at al., 2007) 5

6 Intermittency Transport Model - basic assumptions olver => Fluent => 4 User s Defined calars k transport equation } ω transport equation Modified T turbulence model Intermittency factor (γ) transport equation Local transition onset momentum thickness Reynolds number (Re θt ) transport equation 6

7 Intermittency Transport Model - basic assumptions Transport Equation for Intermittency Factor (γ) ( ργ ) ( ρu jγ ) t Transition ources P x j = P E = F ρ γ P E γ 1 γ 1 γ 2 γ 2 [ F ] 0. 5 γ 1 2 length onset Destruction/Relaminarization ources x E j µ t µ σ f γ 1 = ce 1 Pγ 1 γ 2 = 0. ρ Ω γ F turb E γ 2 = 50 Pγ 2 γ Pγ 06 γ x j The main difference to other intermittency models lies in the formulation of F onset used to trigger the intermittency production where F = F onset _1 f ( ) _1 onset F onset ReV = Re θ c (Piotrowski at al., 2007) ( R ~ ) θ c = f eθ t θc FP θt Re and F θc length could be correlated to the local transition momentum thickness Reynolds number Re θt obtained from the additional transport equation Re Re = R ~ e 7

8 Intermittency Transport Model - missing correlations The key element of the methodology is a relation between Re θc and F length and local momentum thickness Reynolds number Re θt? Those relations were obtained based on numerical experiment! Re ( ) = f e θ c θ t R ~ Re = R ~ e θc FP θt Flow direction F P 525 T3A T3C3 T3B T3C4 T3C1 N T3C2 N T3C5 F length T3C1 T3C2 T3C3 T3C4 T3C5 250 T3A T3B Re θt max wall Re θt max wall 8

9 Intermittency Transport Model - modifications to account for wall roughness (ITM R ) Introduced modifications: For turbulent boundary layer: modification of wall boundary condition for ω and for turbulent eddy viscosity (Hellstein&Laine,1997) R R = ω u 2 τ w = R ν [ 50 / max( K ; K ] = 100 / K min 2 uτ ks K s = ν dla K < 25 dla K 25 µ T a1ρk = MAX ( A1 ; Ω F2 F3 ) 4 150ν F3 = 1 tanh 2 d ω ( F = 1 0 in near wall 3 region ) 9

10 Intermittency Transport Model - modifications to account for wall roughness (ITM R ) Introduced modifications: For turbulent boundary layer: modification of wall boundary condition for ω and for turbulent eddy viscosity (Hellstein&Laine,1997) R R = ω u 2 τ w = R ν [ 50 / max( K ; K ] = 100 / K min 2 dla K 25 For transitional boundary layer: combination of Re θt transport equation with the onset 240 correlation of tripf at al. (2008). for k r /δ * > 0.01 Re Θ uτ ks K s = ν dla K < 25 1 kr t = MIN f Λ * ReΘ twall δ The correlation accounts for the effects of roughness height and density as well as turbulence intensity. µ ƒ Tu = ƒ(tu) ƒ Λ = ƒ(λ R ) T a1ρk = MAX ( A1 ; Ω F2 F3 ) 4 150ν F3 = 1 tanh 2 d ω ( F = 1 0 in near wall 3 ftu 1 Re θc region ) smooth HP_01_20a HP_01_40b HP_01_70 Roughness height s/c 10

11 Calculations of simple flows with rough walls Flat plate flow with zero gradient (Halzer,1974) copper balls with a diameter of d 0 = 1.27 mm equivalent sand roughness k s =0.62 d 0 =0.79 mm Tu=0.4%; U =27, 42, 58 m/s Calculations verified against DEM-TLV (tripf, 2007) and correlation by Mills and Hang (1983) c f = ( ln( x / ks )) ,010 0,009 0,008 U =27m/s Exp DEM-TLV Mills&Hang ITM 0,010 0,009 0,008 U =42m/s Exp DEM-TLV Mills&Hang ITM R 0,007 0,007 C f 0,006 C f 0,006 0,005 0,005 0,004 0,004 0,003 0,0 0,5 1,0 1,5 2,0 2,5 x [m] 0,003 0,0 0,5 1,0 1,5 2,0 2,5 x [m] 11

12 Verification of ITM procedure for turbine blade with wall roughness High pressure turbine vane (tripf, 2007). Type of surface roughness Tu=3.5 %; U =29.8 m/s Test case K [ ] δ * u * τ k s / k s [mm] τ [Pa] [ m / s] [mm] Tu eff [%] Λ R δ HP_01_20a HP_01_40b HP_01_ Condition to induce the response of b.l. (acc. to Zhang, Hodson 04): k s > 0.15% chord >> HP_01_40b 12

13 Verification of ITM procedure for turbine blade with wall roughness ymbols experimental data Lines - num. results (tripf 08) Parameter Nusselt Number Nu c 13

14 Verification of ITM procedure for turbine blade with wall roughness ymbols experimental data Lines - num. results (tripf 08) Parameter Nusselt Number Nu c ITM R - τ ITM R - τ ITM R - τ Exp. - Nu Exp. - Nu Exp. - Nu ymbols experimental data Lines - own num. results Parameter shear stresses τ [Pa] τ [Pa] Nu s/c 0 14

15 teady and unsteady calculations of simple flows with rough walls Calculations for flat plate with pressure gradient (Lou, Hourmouziadis, 2000) ncoming flow separation bubble K s =10-50; Tu=0.6%; U =9 m/s 15

16 teady and unsteady calculations of simple flows with rough walls Calculations for flat plate with pressure gradient (Lou, Hourmouziadis, 2000) incoming flow separation bubble K s =10-50; Tu=0.6%; U =9 m/s Unsteady results: oscillating inflow conditions [ 1 A sin( 2 ft )] U ( t ) = U π in A=13%, f=7hz 16

17 teady and unsteady calculations of simple flows with rough walls Calculations for flat plate with pressure gradient (Lou, Hourmouziadis, 2000) Influence of surface roughness K s =10-50; Tu=0.6%; U =9 m/s 17

18 teady 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 U/U 18

19 Unsteady calculations of N3-60 blade Unsteady results: instantaneous solutions Tu in =0.4% and d=4mm τ/t 0.20 τ/t 0.49 τ/t 0.61 C A A C A C B B B Wake deformation and displacement towards the suction side Difficult task for transition modelling 19

20 Unsteady calculations of N3-60 blade Unsteady results: instantaneous solutions Tu in =0.4% and d=4mm PUIM 3,2 2,8 The time traces of H at the location =0.65 exp. PUIM ITM 2,4 H 2,0 1,6 ITM TUCz Experiment 1,2 0,0 0,4 0,8 1,2 1,6 2,0 τ/t The same start of transition under the wake ome differences in the extend of the turbulent wedge The model indicates transition in separated boundary layer 20

21 Concluding remarks the ITM procedure with proposed correlations for transition 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 framework of transition model has been presented The results of simulations are consistent with experimental data, at least qualitatively The methodology needs further tests and evaluations 21