L. Mangani
MaschinentechnikCC Fluidmechanik und Hydromaschinen
Hochschule LuzernTechnik& Architektur
Technikumstrasse 21, CH-6048 HorwT +41 41 349 33 11, F +41 41 349 39 60
e-mail: [email protected]
Fifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
CONJUGATE HEAT TRANSFER ANALYSIS OF
NASA C3X FILM COOLED VANE
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Presentation outline
2/21
• Background-State of the Art
• Heat Transfer in Turbo-Gas engine
• Developments for heat transfer analysis in
turbomachinery
• Present contribution
• Results and discussion
• Conclusions
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Heat Transfer in Turbo-Gas Engine
3/21
• Heat transfer analysis of turbomachinery aims at:
– Increasing turbomachinery performance:
Efficiency increases with high inlet temperature
– Extending machine working life
– Preventing catastrophical damages
• Cooling systems of:
– Rotor blades
– Stator vanes
– Combustors
– Turbine endwalls
– Stator-rotor cavities
0
' '
w f
y=
Tq = k
y
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca Mangani
OpenFOAM™ Developments
Steady-State all-Mach algorithm
• Steady-state: no artificial time derivative included
• All-Mach flows
• Pressure correction based
Compressible turbulence models
• Low-Reynolds k-ε, k-ω SST, Two-Layer, automatic wall treatment, thermal wall function, anisotropic eddy viscosity
Mangani
Phd thesis 2007
Bianchini
Master thesis 2007
Tools specific for turbomachinery blades and CHT
• Fluid Structure Interaction, Radial equilibrium, total energy equation, rotating reference system
Mangani et al.
ETC 09
ASME IGTI 2008
ASME IGTI 2009
Mangani et al.
ASME-JSME 2007
Mangani
Phd thesis 2007
4/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
OpenFOAM™ Applications & Validations
• Heat Transfer in Turbomachinery devices:
– Turbine trailing edge internal cooling ducts with ribs, pedestals and pins [IGTI 2008, ETC 2009]
• Impingement cooling system devices:
– Film & effusion cooling systems [IGTC 2007, IGTI 2009]
• Subsonic and transonic real engine rotor blades:
– Stator rotor cavity systems [IGTI 2008]
• Conjugate Heat Transfer:
– Internally cooled stator vane [ETC 2009]
– Film cooling: Experimental setup [IGTI 2009]
5/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Present contribution
6/21
• Energy equation solved in terms of temperature (static or total)
• Convective-diffusive equation degenerates into Fourier equation in case of null fluxes – same matrix for solid and fluid domain
• Mutual influence coefficients calculated imposing continuity of heat flux across the boundary
• The temperature values are calculated in both side with the generic grid interface boundary criteria
. .. .
1 11
sf
f w s w
f s
s s sf f f
f s s f
w s fw ss s sf f fs s
f s s f s f
E x tra d ia g C o e ffD ia g C o e ff
kkT T T T
y y
k T kk T k
y y y yT T T T
k k kk k ky y
y y y y y y
Developed algorithm for Conjugate Heat Transfer with Generic Grid Interface
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca Mangani
7/21
Present contribution
•Multiple implicit coupling - ghost cell mechanism
•Contribution of ghost cell calculated via cell-to-cell addressing and weighting factors αi
•Weighting factors based on face overlapping areas
– No explicit coupling between solid and fluid (too slow)
– Needed implicit coupling
Implicit coupling is guaranteed by a special boundary based on couplePatch
– Applied also to Total Energy Equation
– Redefinition of the members valueInternalCoeffs, gradientInternalCoeffs etc..
,1
f p p p i n i
i
w w
,i o i fpA A
,n i n iC C
Domain 1
Domain 2Non conformal interface
p
n1 n2
Generic grid interface boundary criteria
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
• 4-Equations turbulence model k-ε-v2-f
– Starting model [Lars Davidson et al. 2003]
Far way wall correction for v2 production term
– Added realizability constraint for the turbulent time and length scale [Lien et al., Sveningsson]
Present contribution
8/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Present contribution: Test Cases
• Flat plate thermal bounday layer
– Heat transfer coefficient distribution along the stream-wise direction
• Axial symmetric impinging jet with wall heat flux
– Nusselt number distribution along the radius
9/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Film Cooled NASA C3X Vane
• Numerical model simulates experimental setup of Hylton et al.1988.
• NASA-C3X Film and internally cooled linear cascade
– Consists of a stainless steel blade.
– Internally cooled by ten radial channels.
– Three plenums are implemented feeding:
– Two rows of pressure side filmcooling holes.
– Five rows of leading edge shower head holes.
– Two rows of suction side film cooling holes.
10/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Computational Domain
• Following the work of [Garg et al.] the computational span, is only a part of the real span
• The spanwise pitch domain is 7.5d, where d is the diameter of the holes
• Periodic boundary conditions are imposed due to shower-head injection on the ends of the computational span
Periodic
Plenums
Cooling channel
Periodic
Film cooling holes
Shower Head
11/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Computational Grid
• Main flow mesh is the main challenge– Previous work by [Garg et al. 95]
No grid for the plenum and duct holes
– Previous work by [Ledezma et al. 08]
ANSYS CFX Tetra mesh fluid-fluid GGI interface at film cooling hole exit
– Present work:
Fully Hexa structured mesh with multi block strategy, GridPRO™
No GGI fluid-fluid interface between the flow path mesh and film cooling hole exit
11’000 Blocks was used
12/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Computational Grid
• GGI solid-fluid interface between flow, radial cooling channel path and blade
13/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Pressure distribution
• No pressure profiles data from [Hylton et al. 88]
• Experimental pressure distribution only present in [Garg et al. 94]
• Running code #44155
• Turblence Models used:
– Spalart-Allmaras, k-ω SST, k-ε Two-Layer, v2-f
[Garg et al. 94] Present work
14/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Heat Transfer Coefficient
• The reference run code is #44344
• Turbulence models used:– Spalart-Allmaras, k-ω SST, k-ε Two-Layer, v2-f
• No data given for about 25% from leading edge
• No CHT simulation: Average wall temperature imposed based on exp.
HTC=Q/(Tw-T0)
15/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Heat Transfer Coefficient
• BC for the radial cooling channel based on [Ledezma et al. 08]
• Turbulence Models used:– Spalart-Allmaras, k-ω SST, k-ε Two-Layer, v2-f
• No data given for about 25% from leading edge
• CHT simulation
• Wall temperature and HTC evaluation vs. experiment
16/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Heat Transfer Coefficient
• Results analysis:
– Wall temperature profile in good agreement with experiment
– Less agreement for the HTC profile than wall temperature
Three temperature problem
Taw should be preferred as reference temperature for scaling the heat flux
HTC=Q/(Tw-T0)
CHT: Temperature CHT: HTC
NO CHT: HTC
17/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Contour Maps
• Temperature maps
• Sink effect of the radial cooling channel
18/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Results: Streamlines
• Shower head jets influence downstream film cooling
– Lift effect in film cooling in pitch-wise direction
– SH influence more the pressure side film cooling development
19/21
Lucerne University - SwitzerlandConjugate Heat Transfer Analysis Of Nasa C3x Film Cooled Vane
T&A Luca ManganiFifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
Conclusions
• Conjugate heat transfer simulation of a representative first stator cooling vane with a turbulence models assessment was simulated
• OpenFOAM has been improved to predict heat transfer phenomena in gas turbine blade cooling
• Generic Grid Interfacing and implicit conjugate heat transfer module have been developed and validated
• A realizable v2-f turbulence model was implemented
• Loading distributions were found to be in good agreement with experiments
• Good agreement with experimental measurements was also found in terms of wall temperature
20/21
L. Mangani
MaschinentechnikCC Fluidmechanik und Hydromaschinen
Hochschule LuzernTechnik& Architektur
Technikumstrasse 21, CH-6048 HorwT +41 41 349 33 11, F +41 41 349 39 60
e-mail: [email protected]
Fifth OpenFOAM Workshop, June 21-24 2010, Gothenburg, Sweden
CONJUGATE HEAT TRANSFER ANALYSIS OF
NASA C3X FILM COOLED VANE