Turbine Aero-Heat Transfer Studies in Rotating Research Facilities
Multi-scale Method Development for Turbine Heat Transfer ...
Transcript of Multi-scale Method Development for Turbine Heat Transfer ...
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Multi-scale Method Development for Turbine Heat Transfer and Aerodynamics
(MUSAF II, Toulouse, Sept 18-20, 2013)
L. He
Rolls-Royce/Royal Academy of Engineering Professor
of Computational Aerothermal Engineering,
Department of Engineering Science, Oxford University
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Background Problem Statement
- scale disparities in turbine aero-thermal problems
Unsteady Conjugate Heat Transfer (in time)
- fluid-solid interfacing (for periodic unsteadiness & LES)
‘Block-spectral’ Method (in space)
- resolving micro scales (film cooling, surface roughness)
OUTLINE
High Pressure Turbine - ‘Core of the Heart’
High Pressure, High Speed
- Pressure ratio ~ 40+
- HP Turbine shaft ~ 10,000 RPM
- Transonic flow (Mach No >1)
High Temperature - high gas temperature (1800K+),
(for high efficiency & work output)
- Blade metal melts at 1200K!
Multi-scales (in time & space) Fluid – fast convection
Solid – slow conduction (tS / tF ~ 103)
Main flow path – blade chord C
Cooling holes ~ 10-2 C
compressor
High Pressure
(H.P.) turbine
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Timescale Disparity in Aero-Heat Transfer Interaction (wall condition for the energy equation if non-adiabatic ?)
- For high-speed flow with high heat transfer: large T & variations in near-wall/wakes (i.e. work load/losses)
erroneous flow-only (adiabatic) solution
(regardless of flow model fidelities!)
- Fluid-solid ‘Conjugate Heat Transfer’ (CHT)
- STEADY: working with domain dependent stepping
- UNSTEADY: limited by conflicting requirements
Maximum Time Step dictated by resolving fast unsteadiness (fluid);
Minimum Time Scale dictated by covering slow conduction (solid).
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Exp(-S/R)
1.4
1.34
1.28
1.22
1.16
1.1
1.04
0.98
0.92
0.86
0.8
0.74
0.68
0.62
0.56
0.5
Hot-streak
P.S.Heating
URANS (He et al 2004)
LES (He 2013)
HP turbine with combustor exit
hot streaks (Khanal et al 2012)
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(to ‘realign’ mismatched time scales)
Fluid: solved in time-domain;
Solid: solved in frequency domain:
Ts=T0s+ Σ Ascos(wt) + Bs sin(wt)
(T0s As , Bs are all time-independent (“steady”)
Unsteady solid domain solved in a Steady manner
Hybrid Time/Frequency-domain Approach:
Implemented in a density based solver (He 2000) 3-D Unsteady Navier-Stokes in multi-block meshed domain;
Hex cell-centred upwind (AUSM) finite volume;
4-stage Runge-Kutta time-marching;
Local time stepping & multi-grid;
Implicit dual timing for unsteady flow;
(solid domain: fluid energy equation with zero velocity)
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Verification of Conduction and Convection
Solution Capabilities of CFD solver
0
1000
2000
3000
4000
5000
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1N
uP.S. S/S0 S.S.
Fully Turbulent
Trpped on S.S.
Exp (P.S)
Exp (S.S.)
Conduction Solution
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1(R-R1)/(R2-R1)
(T-T
1)/
(T2
-T1
)
Calc (FV CFD)
Analytical
Blade Surface HTC
0
5
10
15
20
0 0.5 1X/L
NUx
Calc
Analytic
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Semi-Analytical Unsteady Interface Method (He and Oldfield, 2009)
Basic assumption: locally 1D semi-infinite solid domain (valid for high frequencies with small ‘penetration depth’ in solid)
Analytical link in harmonics
between heat flux (qw) and temperature (Tw ):
(TFTq – “transfer function” )
Harmonic Balancing (heat flux / temperature continuity):
(n = 0,1,2, ……Nh)
Discrete for fluid side (FD) & Analytical for solid side:
(n = 0,1,2, ……Nh)
Tf Ts
xf xs
Tw
TBC wTqw TTFq ˆ ˆ
nSnF qq )ˆ( )ˆ(
])( ,)ˆ[(f )ˆ( nTqnfnw TFTT
fluid solid
Impact of Unsteady Surface Temperature
on Heat-flux Prediction (single harmonic)
At 10 Hz , ~33% over-prediction in unsteady heat flux
At 100 Hz, ~18% over-prediction
At 1000 Hz, ~6% over-prediction
Heat Flux Time Trace (HTC=3000 W/m**2/K, f = 10 Hz)
-500000
-250000
0
250000
500000
0 180 360 540 720
Time (wt, deg)
q (
W/m
**2)
q without Twall variation
q with Twall variation
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Conjugate Heat Transfer with LES
Basic Hypothesis: Turbulence at a spatial point ‘deterministically’
manifested by the corresponding Fourier spectrum
Tu Intensity: analogue of ‘Deterministic Stress’ for Nh harmonics
Tu Length-scale: Shape of the spectrum
])u()u( )u()u[(2
1)uu( inin
N
1nrnrn
'' h
1, 2, ………... , Nh
FT on the fly input to the semi-analytical interface condition
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Inflow Turbulence Fluctuations
(Synthetically Randomised Vortices)
Short scale
Long scale
Validation for Inflow Turbulence
Development in Duct (Tu=3.5%)
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 1.00 2.00 3.00 4.00 5.00
Tu/T
u0
Rex (x105)
Present LES
DNS (Jacobs & Durbin)
LES Conjugate Heat Transfer (Aerothermal Characteristics, Internal Cooled Nozzle, 30 Fourier modes)
Heat Flux (Quasi-steady vs Unsteady Wall BC)
-500
0
500
1000
1500
2000
2500
3000
0 10000 20000 30000 40000
Nu
q
Time step
Unsteady (harmonic-spectral)
Quasi Steady
Shear Stress (Influence of Heat Transfer on Aerodynamics!)
0
100
200
300
400
500
0 10000 20000 30000
Sh
ear
Str
ess
Time Step
Conjugate HT LES
0
100
200
300
400
500
0 10000 20000 30000
Sh
ea
r S
tre
ss
Time Step
Adiabatic LES
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Spatial Length-scale Disparity in Film-Cooling etc
Macro: Blade Chord (passage P & Vel field)
Micro: Film cooling hole (< 1%C),
(mixing of coolant with mainstream)
Compounding Challenge: Large number of cooling holes
( ~102+ )
Direct solutions with all holes resolved are prohibitively costly!
(Oldfield, 2007)
Macro & Micro scales exist in many problems:
- Film/effusion cooling: Cooling hole vs Blade
- Surface treatment/roughness: Dimple vs Blade
Scale-dependent Solvability
Scale-Dependent Solvability Behaviour
- Locally: micro scales of high gradient (needing high resolution)
- Globally: smooth variation among ‘similar’ meso-structures
‘Block-Spectral’ Model (He 2010)
Resolve micro scales (RANS /LES); Avoid solving large domain with very fine mesh.
Set up spectral block-block variations (pointwise) Simultaneous ‘mapping’ to the full domain;
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Pointwise Spectrum for Block Boundary Points
Main (macro) stream only ‘sees’ small
(micro) blocks through boundary faces
For each boundary point (i, j),
variable changes from block to block
(1-D variation wrt block index).
For NB blocks: )(GF)U()(U
BN
1j,i0j,ij,i
i,j
i,j
i,j
i,j
1
2
3
4
For a given basis function G(), only need to solve enough
blocks to determine the coefficients Fi,j
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i,j
i,j
i,j
1
2
3
4
Pointwise Fourier Spectrum (periodic, or “mirroring”/padding for non-periodic)
)]nsin()B()ncos()A[()U(U Lj,inL
N
1nj,in0j,iL,j,i
F
- Fourier Shape of variation with NF harmonics
- for each mesh point (i,j) for Block L :
i,j
- 2NF+1 blocks to be solved to fix the spectrum
Double Fourier Series Shape (M x N):
- (2M+1)(2N+1) blocks to be solved
)]nsin()msin(D)nsin()mcos(C
)ncos()msin(B)ncos()mcos(A[)U(
JIn,mJIn,m
JIn,mJI
hN,hM
0n,0m
n,mn,mJ,I
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Sample 2D Film-cooling Test Cases
Direct (39 holes) Spectral (4 holes)
Hot (T01)
Cold ( 0.5 T01) 0
0.5
1
1.5
0 0.2 0.4 0.6 0.8 1
X /L
T0
/T
01
Direct (39holes)
FT (10 holes)
FT (7 holes)
FT (4 holes)
1.E-03
1.E-02
1.E-01
1 10 100
L2 Error-Norm
Number of Modes Solved
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Direct Solution
(solving 992 holes)
Block-Spectral
(solving 8 holes)
T01
0.5T01
3D Effusion Cooling (mass & heat transfer via large number of micro holes)
Surface temperature under a distorted infow
Surface Pressure and heat flux (1600 dimples)
(with inlet P0 distortion)
Direct Solution Block Spectral
(Solve 9 dimples)
Non-D Heat Flux (1600 dimples)
0
200
400
600
0 0.2 0.4 0.6 0.8 1
X/L
Nu
Direct Solution (1600 dimples)
Block Spectral ( 21 dimples )
Block Spectral ( 15 dimples )
Block Spectral ( 9 dimples )
Smooth Surface
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(Solve 1600 dimples)
Summary
Two Methods for Multi-scale Problems:
Time scale disparity (fluid-solid heat transfer)
- Harmonic transfer function method:
unified and consistent interfacing condition/framework
for periodic & turbulence unsteady simulations.
Spatial scale disparity (cooling, micro structures)
- Block-spectral method:
macro & micro scales resolved by the same model/numerics
Some Refs: L. He, “Block-spectral Mapping for Multi-scale Solution”,
J. of Computational Physics, Vol.250 (2013).
L. He, “Fourier Spectral Method for Multi-scale Aerothermal Analysis”,
International J. of Computational Fluid Dynamics, Vol.27, No2 (2013).