Automatic Transition Prediction in Unsteady Airfoil Flows Using an Unstructured CFD Code Andreas Krumbein, Normann Krimmelbein, Cornelia Seyfert German Aerospace Center Institute of Aerodynamics.

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Transcript Automatic Transition Prediction in Unsteady Airfoil Flows Using an Unstructured CFD Code Andreas Krumbein, Normann Krimmelbein, Cornelia Seyfert German Aerospace Center Institute of Aerodynamics.

Automatic Transition Prediction in
Unsteady Airfoil Flows Using an Unstructured CFD Code
Andreas Krumbein, Normann Krimmelbein, Cornelia Seyfert
German Aerospace Center
Institute of Aerodynamics and Flow Technology
C²A²S²E Center for Computer Applications in AeroSpace Science and Engineering
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 1
Andreas Krumbein > 28 June 2011
Overview
Introduction
Transition Prediction Coupling Structure
Extension of the eN method for unsteady base flows
Test Cases & Computational Results
Conclusion & Outlook
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 2
Andreas Krumbein > 28 June 2011
Introduction
Transition Prediction in RANS-based CFD of External Flows
Current status of transition prediction in RANS solvers
RANS solvers have become a standard approach for the design and the
aerodynamic analysis of aerodynamic configurations.
Requirement from Aircraft Industry and Research for a long time:
RANS solver with integrated general transition prediction functionality
Automatic: no intervention of the user
Autonomous: as little additional information as possible
Major aims:
Reduction of modeling based uncertainties
Improvement of simulation accuracy
Accuracy of results from fully turbulent computations or from computations with
prescribed transition often not satisfactory
Exploitation of the full potential of advanced turbulence models
Most important, at present, improved simulation of the interaction between
transition locations and separation, especially for high-lift configurations.
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 3
Andreas Krumbein > 28 June 2011
Introduction
Transition Prediction in RANS-based CFD of External Flows
M = 0.2, Re = 2.3x106,
a = -4.0°, iHTP = 4°
Current status of transition prediction in RANS solvers
Incorporated transition prediction has become
inviscid stream
a state-of-the-art technique for various RANS
lines
codes in the last years.
Details of the concepts are different. They have
line of laminar
separation
in common that they are able to be applied to
complex geometries: multi-element configurations,
full aircraft, high-lift configurations, wind turbines, fuselages, etc.
transition lines
Much development and validation work has been carried out and,
today, the approaches have gained a high level of confidence.
Standard approaches of the transition prediction
functionalities regularly used in aircraft industry.
predicted transition lines
Re = 3.5 x 106, Ma = 0.17
Currently, increasing use of advanced approaches at
universities and research organizations.
Growing computer capacities will allow for more complex
geometries and more points.
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 4
Andreas Krumbein > 28 June 2011
Introduction
Transition Prediction in RANS-based CFD of External Flows
Currently most commonly used approaches for 3D RANS simulations
RANS solver + laminar BL code + eN database methods/empirical criteria
RANS solver + laminar BL code + automated stability code + eN methods
RANS solver +
+ eN database methods/empirical criteria
RANS solver +
+ automated stability code + eN methods
RANS solver +
+ transition transport equation models
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 5
Andreas Krumbein > 28 June 2011
Introduction
Transition Prediction in RANS-based CFD of External Flows
Currently most commonly used approaches for 3D RANS simulations
RANS solver + laminar BL code + eN database methods/empirical criteria
RANS solver + laminar BL code + automated stability code + eN methods (1)
 standard approach, industrial applications, standard grids can be used: only cp
RANS solver +
+ eN database methods/empirical criteria
RANS solver +
+ automated stability code + eN methods (2)
 advanced approach, accurate in regions where BL codes can not be applied
RANS solver +
+ transition transport equation models
(3)
 still under test, works well and yields accurate results for streamwise transition
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 6
Andreas Krumbein > 28 June 2011
Introduction
Transition Prediction in RANS-based CFD of External Flows
Current application spectrum
2d airfoils, infinite swept + 3d wings, winglets, fuselages and nacelles
single + multi-element configurations
attached flow + flow with laminar separation
fully validated: Tollmien-Schlichting, cross flow, separation induced transition
validation started: attachment line transition, by-pass transition
All for steady flow problems
Objectives of the talk
Can the existing transition prediction techniques be applied to unsteady flows
and if yes, how?
What are the differences in the results due to the different approaches?
Can some kind of best practice be derived?
Which is the most suitable approach for unsteady flows emphasizing dynamic
stall test cases?
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 7
Andreas Krumbein > 28 June 2011
Transition Prediction Coupling Structure
Iteration of the Transition Points
cycle = kcyc
external BL
approach
cycle = kcyc
internal BL
approach
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 8
Andreas Krumbein > 28 June 2011
Transition Prediction Coupling Structure
Transition Prediction Module
Treatment of separation induced transition
external BL approach
Yields very accurate laminar BL profiles using grids with standard resolution.
BL code stops at the point of laminar separation.
The laminar separation point approximates the transition point if transition is
located downstream of the separation point.
internal BL approach
Needs very fine grid resolution in wall normal direction for sufficient accuracy
of laminar BL profiles including the 1st and 2nd derivatives which are input for
the stability code, ≈ 40 points in prismatic layer of a hybrid grid for streamwise
instabilities.
Stability analysis can be carried out inside the separation bubble.
Sufficiently high resolution of the bubble must be ensured also in streamwise
direction, factor 2÷2.5 compared to normal resolution (≈ 256 points airfoil
contour).
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 9
Andreas Krumbein > 28 June 2011
Transition Prediction Coupling Structure
Unstructured RANS Solver TAU
3D RANS, compressible, steady/unsteady
Hybrid unstructured grids: hexahedra, tetrahedra, pyramids, prisms
Finite volume formulation
Vertex-centered spatial scheme (edge-based dual-cell approach)
2nd order central scheme, scalar or matrix artificial dissipation
Pseudo-time integration: explicit Runge-Kutta or implicit approximate factorization scheme (LU-SGS), multi-grid acceleration, local time stepping, explicit
residual smoothing, low Mach number preconditioning
Physical time integration: dual time stepping using pseudo-time integration for
the inner iterations
Turbulence models:
1- and 2-equation eddy viscosity models (SA type, k-w type)
differential RSM
DES
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 10
Andreas Krumbein > 28 June 2011
Extension of the eN method for Unsteady Base Flows
Steady case
The n factor of a frequency f (circular frequency
wr = 2p f ) describes the ratio of a disturbance‘s
amplitude at position x and the position x0
where the disturbance was first amplified by
integrating its spatial amplification rate ai.
x
 A(w r , x) 
   a i (w r ; ~
n  n(w r ; x)  ln
x ) d~
x

A
(
w
)
 0 r  x0

Ncrit
xtr
From the set of n factor curves for all frequencies in a certain frequency band
the maximum value at the position x, the maximum N factor N, is compared to
the critical N factor Ncrit, which has to be determined experimentally.
N  N ( x )  MAXn(w r ; x )
wr
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 11
Andreas Krumbein > 28 June 2011
Extension of the eN method for Unsteady Base Flows
Unsteady case
In a steady flow, one finds this situation of amplified disturbances at every moment when
time passes.
In an unsteady flow, this situation is only found at time t. At time t +Dt, this situation is
convected downstream due to the unsteadyness.
The Gaster relation tranfers spatial into temporal theory expressing the spatial
amplification rates through the temporal amplification rates wi.
wi ( ~
x (t ))
~
a i ( x (t )) 
vg (~
x (t ))
x
x (t )
x0
x0 (t )
n    a i (~
x ) d~
x
spatial theory

t
d~
x
~
~
wi ( x (t ))
  wi (t ) d t  n( x(t ))
vg
t0
temporal theory
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 12
Andreas Krumbein > 28 June 2011
Extension of the eN method for Unsteady Base Flows
The idea of the convection of amplification rates in an unsteady base flow *,**
n factor evolution between t and Dt:
n( x(t  Dt ))  n( x(t ))  Dn( x(t  Dt ))
 n( x)  Dn( x(t )  Dx)
 n( x)  Dn( x  v g Dt )
t  Dt
 n( x )

~
w
(
t
)
d
t
i

t
 n( x )
 wi (t  Dt )Dt
 time integration scheme for the values of the n factor: n = n(t, wr; x)
n(t , wr ; x)  n(t  Dt , wr ; x  Dx)  n(t , wr ; x)  Dn(t  Dt , wr ; x  Dx)
Radespiel, J. Windte, U. Scholz: „Numerical and Experimental Flow Analysis of Moving Airfoils with Laminar Separation Bubbles‘, AIAA Journal,
Vol. 45, No. 6, June 2007, pp. 1346-1356, also: AIAA 2006-501
**J. Windte, R. Radespiel: „Propulsive Efficiency of a Moving Airfoil at Transitional Low Reynolds Numbers“, AIAA Journal, Vol. 46, No. 9, Sep. 2008, pp.
2165-2177
*R.
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 13
Andreas Krumbein > 28 June 2011
Extension of the eN method for Unsteady Base Flows
Different Approaches for Unsteady Base Flows
• laminar separation from BL code
approximates transition in case of
laminar separation bubble
Application modes of the eN method
RANS + BL(BL code)
•BL steady + transition steady
+ stability code + eN method
•transition location inside laminar
separation bubble possible
• BL unsteady + transition steady
RANS + BL(RANS code) + stability code + eN method
•transition location inside laminar
separation bubble possible
•BL unsteady + transition unsteady
RANS + BL(RANS code) + stability code + unsteady eN method
g-ReQ,t transition transport model
Transport equations for the intermittency value g and the momentum loss Reynolds
number at transition onset
Covers streamwise transition mechanisms due to instabilities and by-pass (criterion) and
laminar separation (specific control of g production at separation)
Unsteadyness is taken into account by the time derivatives of the two variables in the
transport equations.
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 14
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
NACA0012
hybrid grid with 79,000 points, 512 along
contour, 128 in prismatic layer
M = 0.16, Re = 1.8 mio.
a(t) = 10.0° - 10.0° sin(wt), k = pf c/U= 0.1
Tu∞ = 0.083% → Ncrit = 8.59
Spalart-Allmaras (SA) turbulence model
3 periods with all eN approaches
dual time stepping
600 physical time steps per period
300 inner pseudo-time iterations with LU-SGS with 4w multigrid cycle
started at amin from well converged fully turbulent steady solution for amin
transition prediction at the physical time steps
initial phase with reasonably estimated fixed transition locations
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 15
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
NACA0012
Temporal convergence
lift
▪ FT, BL + steady: well converged
▪ RANS + steady: converged
▪ RANS + unsteady: not yet converged during
downstroke between 13 deg and 0 deg
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 16
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
NACA0012
Differences in the results
lift
▪ FT, BL + steady: very similar during upstroke
▪ RANS: formation of stall vortex at lower a
▪ transition: all similar during downstroke, amplitudes different
between 13 deg and 0 deg
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 17
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
NACA0012
Transition locations
Start of dynamic stall vortex found
in experiment at a = 15 deg
separations and
oscillations
differences
due to method
BL code separation
differences due to
representation of BL
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 18
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209 – airfoil of a rotorblade section
hybrid grid with 37,000 points, 940 along
contour, 40 in prismatic layer
DS1 (light stall): M = 0.16, Re = 1.8 mio.
a(t) = 13.0° + 5° sin(wt), k = pf c/U= 0.1
Tu∞ = 0.057% → Ncrit = 9.5
DS2 (deep stall): M = 0.31, Re = 1.2 mio.
a(t) = 13.0° + 7° sin(wt), k = pf c/U= 0.05
Tu∞ = 0.056% → Ncrit = 9.54
SA, Menter k-w SST, SSG/LRR-w
settings as before
all eN approaches
some results with g-ReQ,t model
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 19
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ FT, BL + steady eN: almost identical, transition locations
are separation points
▪ RANS: some qualitative improvement (vortex, moment peak)
▪ RANS + unsteady eN: strong oscillations of upper transition
point
Converged:
DS1 with SA
FT
BL + steady
RANS + steady
RANS + unsteady
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 20
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ FT, BL + steady eN: almost identical, transition locations are
separation points, lift qualitatively OK, moment not as good
▪ RANS + steady eN: strong oscillations of upper transition
point, yields the existance of a moment peak
▪ RANS + unsteady eN: NOT converged, similar to RANS +
steady eN
Converged:
DS1 with SST
FT
BL + steady
RANS + steady
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 21
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ FT, BL + steady eN: almost identical, transition: separations
▪ RANS: NOT converged, strong oscillations of upper
transition point, yield the existance of a moment peak
▪ RANS + unsteady eN: oscillations earlier and stronger than
with steady eN, downstroke reattachment looks best, as with
SA/SST
Converged:
DS1 with RSM
FT
BL + steady
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 22
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ FT, BL + steady eN: very similar, lift and moment
qualitatively OK, first peaks exist near to exp. data
▪ RANS: both approaches very similar, stall vortex too early,
▪ Second peaks do not exist.
Converged:
DS2 with SA
FT
BL + steady
RANS + steady
RANS + unsteady,
upstroke
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 23
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ FT, BL + steady eN: almost indentical, lift and moment
qualitatively OK, both peaks exist near to exp. data
▪ RANS: both approaches very similar, stall vortex too early,
both peaks exist
Converged:
DS2 with SST
FT
BL + steady
RANS + steady
RANS + unsteady,
upstroke
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 24
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ FT, BL + steady eN: very similar, lift and moment
qualitatively OK, first peaks exist near to exp. data,
second peaks very much less pronounced
▪ RANS: both approaches very similar, stall vortex too early,
existance of second unclear.
Converged:
DS2 with RSM
FT
BL + steady
RANS + steady
RANS + unsteady,
upstroke
until
a = 18 deg
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 25
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ Dependance on initial conditions?
▪ Different initializations: FT vs. free stream
▪ There are different temporally converged solutions.
lift
moment
▪ RANS: all not converged
▪ FT, BL + steady: some converged
▪ different: DS1 with SA – FT, BL + steady
DS2 with SA – FT, BL + steady
DS2 with SST – FT
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 26
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
▪ DS1 with RSM + free stream initialization + RANS + steady eN: not converged!
▪ Only here, the direction of the lift loop is represented as in the measurement. Why?
▪ Problem: New DS1 experiment carried out recently using a new model and new oscillation
system both being stiffer  no lift loop anymore  another source of uncertainty
lift
moment
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 27
Andreas Krumbein > 28 June 2011
Test Cases & Computational Results
Pitching Oscillations with Dynamic Stall
OA209
g-ReQ,t model
▪ Also not converged in the third
cycle.
▪ Very similar to the results from
RANS + steady eN.
▪ Differences mainly during the
downstroke, significantly
essentially for DS1.
▪ The results show the high
potential of this modeling
approach.
▪ At present, the reduction of the
computational effort is
appealing.
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 28
Andreas Krumbein > 28 June 2011
Conclusion & Outlook
All results are of preliminary character and will be re-computed in the
nearest future.
Transition can significantly improve the results of dynamic stall simulations.
At present, it seems that light stall simulations – DS1 – are more sensitive to
the effects of transition and improvements are more obvious.
High sensitivity to temporal resolution when transition downstream if
separation is taken into account. New computations with considerably
higher temporal resolution of one oscillation period.
At present, significant interaction between the transition points and the
turbulence model found, which makes a clear assessment impossible. New
computations will use a much finer grid. This seems to be necessary
especially for the RSM.
For DS2, the fully turbulent results seem to match the measured results best.
This was unexpected. Was the flow in DS2 experiment fully turbulent?
The new DS1 measurements will be taken into account for the assessment
based on the new computations.
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 29
Andreas Krumbein > 28 June 2011
Conclusion & Outlook
The approach BL(BL code) + steady eN is not suitable for dynamic stall
simulations and will not be used anymore.
Work program for the new computations:
Fully turbulent, BL(RANS code) + steady eN, BL(RANS code) + unsteady eN, g-ReQ,t(SST)
Finer grid
Increase of the number of periods nT in order to ensure temporal convergence
Reduction of the physical time step Dt per period in order to promote temporal convergence
Reduction of the number of inner iterations ninner per physical time step in order to save
computational time while keeping convergence within the inner iterations
Reduction of the number of transition prediction steps Dntr from one prediction step at every
physical time step, Dntr = 1, to Dntr ≈ 10÷20 in order to save computational time
Initialization with free stream conditions, fully turbulent solution and solution with reasonably
estimated or predicted, fixed transition locations.
Derivation of a best practice combination of these parameters for a reliable, but fast
simulation
29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 30
Andreas Krumbein > 28 June 2011