An Integrated Navier Stokes - Full Potential Free Wake Method for Rotor Flows
Ph. D Work by
Mert Enis Berkman
Advisors: Prof. S. M. Ruffin & Prof. L. N. Sankar
Georgia Institute of Technology
School of Aerospace Engineering
OUTLINE
• Review of Rotorcraft CFD Techniques
Why is a hybrid approach more favorable ?
• Hybrid Solver
• Navier-Stokes Zone
• Full Potential Zone
• Boundary and Interface Conditions
• Wake Model
• Results
• Hover Analysis
Two-Bladed, UH-60A and Tapered Tip Rotors
• Forward Flight Analysis
Two-Bladed, UH60A and H-34 Rotors
• Conclusions
ROTARY WING AERODYNAMICS
• Performance of rotary wings is limited by:
transonic flow (on advancing blade)
stall (on retreating blade)
operation under its own wake.
• The flow field is 3-D, unsteady, viscous and compressible.
• Rotor wake is a distorted, skewed helix that stays in the
vicinity of the rotor and affects entire flow field.
• The rotor wake structure determines performance, vibratory
airloads and acoustics.
• Modeling the wake and its effects remains a very challenging
task.
ROTORCRAFT CFD
Lifting - Line (- Surface) Methods
• Blades are modeled as a lifting-line (or -surface).
• Wake is represented by a network of vortex filaments.
• Routinely used in industry. They need small CPU time, thus
easily incorporated into comprehensive codes as aerodynamics
modules.
• They require table look up for airfoil load data, and are often
quasi-steady.
• They are loaded with empirical corrections.
ROTORCRAFT CFD
Finite-Difference Methods: (Potential, Euler and N-S)
a) Finite-Difference Methods with External Wake Model:
• The flow field is solved near the blade; the effects of the far
wake is modeled.
solved
• They can handle compressible flows.
• They require external coupling with
a wake model to account for far wake.
modeled
ROTORCRAFT CFD
b) Wake Capturing Schemes
• This class of methods attempt to capture the far wake as a
part of the solution.
• They provide high quality detailed flow field solutions.
• They require enormous computer time since they need to
resolve the tip vortex adequately.
• They diffuse the tip vortex too rapidly due to the dissipative
nature of Euler/N.-S. schemes.
• Higher order schemes, overset and/or unstructured grids were
used to conserve vorticity without significant success.
ROTORCRAFT CFD
Vorticity Embedding Technique
• A unique finite difference technique that eliminates wake diffusion.
• Vortex sheets are basically embedded inside a potential flow field
and their effect is confined to a small region.
• The wake is tracked by a Lagrangean approach using “vorticity
markers”.
• The technique is gaining popularity in helicopter industry due to
is efficiency and success in predicton of hovering rotor loads.
• It lacks viscous features.
• It cannot model BVI, dynamic stall and tip vortex generation well.
ROTORCRAFT CFD
c) Hybrid Schemes
• They integrate different methods in different flow regions to
improve solution quality without a big penalty in computer time.
• A hybrid rotor solver developed by Berezin and Sankar uses N.-S.
equations near the blades and full potential equations elsewhere
since viscous effects are negligible away from the blades.
• The method typically shows 40% reduction in CPU time without loss
in accuracy compared to full blown N-S solution.
• This method is available for hovering as well as advancing rotors.
• This scheme requires coupling to a comprehensive code for account
for far wake and trim effects.
ROTORCRAFT CFD
• Moulton and Caradonna integrated the Vorticity Embedding
Technique with a Navier-Stokes solver.
• The resulting method enjoys advantages of high order NavierStokes methods and wake treatment of vortex embedding scheme.
• This scheme can freely convect wakes without diffusion and
account for viscous effects over the blade.
• However, the method is limited to steady-state analysis, it can not
be used to analyze advancing rotors.
ROTORCRAFT CFD
First Generation
Second Generation
Hybrid Approach
Current operational
methodology
Current research
methodology
Proposed research
methodology
Free Wake
Model
Potential
Flow
Euler or N-S
Loads
Compute Inflow
Trim
Trim
Loads
Free
Wake
N-S
Potential,
Euler or N-S
Trim
Loads
HYBRID SOLVER VERSUS OTHERS
A hybrid technique offers the following capabilities:
• Capture viscous phenomena efficiently
• Eliminate tip vortex preservation problem
• Avoid external wake models
• Be applicable to hovering and advancing rotors
• Offer high order accuracy
• No other existing CFD technique combines ALL of the
properties listed above !
OBJECTIVES OF THIS RESEARCH
1. Develop a new hybrid technique that will feature the
capabilities listed.
2. Validate the method by comparison with experimental or
flight test data available for realistic helicopter rotor
configurations.
3. Study the effects of wake model, grid density and spatial
accuracy on the solution quality.
HYBRID SOLVER
N-S zone
FPE zone
Lagrangean Wake
Three Modules:
• Navier-Stokes Zone
• Full Potential Zone
• Lagrangean Wake
HYBRID SOLVER
Navier-Stokes (Inner) Zone
• Viscous features are captured, including separation.
• The near wake is captured as a part of the solution.
• Far wake effects are felt through interface boundaries.
Potential (Outer) Zone
• Viscous effects are negligible away from the blades.
• The inner wake structure is not modeled.
• An induced vortical velocity field due to a concentrated
tip vortex is generated.
Lagrangean Wake
• The tip vortex emanating from each blade is represented
by a series of piecewise linear elements.
• The tip vortex may deform based on local flow.
HYBRID SOLVER
FP
block 1
Kmatch
1
3
2
N.-S.
block 2
A cut in the radial plane
Inner and outer zones
INNER ZONE
• Finite volume technique that uses Reynolds Averaged NavierStokes equations.
• Third order or fifth order accurate terms for inviscid fluxes
crossing cell faces.
• 2nd order accurate modeling of viscous terms.
• MUSCL scheme with Roe averaging.
• Baldwin-Lomax turbulence model.
INNER ZONE
In transformed coordinates, the N.-S. equations may be be written
in differential form after nondimensionalization as

1
q   F  G   H 
R  S  T
Re

Finite volume and finite difference fluxes in generalized coordinates
are related via
 
F  E I  n S
 
R  EV  n S
 
G  E I  n S
 
S  EV  n S
 
H  E I  n S
 
T  EV  n S
for cell faces (i+1/2, j, k) and (i-1/2, j, k)
for cell faces (i, j+1/2, k) and (i, j-1/2, k)
for cell faces (i, j, k +1/2) and (i, j, k-1/2)
INNER ZONE
• Treatment of Inviscid Fluxes
dq
 RHSI  RHSV
dt
RHSI     F    G    H  
RHSV
1
  R   S    T  

Re
 
  E I  n S
Vol
 
 EV  nS
Vol
Roe’s approximate Riemann solver is used to calculate inviscid
fluxes
Fi1/ 2, j,k  0.5FL  FR   C qL  q R 
INNER ZONE
• Treatment of Inviscid Fluxes (cont.)
i-1,j,k
i,j,k
i-1/2,j,k
L
R
i+1,j,k
i+1/2,j,k
A third order spatial accuracy is obtained with a MUSCL scheme
q L  qi  1/ 3(q i1  q i )  1/ 6(q i  q i 1 )
q R  q i  1/ 3(qi 1  q i )  1/ 6(qi 2  qi 1 )
or as an option a fifth order scheme which uses information from
two additional nodes is available.
INNER ZONE
• Treatment of Viscous Fluxes
The viscous fluxes are also calculated with a finite volume scheme.
An eddy viscosity class of models is used to model Reynolds
stresses and turbulent transport of heat flux.
m = mL + mT
Pr = PrL + PrT
INNER ZONE
• Temporal Discretization and Diagonal ADI Factorization
A first order semi-implicit scheme is used in the study.
The viscous fluxes are lagged by a time step.
Beam and Warming’s linearization is done.
A diagonal ADI factorization proposed by Pulliam and Chaussee
is employed to solve the resulting system of equations.
OUTER ZONE
• The unsteady full potential equations are solved in the outer
zone away from the rotor blade.
Consider the continuity equation


t    ( V )  0
The velocity consists of two parts
 

V    Vw
The second term is a superimposed vortical velocity field that is
induced by the rotor wake.
OUTER ZONE
• Along with energy equation and isentropic gas relation, and
after manipulations the governing equations form a second
order hyperbolic PDE as,
  
  x  xt   y  yt  z zt
a 2  tt


 y  z z
 x x   y
• This system is converted in a set of equations to be solved for
perturbation potential.
• A three factor ADI scheme is used to solve the system.
COUPLING OF THE TWO ZONES
A cous tic waves
Vn + a
Vn -a
N .-S. F P
V orticity w aves
Vn
vortex filaments
Entropy wave
Vn
COUPLING OF THE TWO ZONES
• Flow Information Transfer from Inner to Outer Zone
The outer zone requires specification of velocity potential along
all zonal interfaces that separate the two zones.
The normal component of velocity at the interface is passed to
the outer zone.
This condition is used to match the normal derivative of the
potential at the interface.
This type of a condition assures a smooth informtion passage
from inner to outer zone.
COUPLING OF THE TWO ZONES
• Flow Information Transfer from Outer to Inner Zone
The velocity components at the interfaces are found by addition of
potential and wake induced velocities as
 
u N  S   x  Vw  i
 
vN  S   y  Vw  j
 
wN  S   z  Vw  k
FP
N-S
Temperature and density are found from isentropic gas law
at the interface.
COUPLING OF THE TWO ZONES
• Flow Information Transfer from Outer to Inner Zone
Although these relations do not account for information from the
inner zone, they have been shown to pass information
accurately enough in the past for most cases.
In this study characteristic based interface conditions coded by
Mello is also available as an option.
These non-reflecting boundary conditions use Riemann invariants
so that flow information from both sides are used in subsonic
flows.
BOUNDARY CONDITIONS
Computatinal domain covers
1 -2 blade radius above and below the rotor disk
0.6 - 1 blade radius beyond the blade tip
BOUNDARY CONDITIONS
• Inner zone (3 boundaries)
• On blade surface: no-slip or flow tangency
• Inboard: extrapolation from interior
• Outboard: extrapolation from interior
• Outer zone (6 boundaries)
• Inboard: extrapolation from interior
• Outboard: set to free stream conditions
• Plane above rotor disk: set to free stream conditions
• Plane below rotor disk: set to free stream conditions
• Upstream plane: set to free stream conditions
• Downstream plane: set to free stream conditions
BOUNDARY CONDITIONS
• Only one of the rotor blades is resolved in the hybrid technique.
• For hover analysis since the flow field is periodic about each
blade only one blade needs to be resolved by CFD methods.
• In forward flight analysis, all blades need to be resolved in
typical CFD methods.
• In the hybrid method, the far wake of each blade is modeled (not
solved for), therefore the influence of the other blades are
accounted via their wake.
• Significant reduction in computer time and memory requirements
since only one blade is resolved.
WAKE MODEL
• Wake shed from the blade is captured inside the Navier-Stokes
zone in the near field.
• The inner wake is neglected in the Full Potential zone once it
leaves the Navier-Stokes zone.
• Each individual blade’s tip vortex is modeled by a series of
piecewise linear elements.
• These elements are introduced at the inner/outer zone boundary
behind the blade trailing edge and extends for several revolutions
below the rotor plane outside the computational domain.
WAKE MODEL
• The wake elements that lie in the computational domain are
allowed to move with the local flow for hover analysis.
• In forward flight analysis, the wake elements remain fixed at
their predefined position, i.e. they are not allowed to move.
• The induced velocity field due to these vortex filaments is
calculated by Biot-Savart law.
• Two parameters are needed by Biot-Savart law to generate the
wake induced velocity field in the outer zone:
- vortex strength
- wake shape
WAKE MODEL
• The Biot-Savart law is
 

 dl  r
Vw  
3
4

r
elements
P
r
dl
WAKE MODEL
• The tip vortex strength is taken to be either
- the bound circulation at 97-99% blade, or
- the peak bound circulation
• The bound circulation at a blade section is calculated by the KuttaJoukowski theorem.
L = V
• In hover analysis, the tip vortex strength is updated at each iteration
with the change in blade loading.
• In forward flight analysis, the tip vortex changes at every time level
based on current lift variation over the blade.
WAKE MODEL
• To start the solution process either
- a non-contracting classical wake, or
- a contracting prescribed wake
structure is assumed.
Computational domain
Tip vortex
trajectory
Wake element
Wake markers
WAKE MODEL
• In the rigid wake option this wake shape remains unchanged.
• In the free wake option, the wake markers are allowed to move
freely with the flow.
• Inside the computational domain these markers are tracked using
a Lagrangean technique. The following procedure is followed
every time level in the free wake option:
1. determine in which cell each wake marker lies,
2. calculate the local flow speed at these positions,
3. move each marker to its new position
• The remaining wake markers are attached to the last free marker
appropriately.
WAKE MODEL
• Since the wake shape deforms at each time step, ideally, the
wake induced velocity coefficients should be updated at each
time step too.
• However, calculation of these coefficients is computationally
intense. Therefore, only after each 10 degrees of blade rotation
the update is performed based on the latest wake structure.
• In hover analysis this delay does not cause any problems since
a single steady-state solution is sought.
• In forward flight, these updates need to be done at every time step
rendering the free wake option impractical.
VALIDATION STUDIES
• Two-Bladed Rotor in Hover
• UH-60A Rotor in Hover
• Tapered Tip Rotor in Hover
• Non-Lifting Two-Bladed Rotor in High Speed Forward Flight
• UH-60A Rotor in Forward Flight
• H-34 Helicopter in Forward Flight
HOVERING TWO-BLADED ROTOR
• Two-bladed rotor tested by Caradonna and Tung
Rectangular planforn, no twist, NACA 0012 sections, AR = 6
• Non-Lifting Case
(Collective pitch = 0o, Tip Mach No. = 0.52, Reynolds No. = 2 Mil.)
r/R = 68%
r/R = 96%
HOVERING TWO-BLADED ROTOR
• Non-Lifting Case
upper half: hybrid solver
lower half: full Navier-Stokes
• Hybrid solver is twice
as fast as the full NavierStokes solver !
Density
contours
EFFECT OF WAKE MODEL
• Two-Bladed Rotor:
r/R = 68%
(Collective pitch = 5o, Tip Mach No. = 0.794)
r/R = 96%
FULL N.-S. VS. HYBRID SOLVER
• Two-Bladed Rotor:
Collective pitch = 8o,
Tip Mach No. = 0.439
r=50%
Full N.-S. : 1 full revolution
Hybrid : 1/3 revolution
r=80%
r=96%
EFFECT OF NUMBER OF WAKE ELEMENTS
• Two-Bladed Rotor:
(Collective pitch = 8o, Tip Mach No. = 0.612)
r/R = 50%
EFFECT OF WAKE STRUCTURE
• Two-Bladed Rotor:
(Collective pitch = 8o, Tip Mach No. = 0.612)
r/R = 68%
EFFECT OF WAKE STRUCTURE
• Two-Bladed Rotor:
(Collective pitch = 8o, Tip Mach No. = 0.612)
r/R = 96%
TIP VORTEX POSITION
• Two-Bladed Rotor:
(Collective pitch = 8o, Tip Mach No. = 0.612)
Radial Position of the Tip Vortex Variation with Iteration
1.05
iteration
1
rTV /R
0.95
0.9
0.85
0.8
0
50
100
150
200
250
Vortex Age (deg.)
300
350
400
FIFTH ORDER VS. THIRD ORDER
• Two-Bladed Rotor:
(Collective pitch = 8o, Tip Mach No. = 0.612)
r/R = 68%
r/R = 89%
-1.5
-1.5
Experiment
3rd order
5th order
-1
Experiment
3rd order
5th order
-1
-0.5
-0.5
Cp
Cp
0
0
0.5
0.5
1
1
0
0.2
0.4
x/c
0.6
0.8
1
0
0.2
0.4
x/c
0.6
0.8
1
HOVERING UH-60A ROTOR
• Four twisted blades with rearward swept tip and two
different airfoil sections, AR = 15.3.
• Collective pitch=10o, Tip Mach No. = 0.628, Reynolds No.=2.5 Mil.
• A two block H-O grid with 90 chordwise, 43 spanwise and 80
normal nodes.
• Approximately 37% of the nodes lie inside the Navier-Stokes zone.
• Free wake option with 10 wake revolutions modeled.
• Initial wake is non-contracting and updated every 10o of blade
rotation.
• Peak bound circulation used as the tip vortex strength.
HOVERING UH-60A ROTOR
• A total of 2850 iterations were enough to reach steady state.
Experimental
Numerical
CT/s0.085,CQ/s0.0070CT/s0.086,CQ/s0.0074
Sectional Thrust
Coefficient Variation
HOVERING UH-60A ROTOR
Chordwise Pressure Coefficients
r/R=40%
r/R=67%
r/R=87%
r/R=99%
HOVERING TAPERED TIP ROTOR
• Four dual linearly twisted blades, with taper starting at 82% radius.
• Two different airfoil sections and AR=15.3.
• Collective pitch=8.6o, Tip Mach No. = 0.628, Reynolds No.=2.5 Mil.
• Two block H-O grid with 90 chordwise, 43 spanwise and 80
normal nodes.
• Approximately 37% of the nodes lie inside the Navier-Stokes zone.
• Rigid wake option with 10 wake revolutions modeled.
• Initial wake shape is based on the K-T prescribed wake.
HOVERING TAPERED TIP ROTOR
Collective pitch = 8.60, Tip Mach No. = 0.628
r /R= 77.5%
r/R = 94.5%
ADVANCING UH-60A ROTOR
• Tip Mach No. = 0.628, Advance Ratio = 0.3, Reynolds No.=2.5 Mil.
• The blade motion is prescribed by a table, qq(r ,Y).
• Unstable behavior is observed with this blade deformation scheme.
• The blade pitching motion approximated as
q  8.5  7.5cos   1.84sin 
• Rigid wake option with 10 wake revolutions modeled.
• Peak bound circulation used as the tip vortex strength.
ADVANCING UH-60A ROTOR
-2.5
Pressure Coefficients at  = 0o
r/R=67.5%
-2
Ex p-upper
Ex p-lower
Hy b-upper
Hy b-lower
-2
-1.5
-1
Cp
Cp
-0.5
0
0.5
0.5
1
1
1.5
1.5
0.4
-2.5
x /c
0.6
0.8
0
1
0.2
0.4
-2.5
-2
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1.5
0.6
-1
0
0.5
0.5
r/R=94.5%
1
1.5
1
-0.5
0
r/R=86.5%
0.8
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1.5
-0.5
1
x/c
-2
Cp
-1
Cp
-0.5
0
0.2
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1.5
-1
0
r/R=77.5%
-2.5
1.5
0
0.2
0.4
x/c
0.6
0.8
1
0
0.2
0.4
x/c
0.6
0.8
1
ADVANCING UH-60A ROTOR
-2
Pressure Coefficients at  = 90o
r/R=67.5%
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1.5
-1
-0.5
-0.5
0
0
0.5
0.5
1
1
0.2
0.4
-1.5
x/c
0.6
0.8
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1.5
Cp
Cp
-1
0
r/R=77.5%
-2
0
1
0.2
0.4
-1
0.8
1
x/c
-1.5
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
0.6
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1
-0.5
Cp
Cp
-0.5
0
0
0.5
0.5
r/R=86.5%
1
r/R=94.5%
1
0
0.2
0.4
x/c
0.6
0.8
1
0
0.2
0.4
x/c
0.6
0.8
1
ADVANCING UH-60A ROTOR
-2.5
Pressure Coefficients at  =18 0o
r/R=67.5%
r/R=77.5%
-2
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-2
-1.5
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1.5
-1
Cp
Cp
-1
-0.5
-0.5
0
0
0.5
0.5
1
1
0
0.2
0.4
-1.5
x/c
0.6
0.8
0
1
0.2
0.4
-1.5
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1
x/c
0.6
0.8
1
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-1
-0.5
Cp
Cp
-0.5
0
0
0.5
0.5
r/R=86.5%
r/R=94.5%
1
1
0
0.2
0.4
x/c
0.6
0.8
1
0
0.2
0.4
x/c
0.6
0.8
1
ADVANCING UH-60A ROTOR
-4
Pressure Coefficients at  = 270o
r/R=67.5%
r/R=77.5%
-4
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-3
-2
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-3
Cp
Cp
-2
-1
-1
0
1
0
2
1
0
0.2
0.4
x/c
0.6
0.8
1
0
0.2
0.4
-2.5
-4
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-3
-2
x/c
0.6
0.8
1
Exp-upper
Exp-lower
Hyb-upper
Hyb-lower
-2
-1.5
Cp
Cp
-1
-1
-0.5
0
0
r/R=86.5%
1
r/R=94.5%
0.5
1
2
0
0.2
0.4
x/c
0.6
0.8
1
0
0.2
0.4
x/c
0.6
0.8
1
CONCLUDING REMARKS
• The hybrid solver is a very efficient new method for
prediction of complex viscous unsteady flows over
isolated helicopter rotors.
It requires only half to the CPU time compared to a full blown
Navier-Stokes solver over the same grid per time level.
It converges in less number of iterations for hover cases.
Only one blade needs to be resolved for advancing rotors.
The hybrid solver does not need fine grid away from the blades,
has no wake diffusion in the far field due to its unique wake
treatment.
A single method for rotors in hover and forward flight.
RECOMMENDATIONS FOR FUTURE STUDIES
• Inclusion of inner wake
• Newton sub-iterations
• Turbulence modeling
• Adaptive stencil
• Parallel processing
• Coupling with a structural dynamics solver
• Overset grids
Georgia Tech
School of Aerospace Engineering
A Hybrid Flow Analysis for Rotors
in Forward Flight
A Ph.D Thesis Presentation
Zhong Yang
Advisor: L. N. Sankar
School of Aerospace Engineering
Georgia Institute of Technology
June 26, 2000
Georgia Tech
•
•
•
•
•
School of Aerospace Engineering
Outline
Technical Barriers Limiting Rotor Performance
in Forward Flight
Overview of Current Research Methods
Hybrid Methodology and Numerical Procedure
Implementation Details
Results and Discussion
– UH-60A in high speed flight
– AH-1G in low speed descent
• Conclusions and Recommendations
Georgia Tech
School of Aerospace Engineering
Background
• Modeling forward flight phenomena requires
detailed modeling aerodynamics (transonic
flow, dynamic stall, blade vortex interaction),
elasticity, blade dynamics and pilot input.
• First-principles based aerodynamics analyses
(N-S solver) have been available to the
industries, but are computationally expensive.
• In some studies, an open-loop coupling
between CFD solver and the comprehensive
analysis are done.
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School of Aerospace Engineering
Helicopter Aerodynamic Environment
Georgia Tech
School of Aerospace Engineering
Technical Barriers in Forward Flight
• High speed forward flight:
transonic flow, dynamic stall effects
• Low advanced ratios:
strong tip vortices, BVI
• Flow asymmetry:
caused by complex blade dynamics, bending
and torsional deformation
• Problem is multidisciplinary:
aerodynamics, elasticity, blade dynamics and
trim
Georgia Tech
School of Aerospace Engineering
Comprehensive Codes
• e.g. CAMRAD/JA, 2GCHAS, RDYNE,
UMARC, COPTER
– blade element theory
– Various wake models
– Can handle trim, and elastic effects
– These methods are not general enough to model
nonlinear and unsteady effects, except in an
empirical fashion (curve fits or synthesis of airfoil
load tables).
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Potential Flow Methods
• e.g. Caradonna, Chattot, RFS2 by Prichard and
Sankar, FPR by Strawn, HELIX by Steinhoff
– limited to weak shock waves and inviscid flow
– Far wake is modeled as inflow corrections supplied
from an external wake model (free wake model or
a prescribed wake model)
– Vortex embedding techniques are sometimes used.
– Rotor is trimmed, and elastic deformations
accounted for, using a comprehensive code
Georgia Tech
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Euler/Navier-Stokes Methods
• e.g. Wake and Sankar , Srinivasan (TURNS),
Ahmad, Duque and Strawn (OVERFLOW),
Banglore and Sankar, Hariharan and Sankar
– Most methods can capture wake as a part of the
solution.
– Calculations are limited value because of:
 Excessive numerical viscosity
 Significant computational memory and time
 Rotor not trimmed; blade dynamics and aeroelasticity
inadequately modeled.
– Smith, Bauchau and Ahmad coupled NS solvers to
structural dynamics codes.
Georgia Tech
School of Aerospace Engineering
Hybrid Methods
• Berezin (GT), Berkman (GT), Moulton,
Caradonna, and Bangalore (US Army)
– Use the most appropriate models in different flow
regions to retain solution quality
– Large savings in computer time compared to NS
methods
– Berezin coupled hybrid solver to RDYNE to
account for the far wake and trim effects.
– Berkman modeled the entire wake from first
principles, and obtained good results in hover.
Georgia Tech
School of Aerospace Engineering
Hybrid Method (continued)
– Moulton and Caradonna coupled HELIX to
TURNS for modeling rotors in hover.
– Bangalore and Caradonna extended Moulton’s
work to advancing rotor flows through overset
grids.
– Trim and elastic effects were not accounted for in
most of these calculations, excpet in Berezin’s
work (via RDYNE) and Moulton’s work (via
CAMRAD).
Georgia Tech
School of Aerospace Engineering
Research Objectives
• Develop innovative methods , which combine
solution efficiency and accuracy, for modeling
rotors in forward flight.
• Validate the methods by comparisons with
experimental and flight test data for realistic
rotor configurations.
• Investigate the capabilities and limitations of
the numerical models in capturing flow field
physics.
School of Aerospace Engineering
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Hybrid Methodology
N-S zone
FPE zone
Lagrangean Wake
• Navier-Stokes solver:
modeling the viscous
flow and near wake
• Potential flow solver:
modeling the inviscid
isentropic flow
• Lagrangean approach:
convecting vortex
filaments without
diffusion in the FPE zone
and the far field
Georgia Tech
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Navier-Stokes Solver
• Solves the 3-D Reynolds-Averaged NavierStokes equations.
• Scheme is first or second order accurate in
time, third or fifth order in space.
• Numerical viscosity provided through Roe
upwind scheme.
• Effects of turbulence are modeled with a
Baldwin-Lomax eddy viscocity model.
Georgia Tech
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Full Potential Solver
• Solves the continuity equation in finite volume

form
t    V  0
• The velocity field is made of


V    Vwake
• The time-marching scheme is fully implicit,
first order accurate in time, second order
accurate in space except in supersonic regions.
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Boundary and Interface Conditions
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Boundary and Interface Conditions



n  (VNS  Vwake )  n
FP
block 1
Kmatch
1
3
2
N.-S.
block 2


VNS    Vwake
, e from isentropic flow
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Computational Domain
Domain 1
4
blade
3
Conventional N-S Solver
Domain 2
Hybrid Method
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Implementation Details
• CPU time was reduced by performing hybrid
analysis for a single blade.
• The other blades are “seen” by the analysis as
a collection of bound and tip vortices.
• There is no more need to match and patch the
grids around multiple moving, deforming
blades.
• This allows pitching and flapping motion to be
modeled rapidly without need for inter-blade
grid continuity.
Georgia Tech
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Blade Dynamics
• A module for computing the rigid blade
motions in flap and pitch, and the complex
blade deformation due to aeroelastic effects has
been developed.
• For rigid blades, the (x,y,z) positions in space
at any instance in time may be transformed
using Eulerian angles:



xnew  Txold  ABC xold
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Blade Dynamics (continued)
• If the blade is not rigid, the grid motion should
include additional rotations in twist, and
bending deformations:
–Exact Approach:

xelastic_ deformation
 cos q
  0
 sin q
0 sin q 
dx 

1
0 
xr  dy 
 dz  bending
0 cos q  torsion
–Transpiration boundary condition: used in present
calculation.
v  v  n  r  V sin   d z  
b
surface

 dx
elastic

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Wake Model
• In
forward flight, the helical vortices are
carried downward by the induced velocity and
rearward by free-stream velocity.
• Prescribed wake model:
–Inflow  is computed from
Glauert’s theory.
–Wake markers are located
as follows:
xmarker  r cos(   )  Rm x  Rx
ymarker  r sin(    )  Rm y  R y
z marker  z0  Rm z  Rz
Wake marker
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Wake Geometry
Non-distorted wake
Distorted free wake
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Wake Model (continued)
• Free wake model:
–It can model the distortion from the basic helix.
–One option in the code is to search for the computational
cell each wake marker lies in, and calculate local velocities
of the markers by trilinear interpolation. This search can be
costly.
–Another option is to directly use the Biot-Savart Law to
evaluate the self induced velocity.
This option was used here.
 

1  r  dl
v  
4  r 3
Georgia Tech
School of Aerospace Engineering
Tip Vortex Strength
• An
automated procedure is employed for an
initial wake geometry and tip vortex strength.
• The wake geometry and induced flow are
automatically updated at user-specified intervals
(e.g. every 5 degree azimuth)
• As the blade rotates, the bound vortex
circulation is computed from the flow solver by
Kutta-Joukowski theorem:
1
U T   U T2 cCl
2
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Tip Vortex Strength
found as the peak bound circulation
Tip Vortex Strength
Tip Vortex Strength
Positive circulation
distribution
Negative circulation
distribution near the tip
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Rotor Trim
• User supplies CT/s , aTPP and desired moments
(usually zero).
• The supplied tip path plane angle is used to set
blade flapping motion.
•The desired CT/s and moments are achieved
through the adjustment of the collective and
cyclic pitch.
cT  cT (q 0 ,q1c ,q1s )
cM  cM (q 0 ,q1c ,q1s )
y
y
cM x  cM x (q 0 ,q1c ,q1s )
School of Aerospace Engineering
Georgia Tech
Rotor Trim (continued)
• A Newton-Raphson
iterative method is
employed to compute the control settings
changes, and obtain a new guess.
 cT
 q
(0)
 cT 
 0
 
 cM y
cM y   
q 0
c 

 Mx 
 cM x
 q 0

cT
q1c
cM y
q1c
cM x
q1c
cT 
q1s 

cM y 
q1s 

cM x 
q1s 
(0)
 cT 
 q 0 
 



q

 1c 
cM y 
q 
c 
 1s 
 Mx 
(0)
(d )
 q 0   q 0   q 0 
q   q   q 
 1c   1c   1c 
q1s  q1s   q1s 
(1)
(0)
(0)
Georgia Tech
School of Aerospace Engineering
Validation Studies
• 2-D code Validation Studies (not documented)
• UH-60A Model Rotor in High Speed Forward
Flight
• AH-1G Flight Test Rotor in Descent
• OLS Model Rotor in Descent
Georgia Tech
School of Aerospace Engineering
UH-60A in High Speed
Forward Flight
• Tested in the DNW tunnel in Holland
• Complex aerodynamic design: nonlinear twist,
several asymmetric airfoils, and swept tip
• Nonlinear elastic deformations
Georgia Tech
School of Aerospace Engineering
UH-60A in High Speed
Forward Flight
• Validation case:
–Advance ratio m=0.3
–Tip Mach number Mtip=0.628, CT/s= 0.082
–The blades were trimmed to eliminate one-per-rev
flapping.
–H-O multi-block grid: After grid sensitivity
studies, a 90x44x80 (NS zone: 62x44x44) grid was
chosen for optimum combination of accuracy and
computational efficiency.
Georgia Tech
School of Aerospace Engineering
Measured Torsional Deformations
q  11.5  1.84 cos
 7.5 sin   q elastic(r , )
Modeled
using
Transpiration
Velocity
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School of Aerospace Engineering
Grid around the UH-60A Blade
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CP at =00
(r=67.5%R and 94.5%R)
-2
-1.5
r/R=67.5%
r/R=94.5%
-1.5
-1
-1
-0.5
-0.5
Cp
Cp
0
0
0.5
0.5
1
1.5
1
0
0.2
0.4
0.6
x/c
0.8
1
0
0.2
0.4
0.6
x/c
0.8
1
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CP at =1200
(r=67.5%R and 94.5%R)
-1.5
-1.5
r/R=67.5%
Cp
r/R=94.5%
-1
-1
-0.5
-0.5
Cp
0
Cp *
0
0.5
0.5
1
1
1.5
1.5
0
0.2
0.4
0.6
x/c
0.8
1
0
0.2
0.4
0.6
x/c
0.8
1
School of Aerospace Engineering
Georgia Tech
CP at =2700
(r=68%R and 94.5%R)
-3.5
-2.5
r/R=67.5%
-3
-2
r/R=94.5%
-2.5
-1.5
-2
-1
-1.5
Cp
Cp -0.5
-1
-0.5
0
0
0.5
0.5
1
1
1.5
1.5
0
0.2
0.4
0.6
x/c
0.8
1
0
0.2
0.4
0.6
x/c
0.8
1
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Mach Number Contour at r=96%R
(Blade at Y=900)
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Sectional Normal Load at r=78%R
(with and without elastic deformation)
1.5
r/R=78%
hybrid w ithout elastic
hybrid w ith elastic
experiment
1.2
0.9
Cn
0.6
0.3

0
0
45
90
135
180
225
270
315
360
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Sectional Normal Load at r=92%R
(with and without elastic deformation)
1
r/R=92%
hybrid w ithout elastic
hybrid w ith elastic
experiment
0.8
0.6
Cn
0.4
0.2
0

-0.2
0
45
90
135
180
225
270
315
360
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Sectional Normal Load at r=78%R
(Comparison with Bangalore and Caradonna)
1.5
r/R=78%
hybrid w ith elastic
experiment
Results of Bangalore et al
1.2
0.9
Cn
0.6
0.3

0
0
45
90
135
180
225
270
315
360
School of Aerospace Engineering
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Sectional Normal Load at r=92%R
(Comparison with Bangalore and Caradonna)
1
r/R=92%
hybrid w ith elastic
experiment
0.8
Results of Bangalore et al
0.6
Cn
0.4
0.2
0

-0.2
0
45
90
135
180
225
270
315
360
Georgia Tech
School of Aerospace Engineering
AH-1G in Low Speed
Descending Flight
• Flight test done at NASA Ames
• Two-bladed rectangular planform rotor
• Linear twist is -100
• Several calculations have been reported:
–Hernandez used FPR coupled with
CAMRAD/JA
–Ramchandran applied HELIX-II
–Ahmad used Chi-TURNS with Chimera grid
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AH-1G in Low Speed
Descending Flight (continued)
•Validation case:
–Advance ratio m=0.19
–Tip mach number Mtip=0.65, CT/s =0.0713,
aTPP = -1.870
–The first blade harmonics from flight test:
q0
6.00
q1s
-5.50
q1c
1.70
1s
-0.150
1c
2.130
q1c
2.50
1s
-0.150
1c
2.130
–After trimming:
q0
8.00
q1s
-6.50
–H-O multi-block grid: 90x43x80
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CP at r=91%R (=900)
Due to input airfoil imperfections
-2
-1.5
-1
-0.5
Cp
0
0.5
1
1.5
0
0.2
0.4
0.6
x/c
=900
=900
(results of Ahmad et al)
(hybrid method)
0.8
1
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CP at r=91%R (=1050 and =2700)
-2
-3
-1.5
-2
-1
-1
-0.5
Cp
Cp
0
0
0.5
1
1
1.5
2
0
0.2
0.4
0.6
x/c
=1050
0.8
1
0
0.2
0.4
0.6
x/c
=2700
0.8
1
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Sectional Normal Load at r=97%R
(with and without trimming)
0.6
r/R=97%
0.5
Flight test data
Hyb. (trimmed)
Hyb. (no trimming)
0.4
Cn
0.3
0.2
0.1

0
0
90
180
270
360
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Sectional Normal Load at r=99%R
(Comparison with Ahmad and Duque)
0.5
r/R=99%
0.4
Results of Ahmad et al.
Flight test data
Hyb. Method (trimmed)
0.3
Cn
0.2
0.1
0

-0.1
0
90
180
270
360
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Sectional Normal Load at r=99%R
(with different wake models)
0.5
r/R=99%
Flight test data
Hyb. (free w ake)
Hyb. (prescribed)
Hyb. (uniform)
0.4
0.3
Cn
0.2
0.1
0

-0.1
0
90
180
270
360
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Sectional Normal Load at r=99%R
(with different parameters of free wake model)
0.5
r/R=99%
Cn
0.4
Flight test data
Hyb. (0.2, 5 degree)
0.3
Hyb. (0.2, 10 degree)
Hyb. (0.1, 5 degree)
0.2
0.1
0

-0.1
0
90
180
270
360
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Wake Shed from Blade at Y=2700
25
10
free wake
prescribed wake
20
6
15
Y
Z
10
5
4
2
Rotor disk
0
0
-5
-2
-10
-4
-15
-6
-20
-8
-10
-25
-10
free wake
prescribed wake
8
0
10
20
30
40
-10
50
X
0
10
20
free wake
prescribed wake
4
3
z
2
Rotor Disk
1
0
-1
-2
-3
-4
-5
-15
-10
-5
30
X
5
0
5
y
10
15
40
50
Georgia Tech
• Blade at
Y=2700
• Free wake
model
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Tip Vortex Visualization
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Tip Vortex Visualization
• Blade at
Y=2700
• Prescribed
wake model
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OLS 1/7 Scale Model Studies
• The 1/7 scale model AH-1 rotor experiment
was tested by Splettstoesser et al.
• Two-bladed rectangular planform rotor
• Linear twist is -8.20.
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OLS 1/7 Scale Model Studies (continued)
• Validation case:
–Advance ratio m=0.164
–Tip mach number Mtip=0.664, CT/s0.0783,
aTPP= -10
–The first blade harmonics from Strawn et al:
q0
q1s
q1c
 1s
 1c
0
6.140
-1.390
0.90
0.00
-1.00
0.50
–Coarse H-O multi-block grid: 90x43x80 (NS
zone: 62x43x44)
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CP at r=95.5%R (=00 and =450)
-1.5
-1.5
Chordwise Pressure for BVI Case (r/R=0.955, Psi=45)
Chordwise Pressure for BVI Case (r/R=0.955, Psi=0)
Cp
-1
-1
-0.5
-0.5
Cp
0
0
0.5
0.5
Hybrid Method (low er)
Hybrid Method (low er)
Hybrid Method (upper)
1
1
Hybrid Method (upper)
Experiment
Experiment
1.5
1.5
0
0.2
0.4
0.6
x/c
=00
0.8
1
0
0.2
0.4
0.6
x/c
=450
0.8
1
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CP at r=95.5%R (=900 and =1350)
-1.5
-1.5
Chordwise Pressure for BVI Case (r/R=0.95, Psi=135)
Chordwise Pressure for BVI case (r/R=0.955, Psi=90)
Cp
-1
-1
-0.5
-0.5
Cp
0
0
0.5
0.5
Hybrid Method (low er)
Hybrid Method (low er)
1
1
Hybrid Method (upper)
Hybrid Method (upper)
Experiment
Experiment
1.5
1.5
0
0.2
0.4
0.6
x/c
=900
0.8
1
0
0.2
0.4
0.6
x/c
=1350
0.8
1
Georgia Tech
School of Aerospace Engineering
Conclusions
• A combination
of Navier-Stokes, potential flow and
free wake methods can be used to model rotors in
forward flight, with input from an elastic analysis.
• Inclusion of torsional deformations was found to be
extremely important. The AH-1G study, where elastic
deformation was not available, gave less satisfactory
results.
• At the advance ratios considered (m >0.16), free wake
and prescribed wake based inflow models gave
comparable results, even though the vortex geometry
was entirely different and BVI phenomena were
present.
Georgia Tech
School of Aerospace Engineering
Conclusions (continued)
• Measured
data regarding blade dynamics is often
inaccurate, or simply not available. A trim analysis
should always be done as part of any forward flight
analysis, based on user supplied CT/s, aTPP and rolling
moment information.
• In this work, methods have been developed for
handling all of these important aspects of the analysis.
Georgia Tech
School of Aerospace Engineering
Recommendations
• Transpiration BC is very approximate and can handle
only small deformations. Improved grid deformation
algorithms are needed.
• The Baldwin Lomax model is inadequate for
modeling dynamic stall. Improved turbulence and
transition models must be developed and validated.
• Biot-Savart law will occasionally produce velocity
spikes when a marker is very close to a computational
node. This can lead to unrealistically high velocity, and
low density values. Alternate approaches for
computing the rotational component of velocity must
be explored.
CFD Research Corporation
215 Wynn Dr. , Huntsville, AL 35805
(256) 726-4800
FAX: (256) 726-4806 www.cfdrc.com
FIRST-PRINCIPLES BASED HIGH ORDER
METHODOLOGIES FOR ROTORCRAFT
FLOWFIELD STUDIES
Nathan Hariharan
CFD Research Corporation
Huntsville, AL
Lakshmi Sankar
Georgia Institute of Technology
Atlanta, GA
AHS 55th Annual Form & Technology Display
Montreal, Canada
May 27, 1999
OUTLINE
•
Background
•
High Order Methods
- Fifth Order ENO
- Discontinuous Galerkin (DG) Scheme
- Seventh Order ENO
•
Overset Refinement
•
Results and Discussions
•
Conclusions and Recommendations
OUTLINE
•
Background
•
High Order Methods
- Fifth Order ENO
- Seventh Order ENO
•
Overset Refinement
•
Results and Discussions
•
Conclusions and Recommendations
ROTORCRAFT FLOWFIELD SIMULATION
•
First-Principles Based Methods
- High Order Methods
- Vorticity Confinement
•
Analytical Methods
- HELIX /Hybrid analysis
- Design Codes, such as CAMRAD
ROTORCRAFT FLOWFIELD SIMULATION
First-Principles Based Methods
•
Direct Solution of Euler/NS Equations Including Vorticity
•
Vortex Formation, Convection, and Interaction
•
Necessity of First-Principles for Next Generation Rotorcraft
- Advanced Tip Shapes
- Active Devices to Enhance Aerodynamic Efficiency,
Decrease Acoustic Signal
- Blade-Vortex Interaction, Vortex Miss-Distance, etc.
OBJECTIVES
•
Examine the ability of first-principles Euler/NS methodologies to capture
rotor-blade tip vortices.
•
Develop 3rd,5th spatial order, compact stencil, Discontinuous Galerkin
methodology.
•
Compare the vortex diffusion characteristics of DG with ENO for a 3D
rotor computation. Analyze the relative computational speed, memory
overheads.
•
Develop vortex tracking grids for blade tip vortices with unsteady the
“vortex grids” embedded inside the main grid.
•
Capture the tip-vortex for the first 180 degrees with less than 10-20%
diffusion, enabling truly first-principles based blade vortex interactional
studies.
OBJECTIVES
•
Examine the ability of first-principles Euler/NS methodologies to
capture rotor-blade tip vortices.
•
Develop vortex tracking grids for blade tip vortices with
unsteady the “vortex grids” embedded inside the main grid
(overset refinement).
•
Compare the vortex diffusion characteristics of DG with ENO for
a 3D rotor computation. Analyze the relative computational
speed, memory overheads.
•
Capture the tip-vortex for the first 180 degrees with less than 1020% diffusion, enabling truly first-principles based blade vortex
interactional studies.
ROTOR IN HOVER
Ceradonna-Tung Rotor Blade
ROTOR IN HOVER
Ceradonna-Tung Rotor Tip Vortex
Top View
Side View
ROTOR IN HOVER
Tip Vortex Capture (Fifth Order)
ROTORCRAFT FLOWFIELD SIMULATION
First-Principles Based Methods
•
Fifth Order ENO ( H-H grid, Caradonna-Tung Rotor)
Top View
Side View
Vorticity Iso-Surfaces Showing the Tip Vortex
•
Compact Scheme Issues
Fifth Order Stencils for Computing Left and Right Primitive Variables
HIGH ORDER NAVIER-STOKES FORMULATION
•
NS Equations in Moving Finite Volume Framework




6 
6

qJ    VF  VG q  F  S   Fv  S
t
i1
i1
•
Roe Scheme for Inviscid Fluxes
F
•
F1qL   F1qR 
 A qR  qL 
2
Baseline Fifth Order ENO Scheme (Third Order Temporal Accuracy,
Newton Iterative Scheme)
Fifth Order Stencils for
Computing Left and Right
Primitive Variables
HIGH ORDER NAVIER-STOKES
FORMULATION (DG)
u
t
•

u
x
0
Assume an Approximate Form of Local Solution, let
n 3
u i  Vi x, t    ai, j t b j x 
i 0
where
ai,j are the moments
bj = {b0, b1, b2, …} are some basis functions
n=3 is the third order accurate approximation
i as in the below figure for 1D case
i
xi-1
xi+1
xi
xi-1/2
Stencil for DG Method
xi+1/ 2
xci
•
Using the Classical Galerkin Technique, One Minimizes the Error by,
 u u 
  dx  0
 t x 
 bk x 
i
DISCONTINUOUS GALERKIN FORMULATION
3-D Euler Equation

Ut    F  0
•
Quadrature-free approach (Atkins and Shu)
N
 
 bk  v i, j t b jJid  
i
i0
i


bk  Ji1FiJid 
0  k  N,
Ji 
i
0  i  I
x, y, z 
 , ,  

1 R
b
J
F

J
d
s
0
 k i i
i
DISCONTINUOUS GALERKIN FORMULATION
•
Three One-Dimensional Solutions in psi, eta, and tau
Directions
v F

0
t 
v F

0
t

v F

0
t 
bk  1, , 2, 3
v  a0  a1  a22  a33
•
Third Order Explicit Runge-Kutta Time Stepping
DISCONTINUOUS GALERKIN FORMULATION
Memory Management
•
Fourth Order (in 1-D Sense) Solution Requires Storage Of:
- a0-a9
- 10 for each independent variable
- 5 variable - 50 for each time-level stored
- 3 time level - 150 elements for each cell
•
Optimal Implementation Depends on Machine/Environment
•
Current Implementation
- for each grid
-- read data from disk
-- update a0-a9 for all time level
-- write data to disk
- next grid
-- (similar to OVERFLOW)
UNSTEADY OVERSET FRAMEWORK
3D, Unsteady, Overset Solver
Exp
ent
Exp
eerim
rimen
t
Euler-First Rev
Euler_516
Euler- 1/2 Rev
Eu
ler_
Lat
er 696
4
3
Cp
2
8
Experiment
Experimental
Euler
Euler_366
6
Cp
4
1
2
0
0
-1
-2
-2
-4
-3
PSI=6
-6
PSI=156
-4
-8
0.1
0.325
0.55
x/R
0.775
1
0.1
0.325
0.55
x/R
0.775
1
Y 6
Y56
Instantaneous Cp Distribution on the Crownline of Airframe when Rotor is at an Azimuth of PSI = 156°
OVERSET REFINEMENT
•
Wing-Vortex System
•
Vortex Grid Adaptation
Wing Components Across
Vortex Grid System
•
Additional Overset Grids
•
Combination of Both. Provide Enough Points by Oversetting.
OVERSET REFINEMENT
Vortex Grid Adaptation
Initial
Top View
Final
Movement of a Streamwise Plane
Side View
Tip Vortex
Schematic of Unsteady Vortex Grid System
OVERSET REFINEMENT
Vortex Grid Adaptation
•
Wing-Vortex Grid (Vortex Grid 100*30*30)
Wing Vortex Grid System
OVERSET REFINEMENT (cont.)
Vortex Grid Adaptation
•
Vorticity Iso-surface
Top View of the Tip Vortex
Side View of the Tip Vortex
MECHANISM OF 3D VORTEX STRUCTURE
VORTEX CONVECTION DISCONTINUOUS GALERKIN
Vortex Grid 100*30*30, Mach No = 0.4
a. x/c=0.1
b. x/c=0.5
c. x/c=0.9
VORTEX CONVECTION DISCONTINUOUS GALERKIN
Vortex Grid 100*30*30, Mach No = 0.4
a. x/c=1.0
•
b. x/c=2.0
c. x/c=3.0
Retains Vortex Up to Four Chord Lengths for the Given Grid
VORTEX CONVECTION DISCONTINUOUS GALERKIN
•
Cannot Use DG Methods Like ENO Methods (for high order
projection only)
•
The Mass-Matrix Dependency of Solution on its High Order
Moments is a Central Characteristic of this Method
VORTEX CONVECTION - FIFTH ORDER
ENO
Vortex Grid 100*30*30, Mach No = 0.18,
Eighteen Chord Lengths
Original and Adapted Vortex Grid
Streamwise Momentum Contours Across Spanwise Section of the Vortex Grid
VORTEX CONVECTION - FIFTH ORDER
ENO (cont.)
Comparison of Axial (black) and Tangential (red) Momentum Variation Across the Vortex
SEVENTH ORDER ENO
•
Seven Point Stencil
Seventh Order Stencil for Smooth Flow Conditions
•
One Sided Stencil Near Boundaries. Uniform High Order
Accuracy
•
Third Order Temporal Accuracy
VORTEX CONVECTION - SEVENTH
ORDER ENO (cont.)
•
Stability
- Same as Fifth Order ENO - One Chord Length Every
(50/Mach No.) Iterations
•
CPU Requirements
•
SCHEME
CPU/TIME
ITERATION
Fifth ENO
13.5 seconds
Seventh ENO
17.2 seconds
27% More CPU for Seventh Order
VORTEX CONVECTION - SEVENTH
ORDER ENO (cont.)
Vortex Grid 100*30*30, Mach No = 0.18, Eighteen Chord
Lengths (~180 degrees of revolution for a rotor of AR=6)
U-Momentum Contours Across a Spanwise Section of the Vortex Grid
U, W Momentum Variation Across the Vortex at Various Streamwise Sections
VORTEX CONVECTION - SEVENTH
ORDER ENO (cont.)
Vortex Grid 100*30*30, Eighteen Chord Lengths,
Skewed Grid
Mx=0.04
Mx=0.18
U-Momentum Contours Across a Normal Plane of the Vortex Grid
U, W-Momentum Variation Across the Vortex at Various Streamwise Stations
VORTEX CONVECTION - SEVENTH
ORDER ENO (cont.)
Vortex Grid 100*30*30, Eighteen Chord Lengths,
Skewed Grid
U-Momentum Contours at Several Streamwise Stations
VORTICITY TRANSFER ACROSS
OVERSET GRIDS
(ENO Schemes)
Grid-2
Interface_In
Tip Vortex
Trajectory
Interface_Out
Hole Boundary for Grid-1
Grid-1
Schematic of the Vortex Trajectory through the Main and Vortex Grid
•
High Order Near Boundaries (one-sided stencils)
•
Reduced Order Near Hole Boundaries (...can be high order)
VORTICITY TRANSFER ACROSS
OVERSET GRIDS (cont.)
Interface_In
1.8
1
Grid-2
Grid-1
0.5
Grid-1
Grid-2
1.6
Vx/Vinf
Vz/Vinf
1.4
0
x/c ~ 0.1
x/c ~ 0.1
-0.5
1.2
-1
1
-1.5
0.8
-1
-0.5
0 y/c 0.5
1
1.5
-1
-0.5
0 y/c 0.5
1
1.5
VORTICITY TRANSFER ACROSS
OVERSET GRIDS (cont.)
Interface_Out
Interface_Out
y
x
Grid-2
Tip Vortex
Trajectory
Hole Boundary for Grid-1
Grid-1
0.8
1.3
0.6
1.25
Grid-1
Grid-2
Vz/Vinf
0.4
Grid-2
Grid_1
Vx/Vinf
1.2
0.2
1.15
0
x/c ~ 4.0
1.1
x/c ~ 4.0
-0.2
1.05
-0.4
1
-0.6
0.95
-0.8
-1
-0.5
0
0.5
y/c
1
1.5
-1
-0.5
0
0.5
y/c
1
1.5
VORTEX CONVECTION - SEVENTH
ORDER ENO
Vortex Grid 300*30*30, Fifth Chord Lengths
(~ 3-4 half-revolutions for a rotor of AR=6)
x/c=2
x/c=25
x/c=50
Axial-Momentum Iso-Surface Showing the Vortex. Graphs Show Axial (black) and
Tangential (red) Momentum Distribution across Vortex
SUMMARY
•
A fourth order spatial and third order temporal, 3-D,
Discontinuous Galerkin scheme was implemented in unsteady
overset settings and was proven feasible.
•
The efficiency of self-adaptive vortex-grid vortex grid
technology was proven using tip vortex generated over a wing.
•
Vortex capturing using a wing grid-vortex grid overset system
was undertaken using a baseline fifth order spatial/third order
temporal ENO scheme.
•
The behavior of three dimensional vortices was analyzed in
detail and the importance of capturing the axial momentum
variation of the tip vortex was elucidated. Vorticity transfer
characteristics between overset grids in a high order setting
were analyzed.
SUMMARY (cont.)
•
A seventh order ENO methodology was implemented in
extension to a baseline 5th order scheme.
•
An ambitious objective of identifying and proving a high order
overset method to capture blade tip vortices over 180 degrees
with less than 10% dissipation has been achieved and
bettered in a demonstration of capturing the wing tip vortex
over fifty chord lengths with negligible dissipation of the vortex.
CONCLUSIONS
•
3D Euler/NS Vortex Capturing has to Resolve the Axial
Component Across the Vortex. Otherwise the Captured Vortex
Resorts to a Wake-Like Mode Triggered by Numerical
Dissipation.
•
A Combination of High Order Method and Overset
Refinement/Adaptation is Highly Efficient and Ideal for
Rotorcraft Tip Vortex Resolution.
•
It is Possible to Capture Tip Vortices up to 3-4 Half Revolutions
(or even 5-6 revolutions) with Grid Sizes Small Enough to Run
with Workstations.
CONCLUSIONS (cont.)
•
First-principles Based Euler/NS Simulations with Overset
Refinement have Reached a Point Where They Can be Used
in Routine Rotorcraft Computation.
•
ENO-based Methods are Ideal for Rotorcraft Computations
such as Forward Flight BVI, Evaluation of Tip Shapes, Active
Devices etc. (relatively well known vortex structure).
Georgia Tech
School of Aerospace Engineering
Rotorcraft Research
at
Georgia Tech
L. N. Sankar
School of Aerospace Engineering
Georgia Institute of Technology
* This work was funded by the National Rotorcraft Technology
Center (NRTC) and RITA
Http://www.ae.gatech.edu/~lsankar
Georgia Tech
School of Aerospace Engineering
Outline
• Overview of all the Rotorcraft Center Tasks
• Rotorcraft CFD Research by the Present
Investigator and Coworkers being funded under
NRTC and RITA
• Related research activities
– Wind Turbines
– Compressor Flow Control
– Circulation Control
Project Title : Active Rotorcraft Blade Tips for Tip Vortex Core Modifications
Project Number: GT 1.1
PI: N. Komerath nkomerath@ae.gatech.edu, S. Dancila sdancila@ae.gatech.edu, L. Sankar lsankar@ae.gatech.edu
Technical barriers/problems :
• Rotor blade tips substantially affect blade
performance.
• Passive and active modifications may be necessary to
improve the performance and noise characteristics
of rotors.
Objectives :
• Systematically study through experiments a number
of passive and active tip shapes.
• Perform computational studies to further understand
the flow physics near the blade tip, and how/if active
and passive control strategies may be beneficial.
• Develop and demonstrate innovative active and
passive control methods for modifying flow field in the
vicinity of the rotor tip, and in the wake.
Key Milestones
milestones
• Detailed wake field measurements for an
advancing rotor.
• Computational and experimental modeling
of several passive control concepts
• Preliminary CFD studies of active control
concepts
01
02
03
‘01 Accomplishments :
• Deatiked wake measurements were done for a
baseline rotor.
• Algorithmic improvements were done to the
TURNS analysis, in collaboration with Task 1.2
• Preliminary numerical results were obtained for
the wake structure behind a baseline rotor.
‘02 Plans :
• PIV measurements will be done for new baseline
and rounded-tip rotors in forward flight
•Detailed Analysis, modeling and implementation
of piezoelectric actuation for blowing modulation
on blade tips will be done.
• CFD studies done in support of the experiment.
Project Title : First-Principles based Modeling of Rotors in Hover, Forward Flight, and Maneuver Project Number: GT 1.2
PI / tel /e-mail L. Sankar, S. Ruffin, D. Peters lsankar@ae.gatech.edu, 404-894-3014; sruffin@ae.gatech.edu 404-894-8200
Technical barriers/problems :
• First principles based models of rotors in hover
and forward flight suffer from numerical
errors such as dispersion, and diffusion.
• Physics of the flow (e.g. tip vortex formation)
can not be adequately modeled until these errors are
minimized.
• Strategies are needed for tightly coupling
these methodologies to trim and aeroelastic
models.
Experiment
TURNS-STVD6-WENO5
CQ/s
Objectives :
• Develop spatially, and temporally accurate algorithms.
• Develop embedded and adaptive grid
based methods for tracking vortices.
• Validate methodology with data for rotors in hover
and forward flight.
CT/s
0
Key Milestones
milestones
• Hover methodology development.
• Forward flight method development,
and validation against UH-60A airloads.
• Adaptive grid method development
01
02
03
0.02
0.04
0.06
0.08
0.1
0.12
‘01 Accomplishments :
• 4th, 6th, and 8th order algorithms were evaluated for
rotors in hover.
• Preliminary calculations were done for UH-60A
rotor.
• Two papers were published; improved methods
were made available to industries.
‘02 Plans :
• Complete hover studies; implement higher order
metrics and load integration.
• Improve UH-60A results with measured blade
dynamics
• Begin adaptive grid based vortex tracking.
Project Title: Simulations of Unsteady Flow-Rotor Interactions to Predict Dynamic Loading in a Turbulent Environment Proj No. GT 1.3
PI M. Smith, S. Menon marilyn.smith@ae.gatech.edu, 404894-3065 suresh.menon@ae.gatech.edu, 404-894-9126
Technical Barriers, Problems:
• Modern rotorcraft rotor and airframe loading is not wellpredicted by RANS methods.
• Existing turbulence models developed for steady flows
• LES provides the opportunity to investigate turbulence
models in unsteady flows at the small-scale level where
experimental methods cannot provide data
Velocity Profiles at X=1.6, Z=0
1
Baldwin-Lomax
Degani-Schiff
Johnson-King
Spalart-Allmaras
0.8
0.6
Y

0.4
0.2
Objective(s):
• Extend and validate LES methods for unsteady flows of
interest.
• Compare RANS, LES, and experimental data for steady and
dynamic stall situations
• Use LES to determine how to modify RANS turbulence
models
Tasks (CY)
• LES code extension and
validation
• Extend RANS codes to include
variety of turbulence models
01
02
03
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Velocity
2001 Accomplishments:
• LES code extended to include BC/IC for wing geometry
• Ability of different grid-types: H,C,O and embedded
investigated for application to LES of pitching wings
• Evaluate steady semi-infinite
wing
• RANS turbulence model study conducted, RANS codes
underway to update turbulence models, RANS steady
testing begun.
• Evaluate unsteady semi-infinite
wing
• Compare LES with RANS and experiments for steady semiinfinite wing..
• Evaluate steady finite wing
2002 Plans
• Begin evaluation for dynamic stall of semi-infinite wing..
Project Title : Efficient and Affordable Joining of Composites
Project number: GT 2.1
PIs : Armanios, (404) 894 8202, erian.armanios@ae.gatech.edu, Dancila (404) 894 8197, stefan.dancila@ae.gatech.edu
and Makeev (Delta), 404) 714 3655, andrew.makeev@delta.com
Technical barriers/problems :
• Premature failure of joints
- Boundary layer distribution of interlaminar stresses
- Presence of peel stress
•Lack of understanding of interacting failure mechanisms
- retro-fit fixes
•Lack of reliable tools for failure prediction
Objectives :
• Development of affordable composite joint concept
• Isolate mechanism driving premature failure
• Development of associated predictive failure models
• Stress-based
• Strain energy release based
Key Milestones
milestones
• Development and validation of analytical
Models for interlaminar stresses
• Performance of parametric studies
•Manufacturing and testing under monotonic
And fatigue loading
•Identification of associated damage growth/
Crack resistance mechanisms
01
02
03
Nested overlap concept leading to compressive peel stress
‘01 Accomplishments :
•Nested-overlap concept developed
-achieved compressive peel
•Corrugated interface
- testing
•Edited special volume on bonded joints
- FAA, ASTM
•’02 Plans :
•Validation of nested-overlap concept
-Manufacturing and testing
•Improved corrugated concept
•Edit follow-up volume on bonded joints
Project Title: Phenomenological & First Principles Based Models for Complete Helicopters
Project No. GT 3.1
PI M. Smith, L. Sankar, S. Ruffin msmith@ae.gatech.edu, 404894-3065 lsankar@ae.gatech.edu, 404-894-3014; sruffin@ae.gatech.edu 404-894-8200
Technical Barriers, Problems:
• Modern rotorcraft have adverse rotor-airframe, and rotorempennage interactions, which are not clearly understood.
• Existing methods based on panel methods and lifting line
theory can not model these interactions well.
• In some instances, the unsteady airloads on the tail due to
the wake can cause tail fatigue, and/or loss of directional
control.
Objective(s):
• Develop rapid first-principles based methods for modeling
complex fuselage shapes.
• Develop hierarchy of methods for coupling rotor
aerodynamics to fuselage aerodynamics.
• Use the computational tools to improve the aerodynamic
characteristics of rotorcraft.
Tasks (CY)
• Unstructured & Cartesian
Fuselage Analysis
• Incorporation of rotating force
field model
• Replacement of body force with
individual blades
01
02
03
2001 Accomplishments:
• Several unstructured grid methodologies, and an adaptive
Cartesian grid based method were evaluated for use in
rotor-airframe interactions.
• A seventh order accurate method (developed under Task
1.2) was modified for modeling rotor-airframe interactions.
2002 Plans
• Couple Fuselage method
w/CSM
• Apply the unstructured grid method, and the Cartesian grid
based method to ROBIN fuselage.
• Evaluate other features (vortex
modeling, turbulence. modeling,
etc.)
• Couple the rotor solver to the fuselage analyses, obtain
preliminary results.
Project Title : Damage Tolerance Analysis of Stiffened Composites and Rotor Hubs
Prof. E. Armanios (GT) / 404 894-8202
Dr. A. Makeev (Delta) / 404 714 3655
Technical barriers/problems :
•Absence of general damage tolerance analysis methodology
• Absence of efficient and accurate models to predict interlaminar
stresses and energy release rates
• Finite element based techniques for evaluation of energy release rate
components not convergent
5
Project Number: GT 5.2
Prof. A. Badir (CAU) / 404 880 6900
t yb
u0
, GPa
4
ABAQUS, 1098 variables
3
ABAQUS, 15972 variables
BEM, 144 variables
BEM, 896 variables
Objectives :
• Development of cost effective, reliable models for damage tolerance
analysis of rotorcraft composites
2
1
x
b
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1
Key Milestones
milestones
• Analysis for structures of simple
geometry
• Extension of the analysis to nonlinear
tapered flexbeams
• Development of a 3D model for
composites
01
02
03
‘01 Accomplishments :
•Simple damage tolerance analysis methodology
identified
• Simple boundary element models for composites
developed
‘02 Plans :
• Incorporation of higher order elements
• Large systems capability based on global/local
FEM/BEM
• Selection of efficient and accurate fracture
mechanics analysis techniques for composites
Project Title : COMPOSITE BEAM CROSS-SECTIONAL OPTIMIZATION
Project Number: GT 5.3
V. V. Volovoi & D. H. Hodges / 404-894-9811 & -8201 / Vitali.Volovoi@ae.gatech.edu & Dewey.Hodges@ae.gatech.edu
Technical barriers/problems :
Baseline and
• Design space for composite rotor blades vast and mainly
design variables
unexplored
• Traditional design based on evolutionary changes of existing
layouts; inherently leads to sub-optimal configurations
• Industry is yet to exploit elastic couplings
Optimized configuration
• Optimal design of rotor blades is a tightly coupled
interdisciplinary problem
• 3-D structural optimization of rotor blades is not feasible
Objectives :
Stress field assessment
for various loads
• Apply cross-sectional analysis based on a rigorous asymptotic
framework to design rotor blades with desired properties
• Compliment evolutionary rotor blade design with
conceptually new designs
• Develop numerical methods that produce models suitable
for practical rotor blade cross-sectional configurations
‘01 Accomplishments :
Key Milestones
• Stand-alone parametric model of a rotor-blade has
Milestones
been created
Tasks
01
02
03
04
05
•This model has been connected with VABS and and an
Parametric optimization:
SimpleIntermediate
Example example
Proof of concept
sizing
optimizer in an automatic fashion
Modeling Manufacturing
•Tools for convenient assessment of stress distribution
Industry survey
Formal Set of constraints
constraints
over the cross section were developed.
Accounting for
Visualization/Stress recovery
Using as optimization constraints
Stress distribution
•This optimization environment was tested on a simple
Library of traditional
Accumulating
Database
lay-outs
example
‘02 Plans :
Global optimization
Aeromechanics example
• Increase the fidelity of the model, consider several
UCAR Proto/ Demo
Topological
Proof of concept
Optimization
other objective functions
• Consider an example with discrete variables
Robust Design
Probabilistic optimization
• Investigate the robustness of the solution
Project Title : Wakes of Rotorcraft Maneuvering in Ground Effect
Project Number: GIT 8.1
N.M. Komerath, GIT 404-894-3017 ; A.T. Conlisk, OSU 614-292-0808
Technical barriers/problems :
• Multiple time scales of unsteadiness associated with
ground vortex phenomena.
• Origin of the ground vortex.
• Influence of flight condition on parameters such as
thrust and load.
Objectives :
• Develop physically-based models for rotor wake
behavior in ground effect, with unsteadiness due to
maneuvers or gusts.
• Understand time scales of unsteadiness, including
ground vortex, and vortex interactions.
• Use findings to improve the aerodynamics in reducedorder flight simulation models.
Key Milestones
milestones
•Experiments – wake distortion
•Experiments on time lag in inflows
and loads
•Experiments: fuselage loads
•Computation: loads and wake
deflection; reduced-order model
01
02
03
‘01 Accomplishments :
•Flow visualization experiments successful in
capturing steady (cleanly periodic) and unsteady
test cases
•Computation modeled wake geometry in hover and
forward flight IGE.
•Computation captures thrust variation due to
vortex interaction effects in inflow.
‘02 Plans :
•Quantify flow field of rotor wake & ground vortex.
• Quantify time scales of unsteadiness.
• Fuselage loads experiment & computation
Project Title: Limit Detection and Limit Avoidance Methods for Carefree Maneuvering
PIs: J.V.R. Prasad & A.J. Calise tel: (404) 894-3043, (404)894-7145
Technical Barriers/Problems:
• Current limit prediction methods are based on the
availability of an accurate simulation model of the vehicle.
• ‘Dynamic trim’ based limit prediction is not
applicable to the transient limit parameter predictions.
• It is not clear how to provide cues for multiple and
conflicting limit parameters in multiple control axes.
• An effective limit cueing system will facilitate full
exploitation of flight envelope with reduced pilot
workload for highly reliable and safe operations of rotorcraft.
• Objectives:
• Develop adaptive algorithms for prediction of limit
parameters that reach limit boundaries during dynamic trim.
• Develop algorithms (in collaboration with Prof. Horn of
Penn State) for prediction of limit parameters that reach
limit boundaries during transient part of the response.
• Develop approaches to combine pilot cueing and limiting
using AFCS for envelope protection.
• Carry out simulation and flight test evaluations in
collaboration with industry and government labs.
• Investigate potential applications of the envelope limiting
algorithms to UAVs using the UAV test bed at Georgia Tech.
Key Mile Stones:
Milestones
Adaptive limit prediction algorithms
Simulation evaluation of adaptive algorithms
Transient limit detection algorithms
Combined pilot cueing and limiting using AFCS
Piloted simulation and flight test evaluations
Potential UAV applications
01
02
03
04
05
Project Number: GT 8.2
Adaptive
Limit
Detection
Control Inputs
and
Vehicle States
Estimation of Future
Limit Variables
Limit
Avoidance
Adaptive Limit Detection
and Avoidance
CY ‘01 Accomplishments:
• Developed a neural net based adaptive limit
parameter prediction method
• Carried out simulation evaluations of the adaptive
algorithms using the Generalized Tilt Rotor (GTR)
simulation model.
• Developed a method for extraction of dynamic trim
maps directly from time response data.
• Developed a method for limiting using the automatic
flight control system for UAV applications.
CY ‘02 Plans:
• Adaptive algorithms using nonlinearly parameterized
neural networks
• Combined pilot cueing and limiting through AFCS.
• Flight test evaluations of envelope limiting using the
AFCS on our UAV helicopter test bed.
Project Title: Deformable Wake Dynamics for maneuvering Flight Simulation
PIs: J.V.R. Prasad & D.A. Peters tel: (404) 894-3043, (314)935-4337
Project Number: GT 9.1
Climb
Technical Barriers/Problems:
• Wake distortion effects are the primary source
of the off-axis response behavior observed in maneuvering flight.
• Finite state inflow models offer a viable alternative in terms of
accuracy and computational expense.
• Development of accurate models to capture the essential
physics of wake distortion effects on the flow behavior
at and off the rotor are important for development and
evaluation of model decoupling flight control laws and for
effective use of piloted simulation for various aircraft
subsystem development and pilot training.
Objectives:
• Development of inflow models to capture wake bending,
skew and spacing dynamics during transient maneuvers.
• Development of inflow models for inflow off the rotor.
• Integration of refined inflow models into a comprehensive
flight simulation program and carry out simulation evaluations.
• Correlations with available wind tunnel and flight test data.
• Transition of inflow models to govt. labs and industry.
Key Mile Stones:
Milestones
Wake dynamics modeling in hover
Wake dynamics modeling in forward flight
Wake bending and skew coupling
Modeling of inflow off the rotor
Correlations with test data and model refinements
Transitions to industry and govt. labs
01
02
03
04
05
Hover
Forward Flight
Pitch Up
Rotor Dynamic Wake
Distortions during
Transitional Flight From Hover
CY ‘01 Accomplishments:
• Formulated a reduced-order wake distortion
model for transitional flight from hover
• Extracted time constants of the model using
results from vortex tube theory
• Carried out model validations through
comparison of simulation predictions using
GENHEL with the Black Hawk flight test data
CY ‘02 Plans:
• Development of reduced order wake distortion
models for forward flight
• Development of reduced order models for
inflow off the rotor
• Model validations using flight test data
Project Title : Neural Network Based Adaptive Flight Control
PI’s: Prof. A.J. Calise and Prof. J.V.R. Prasad
Tel: (404)894-7145, 3043
Linear
controller
Technical barriers/problems :
• Gain scheduled control designs are awkward and difficult
to apply to high bandwidth UAV control design
• Adaptive control using neural nets offers a viable
alternative and is adaptive to parameter uncertainty
• High bandwidth adaptive control will have to also
address more difficult issues related to time delays,
unmodeled dynamics and actuator saturation
Basic research in limited authority adaptive output
feedback
Research in active rotor control (Boeing Mesa)
Applications of high bandwidth adaptive flight control
(Bell and NASA Ames)
Experimental demonstrations using the R-50
03
Helicopter
‘01 Accomplishments :
• Development and improvement to an approach
to output feedback adaptive control
• Development of an adaptive approach for
vibration suppression
• Implementations on the R-50 helicopter and
laboratory demonstration in vibration
suppression. We are getting to higher
bandwidths.
Key Milestones
01 02
Model
Inversion
Adaptive
NN/FL
Objectives:
• Extend our current research to the case of adaptive output
feedback control, permitting robustness to unmodeled
dynamics
• Develop and approach to directly deal with control limits
and in an adaptive control setting
• Validation in both simulation and flight experiments,
• Collaborative efforts with both industry and government
labs
• Pursue technology transition opportunities
Milestones
Project Number: 9.3
04
05
‘02 Plans :
• Continue to refine NN based adaptive output
feedback control
• Continue to develop our approach to vibration
suppression and its application
• Continue Flight testing and higher bandwidths.
This will include closing outer loops that
control velocity, flight direction and position
• Pursue technology efforts with industry in UAV
high bandwidth rotary wing flight control and
active vibration control.
• Continue to aggressively pursue rapid
developing technology transfer opportunities,
and leveraging with other NASA/Air Force
/DARPA programs
Project Title : Elastically Tailored Smart Composite Rotor Blades
Project Number: GT 5.1
PI: E Armanios earmanios@ae.gatech.edu, S Dancila sdancila@ae.gatech.edu, O Bauchau obauchau@ae.gatech.edu
Technical barriers/problems :
•Change of linear twist of 20+ degrees required between cruise
and hover to optimize performance in both regimes on typical
tiltrotor configuration (Nixon et al. )
•Closed cell composite beams - insufficient level of coupling
while meeting torsional stiffness stability requirements
•Open cell composite beams – appropriate level of coupling but
insufficient torsional stiffness
•Need for a structural concept that provides adequate level of
coupling without weight or stability penalties
•Need for efficient piezoelectric actuator amplification
strategies/mechanisms
Objectives :
•Improve the performance of rotor blades by combining elastic
tailoring and piezoelectric actuation
•Develop configurations functional and efficient on tailored active
rotor blades at full scale
Key Milestones
milestones
•Systematic investigation of star cross
section beams
•Modeling and analysis of tailored beams
for blade flap hinge
•Modeling and analysis of hinge tensiontorsion beam warping actuation using
piezoelectric stack actuators
01
02
03
‘01 Accomplishments :
•Systematic investigation of tailored star cross section
beams
•Fundamental understanding – tailoring the entire blade
structure not effective
•New approach:
•Untailored blade spar - high torsional stiffness
•Extension-twist coupled deformation of trailing edge
blade section (flap)
‘02 Plans :
•Modeling and analysis of flap hinge tailored beams
•Modeling and analysis of hinge tension-torsion beam
warping actuation using piezoelectric stack actuators
CFD Activities by the
Present Investigator and Coworkers
• Spatially High Accuracy Algorithms for
improved tip vortex modeling and
performance predictions.
• Efficient Airloads Prediction methods for
Rotors in Forward Flight .
• Modeling of Complete Rotor-Airframe
Configurations.
•
•
•
•
•
•
C
on
Rectangular plan form, Aspect Ratio=6
fig
NACA 0012 airfoil sections
ur
Untwisted rotor
ati
Tip Mach No. 0.388, corresponding
to a rotor rpm of
on
1100.
St tested by McAlister.
This rotor has been extensively
Wake survey LDV data are
udavailable.
Surface pressure and thrust
ie data for a similar
configuration tested by Caradonna et al are also
d
available.
Need for High Accuracy Algorithms
• Many industry standard codes (e.g. TURNS,
OVERFLOW) have low order spatial
accuracy which leads to excessive numerical
diffusion, and dispersion.
• A very fine grid, and large CPU resources are
needed to reduce these errors.
• High order algorithms are an effective way of
reducing these errors and achieving accurate
solutions on moderately fine girds.
Problems with Existing Methods
• Numerical dissipation
–Dissipation causes a gradual decrease in the
amplitude of an acoustic wave or the
magnitude of the tip vortex as it propagates
away from the blade surface.
–The computed vortical wake, in particular,
diffuses very rapidly due to numerical
dissipation
Problems with Existing Methods
•
Numerical dispersion
– Dispersion causes waves of different wavelengths
originating at the blade surface to incorrectly
propagate at different speeds.
– Because of dispersion errors, the waves may distort
in nonphysical manner as they propagate away from
the blade surface.
Model Problem
Propagation of a 1-D wave
• Consider the following
simple PDE:
Initial Condition at t=0:
The exact solution:
u u

0
t x
u ( x, t  0)
u ( x, t )  e
x2

 e 16
2

x t 

16
Initial Solution
1.2
1
0.8
u
0.6
0.4
0.2
0
-100
-75
-50
-25
0
25
50
75
100
How well do the 3rd order schemes in
OVERFLOW, TURNS, and CFL3D do?
1.2
Upwind, T=50
1
Dissipation
0.8
Exact
u
0.6
0.4
Dispersion
0.2
0
-0.2
0
25
50
75
100
What happens at later time levels?
1.2
Upwind, T=100
1
0.8
Exact
u
0.6
0.4
0.2
0
-0.2
-0.4
50
75
100
x
125
150
A Possible Cure
• Compute the spatial derivatives with a
sufficiently high order finite difference
approximation (Text book solution)
• Further optimize the coefficients in the finite
difference form by minimizing the dissipation
and dispersion errors (low dispersion schemes
by Tam; Nance and Sankar).
nce of a Spatially Fourth Order Algorithm for this
1.2
1.2
STVD-4, T=50
1
0.8
STVD-4, T=150
1
Exact
0.8
Exact
0.6
u
u
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
0
25
50
75
100
-0.2
100
125
150
x
175
200
Application to a Fixed Wing
-5
-4
Experiment
Fifth Order
Third Order
Cp
-3
-2
% Semi-span = 89
-1
0
1
0
0.2
0.4
0.6
0.8
1
x/c
Surface Pressure Distribution
89% Span
Surface Pressure Distribution
97% Span
-5
-4
Experiment
Fifth Order
Cp
-3
Third Order
-2
% Semi-span= 97
-1
0
1
0
0.2
0.4
0.6
x/c
0.8
1
Tip Vortex Velocity Field
Downwash one chord length downstream
0.8
0.6
Vz/Vinf
0.4
0.2
3rd order
MUSCL
0
-0.2
x/c = 1.0
-0.4
-0.6
-0.8
-0.8 -0.6 -0.4 -0.2
0 0.2
y/c
0.4 0.6
0.8
Downstream of 5 chord lengths, the vortex quickly
Diffuses, even with the 5th order scheme.
Axial Velocity in the
Core of the Tip Vortex
1.6
Vx / Vinf
1.4
x/c = 0.5
1.2
1
0.8
0.6
-0.8 -0.6 -0.4 -0.2
0 0.2
y/c
0.4 0.6 0.8
Axial velocity field is well predicted by the 5th order
Scheme, up to 1 chord length in the wake.
OVERSET REFINEMENT
•
Wing-Vortex System
•
Vortex Grid Adaptation
•
Additional Overset Grids
•
Combination of Both. Provide Enough Points by Oversetting.
Wing Components Across
Vortex Grid System
OVERSET REFINEMENT
Vortex Grid Adaptation
Initial
Top View
Final
Movement of a Streamwise Plane
Side View
Tip Vortex
Schematic of Unsteady Vortex Grid System
OVERSET REFINEMENT
Vortex Grid Adaptation
•
Wing-Vortex Grid (Vortex Grid 100*30*30)
Wing Vortex Grid System
OVERSET REFINEMENT
Before
Vortex Grid Adaptation
After..
Top View of the Tip Vortex
Side View of the Tip Vortex
VORTEX CONVECTION - SEVENTH
ORDER ENO (cont.)
Vortex Grid 100*30*30, Eighteen Chord Lengths,
Skewed Grid
U-Momentum Contours at Several Streamwise Stations
RITA and NRTC Activities on High Order Algorithm
• Spatially high order algorithms (4th, 5th, 6th, 7th, 8th)
have been systematically implemented in public
domain codes such as TURNS, OVERFLOW.
• In most instances, the change from the user
perspective is a simple flag in the make file.
• Computer time does increase (per point per time step)
by 10% to 20% with the higher order methods,
compared to 3rd order MUSCL schemes.
• This increase is offset by the ability obtain accurate
results on relatively coarse grids.
Performance of the UH-60A Rotor
Grid Size 149x89x61(808K)
0.01
0.8
Experiment
0.009
0.7
0.008
CQ/s
TURNS-STVD6-WENO5
0.007
0.6
0.006
0.5
Experiment
FM
0.005
TURNS-STVD6-WENO5
0.4
0.004
0.3
0.003
0.2
0.002
0.001
0.1
CT/s
0
0
0.02
0.04
0.06
0.08
0.1
0.12
CT/s
0
0
0.05
0.1
• Error of 0.01-0.02 in FM; well within 100 lb. or 200 lb. error in
0.15
thrust;considered very good by industry.
• Tip loads still not satisfactory due to highly stretched grids. Work
must be done to improve performance of high order algorithms on
highly stretched grids. This is critical to rotor tip design.
Efficient Methods for High Speed Forward
Flight
 Modeling high speed forward flight phenomena requires detailed
modeling aerodynamics (transonic flow, dynamic stall), elasticity,
blade dynamics and pilot input.
 First-principles based aerodynamic analyses (Navier-Stokes,
Potential Flow) have been available to the industries for some
time, but are computationally expensive, and require several
days of turn-around time.
 In some studies, an open-loop coupling between aerodynamics
and the other effects are done.
 Trim, elasticity, blade dynamics, wake are handled by the
comprehensive analysis
 Viscous flow, transonic effects handled by CFD.
Hybrid Methods for Rotors in
Forward Flight
• This method integrates the most appropriate models in
different flow regions to retain solution quality.
• A large reduction in computer time is reached.
• Related Prior Work
– Berezin coupled hybrid solver to RDYNE to account for the far wake
and trim effects.
– Berkman (under Sikorsky support) modeled the entire wake from first
principles, and obtained good results in hover.
– Moulton and Caradonna coupled HELIX to TURNS for modeling
rotors in hover.
– Bangalore and Caradonna extended Moulton’s work through overset
grid for advancing rotor flows.
School of Aerospace Engineering
Georgia Tech
Hybrid Methodology
N-S zone
FPE zone
Lagrangean Wake
• Navier-Stokes solver for
modeling the viscous flow
and near wake
• Potential flow solver for
modeling the inviscid
isentropic flow
• Lagrangean approach for
convecting vortex
filaments without
diffusion in the potential
flow zone and the far field
School of Aerospace Engineering
Georgia Tech
Implementation Details
• CPU time was reduced by performing hybrid
analysis for a single blade.
• The other blades are “seen” by the analysis as
a collection of bound and tip vortices.
• There is no more need to match and patch the
grids around multiple moving, deforming
blades.
Georgia Tech
School of Aerospace Engineering
Implementation Details (Cont.)
• This allows pitching and flapping motion to be
modeled rapidly without need for inter-blade
grid continuity.
• The solutions are manually trimmed outside
the flow solver, once every revolution.
• Elastic deformations are included, where
available.
Georgia Tech
School of Aerospace Engineering
Blade Dynamics
• A module to cope with the rigid blade motions in flap
and pitch, and the complex blade deformation due to
aeroelastic effects has been developed.
• For rigid blades, the (x,y,z) positions in space at any
instance in time may be transformed using Eulerian
angles:



xnew  Txold  ABC xold
• If the blade is not rigid, the grid motion should
include additional rotations in twist, and bending
deformations.
Georgia Tech
School of Aerospace Engineering
Wake Model
• Wake markers may lie inside the grid, or outside.
•Rigid wake model is used by default.
• Free wake model that can model the distortion from a
basic helical shape is also available.
•We use Biot-Savart Law to evaluate the self induced
velocity.
•We have also programmed Steinhoff’s Clebsch
formulation
Georgia Tech
School of Aerospace Engineering
UH-60A in High Speed Forward Flight
• Validation case:
–Advance ratio m=0.3
–Tip mach number Mtip=0.628
–The blades were trimmed to eliminate oneper-rev flapping.
q  11.50  1.84 0 cos  7.50 sin
–H-O multi-block grid: 90x44x80 (NS zone:
62x26x44)
School of Aerospace Engineering
CP at =00 (r=68%R and 94.5%R)
Georgia Tech
CP
Hyb. Method (Lower)
r=68% R.
-2
Hyb. Method (Upper)
Exp. (Upper)
-1.5
Exp. (Lower)
-1
-0.5
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
0
x/c
0.5
1
1.5
-1.2
CP
r=94.5%R.
Hyb. Method (Lower)
Hyb. Method (Upper)
-1
Exp. (Upper)
Exp. (Lower)
-0.8
-0.6
-0.4
-0.2
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
0
0.2
0.4
0.6
0.8
x/c
CP at =1200 (r=94.5%R)
-1.5
r/R=94.5%
-1
-0.5
Cp
0
0.5
1
1.5
0
0.2
0.4
0.6
x/c
0.8
1
School of Aerospace Engineering
CP at =2700 (r=68%R and 94.5%R)
Georgia Tech
-3.5
CP
r=68% R.
Hyb. Method (Lower)
-3
Hyb. Method (Upper)
-2.5
Exp.
(Upper)
Exp. (Lower)
-2
-1.5
-1
-0.5
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
0
0.5
x/c
1
1.5
-2.5
CP
r=94.5%R.
Hyb. Method (Lower)
Hyb. Method (Upper)
-2
Exp. (Upper)
-1.5
Exp. (Lower)
-1
-0.5
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
0
x/c
0.5
1
1.5
Georgia Tech
School of Aerospace Engineering
Mach Number Contour at r=96%R
(Blade at Y=900)
School of Aerospace Engineering
Georgia Tech
Sectional Thrust Coefficient at r=78%R
1.2
Cn
r/R=78%
1
0.8
0.6
0.4
hybrid, rigid
hybrid, elastic
0.2
experiments
ψ
0
0
-0.2
90
180
270
360
School of Aerospace Engineering
Georgia Tech
Sectional Thrust Coefficient at r=92%R
1
Cn
r/R=92%
0.8
0.6
0.4
hybrid, rigid
0.2
hybrid, elastic
experiments
ψ
0
0
-0.2
90
180
270
360
Modeling complete helicopter configurations
• Motivation:
– Helicopter configurations are often
complex in shape, full of corners and
edges.
– Present overset methods require
considerable CPU time, and a very large
number of overset blocks.
– Design studies require quick turn around
time, and the ability to model local changes
to the geometry.
Prior Work
•
•
•
•
OVERFLOW
Ganesh Rajagopalan’s work.
Steinhoff’s Cartesian grid based approach
Other Cartesian grid based approaches (e.g.
SPLITFLOW)
• Georgia Tech CHIMERA approach
Proposed Approach
• Model the fuselage using an unstructured
grid approach.
– We are starting with USM3D and/or FUN3D
• Model the main and tail rotors using
structured grid methods.
– We will be using GT codes for start.
• Tightly couple these two approaches using
Georgia Tech version of the CHIMERA
scheme.
2
Experiment
1.5
Euler
1
Cp
0.5
0
-0.5
-1
-1.5
0.1
0.95
1.8
x/R
Experiment
Experiment
Euler
Euler_354
10
8
6
Cp
3.5
Mean surface pressure
distribution along the crown
line of the airframe
12
PSI=174
4
2
0
-2
0.2
2.65
0.3 0.4
0.5 0.6 0.7
x/R
0.8 0.9
1
Instantaneous surface
pressure distribution along
the crown line
Modeling for Hover, Forward Flight, maneu
• This task is a continuation of prior work by
– Nathan Hariharan (ENO, adaptive CHIMERA)
– Ebru Usta (STVDx schemes)
– Zhong Yang (Hybrid Approach)
• Basic algorithm developments done under
the Center funding will feed into applied
work with industry partners.
Active Control of Rotors
• Joint task with Dr. Komerath and Dr. Dancila
• We will be computationally investigating
various tangential and normal jet concepts.
• Starting point is the circulation control airfoil
research being done at Georgia Tech under
NASA support.
Related Research
• Wind Turbine Aerodynamics
• Compressor Flow Control
• Circulation Control Airfoil Research
School of Aerospace Engineering
Georgia Tech
Results for the Phase II Rotor
20
Generator Power[kw]
15
10
5
0
0
-5
-10
NREL
NREL experiment
experiment
N-S
N-S Solver
Solver
Hybrid
Hybrid Code
Code
Lifting
Lineresults
results
AeroDyn
5
15
10
Wind Speeds[m/s]
20
25
School of Aerospace Engineering
Georgia Tech
RESULTS for the Phase III Rotor
Generator Power[kw]
NREL Test data
AeroDyn
Present Hybrid code
20
15
10
5
0
0
5
10
Wind Speed[m/s]
15
20
School of Aerospace Engineering
Georgia Tech
The NREL Blind Run Comparison
• The Phase VI Rotor
•Full Scale Wind Tunnel Tests at NASA Ames
•Chordwise pressure tap at 0.3, 0.47, 0.63, 0.8, 0.95R
-0.5
C
0.8C
0.03m
Measured Point
0.5
School of Aerospace Engineering
Georgia Tech
Blind Run Comparison (I)
Upwind Condition, Zero Yaw
95% Span Normal Force Coefficient
3
2.5
NREL
2
Present Simulations
1.5
1
0.5
0
5
10
15
20
25
Wind Speed (m/s)
The 95%R Normal Force Coefficients
30
School of Aerospace Engineering
Georgia Tech
Blind Run Comparison (II)
Upwind Configuration, Zero Yaw
Root Flap Bending Moment (Nm)
5000
4000
3000
2000
NREL
Present Methodologies
1000
0
5
10
15
20
25
30
Wind Speed (m/s)
Flap Bending Moment for One Blade
School of Aerospace Engineering
Georgia Tech
Blind Run Comparison (II)
Upwind Configuration, Zero Yaw
8000
UIUC/Enron-C
UIUC/Enron-UIUC
ROTABEM - DTU
Loughborough University
Global Energy Concepts, LLC
Windward (1)
Windward (2)
Windward (3)
ECN
NASA Ames
Teknikgruppen AB
RISOE -- HawC
Risoe NNS
DTU1
Georgia Tech
Glasgow University
TU Delft
NREL
Root Flap Bending Moment (Nm)
7000
6000
5000
4000
3000
2000
1000
0
5
10
15
20
Wind Speed (m/s)
25
30
Circulation Control Concept
• Advanced CCW Airfoil: 0 - 90 degree small CCW
flap
•Maintain the high lift when taking off and landing with
large flap angle and jet blowing
• Reduce the drag when cruise with 0 flap angle and
non-blowing.
The CCW Airfoil Shape
0.5
0.4
0.3
Jet Slot Location
0.2
0.1
0
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-0.2
30 degree integral flap
-0.3
-0.4
-0.5
• To Maintain the high-lift characteristics of CCW
Airfoil while greatly reduce the drag and noise
compared to large angle flap
1
The Variation of Lift Coefficient with the Angle of Attack
4
Leading Edge Stall
Cmu=0.1657
3
Cmu=0.111
Cl
Cmu=0.0566
2
Cmu=0.0
1
0
-2
0
2
4
6
Angle of Attack
8
10
12
STEADY JET RESULTS
Computed vs. Measured Variations of Lift Coefficient with
Momentum Coefficient
5
4
Cl
3
2
Cl, Computed
Cl, Measured
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Cm
Angle of Attack 0 degree, Integral Flap 30 degrees
The Stream Function Contours for the
No-Blowing Case
The Stream Function Contours for the
Blowing Case, Cm=0.1657
Concluding Remarks
• A snapshot of some of the ongoing CFD research
at Georgia Tech has been presented.
• Sikorsky and United Technologies have been
partners in many of our efforts.
• This has lead to fruitful interactions with Dennis
Hiff, Brian Wake, Chip Berezin, Mike Torok, Bob
Moffitt, Ebru Usta (UTRC Intern), Nathan
Hariharan, and Alan Egolf.
• We look forward to continued collaboration with
Sikorsky researchers on areas of importance to
Sikorsky/United Technologies, and to NRTC.