The
interaction
between
the
shock
wave
and
boundary
layer
of
transonic
wings
can
trigger
periodic
self-excited
oscillations,
resulting
in
buffet.
Buffet
severely
restricts
flight
envelope
civil
aircraft
is
directly
related
to
their
aerodynamic
performance
safety.
Developing
efficient
reliable
techniques
for
buffet
onset
prediction
crucial
advancement
aircraft.
In
this
study,
utilizing
a
comprehensive
database
supercritical
airfoils
generated
through
numerical
simulations,
convolutional
neural
network
(CNN)
model
firstly
developed
perform
classification
based
on
flow
fields.
After
that,
employing
explainable
machine
learning
techniques,
including
Gradient-weighted
Class
Activation
Mapping
(Grad-CAM),
random
forest
algorithms,
statistical
analysis,
research
investigates
correlations
supervised
CNN
features
key
physical
characteristics
with
separation
region,
wave,
leading
edge
suction
peak,
post-shock
loading.
Finally,
metric
established
good
generalization
accuracy,
providing
valuable
guidance
engineering
design
Physics of Fluids,
Journal Year:
2025,
Volume and Issue:
37(1)
Published: Jan. 1, 2025
Based
on
the
framework
of
field
inversion
and
machine
learning,
an
adaptive
modification
for
Reynolds-Averaged
Navier–Stokes-based
turbulence
models
is
proposed
simulation
low-pressure
turbine
cascades
involving
flow
separation.
This
method
adjusts
results
by
modifying
source
terms
correspondingly
at
different
spatial
locations.
First,
specific
regions
are
obtained
Gaussian
mixture
adaptively
according
to
baseline
distribution
correction
term
inferred
ensemble-based
with
effective
utilization
high-fidelity
data.
Then
a
corrective
model
form
quantities
calculated
established
Gradient
Boosting
Decision
Tree
used
T106
cascade
cases.
The
demonstrate
that
modified
model,
reduced
deficiency
predicting
load
can
be
obtained.
also
predict
more
accurate
separation
onset
damping
eddy
viscosity
in
separated
region
case
out
training
set.
With
added
solely
region,
computational
cost
compared
full-field
inversion,
possibly
applied
simulating
three-dimensional
considering
rotation
effects.
Physics of Fluids,
Journal Year:
2025,
Volume and Issue:
37(2)
Published: Feb. 1, 2025
Transonic
axial
compressor
flows
exhibit
complex
turbulence
structures
that
pose
significant
challenges
for
traditional
models.
In
recent
years,
neural
network-based
models
have
demonstrated
promising
results
in
simulating
these
intricate
flows.
However,
often
lack
interpretability,
a
crucial
aspect
of
understanding
the
underlying
physical
mechanisms.
Symbolic
regression,
capable
training
highly
interpretable
models,
offers
potential
solution
to
elucidate
mechanisms
underpinning
this
study,
we
employ
evolutionary
symbolic
regression
interpret
tensor
basis
networks
(TBNNs)
and
develop
explicit
transcendental
Reynolds
stress
(ETRSM)
transonic
Our
are
trained
on
inputs
outputs
pre-trained
TBNN.
We
introduce
method
independently
predicts
coefficients
each
basis,
significantly
reducing
computational
costs
enhancing
rationality
prediction
process.
six
models:
three
algebraic.
Through
rigorous
fluid
dynamics
(CFD)
simulations,
demonstrate
an
exceptional
ability
TBNN,
while
algebraic
show
limited
success.
The
ETRSM,
characterized
by
high
interpretability
transferability,
effectively
interprets
TBNN
achieves
comparable
accuracy
TBNN-based
compressors.
These
underscore
industry-level
CFD
problems
highlight
importance
incorporating
additional
features
such
Furthermore,
separates
individual
coefficients,
costs.
Physics of Fluids,
Journal Year:
2025,
Volume and Issue:
37(3)
Published: March 1, 2025
Reynolds-averaged
turbulence
models
have
become
one
of
the
most
important
and
popular
techniques
for
practical
engineering
applications
in
aeronautics
astronautics.
However,
poor
performance
prediction
flow
separations
restricts
its
application
ranges
due
to
traditional
linearity
equilibrium
hypotheses
that
constitute
equation
Reynolds
stress
modeling.
In
this
study,
an
artificial
neural
network-based
quadratic
constitutive
(ANN-QCR)
model
is
proposed
simulating
turbulent
flows
with
by
using
field
inversion
machine
learning
technique
(FIML)
high-fidelity
experimental
data.
particular,
decomposed
into
linear
non-linear
parts,
respectively.
The
former
evaluated
Spalart–Allmaras
a
correction
factor
imposed
on
production
term
account
non-equilibrium
effect,
while
latter
self-calibrated
factor.
These
factors
are
predicted
network
(ANN)
depending
local
features.
unified
framework
FIML
updates
weights
ANN-QCR
directly
gradient-based
discrete
adjoint
method,
ensuring
consistency
between
training.
data-augmented
well
validated
through
several
separated
induced
adverse
pressure
gradients,
shock
wave
boundary
interfaces,
higher
angles
attack,
numbers
(Re).
With
optimization
target
at
lift
coefficients,
established
also
improves
predictive
other
quantities,
such
as
drag
coefficients
distributions.
addition,
captures
development
separation
bubbles
better
increase
angle
attack.
Benefiting
from
compatibility
convergence
forward
simulation,
generalization
capability
present
successfully
various
numerical
simulations
problems
across
wide
range
attack
good
accuracy.
Physics of Fluids,
Journal Year:
2024,
Volume and Issue:
36(3)
Published: March 1, 2024
This
work
introduces
an
ensemble
variational
method
with
adaptive
covariance
inflation
for
learning
nonlinear
eddy
viscosity
turbulence
models
where
the
Reynolds
stress
anisotropy
is
represented
tensor-basis
neural
networks.
The
ensemble-based
has
emerged
as
important
alternative
to
data-driven
modeling
due
its
merit
of
non-derivativeness.
However,
training
accuracy
can
be
affected
by
linearization
assumption
and
sample
collapse
issue.
Given
these
difficulties,
we
introduce
hybrid
method,
which
inherits
merits
in
non-derivativeness
analysis.
Moreover,
a
scheme
proposed
based
on
convergence
states
alleviate
detrimental
effects
collapse.
capability
model
tested
flows
square
duct,
over
periodic
hills,
around
S809
airfoil,
increasing
complexity
data
from
direct
observation
sparse
indirect
observation.
Our
results
show
that
learn
relatively
accurate
network-based
scenarios
small
size
variances,
compared
Kalman
method.
It
highlights
superiority
practical
applications,
since
sizes
reduce
computational
costs,
variance
ensure
robustness
avoiding
nonphysical
samples
stresses.