gas turbine analysis

1. The
measured
temperature
profile
provided
to
you
is
not
the
actual
temperature
profile
of
the
gas.
There
is
heat
transfer
from
the
viscous
dissipation
of
gas
onto
the
thermocouple
bead,
leading
to
a
higher
temperature
reading
than
the
actual
static
temperature.
Normally
this
is
not
an
issue,
however,
because
we
are
measuring
high
speed
flow,
the
viscous
dissipation
is
not
negligible.
There
are
three
equations
that
can
be
used
to
describe
this
phenomenon:
푇! = 푇! +
푉!
2푐!
푇! = 푇! + 푟
푉!
2푐!
푇!
푇!
=
푃!
푃!
!!!
!
The
first
equation
is
the
relationship
between
the
total
and
static
temperature.
The
total
temperature
is
the
temperature
of
the
gas
if
it
were
to
be
isentropically
brought
to
rest,
in
other
words,
the
kinetic
energy
would
be
completely
converted
into
thermal
energy.
The
second
equation
describes
how
the
static
temperature
relates
to
the
temperature
that
was
measured
with
the
thermocouple.
The
variable
“r”
is
called
the
recovery
factor,
and
for
this
experiment
you
can
set
the
value
of
this
term
to
0.7.
The
last
equation
describes
the
ratio
of
total
and
stagnation
temperatures
and
pressures,
where
k
is
the
ratio
of
specific
heats.
The
equation
below
was
found
by
eliminating
the
total
temperature
and
the
velocity
from
the
three
equations
above.
The
static
temperature
can
then
be
solved
for
and
used
to
calculate
the
velocity
and
temperature.
The
profile
data
provided
on
moodle
gives
the
difference
between
the
total
and
static
pressures,
and
you
should
have
the
value
of
the
ambient
pressure
reading
from
the
day
of
the
experiment.
푇! = 푇! 푟
푃!
푃!
!!!
!
− 1 + 1
The
equations
below
could
be
useful
in
calculating
the
required
results
for
your
presentation.
The
analysis
of
the
turbine
and
compressor
are
straight
forward,
however
the
analysis
of
the
combustor
and
nozzle
are
a
little
more
involved.
The
combustor
is
not
a
perfect
combustor,
and
will
have
an
efficiency
of
less
than
one.
푄!"#$ = 휂!"#$푚!퐿퐻푉
푄!"#$ = 푚!"#ℎ!"# − 푚!"ℎ!"
To
analyze
the
nozzle
and
evaluate
the
total
mass
flow
rate
through
the
engine,
the
temperature
and
velocity
profile
at
the
exit
of
the
nozzle
need
to
be
evaluated.

2. 휂!! =
푚!"!
푉!
2
푚!퐿퐻푉
Thermal
efficiency
푚 = 휌푉푑퐴 = 휌푉푟푑푟푑휃
Mass
flow
rate
푡ℎ푟푢푠푡 = 푚푉 = 휌푉!푑퐴 = 휌푉!푟푑푟푑휃
Thrust
of
the
engine
푚
푉!
2
= 휌
푉!
2
푑퐴 = 휌
푉!
2
푟푑푟푑휃
The
kinetic
energy
flux
As
you
go
through
the
analysis,
ask
yourself
if
your
data
makes
sense.
What
values
are
you
expecting,
and
what
are
some
ways
to
estimate
the
values
to
check
your
calculations?
This
will
help
you
spot
any
gross
errors.