Chapter 1 :
Working Principles
Turbomachine exchanger energy between continuous
flow of a
fluid and
cont machine
a .
rotating component
* Puer machines
receiving
↳ in
comp .
Fluid) water ,
oil ...
)
Pump (chopter 87
↳ Compressible high pressure
increase -
Compressor
"
Low
presur
increase -
fan 1 Chopter 3)
* Pover
delivering machines
↳
woter-hydraulis /chapter 9) turbine
↳ Steam -
>Steam Limbine (Chapter 6
↳ Air ) Wind turbine (Chapter 10)
Jotmag .
↳
gas
. -
# Basis laws
for
stationary dut parts
o
woll velocity
=
↳ channel between
stationary blades
f
conservation
*
of mas
?
Steady flow -mass in= mess out
& As Va dt =
PrAr vidt
or mout Min (t
pAw
= =
=
* Conservation
of momentum
Newton 2 with C
law s
change in momentum
per
time unt mess
equals sum
of applied face
change momentum
: As d -Pittdt
-
政 Aα - .W ,Aii ☆ - ƩF
な
= P
=> in/v-i) =
z
for elementary partdx , minentam lau
projected on x dis dz
_ u
(p Edp(dt p(A + dA)dxg1z1x
-
in 10 do v) (p dp)(A dt)
pt +
+ + +
+
-
-
-
=
-neglect higher order ? = d)
, .
unt
>
-
JeAde =
-Adp-pAdudevt + dp + du = 0 / Bernali
equation (
~
if j =
+
integrate dong streamline : + u = c
Now take
friction and
activene into account ?
rCisumference
-
Sheor
[0dx
~
+ face rota in
fluid
뛔
nooker,
te
ㅇ
_
PAv
_
dW
dqiu
+
= -
Then Beinarulli : dvC +
jdp + dV +
dqu =
dw
# conservation of energy
T law of thermodynamics
increase in C mass heat and work supplied
- E
of syst .
W .
equale sum
of
* Q =
dg in (Heat per tims unit)
* w =
dFv = dwi/wok per time unit
* E =
e + Ev2 (intend + KE = Fund mech ES
.
.
energylaur : in (E dE + E)
pAv -(p dp)(A + + dA)(v + dv)
yAdxgt Äv w+ q
-
=
+
-
①
ㅇ
No work doe
by pressure force and
frictio firs on duct worl ?
=> m
in &E =
=M - inRid -
indu + w+ Q
‰ dSe )
2 +
崎 + v = dw +
p
e M
h
+
=
dih + e + Ul =
dwd
_
Kim E . .
Gov.
pot
E .
↑ Zie ook Rest .
8
支
, laws for Rotating
* Basic duct
part
* Work and with c
Energy equations in a
rotating from angular vebrity
in Relative vel .
-
frame rotating of Cont
angular
Some basic laws introduce
But
Centrifugal Coriolis
force
~
+
2 h n
"
-D
w
= t 5 rm 챗
" 맑
) put frame
p
O "
Relation between absolute dr and
displacement
Relative Gr
dn = ☆ r 011+ S
→= 5 旭 +
-
differentition is
applied to find relation between als aus andrel
+δ( ++∞ )
d
= 8
@ = 旭 ++ =②+ 1 ※ ++ω * ]
아
e
+
= ≥ ( ㎡ r τ * 1+ * r +
イ
antn 2旭 + 回
… ㅠ
、
arch
Co
-
cf 패
-
Ladditiond
-
man EF marl=
=
EFt MCI
+
term in Relotive frome 8
·
Centrifuge face : -x =
2 Aw
Coriolis
Jorce : Co -
-
Also 1 addit term
eg ?
RHS
.
of momentum
pAdx[T pAstrar ptr d pAdt
&
=
=
the addit Term .
↳ her dx dr and =
u = er
σ
inotcorioi
force ([ =
-2E) ~ Caridir das no work in streamline in relative
- and dang i from
r
*
jadx(a
=
becaus
=> Work
eg.
: dw +
Edp ++ dar = diuc + dW
↳
in rel .
from dW = o since For
within the
roter
perform no work
frame
=>
Energy .:
eg
d1w2 dh +u + = d1ut +
dq d
an
+ that is
turning with the rotor ?
."
var
" in gravity pot . E
negligible : du = o
鼠
鼠
飛
一
, & Moment in the obsolute Rotor Work
of momentum from
~ Meridiaal section contains the o
Um Fra + Vr) and No
* Closed Rotor
Moments Pos Sense
running
Moment at showd and hub
*
Mo :
of friction forces on rotor
by flied that does not
flow throug rotor
* Dis
fiction always broking so zo
* M : moment
of pressins and
friction forces ot blac surfaces and end well
by roter
on
fluid
Driving mochin
mochine 30
e
Driven
;
· e
/Pur
receiving e
,
*
Mchoff : moment
by Motor Generator on
shaft
machine
driving machine driven machine
-Dewen >o = o :
,
*
=M Md
Moment Balance of mot Mstoft
= Mchaft
rotor
parts M M
= .
machine
☆ 。 √
Driving
Bhoft =
Prot -Pl
M
Msheft und
- = -
-
Consider now a CV/ inlet 1 - outlet 2)
take momentum balance in de
frame
P
α
m lv _ v ) = I
moment
of momentum bolance
~
areee deee
à lrxěa- iEs v ) = xF
ocial
M
Project on Tã % => in /M2Nou -
(1Vru) = M
radial
↳ minent of
C
Pressure
Assumed shea stresses inlet
no o
fricti
~
faces
and outlet as distation of flow .
Fang
of the locations is small
-Power from the momentM
rotor to
flow by
·
· = M/U2 Vau- Un (10) =
Prot
瓦加
-Work done
per
unit moss on the
flow by M
U2 Nau-Un = An
8
Prhoft = Prot - Pet = AWchoft = =AN + Siem
Working Principles
Turbomachine exchanger energy between continuous
flow of a
fluid and
cont machine
a .
rotating component
* Puer machines
receiving
↳ in
comp .
Fluid) water ,
oil ...
)
Pump (chopter 87
↳ Compressible high pressure
increase -
Compressor
"
Low
presur
increase -
fan 1 Chopter 3)
* Pover
delivering machines
↳
woter-hydraulis /chapter 9) turbine
↳ Steam -
>Steam Limbine (Chapter 6
↳ Air ) Wind turbine (Chapter 10)
Jotmag .
↳
gas
. -
# Basis laws
for
stationary dut parts
o
woll velocity
=
↳ channel between
stationary blades
f
conservation
*
of mas
?
Steady flow -mass in= mess out
& As Va dt =
PrAr vidt
or mout Min (t
pAw
= =
=
* Conservation
of momentum
Newton 2 with C
law s
change in momentum
per
time unt mess
equals sum
of applied face
change momentum
: As d -Pittdt
-
政 Aα - .W ,Aii ☆ - ƩF
な
= P
=> in/v-i) =
z
for elementary partdx , minentam lau
projected on x dis dz
_ u
(p Edp(dt p(A + dA)dxg1z1x
-
in 10 do v) (p dp)(A dt)
pt +
+ + +
+
-
-
-
=
-neglect higher order ? = d)
, .
unt
>
-
JeAde =
-Adp-pAdudevt + dp + du = 0 / Bernali
equation (
~
if j =
+
integrate dong streamline : + u = c
Now take
friction and
activene into account ?
rCisumference
-
Sheor
[0dx
~
+ face rota in
fluid
뛔
nooker,
te
ㅇ
_
PAv
_
dW
dqiu
+
= -
Then Beinarulli : dvC +
jdp + dV +
dqu =
dw
# conservation of energy
T law of thermodynamics
increase in C mass heat and work supplied
- E
of syst .
W .
equale sum
of
* Q =
dg in (Heat per tims unit)
* w =
dFv = dwi/wok per time unit
* E =
e + Ev2 (intend + KE = Fund mech ES
.
.
energylaur : in (E dE + E)
pAv -(p dp)(A + + dA)(v + dv)
yAdxgt Äv w+ q
-
=
+
-
①
ㅇ
No work doe
by pressure force and
frictio firs on duct worl ?
=> m
in &E =
=M - inRid -
indu + w+ Q
‰ dSe )
2 +
崎 + v = dw +
p
e M
h
+
=
dih + e + Ul =
dwd
_
Kim E . .
Gov.
pot
E .
↑ Zie ook Rest .
8
支
, laws for Rotating
* Basic duct
part
* Work and with c
Energy equations in a
rotating from angular vebrity
in Relative vel .
-
frame rotating of Cont
angular
Some basic laws introduce
But
Centrifugal Coriolis
force
~
+
2 h n
"
-D
w
= t 5 rm 챗
" 맑
) put frame
p
O "
Relation between absolute dr and
displacement
Relative Gr
dn = ☆ r 011+ S
→= 5 旭 +
-
differentition is
applied to find relation between als aus andrel
+δ( ++∞ )
d
= 8
@ = 旭 ++ =②+ 1 ※ ++ω * ]
아
e
+
= ≥ ( ㎡ r τ * 1+ * r +
イ
antn 2旭 + 回
… ㅠ
、
arch
Co
-
cf 패
-
Ladditiond
-
man EF marl=
=
EFt MCI
+
term in Relotive frome 8
·
Centrifuge face : -x =
2 Aw
Coriolis
Jorce : Co -
-
Also 1 addit term
eg ?
RHS
.
of momentum
pAdx[T pAstrar ptr d pAdt
&
=
=
the addit Term .
↳ her dx dr and =
u = er
σ
inotcorioi
force ([ =
-2E) ~ Caridir das no work in streamline in relative
- and dang i from
r
*
jadx(a
=
becaus
=> Work
eg.
: dw +
Edp ++ dar = diuc + dW
↳
in rel .
from dW = o since For
within the
roter
perform no work
frame
=>
Energy .:
eg
d1w2 dh +u + = d1ut +
dq d
an
+ that is
turning with the rotor ?
."
var
" in gravity pot . E
negligible : du = o
鼠
鼠
飛
一
, & Moment in the obsolute Rotor Work
of momentum from
~ Meridiaal section contains the o
Um Fra + Vr) and No
* Closed Rotor
Moments Pos Sense
running
Moment at showd and hub
*
Mo :
of friction forces on rotor
by flied that does not
flow throug rotor
* Dis
fiction always broking so zo
* M : moment
of pressins and
friction forces ot blac surfaces and end well
by roter
on
fluid
Driving mochin
mochine 30
e
Driven
;
· e
/Pur
receiving e
,
*
Mchoff : moment
by Motor Generator on
shaft
machine
driving machine driven machine
-Dewen >o = o :
,
*
=M Md
Moment Balance of mot Mstoft
= Mchaft
rotor
parts M M
= .
machine
☆ 。 √
Driving
Bhoft =
Prot -Pl
M
Msheft und
- = -
-
Consider now a CV/ inlet 1 - outlet 2)
take momentum balance in de
frame
P
α
m lv _ v ) = I
moment
of momentum bolance
~
areee deee
à lrxěa- iEs v ) = xF
ocial
M
Project on Tã % => in /M2Nou -
(1Vru) = M
radial
↳ minent of
C
Pressure
Assumed shea stresses inlet
no o
fricti
~
faces
and outlet as distation of flow .
Fang
of the locations is small
-Power from the momentM
rotor to
flow by
·
· = M/U2 Vau- Un (10) =
Prot
瓦加
-Work done
per
unit moss on the
flow by M
U2 Nau-Un = An
8
Prhoft = Prot - Pet = AWchoft = =AN + Siem
