pengetahuan tentang sentrifugal
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Transcript of pengetahuan tentang sentrifugal
4
Introduction
• Slightly less efficient than axial-flow compressors• Easier to manufacture• Single stage can produce a pressure ration of 5 times that of a
single stage axial-flow compressor• Application: ground-vehicle, power plants, auxiliary power units• Similar parts as a pump, i.e. the impeller, the diffuser, and the
volute• Main difference: enthalpy in place of pressure-head term• Static enthalpy (h) and total (stagnation) enthalpy (ho)
8
Introduction
( ) ( )
kRTc
T
T
k
kRTTTChhV
Vhh
p
=
−
−=−=−=
+=
2
000
2
2
0
11
222
2
• For an ideal gas with constant specific heat
9
Introduction
20
022
2
02
2
2
11
11
2
11
2
Mk
T
T
T
T
kM
c
V
T
T
k
cV
−+=
−
−==
−
−=
• For an ideal gas with constant specific heat
10
Introduction
( ) ( )
( ) ( )
( ) ( )1120
120
0
11
00
1
0
2
11
2
11
,
−
−
−−
−+=
−+=
=
=
k
kk
kkk
Mk
Mk
p
p
T
T
p
p
T
T
ρρ
ρρ
• For an isentropic process
11
Introduction
( )
( )11
0
*
1
0
*
0
*
1
2
1
2
1
2
−
−
+=
+=
+=
k
kk
k
kp
p
kT
T
ρρ
• For the critical state (M=1)
14
Introduction
• The Specific Shaft Work into the Compressor
The specific shaft work
0.96
m
m
E η
η
=
=
15
Introduction
• Compressor Efficiency:– The ratio of the useful increase of fluid energy divided by the
actual energy input to the fluid
– The useful energy input is the work of an ideal, or isentropic, compression to the actual final pressure P3
17
Introduction
0103
01
TT
TT
E
E iic −
−==η
• The Compressor Efficiency
• No external work or heat associated with the diffuser flow, i.e.
03020302 , TThh ==
18
Introduction
1
01
'22
01
03 1
−
+=
kk
mp
ct
TC
VU
p
p
ηη
• The Overall Pressure Ratio
• The compressor efficiency from experimental data• Slip exists in compressor impeller
2'2 tst VV µ=
19
Introduction
−
−=22 cot1
163.01
βϕπµ
Bs n
• The Slip Coefficient (Stanitz Equation)
• More relations in Appendix E• But, Stanitz equation is more accurate for the practical
range of vane angle; i.e.
02
0 9045 << β
20
Introduction
• Total pressure ratio from:– Ideal velocity triangle at the impeller exit– The number of vanes– The inlet total temperature– The stage and mechanical efficiencies
• Mechanical efficiency accounts for– Frictional losses associated with bearing, seal, and disk
friction– Reappears as enthalpy in the outflow gas
21
Impeller Design
• The impeller design starts with a number of unshrouded blades (Pfleiderer)
• Flow is assumed axial at the inlet• Favorable to have large tangential velocity at outlet
(Vt2’)
• Vanes are curved near the rim of the impeller (β2 <90o)
• But, they are bent near the leading edge to conform to the direction of the relative velocity Vrb1 at the inlet
22
Impeller Design
• The angle β1 varies over the leading edge, since V1 remains constant while U1 (and r) varies (V1 assumes uniform at inlet)
• At D1S, the relative velocity Vrb1=(V12+U1
2)0.5 and the corresponding relative Mach number MR1S are highest
• For a fixed set of, N, m,Po1, and To1, the relative Mach number has its minimum where β1S is approximately 32o (Shepherd, 1956)
23
Impeller Design
• Choose a relative Mach number at the inlet
( )
SSR
SRSrb
Ma
VM
Mk
TT
kRTa
aMV
111
11
21
011
11
111
sin :noMach inlet Absolute
211 :eTemperatur Static
:Speed Acoustic
β==
−+=
=
=
24
Impeller Design
011
011
32cos
32sin
SrbS
Srb
VU
VV
=
=• Calculation of V1 and U1S
• Calculation of the shroud diameter
N
UD S
S1
1
2=
25
Impeller Design
21
11
211
4
−=
V
mDD SH πρ
• Calculation of the hub diameter by applying the mass flow equation to the impeller inlet
• Calculation of density from the equation of state of a perfect gas
1
11 RT
p=ρ
26
Impeller Design
• Calculation of static temperature and static pressure
( )
( )( )1
21
011
21
011
211
211−
−+
=
−+=
kk
Mk
pp
Mk
TT
27
Impeller Design
= −
HH U
V
1
111 tanβ
• The fluid angle at the hub
• The vane speed at the hub
21
1H
H
NDU =
28
Impeller Design
1 1
12
13
4
12
12 1
4
Inlet flow rate:
Output head H:
Dimensional specific speed:
( from Table 3 in appendix A)
i
s
SS
Q m
H E g
NQN
H
D QD D
H
ρ==
=
=
&
• The outlet diameter D2
29
Impeller Design
( )9.085.0 : velocityl tangentiaideal The
: velocityl tangentiaactual The
:nsferEnergy tra The
:Aappendix in 3 Table From
'22
2'2
C
−==
=
=
ss
tt
t
C
im
VV
UEV
EE
µµ
ηη
η
• The ideal and actual tangential velocities
30
Impeller Design
( )
−
−=
=
≤≤=−=
−
22
2
212
2222
222
cot1
163.01
tan
35.023.0
βϕπµ
β
ϕϕ
Bs
trb
nrb
nrb
ttrb
n
V
V
UV
VUV
• The vane angle and the number of vanes
32
Impeller Design
pC
VTT
2
22
022′−=
• The static temperature T2 is used to determine density at the impeller exit
Vr
mb
n2222 2πρ
&=
33
Impeller Design
• The optimal design parameters by Ferguson (1963) and Whitfield (1990) from Table 5.1
• Table 5.1 Should be used to check calculated results for acceptability during or after the design process
34
Diffuser Design
• A vaneless diffuser allows reduction of the exit Mach number
• The vaneless portion may have a width as large as 6 percent of the impeller diameter
• Effects a rise in static pressure• Angular momentum is conserved and the fluid path is
approximately a logarithmic spiral• Diffuser vanes are set with the diffuser axes tangent to the
spiral paths with an angle of divergence between them not exceeding 12o
36
Diffuser Design
• Vanes are preferred where size limitations matter
• Vaneless diffuser is more efficient
• Number of diffuser vanes should be less than the number of impeller vanes to:– Ensure uniformness of flow
– High diffuser efficiency in the range of φ2 recommended
37
Diffuser Design
• The mass flow rate at any r (in the vaneless diffuser)
( )n
nr
Vrbm
rrrVV
ρπ2
32
=≤≤=
&
38
Diffuser Design
222
constant
nn
n
VrrV
rV
ρρρ
==
• For constant diffuser width b
• The angular momentum is conserved in the vaneless space
22 ′= tt VrrV
39
Diffuser Design
12 >′M• Typically, the flow leaving the impeller is supersonic
• Typically, the flow leaving the vaneless diffuser is subsonic
0.13 <M
40
Diffuser Design
αcosVVV nr ==
• Denote * for the properties at the radial position at which M=1 (The absolute gas angle, α, is the angle between V and Vr)
• The continuity equation
**** coscos αραρ VrrV =
41
Diffuser Design
*
*tantan
ρα
ρα =
• The angular momentum equation
• Dividing momentum by continuity relations
*** sinsin αα VrrV =
42
Diffuser Design
2
0
1
**
21
1 ,
Mk
TT
T
Tk
−+=
=−
ρρ
• Assuming an isentropic flow in the vaneless region
• For M=1
1
2 0*
+=
k
TT
43
Diffuser Design
( )11
2* 2
11
1
2−
−+
+=
k
Mk
kρρ
• Substituting in the density relation
• Substituting in the absolute gas angle relation
( )11
2*
2
11
1
2tantan
−−
−+
+=
k
Mk
kαα
44
Diffuser Design
21
2**
21
***
**
2
2
2
11
1
2
sin
sin
sin
sin
−
′
′
−+
+=
===
==
Mk
kM
r
r
T
TM
a
a
a
V
V
V
r
r
MM
αα
αα
αα• The angle α* is evaluated by
45
Diffuser Design
21
222
22
**
2
11
1
2
sin
sin−
′′
−+
+= M
k
kM
r
r
αα
• The radial position r* is determined by
• The angle α3* is evaluated by
( )112
3*
3 2
11
1
2tantan
−−
−+
+=
k
Mk
kαα
46
Diffuser Design
21
233
33
**
2
11
1
2
sin
sin−
−+
+= M
k
kM
r
r
αα
• Finally r3 is determined by
• The volute is designed by the same methods outlined in chapter 4
47
Performance• Typical compressor characteristics
cte.01
=T
N
01
01
p
Tm&
02
01
p
p Surge line
.cte=ηmaxη
Choke line
C B
A
48
Performance
• The sharp fall of the constant-speed curves at higher mass flows is due to choking in some component of the machine
• The low flows operation is limited by the phenomenon of surge
• Smooth operation occurs on the compressor map at some point between the surge line and the choke line
• Chocking is associated with the attainment of a Mach number of unity
49
Performance
• In the stationary passage of the inlet The sharp fall of the constant-speed curves at higher mass flows is due to choking in some component of the machine
• The low flows operation is limited by the phenomenon of surge
• Smooth operation occurs on the compressor map at some point between the surge line and the choke line
• Chocking is associated with the attainment of a Mach number of unity
50
Performance
• In the stationary passage of the inlet or diffuser for a Mach number of unity
a =
a kRT=• The temperature at this point
( ) 20
11
2
kT T M
−= +
51
Performance
• By setting M=1
a =
12
t tt
km A p
RT
= ÷
&
• The chocking (maximum) flow rate
*0
2
1 tT T Tk
= = +
52
Performance
• The throat pressure (isentropic process)
a =
2 21 1
01 2 2rbV U
h h= + −
• The chocked flow rate in impeller (use relative velocity instead of absolute velocity)
( )1k k
tt in
in
Tp p
T
−
= ÷
53
Performance
• The critical temperature
a =
( )( )
11
2 12 2
0101 01
21
1 2
k
k
tp
k Um A p
RT k C T
+−
= + ÷ ÷ ÷+ &
• The throat mass flow rate (isentropic process)
( )2
* 01
01
21
2 1 tp
TUT T
C T k
= + = ÷ ÷ +
54
Performance
• The chocked mass flow rate in stationary components is independent of impeller speed
• The point A in the characteristic curve represents a point of normal operation
• An increase in flow resistance in the connected external flow system results in decrease in and increase in
• Causes increase in head or pressure• Further increase in external system produces a decrease in
impeller flow (beyond point C) and surge phenomena results
2nV
2tV
55
Performance
• The at some point in the impeller leads to change of direction of and an accompanying decrease in head.
• A temporary flow reversal in the impeller and the ensuing buildup to the original flow condition is known as surging.
• Surging continues cyclically until the external resistance is removed.
• Surging is an unstable and dangerous condition and must be avoided by careful operational planning and system design.
2rbV
78
TURBOMACHINERY BASICSCENTRIFUGAL COMPRESSOR
Hasan Basri
Jurusan Teknik MesinFakultas Teknik – Universitas Sriwijaya
Phone: 0711-580739, Fax: 0711-560062Email: [email protected]