Modern State of the Universal Modeling for Centrifugal Compressors

Abstract

The 6th version of Universal modeling method for centrifugal compressor stage calculation is described. Identification of the new mathematical model was made. As a result of identification the uniform set of empirical coefficients is received. The efficiency definition error is 0,86 % at a design point. The efficiency definition error at five flow rate points (except a point of the maximum flow rate) is 1,22 %. Several variants of the stage with 3D impellers designed by 6 th version program and quasi three-dimensional calculation programs were compared by their gas dynamic performances CFD (NUMECA FINE TURBO). Performance comparison demonstrated general principles of design validity and leads to some design recommendations.

Full text

Abstract—
The 6th version of Universal modeling method for
centrifugal compressor stage calculation is described. Identification
of the new mathematical model was made. As a result of
identification the uniform set of empirical coefficients is received.
The efficiency definition error is 0,86 % at a design point. The
efficiency definition error at five flow rate points (except a point of
the maximum flow rate) is 1,22 %. Several variants of the stage with
3D impellers designed by 6
th
version program and quasi three-
dimensional calculation programs were compared by their gas
dynamic performances CFD (NUMECA FINE TURBO).
Performance comparison demonstrated general principles of design
validity and leads to some design recommendations.
Keywords—
Compressor design, loss model, performance
prediction, test data, model stages, flow rate coefficient, work
coefficient.
N
OMENCLATURE
b
width
r
c
radial velocity
w
c
resistance force coefficient
D
diameter
i angle of incidence
Kn
specific speed
l
blade heght
w
М
Mach number
p
pressure
R
gas constant
R
radius
Re
u
Reynolds number
Rz
roughness
S
area
t
blade pitch
T
temperature
u
blade speed
i
X
empirical coefficient
w
relative velocity
bl
β
blade angle related to tangential direction
β
flow angle related to tangential direction
z
number of blades
Yuri Borisovich Galerkin is with the S.-Peterbugd Poltechnical Yniversity,
Russian Federaton, S-Peresburg, Polytechnical st. 29 (phone: +7-921-942-73-
40; fax: 8-812-552-86-43; e-mail: yuiri_galerkin@ mal.ru).
Kristina Valerievna Soldatova is with the S.-Peterbugd Poltechnical
Yniversity, Russian Federaton, S-Peresburg, Polytechnical st. 29 (phone: +7-
905-220-50-70 fax: 8-812-552-86-43; e-mail: buck02@list.ru).
Aleksandr Aleksandrovich Drozdov is with the S.-Peterbugd Poltechnical
Yniversity, Russian Federaton, S-Peresburg, Polytechnical st. 29 (phone: +7-
951-680-59-64; fax: 8-812-552-86-43; e-mail: a_drozdi@ mal.ru).
ϕ
flow rate coefficient
T
ψ
work coefficient
ζ
losses efficiency
m
ε
compressibility coefficient
Subscripts
1 impeller inlet
2 impeller exit
bl blade
des design
m meridional
p pressure side
s suction side
thr throat
І.
G
OAL AND
O
BJECTS OF
M
ODELING
OTAL power of centrifugal compressors installed is
measured by dozens and dozens MWt in industrial
countries. The simplest of centrifugal compressors for pipe
line industry is shown in Fig. 1.
These machines have power in range 4-32 MWt, exit
pressure to 12,5 MPa, number of stages up to 8 in one body.
Compressors for other industries are more complicated
usually.
Power consumption depends on many factors but the sound
gas dynamic design is the first of them. Design procedure
consisted of more or less proven rules to establish main flow
path dimensions at pre-PC era. Numerous model tests at
special test rigs were obligatory before new compressor
fabrication.
The modern gas dynamic design becomes easier and more
reliable. I.e. given compressor pressure ratio is guaranteed at
given mass flow rate with good efficiency. Experimental
check and improvement followed are not obligatory in many
cases [14], [15]. Three-step numerical procedure is applied
usually. The first step of design consists of some mean line
field type calculations to find the best flow path main
dimensions.
The TU SPb R&D “Laboratory of compressor problems”
was very active in 1960 – 1980
th
. The TU SPb compressor
school founded by Prof. K. Seleznev is one of the leading
Russian R & D centers [13]. Flow behavior study has lead to
the physical model formulation and its mathematical
description. The design procedure scientific background and
practical application are well presented [1]-[6], [8]-[10]. Fig. 2
shows that measured and calculated velocity diagrams at
impeller blades are rather similar at design flow rate – but the
exit area where the wake is formatted [12].
Modern State of the Universal Modeling for
Centrifugal Compressors
Y. Galerkin, K. Soldatova, A. Drozdov
T
World Academy of Science, Engineering and Technology
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150International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000587
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Fig. 1 Typical two-stage pipe line centrifugal compressor
Fig. 2 Measured (solid) and non viscid calculated velocity diagrams
at 2D impeller blades
This similarity has proved Q3D non viscid calculation
effective application. A powder paint inserted in a flow path
sticks to surfaces where shear stress are close to zero. This
way wake and separation zones formation can be visualized.
Fig. 3 demonstrates flow behavior in the 2D impeller with
work coefficient
T
ψ ≈
0,65.
3D wake zone at the second part of the suction side of the
blade is visible. Flow separation never occurs at hub/shroud
surfaces and impeller blade pressure sides, etc. Flow
visualization at Fig. 4 demonstrates wake zone and secondary
flows on a suction side of an impeller at close to surge flow
rate and flow separation in a vane diffuser at a design flow
rate.
Fig. 3 Low shear stress zones in a 2D impeller
Fig. 4 Flow visualization in stage components
Suction side of a 2D impeller blade, surge flow rate and flow
separation zone in a vane diffuser
ІІ.
U
NIVERSAL
M
ODELING
B
ASIC
F
EATURES AND
A
CHIEVEMENTS
Based on the physical model the field type Universal
modeling method is well presented to specialists ([7]-[10],
[14], [15]) so the basic information is presented below only.
The math model identification is based on gas dynamic
performances of model stages. Loss of a head is calculated on
each surface of a flow path and is summarized. Shear stress
force coefficient and mixing loss coefficients are presented as
functions of flow velocity gradients along surfaces and along
normal direction. A velocity diagram of non viscid flow is
described schematically. Inlet and exit velocities at two sides
of a blade are used for calculations (are marked with dots at
Fig. 5).
World Academy of Science, Engineering and Technology
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151International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000587
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Fig. 5 Velocity diagram of non viscid flow on an impeller blade and a
scheme of flow separation
A friction force coefficient is presented is (a sample for a
suction side):
2 2
2 1
/
1 4 1
/
i i
X X
s s
ws f i i
bl s
w u w
c с X X
R D w
 
   
 
= − + −
   
 
   
 
. (1)
Two members of (1) present normal
2
2
/
/
s
bl
w u
R D
 
 
 
and
tangential
2
1
1
s
s
w
w
 
−
 
 
velocity gradients. The basic value of the
drag force coefficient
f
с
is the coefficient of a thin plate
[11]:
1/ 7
0.0307
Re
f i
w
с X=
- hydraulically smooth surface, (2)
2.5
1
1
1.89 1.62 lg /
=
 
+ ⋅
 
 
f i
bl
с X
Rz l
- rough surface. (3)
Empirical coefficients gradients
i
X
are subjects of model
identification by balance of calculation and measured
performance curves. Their numbers
i
are individual and show
coefficient’s position in the equations. Equations (4), (5)
connect drag force coefficients on both blade surfaces with the
friction loss coefficient of impeller blades and the last one
with an efficiency loss:
2 2
1 1
2p
bl s
fr prof m ws s wp p
thr thr
w
z S w
c w c w
Ф w w
 
   
 
ζ = ε +
   
 
π   
 
, (4)
2
1
2
fr prof
fr prof
T
w
ζ
 
∆η =
 
ψ
 
. (5)
Friction loss coefficients for hub and shroud surfaces are
calculated on the same principle. The physical model is based
on the absence of flow separation everywhere in an impeller
but a suction side of a blade. The separation point is calculated
by (6):
2
1 2
/
1 4 /
i
X
s s
s i i
s bl
w w u
w X X
w R D
 
 
 
= = +
 
 
 
 
ɺ
. (6)
The normalized normal velocity gradient presents in (6) and
reflects Rossby number influence on a boundary layer
condition. Mixing loss coefficient corresponds to scheme of
sudden expansion:
2
12
2
1 1
sin
зr
mix i s
wc
X w
w w
 
= −
 
 
ɺ
ζ β
. (7)
The empirical equations and the proper coefficients
i
X
serve for off-design regimes calculation and take into account
3-D flow character and compressibility influence. The
equations for stator elements of a stage also present in the
math model. The 4th version of computer programs was widely
used in academic and design practice. Several dozens of
compressor with delivery pressure up to 12,5 MPa, number of
stages 1-8, power up to 25 MWt were designed for some
Russian and foreign manufacturers. Amount of compressor
installed exceeds 400 pieces with total power close to
5 000 000 KWt. In all cases the design parameters were
achieved without model tests. But one problem existed for a
designer.
The math model basic principle is that empirical
coefficients
i
X
are independent of a stage parameters and
similarity criteria. It means that a single set of
i
X
must
describe gas dynamic performances of any stage at any
condition with accuracy of experiments. The 4th version
accuracy for design point efficiency is inside 2% that is not
sufficient for design practice. There are different sets of
i
X
for different types of model stages participated in
identification process. A designer had to choose proper sets
for the designed objects. This disadvantage also pointed out
that the physical and math models do not reflect all important
factors.
ІІІ.
N
EW
V
ERSION OF
M
ATH
M
ODEL
I
DENTIFICATION AND
V
ERIFICATION
R
ESULTS
The situation was revised and several important novels
were introduced in 5th version [7]-[10], [14], [15] and in the
next, 6th one too [10]. The flow path main dimensions input
are more precise and complete – for 3-D impellers especially.
World Academy of Science, Engineering and Technology
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Velocity diagram schematization (Fig. 5) is made on the base
of numerical experiment by Q-3-D calculations [7], [8].
Leakage in labyrinth seals is taken into account, etc. The main
novel in the math model is connected with mixing losses
calculation. The empirical coefficient
i
X
in (6) is presented
as a function of two gas dynamic parameters of an impeller:
2
1
1 1
i
i
X
X
mix i i T des i
w
X X X X w
 
 
 
= + ⋅ + −
 
 
 
 
ψ
. (8)
The new model identification was made with the use of 37
tests of 8 basic model stages with parameters
des
Φ
= 0,028 –
0,075,
T d es
ψ
= 0,42-0,75 tested at
u
M
=
0,60 – 0,86. Basic
stages have variants with different hub ratio, vaneless diffuser
width, number of diffuser vanes, impeller blade trailing edge
configuration.
Fig. 6 Results of the 6th version model identification
Measured performances – stroke lines, calculated performances –
solid lines
The identification was made for all tests and a single set of
the empirical coefficients was created. The average accuracy
of efficiency calculation for all 37 tests is 1,09% - all flow rate
range but the stall regime. The last is not important for
industrial compressors. The average accuracy for design flow
rate is 0,88%. Fig. 6 presents graphic information about
matching of measured and calculated performances.
Three compressors were chosen for the new model
verification. The 4-stage booster pipe line compressor – Fig. 7
– with optimal specific speed of stages
0,5 0, 75
/
ndes des Tdes
K= Φ
ψ
[13] was designed by the Universal modeling method.
Fig. 7 Flow path scheme of the 16 MWt compressor with delivery
pressure 7,45Mpa
Good correlation of measured and calculated performances
was expected – Fig 8.
Fig. 8 Sample 1 of gas dynamic performance modeling. Four stage
16 MWt compressor with delivery pressure 7,45M. P▲ –modeling, ♦
- test data
The two – stage booster compressor with parameters close
to the compressor above was quite unusual as the higher
pressure rise was achieved in two stages only. As result
specific speed was very far from optimal range. The first stage
parameters were
des
Φ
= 0,028,
T des
ψ
= 0,82. As result – very
narrow channels with high level of friction losses and impeller
blades with exit angle
2
bl
β
= 1040 – Fig. 9.
The second example compressor was designed by the
Universal modeling method too (4th version), but its stages had
no analogs. Anyway, the compressor demonstrated design
parameters at the plant test and at the installation. The most
satisfactory performance modeling result is shown at Fig. 10.
The third sample compressor was designed by its
manufacturer on the base of model stages designed decades
ago. Fig. 11 shows unusual now a meridian shape of impeller
channels with
2 1
b b
∼
. It leads to excessive flow deceleration
2 1
/ 0,5
w w <
(recommendation [7]
2 1
/ 0,60 0,65
w w ≥ − ).
World Academy of Science, Engineering and Technology
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Fig. 9 Scheme of the flow path of two stage 16 MWt compressor
with delivery pressure 7,45MP
Fig. 10 Sample 2 of gas dynamic performance modeling. Two stage
16 MWt compressor with delivery pressure 7,45MP
Fig. 11 Scheme of the flow path of four stage 16 MWt compressor
with delivery pressure 7,45MP. Outdated design
High mixing losses lead to low efficiency. Anyway, the
modeling result is satisfactory in this case too - Fig. 12.
Fig. 12 Sample 3 of gas dynamic performance modeling. Outdated
four stage 16 MWt compressor with delivery pressure 7,45MP
One more object of calculations was the tested stage with
3D impeller and vaneless diffuser. Gas dynamic performances
are compared at Fig. 13.
ІV.
S
AMPLE OF
O
PTIMIZATION
P
RACTICE
Results of identification and verification of the 6th version
of the model demonstrate its validity. It gives the possibility to
optimize main flow path dimensions by variants’ comparison.
Several important aspects of design cannot be solved by the
simplified approach of Universal modeling though. The
attractive way is to apply CFD calculations to the problem.
The test results shown at Fig. 14 are compared with
NUMECA FINE TURBO calculated performances – Fig. 15.
The result of the calculation is quite typical. CFD
calculations overestimate work coefficient and underestimated
incidence losses at negative incidence angle (
des
Φ > Φ
). The
same results were obtained with ANSYS CFX application and
with other types of stages. The common positive result is that
efficiency prediction is quite satisfactory at
des
Φ ≈ Φ
.
The stage with
des
Φ
= 0,105,
T des
ψ
=0,56 was designed on
principles [13] and optimized by 6th version computer
program. Several approaches of 3D impeller configuration
choice were compared by calculations of efficiency at
des
Φ ≈ Φ
. The important problem is 3D configuration choice.
The “geometry” principle is quite simple. Blade angles are
linear functions of meridian length. The alternative is to
choose blades’ configuration by velocity diagram
optimization. The compared functions
(
)
bl m
f l
β
=are
presented at Fig. 16. CFD calculation has shown that
des
η
is
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0,4% higher in the second case and the advantage is higher at
des
Φ > Φ
.
Fig. 13 Model stage with 3D impeller and vaneless diffuser gas
dynamic performances. Dots – test, solid – calculation 6
th
version
Universal modeling
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
0.060 0.070 0.0 80 0.090 0.100 0.110 0.120 0 .130
Ф
η
Fig. 14 Model stage with 3D impeller and vaneless diffuser gas
dynamic performances. Red – test, blue – CFD calculation
There is the opinion that increase of the work coefficient
along trailing edge from hub to shroud direction in 3D
impellers can improve flow uniformity and diminish head
losses in diffusers. The impeller variant with
(
)
2T des
f b const
ψ
= =
was compared with the variant with
1,03
T des s T des h
ψ ψ
=
.
It appeared that the flow field uniformity is inferior in case
of
(
)
2
var
T des
f b
ψ
= = but the stage efficiency is higher at
0,2% anyway.
VІ.
C
ONCLUSION
Several other problems were studied by variants’
comparison. It could be concluded that general rules well
proven in previous designs are valid for high flow rate stages
with 3D impellers too. Some details of design are constantly
improved by variants’ comparison and more precise design
recommendations are formulated as result.
Fig. 15 3D impeller meridian shape and two variants of blade
configuration defined by function
(
)
bl m
f l
β
=
(a) (b)
Fig. 16 Absolute velocity field at the impeller outlet.
(a)
1,03
T des s T des h
ψ ψ
=
, (b)
(
)
2T des
f b const
ψ
= =
R
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155International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000587
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World Academy of Science, Engineering and Technology
International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering Vol:9, No:1, 2015
156International Scholarly and Scientific Research & Innovation 9(1) 2015 scholar.waset.org/1999.8/10000587
International Science Index Vol:9, No:1, 2015 waset.org/Publication/10000587