Engineering, 2010, 2, 658-664
doi:10.4236/eng.2010.28084 Published Online August 2010 (http://www.SciRP.org/journal/eng).
Computer-Aided Solution to the Vibrational Effect of
Instabilities in Gas Turbine Compressors
Ezenwa Alfred Ogbonnaya1, Hyginus Ubabuike Ugwu2, Charles Agbeju Nimibofa Johnson3
1Department of Marine Engineering, Rivers State University of Science and Technology, Port Harcourt, Nigeria
2Department of Mechanical Engineering, Michael Okpara University of Agriculture (MOUA), Umuahia, Nigeria
3Department of Marine Engineering, Niger Delta University, Bayelsa, Nigeria
Received March 25, 2010; revised June 24, 2010; accepted June 28, 2010
Abstract
Surge and stall are the two main types of instabilities that often occur on the compressor system of gas tur-
bines. The effect of this instability often leads to excessive vibration due to the back pressure imposed to the
system by this phenomenon. In this work, fouling was observed as the major cause of the compressor insta-
bility. A step to analyze how this phenomenon can be controlled with the continuous examination of the vi-
bration amplitude using a computer approach led to the execution of this work. The forces resulting to vibra-
tion in the system is usually external to it. This external force is aerodynamic and the effect was modeled
using force damped vibration analysis. A gas turbine plant on industrial duty for electricity generation was
used to actualize this research. The data for amplitude of vibration varied between -15 and 15 mm/s while the
given mass flow rate and pressure ratio were determined as falling between 6.1 to 6.8 kg/s and 9.3 to 9.6 re-
spectively. A computer program named VICOMS written in C++ programming language was developed.
The results show that the machine should not be run beyond 14.0 mm vibration amplitude in order to avoid
surge, stall and other flow-induced catastrophic breakdown.
Keywords: Computerized Solution, Instabilities, Vibration, Gas Turbine Compressors, Operational Limits
1. Introduction
The economics of power generation with gas turbines
(GT) is now quite attractive due to its low capital cost, its
high reliability and flexibility in operation. Another out-
standing feature is its capability of quick starting and
using wide variety of fuel from natural gas to residual oil
or powdered coal. Due to better material being made
available and with the use of adequate blade cooling, the
inlet gas temperature of the turbine blades can now ex-
ceed 1200°C as a result of which the overall efficiency of
GT plant can be 35%. This is almost the same as that of a
conventional steam power plant. Based on these devel-
opments, occurrence of instabilities in the compressor
system would no doubt result to performance deteriora-
tion of the overall efficiency of the GT. There are two
basic types of instabilities that could be encountered in
the GT compressor system namely the rotating stall and
surge. Both types of instabilities have damaging conse-
quences to the compressor.
According to Iwakiri, et al. [1], rotating stall causes
the compressor to operate with extremely low frequen-
cies resulting in excessive high internal temperature that
has an adverse effect on blade life. Surge causes severe
problems such as excessive pressure built-up at the inlet
and cyclic loading on the compressor. These instabilities
might lead to the inability of the compressor blade to
produce the required loading and the engine might sus-
tain catastrophic damage as a result of the excessive vi-
bration [2].
1.1. Other Approaches/Techniques
1) Lu, et al. [3] and Okada et al. [4] presented a draft on
“Stall Inception in Axial Flow Compressor”. A compre-
hensive measurement and theoretical analyses was used
to determine which of the two types of instabilities (ro-
tating stall or surge) would occur in a particular situation.
2) Ogbonnaya and Johnson [5] dealt specifically on
surge and rotating stall. In their work, a theoretical com-
pressor system was modeled followed by experimental
results and comparison with theory was presented to

E. A. OGBONNAYA ET AL. 659
analyze the characteristics of these instabilities. The
model was used to predict whether a surge or stall would
occur at stall limit. Similarly, Iwakiri et al. [1] and
Huabing et al. [6] carried out similar work on rotating
stall on centrifugal and axial compressors respectively.
1.2. Approach Used in this Present Work
This paper provides a computerized approach to monitor
the vibration effects of instabilities generally in a GT
compressor system. A program named “VICOMS” writ-
ten in the C++ programming language was used to bring
it to fruition. VICOMS stands for Vibration Instabilities
of Condition Monitoring System. It further provides a
detailed description of these phenomenon/threats and
their consequences. Also, this present work looks at gen-
eral instabilities including galloping, flutter in GT com-
pressors. Accoding to Rao [7], Flutter is a form of self
excited stall which can occur when the section of the
blade is just beginning to stall.
1.3. Causes of Instabilities
The degradation of fouling is one of the causes of GT
performance deterioration. It results to instability in the
compressor system. Fouling is known as the source of
about 70-85% of performance deterioration of GT engine
[8]. Morini, et al. [9] developed a stage by stage model
to investigate the effect of compressor and turbine stage
deterioration. It was observed that compressor fouling is
the most common source of loss in a GT system per-
formance.
Fouling is defined as the deposition process of air
borne particle on the blade surfaces. In GT compressor,
foulant tends to deposit on the compressor blades as the
air flowing into the compressor get contaminated which
may cause malfunction of the blade profile and as well
affect the compressor flow coefficient [10]. The rate at
which this fouling takes place is difficult to quantify be-
cause it depends not only on the types and quantities of
materials ingested, but also on the peculiar properties of
the substances that cause them to stick [11].
Under design operating condition, most stage would
operate at design flow coefficient and at a high isen-
tropic efficiency. When the flow coefficient is to the
right of the characteristics curve as shown in Figure 1,
the stage is lightly loaded and extreme right point is
known as choke point. To the left of the characteristic
curve is a region where aerodynamic stall occurs (surge
region).
As fouling drops, the mass flow rate (flow coefficient)
in the first stage affects the performance of the later
stages as the operating point on the first stage character-
istic curve move toward the left, thus increasing the
Heavy stage
loading
m
o
P
o
T
.
Li
g
ht sta
g
e
Design point
Surge line
1
P
a
P
Fouled
Figure 1. Compressor stage characteristics during fouling
[12].
pressure ratio as shown in Figure 1. This causes a high
density at the inlet to the second stage. Thus, there will
be further reduction in second stage flow coefficient
(mass flow rate). If this effect progresses throughout the
successive stages, a later stage will stall aerodynamically
and trigger surge.
2. Materials and Method
Data were collected on hourly basis for a period of ten
months from an operational GT used for electricity gen-
eration. The data were sampled and the mean taken for
monthly basis. The GT is a 75MW plant called AFAM
III, GT17, TYPE 13D located near Port Harcourt in Riv-
ers State of Nigeria. The characteristics of the GT is
shown in Appendix A.
Any machine handling fluid will vibrate due to reac-
tion of the blade and vanes of the fan or impeller striking
the media of operation. This vibration is rarely trouble-
some except that they exert some part of the machine or
dotting to resonance and it is vibration due to aerody-
namic force. When a system is subjected to a force harm-
onic excitation, its vibration response takes place at the
same frequency as that of the excitation. Common sour-
ces of harmonic excitation are imbalance in rotating ma-
chines, forces produced by reciprocating machines, or
the motion of the machine itself. Figures 2 and 3 show a
compressor model and the free body diagram of a GT
engine, respectively [13,14].
According to Ogbonnaya [14], Rao [15], Dukkipati
and Srinivas [16], the equation of motion that leads to the
circumstances on instabilities of s single degree of free-
dom system is considered as follows:
0mx cx kx


 (1)
For the model shown in Figures 2 and 3 the equa-

E. A. OGBONNAYA ET AL. 660
K

C-damper
Direction of
shaftrotation
m
Figure 2. Compressor Model.
.
xC Kx
F
0
cost
..
xm
Figure 3. Free body diagram of the Compressor Model.
tion of motion may be expressed as follows:
ΣF = ma =
..
xm
F0cost +  – k (dst + x) =
..
xm
F0cost +  – kdst + kx =
..
xm (2)
But  = kdst substituting into Equation (2)
F0cost + kdst – kdst + kx =
..
xm (3)
 F0cost + kx =
..
xm
and
..
xm + kx = F0cost (4)
For damping force analysis
.
x
C
Putting
.
x
C
into Equation (4)
Ferdinand and Johnston [17] showed that
..
xm +
.
xC + kx = Focost (5)
Dividing through by m, we have
.
cos
..
x
m
k
x
m
c
m
t
Fo
x

 (6)
where:
2
n
m
k
, 2  
m
c
Substituting back into Equation (6), we have
.cosF
..
x
2
n
x 2 o
m
t
x

 
(7)
The complementary function, i.e., solution of
is; 0
..
x
2
x 2  n x 
t
e
t
eX 




















2 -
2
-
2
C
-
2
-
1
C
1



t
etX
 
 212 C C









tt
t
eX
22
sin B
22
cosA
3


The general solution of Equation (7) can be obtained
thus:
 tDD  cos
M
F
x 20
22 
and 22
0
D2 D
tcos
M
F



x
since f (D2) cost = f ( – 2) cost,



t
D
X
n
n



cos
M
F
4
- D2
0
2222
22













 4
cos -t Dsin 2
M
F
2
2222
22
0












n
n


 












2
2222
2
2222
0
4
-t cos 4
M
F


n
n
where 








22
2
tan
n



The total solution is the sum of the transient solution
(complementary function) and general solution (steady
state solution) but the transient solution decreases expo-
nentially with time (refer to X1, X2, X3). Thus, when
harmonic solution is considered, we have:

















 


tX
n
ncos
4
4
M
F
2
2222
2
2222
0
which,

E. A. OGBONNAYA ET AL. 661
Frequency, F = Hz


2 and vibration displacement am-
plitude.
 42
22
n
22
0
 

M
F
X (8)
From the referenced GT plant, it was possible to read
out the vibration amplitude directly from the machine
other than the aerodynamic force resulting to the vibra-
tion. It is therefore necessary to determine the correspo-
nding aerodynamic force resulting to vibration. Hence,
from Equation (8) making aerodynamic force, F0, the
subject of formula we have:

2
22
n
22
0 4 XM
 F (9)
where;
F0 = aerodynamic force (N)
M = mass of the shaft (kg)
X = vibration displacement amplitude (mm/s)
 = force frequency (Hz)

n = natural frequency (rad/s)
µ = product of coefficient of damping (Nsm-1).
This is the equation used to model the flowchart and
consequently design the program to simulate a solution
to the vibration effects of instabilities in GT compres-
sors.
Figure 4 shows the flowchart for VICOMS written in
C++ language for obtaining the aerodynamic force re-
sulting to vibration in the GT system. It has one loop as
shown and can go round several iterations until the first
speed is equal to or less than the last speed to make the
program stop. This is when the surge would have been
uncontrollable as to cause damage to the plant. Hence,
VICOMS would predict when the GT should undergo
maintenance check.
The flowchart in Figure 4 led to the evaluation of the
computer program code written in C++ programming
language. The program helped in the calculation of aero-
dynamic force as stated in Equation (9).
3. Results and Discussion
The readings of vibration amplitude of the two end bear-
ings of the compressor unit in a GT plant on industrial
duty for electricity generation was taken with the corre-
sponding mass flow rate, pressure ratio, shaft speed and
active load. These readings are shown in Table 1. It was
observed that the GT was run above its critical speed
value of 3000 rpm.
Figure 5 shows the vibration amplitude as a function
of time. From this result, it is observed that the disturb-
ing force has an oscillatory nature. The force varies as a
Start
Declare / Define
variables used
1 – 1,

n
– 314
Input first, speed last speed
and step value

n
= 2N / 60
Input active load
Input X
1
[ i ] and X
2
[ i ]
 
2
22
n
22
4m i
1
X i
01 





 F
 













 2
22
n
22
4m i
2
X i
02
 F
Print speed, frequency, active load X
1
,
X
2
, and F
01
and F
02
1 = 1 + 1
First speed = first speed + step Val
Is
Firstspeed < = lastspeed
Stop
Yes
N
O
Figure 4. Program flow chart for a VICOMS.
sinusoidal function of time and the wave form.
The wave form shows that it is a steady state vibra-
tion. The graph further depicts that the maximum am-
plitude which the engine can withstand is 15 mm de-
spite running above its critical speed. Figure 6 depicts
the general operation of a compressor under surging
condition. It also shows that the region from point A to
B implies a stable operation without surge or stall.
There is a reverse flow from B, which would lead to
surge. The flow again recovers from C to D yielding a
normal flow; which within the compressor depicts a
normal operating range.
The graph obtained is also in conformity with that giv-
en in Ogbonnaya and Johnson [5]. The minor difference
in profile between B and C could be attributed to the size
of the engine and environmental conditions [14] where
the engines are being used.

E. A. OGBONNAYA ET AL. 662
Table 1. Reading showing the data taken from AFAM III,
GT 17, TYPE 13D.
m
(kg/s) rp
Shaft
Speed
(RPM)
Active
Load
Fre-
quency
(Hz)
Vibration
Amplitude
(mm/sec)
Brg1Brg.2
6.49 9.30 3005 50 51.2 4.8 −15.0
6.7 9.40 3053 50 51.3 4.8 15.0
6.2 9.30 3051 50 51.2 4.6 −15.0
6.8 9.50 3080 50 51.3 4.9 10.0
6.4 9.60 3063 50 51.0 4.9 15.0
6.3 9.50 3063 50 50.4 5.1 −15.0
6.1 9.40 3074 45 51.1 5.1 15.0
6.3 9.50 3076 40 51.3 5.3 7.0
6.5 9.40 3077 40 56.7 5.0 −15.0
6.66 9.40 3081 36 51.5 5.1 6.40
20
15
10
5
0
-5
-10
-20
Amplitude of Vibration (mm)
Time in Hours
Figure 5. Amplitude of vibration as a function of time.
3090
3080
3070
3060
3050
3040
3030
3020
3010
3000
Compressor Speed (rpm)
6 6.2 6.4 6.6 6.8 7
Mass flow Rate (kg/sec)
Figure 6. Speed against flow rate.
This analysis shows that running the compressor within
the regions of B and C should be avoided. This region
would correspond to speeds between 3051 and 3053 rpm.
4. Conclusions
A work has been carried out on the computerized solu-
tion of instabilities in GT compressor. The test engine is
AFAM III, GT 17, TYPE 13D.
The compressor system suffered surge and stall, which
resulted to instabilities in the test engine due to fouling.
It was shown that fouling leads to the stuffing of the
compressor stages. This also results in the reduction of
the compressor surge margin and dramatic instability of
the operation of the whole GT compressor system, cul-
minating to vibration.
The mass flow rate, pressure ratio, shaft speed and vi-
bration amplitude in the system were collected from the
two end bearings of the compressor system in the GT
plant. A model was consequently developed to analyze
the data collected in order to determine the correspond-
ing aerodynamic force causing vibration in the system.
The mathematical model was used to run a program code
named VICOMS written in C++ programming language.
The results and the graph showed that the GT should not
be run beyond 14 mm.
5. Acknowledgements
The authors wishes to acknowledge the efforts of Messrs.
Woji, John and Ebunuoha, Chigozie for their immense
contributions to the success of this research project. They
visited the thermal stations for the experimentations and
data collection associated with this work. They are
equally appreciative of the efforts of Mr. Jeffrey Mukoro
and Chike in typeseting, proof-reading and editing the
manuscript.
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E. A. OGBONNAYA ET AL. 663
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E. A. OGBONNAYA ET AL. 664
Appendix A: Characteristics of afam iii, gt 17, type 13d
NAME OF EQUIPMENT:BROWN BOVIERI- SULZER TURBO MESCHINER;
MANUFACTURER:ABB now ALSTOM
TYPE: 13D
CAPACITY: 75MW
CRITICAL SPEED:3000RPM
TYPE OF COMPRESSOR:VA 14017
DESISGN OF COMPRESSOR:AXIAL
NO. OF STAGES:17
AIR PUMPING CAPABILITY:295 m3/s
Nomenclature:
M = Lumped mass of shaft (kg)
X = Vibration displacement amplitude (mm)
 = 7
22
N = Cycle per minute
F0 = Aerodynamic force (N)
X
= Vibration velocity amplitudes (mm/s)
S = Boundary condition (varying between 1 and 2)

n = Natural damped frequency (rad/s)
W = Weight of the compressor rotor shaft (KN/kg)
K = Shaft stiffness (KN/m)
C = Damping coefficient (KN s/m)

st = Elongation (m)
 = Frequency (Hz)
α = Inlet flow angle 
o (degree)
Eo = Cascade collection efficiency (%)
rp = Pressure ratio
m = Mass flow rate (kg/s)