Alstom Power Steam Turbine Cooling Analysis

Gabriel Marinescu
Alstom Power,
Baden 5401, Switzerland
e-mail: gabriel.marinescu@power.alstom.com
Peter Stein
Alstom Power,
e-mail: peter.stein@power.alstom.com
Michael Sell
Alstom Power,
e-mail: michael.sell@power.alstom.com
Natural Cooling and Startup
of Steam Turbines: Validity
of the Over-Conductivity
Function
The temperature drop during natural cooling and the way in which the steam turbine
restarts have a major impact on the cyclic lifetime of critical parts and on the cyclic life
of the whole machine. In order to ensure the fastest startup without reducing the lifetime
of the turbine critical parts, the natural cooling must be captured accurately in calcula-
tion and the startup procedure optimized. During the cool down and restart, all turbine
components interact both thermally and mechanically. For this reason, the thermal ana-
lyst has to include, in his numerical model, all turbine significant parts—rotor, casings
together with their internal fluid cavities, valves, and pipes. This condition connected
with the real phenomenon lead-time—more than 100 hours for natural cooling—makes
the analysis time-consuming and not applicable for routine projects. During the past
years, a concept called “over-conductivity” was introduced by Marinescu et al. (2013,
“Experimental Investigation Into Thermal Behavior of Steam Turbine Components—
Temperature Measurements With Optical Probes and Natural Cooling Analysis,” ASME
J. Eng. Gas Turbines Power, 136(2), p. 021602) and Marinescu and Ehrsam (2012,
“Experimental Investigation on Thermal Behavior of Steam Turbine Components: Part
2—Natural Cooling of Steam Turbines and the Impact on LCF Life,” ASME Paper No.
GT2012-68759). According to this concept, the effect of the fluid convectivity and radia-
tion is replaced by a scalar function K(T) called over-conductivity, which has the same
heat transfer effect as the real convection and radiation. K(T) is calibrated against the
measured temperature on a Alstom KA26-1 steam turbine (Ruffino and Mohr, 2012,
“Experimental Investigation on Thermal Behavior of Steam Turbine Components: Part
1—Temperature Measurements With Optical Probes,” ASME Paper No. GT2012-
68703). This concept allows a significant reduction of the calculation time, which makes
the method applicable for routine transient analyses. The paper below shows the theoreti-
cal background of the over-conductivity concept and proves that when applied on other
machines than KA26-1, the accuracy of the calculated temperatures remains within
15–18
C versus measured data. A detailed analysis of the link between the over-
conductivity and the energy equation is presented as well. [DOI: 10.1115/1.4030411]
Introduction
In order to design reliably a steam turbine for fast starting and
flexible operation, it is essential to understand the thermal behav-
ior of the turbine components during natural cooling and startup.
The thermal stress arising during startup is in close connection
with the temperature gradient, when the machine cools down from
nominal condition to standstill condition. The stress calculations
proved a significant impact of the natural cooling on the cyclic
life, especially on the turbine rotor.
On the other side, the transient analysis of steam turbines faces
a big challenge regarding the calculation time. Typically, the cool-
ing time of a steam turbine is 100 hours or more, which makes an
accurate calculation time consuming, presently not applicable for
routine projects. A concept called over-conductivity that reduces
significantly the calculation time was introduced in Refs. [1] and
[2]. The main idea of this concept is a scalar function K(T) that
multiplies the fluid conductivity of each finite element within the
turbine cavities. K(T) is calibrated in such a way that it renders the
same heat transfer effect as the real convection and radiation. As
K(T) was calibrated on a Alstom KA26-1 steam turbine (see
Ref. [2]), a verification of the results’ accuracy on other machines
is mandatory. The paper below shows the robustness of the over-
conductivity function when applied on three different machines,
other than the KA26-1 turbine used for calibration. The results
show that the deviation of the calculated temperatures versus
measurements—including the rotor critical locations—remains
within a bandwidth of 15–18
C. Additionally, the paper shows
the close link between the over-conductivity function and the
energy equation.
The Natural Cooling Process
For a steam turbine (see Fig. 1), the natural cooling starts once
the control valve closes. The natural cooling is a time dependent
process that can last more than 100 hours. During this process, the
heat is released gradually from the hot components to the cold
components and from there to environment, until the whole tur-
bine reaches the ambient temperature. Typically, the following
three phases define the natural cooling as a physical process:
• Phase 1: The control valve starts to close, the turbine cavity
is evacuated and remains for several hours at condenser pres-
sure, below the ambient pressure.
• Phase 2 called steam ingestion phase: The glands system is
maintained in service feeding the turbine cavity with steam.
• Phase 3: Once the ingestion phase ends, the condenser pump
shutdowns, the ambient air enters the turbine cavity, and the
pressure increases to ambient pressure.
Contributed by the Turbomachinery Committee of ASME for publication in the
JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 14,
2014; final manuscript received April 18, 2015; published online May 12, 2015.
Editor: David Wisler.
Journal of Engineering for Gas Turbines and Power NOVEMBER 2015, Vol. 137 / 112601-1
Copyright VC 2015 by ASME
Downloaded From: http://gasturbinespower.asmedigitalcollection.asme.org/ on 05/12/2015 Terms of Use: http://asme.org/terms

During steam ingestion, the steam flows at critical condition
through each gland and expands into the turbine cavity. There, it
is driven by the kinetic energy and the temperature gradient. After
the ingestion phase ends, only the temperature gradient drives the
steam flow. During the whole natural cooling period, the rotor
runs at low speed (barring gear mode).
Research Status on Natural Cooling
The main difficulty of the turbine cooling calculation is how to
define the thermal boundary conditions at the fluid–metal inter-
face, especially during the natural cooling. The almost negligible
pressure gradient in the turbine cavity and the very long integra-
tion time (more than 100 hours) prevents to efficiently use the tra-
ditional tools of computational fluid dynamics. Solutions to
overtake these difficulties are presented below.
In 2011, Spelling et al. [3] presented a calculation method
based on a node-centered finite-volume technique on each con-
duction domain. The method was applied extensively for different
transient regimes, including natural cooling, but no details about
the thermal boundary conditions on the fluid–metal interface are
given.
In 2014, Mukhopadhyay et al. presented a very interesting
paper [4] about the transient conjugate heat transfer analysis of a
3D steam turbine casing. The comparison versus measured data
shows a good accuracy for the turbine cooling phase. Being a con-
jugate heat transfer approach, no heat transfer coefficients (HTCs)
were required on the fluid–metal interface. The calculation did not
include the natural cooling.
Regarding the numerical results validation, Mohr and Ruffino
presented, in 2012, an experimental method to measure the rotor
temperature with optical probes during natural cooling [5]. The
thermal survey was conducted on an Alstom KA26-1 IP (interme-
diate pressure) steam turbine with optical probes for the rotor tem-
perature and with standard thermocouples for inner and outer
casing temperatures (see Fig. 2).
Starting from these measurements, Marinescu and Ehrsam [2]
modeled the KA26-1 natural cooling process introducing a func-
tion K(T) called over-conductivity,
kÃ
ðTÞ ¼ KðTÞ Á kairðTÞ (1)
This function allowed modeling the transient heat transfer process
of the whole machine with 12–15
C accuracy along 96 physical
hours.
The over-conductivity function was calibrated in such a way
that it replaces the effect of the transient convection within the
turbine cavities by an equivalent higher conductivity, rendering
on each finite element the same heat transfer effect. The method
has the advantage to be fast enough and consequently applicable
for routine projects, but raised a question on the validity when
applied on other machines.
Natural Cooling and the Over-Conductivity Function
The over-conductivity function K(T) was presented in detail in
Ref. [2]. This approach allows the heat transfer calculation within
the turbine cavities, where the pressure gradient is negligible and
the temperature gradient drives the fluid flow. K(T) is defined as a
second-degree polynomial function of the local temperature
KðTÞ ¼ a1T2
þ a2T þ a3 (2)
The constants a1, a2, and a3 are calculated based on the measured
temperatures on a specific steam turbine unit. Applied for each
thermocouple, presented in Fig. 2, the calculation algorithm pre-
sented in Ref. [2] gave a corresponding Kj(T) function, where j is
the thermocouple index (see Fig. 3). The averaged K(T) is the
over-conductivity function. Obviously, always K(T) 1.
At this point the following two remarks must be noted:
• The scatter of the Kj(T) functions at high temperatures (tem-
perature/live steam temperature above 0.55) is an indication
that at high temperatures, the pressure gradient is not fully
negligible. This scatter defines the method accuracy.
• K(T) was established based on the natural cooling tempera-
tures measured on an Alstom KA26-1 IP steam turbine. That
means this function includes the effect of the internal radia-
tion specific to this machine. But the internal radiation is not
the same on other machines. This is the second limitation of
the over-conductivity function.
Fig. 2 Alstom KA26-1 IP steam turbine instrumentation
Fig. 3 The over-conductivity function (source: Ref. [1])
Fig. 1 Alstom KA26-1 IP steam turbine during instrumentation
(source: Ref. [1])
J_ID: GTP DOI: 10.1115/1.4030411 Date: 12-May-15 Stage: Page: 2 Total Pages: 9
112601-2 / Vol. 137, NOVEMBER 2015 Transactions of the ASME

Over-Conductivity and the Energy Equation
The over-conductivity function presented in Eq. (1) can supply
important qualitative data regarding the flow pattern within the
turbine cavity. As long as, during natural cooling, the pressure
gradient of the fluid is almost negligible, the temperature gradient
is the flow driver. Consequently, we can assume an equivalent ve-
locity V proportional with the fluid temperature gradient rT,
V ¼ fðT; pÞ Á rT (3)
Equation (3) is applicable only within the fluid domain, and does
not include the tangency condition on the fluid–metal interface.
For this reason, V in the paper below is called “equivalent veloc-
ity” and could be interpreted as velocity of the heat wave traveling
in the turbine cavity.
The parameter f(T, p) is a scalar function of pressure and local
fluid temperature. Equation (3) relies on the fluid behavior during
natural cooling—as long as the fluid temperature is constant, the
velocity is zero. Starting from Eqs. (1) and (3), we will show how
the f(T, p) analytical equation can be found. In this order, let us
write the energy equation for axisymmetric domains in two ways.
(a) The standard form
qcp
@T
@t
þ u
@T
@x
þ v
@T
@r

¼ k
@2
T
@x2
þ
@2
T
@r2

þ U (4)
where
U ¼ 2l
@v
@r
2
þ
v
r
2
þ
@u
@x
2
À
1
3
Á r Á Vð Þ2
#
þ l
@v
@x
þ
@u
@r
2
(5)
is the dissipation function. U captures the friction effect,
fully negligible for the natural cooling, as we will see at
the end of this section. If we neglect U and separate the
velocity and the temperature gradient, then Eq. (4)
becomes
qcp
@T
@t
þ qcpV Á rT ¼ k Á DT (6)
(b) The form corresponding to the finite element assump-
tion, which means V ¼ 0 and the convection and radia-
tion effect wrapped up within an equivalent fluid
conductivity kÃ
qcp
@T
@t
¼ kÃ
Á DT (7)
But a link between kÃ
and k was already defined in Eq. (1).
Then comparing Eqs. (6), (7), and (1) we get
kÃ
¼ 1 À fðT; pÞ Á
qcp
k
Á
rT Á rT
DT

Á k (8)
which gives the final equation of f(T, p)
fðT; pÞ ¼
k
qcp
Á 1 À KðTÞð Þ Á
DT
rT Á rT
(9)
As long as K(T) 1, the temperature Laplacian DT gives the
f(T, p) sign. That means for the finite elements that cool down
DT 0 and then f(T, p) 0. Conversely, for the finite elements
that heat up DT 0 and then f(T, p) 0. Because K(T) and the
temperature gradient rT are time- and space-dependent, the func-
tion f(T, p) is time- and space-dependent as well.
The 2D transient analysis was conducted using a finite element
model, where the mesh includes both metal parts and fluid parts
(see Fig. 4).
On the metal parts, the conductivity was declared to be metal
conductivity; meanwhile on the fluid parts, the conductivity was
declared according to Eq. (1). All boundary conditions both for
initial state and transient regime were kept the same as presented
in Ref. [1]. The finite element model was run as follows:
• a first run dedicated to natural cooling, for which the results
are presented below
• a second run dedicated to startup, for which the results are
presented in the section entitled Startup and the Over-
Conductivity Function
The natural cooling run supplied the time variation of the nodal
temperature and nodal temperature gradient based on which we
succeeded to visualize the behavior of the over-conductivity func-
tion K(T) and the fluid equivalent velocity V at several locations
within the turbine cavity (see points A, B C, D, and E on Fig. 5).
Figure 6 shows the time variation of the temperature gradient
module calculated at A, B, C, D, and E. As expected, on a large
time scale, all gradients diminish and converge to zero. The con-
vergence rate is not uniform, which means the temperature of the
Fig. 4 The mesh of the finite element model
Fig. 5 Position of points A, B, C, D, and E

metal parts does not diminish at the same rate. The order of mag-
nitude ranges within 0–0.20
C/mm.
Figure 7 shows the time variation of the temperature Laplacian
DT calculated at the points mentioned above. It is interesting to
see that at point E, the Laplacian changes the sign at approx.
14 hours after natural cooling start. The negative Laplacian is in
connection with the vacuum in the turbine cavity during the steam
ingestion phase. Vacuum means the fluid expands and the fluid
temperature drops below the metal temperature. Once the steam
ingestion ends, the steam is replaced gradually by ambient air and
the radiation from the hot parts (rotor and inner casing) prevails.
The Laplacian increases up to a time (approx. 42 hours after
natural cooling start) when the heat lost to ambient becomes more
important and the temperature drops down to ambient—both the
Laplacian and the gradient tend to zero.
Figure 8 shows the time variation of the function f(p,T) defined
in Eq. (9) and calculated at A, B, C, D, and E. Being a proportion-
ality factor between the equivalent velocity and the temperature
gradient on the same direction, it is not mandatory to diminish to
zero. The divergent variation of the function f at points A, B, and
E confirms that within the turbine cavity, the temperature gradient
drops down faster than the equivalent velocity.
Based on these results, we can find the time variation of the
equivalent velocity in the turbine cavity and explain the flow pat-
tern. Figure 9 shows the variation of the equivalent velocity and
its components at point A.
The negative radial velocity within the first 14 hours is an indi-
cation that during the first hours, after natural cooling start, the
rotor and inner casing cool down faster than the valve. At almost
40 hours after natural cooling start, the radial component of the
velocity exceeds the axial component mainly because the heat lost
radially through outer casing is bigger than the heat lost axially
through bearings. This tendency remains valid for more than
100 hours. The equivalent velocity ranges within 0.02 m/s–0.04 m/
s. Finally, we have to note that as long as the numerical model
does not include the mass and the impulse equations, the equiva-
lent velocity is not applicable on the fluid–metal interface.
Startup and the Over-Conductivity Function
The turbine startup includes a phase called “steam quality
check” (see Ref. [6] and Fig. 10), when the control valve is closed
and there is no active flow in the turbine cavity. In this case, the
standard tools for heat transfer analysis are not applicable. Many
times, after steam quality check, a prewarming phase follows to
heat the turbine rotor before ramping up the turbine. The pre-
warming can last from few tens of minutes up to few tens of
hours. The impact of the prewarming temperature and lead time
on the turbine rotor cyclic life was analyzed in Ref. [6].
As long as, during the steam quality check phase, the turbine
cavity is closed, the gradient of the fluid pressure is negligible.
Only the temperature gradient drives the fluid flow. That means
the over-conductivity function is applicable and can be used to
calculate the transient temperature map of the whole machine.
At cold start, the condensation condition is fulfilled on the
internal faces of the machine. In order to get accurate calculated
temperatures, it is mandatory to take the steam condensation into
account.
Fig. 6 Variation of the temperature gradient module $Tj j
Fig. 7 Time variation of the Laplacian function DT
Fig. 8 Time variation of the function f(p,T)
Fig. 9 Time variation of the velocity module and its compo-
nents at point A

The same Alstom KA26-1 IP turbine was used to model the
transient heat transfer during startup. The machine was stabilized
at cold condition before startup, all thermocouples indicating
17–20
C. The startup consisted of the following (see Fig. 10):
• t1: gas-turbine ignition.
• t2: the glands system was switched ON, the control valve
being closed. On this machine, only the steam quality was
verified, prewarming phase not applied.
• t3: the control valve started to open. The acceleration phase
started. The rotor speed increased to grid synchronization.
• t4: idle regime. The rotor speed reached the synchronization.
The machine was ready for ramp-up.
• t5: the machine reached 10% power regime.
The same over-conductivity function K(T) was used to model
the heat transfer in the turbine cavities. It must be noted that dur-
ing natural cooling the operating points, corresponding to each
thermocouple, travel from high to low temperatures; meanwhile
during startup, the same operating points travel from low to high
temperatures, all of them remaining on the same K(T) curve (see
Fig. 11). For example, the cold start test started on Dec. 11, 2010
at 16:33. The position of the operating points can be seen succes-
sively at 16:33, 16:58, and 17:06. Conversely, the natural cooling
test started on Dec. 13, 2010. The position of the operating points
can be seen successively at 18:44, 19:48, 00:58, and 10:15.
The turbine glands were modeled following the physics of the
steam flow including the condensation phenomenon. During
startup from time t1–t5, the pressure in suction cavity is always
below the ambient pressure, meanwhile in the pressure cavity it is
above the pressure in the turbine cavity and suction cavity. Conse-
quently, there is steam ingestion in the turbine cavity, as presented
in Fig. 12. From time t5 to base load, the steam pressure in the tur-
bine cavity is higher than the pressure in the pressure cavity, and
hence the primary flow changes the direction.
The thermal boundary conditions were calculated at each inte-
gration timestep using the average equation of mass and energy
conservation. For example, on passages 11–12 (see Fig. 12), the
energy equation is
M12hÃ
12 ¼ M11hÃ
12 þ HTC11 Á ðTm À TÞ þ Windage (10)
At station 30, the mass and energy conservation equations are
M30 ¼ M12 þ M22
M30hÃ
30 ¼ M12hÃ
12 þ M22hÃ
22
(11)
Figure 13 shows the temperature map at 30 min after the glands
system is switched ON, when the turbine cavity is closed. A
slightly higher temperature at the hot gland side versus the cold
gland side can be seen because the room available on the hot side
is smaller than the cold side.
Figure 14 shows a comparison between the measured and cal-
culated temperature at thermocouple T24.1. The maximum devia-
tion ranges within 0–18
C and occurred mainly due to
condensation, which distributes the heat asymmetrically around
the inner casing; meanwhile, the finite element modes assumed an
axisymmetric inner casing. We note as well the “bump” of tem-
perature variation between t3 and t4 that captured the effect of
higher steam mass flow required during the rotor acceleration.
Validity of the Over-Conductivity Function
The over-conductivity function K(T) was calibrated based on a
Alstom KA26-1 IP turbine data (see Ref. [2]). In order to verify
how much this function is dependent upon the turbine configura-
tion, the following machines were selected for verification [7]:
(a) Alstom 460 MW HP (high pressure) turbine. This is a HP
50 Hz, single-flow class machine (see Fig. 15).
The outer casing was instrumented with thermocouples
(Th22, Th32, Th42, and Th52). The valves were
Fig. 10 Temperature variation at thermocouples T11.1, T24.1,
Tm33, and Tm42 (source: Ref. [6])
Fig. 11 Startup and natural cooling on over-conductivity
diagram Fig. 12 Gland steam flow from time t1 to t5

instrumented as well with thermocouples (ThV04, ThV07,
and ThV09).
(b) Alstom 1100 MW HP turbine. This is a HP 50 Hz, single-
flow class machine (see Fig. 15).
On this machine, the turbomax indication was compared
against the calculated temperature at the same location.
Turbomax is a temperature sensor located on the inlet spiral
(see the indication “Turbomax” in Fig. 16).
(c) Alstom 1100 MW IP turbine. This is a 50 Hz, IP double-
flow class machine (see Fig. 17).
The turbomax indication was also used to compare the calcu-
lated temperature versus measurements. Due to the double-flow
configuration of this machine, the exhaust columns and the control
valve were separated from the outer casing and a condition of
equal heat flux from the axisymmetric domains to plain domains
was imposed.
All thermal models used the K(T) function (2) and followed the
same calculation process.
In order to prepare a consistent set of input data, all three
machines were operated for natural cooling in the same way:
Fig. 13 Temperature distribution at 30 min after the glands system is switched ON
Fig. 14 Measured and calculated temperature at T24.1
Fig. 15 Alstom HP 460 MW turbine. Temperature distribution
at base load regime.

(a) Each machine was stabilized more than 12 hours at base
load.
(b) At natural cooling start (time ¼ 0), the control valve closes.
The turbine cavity is evacuated and remains at the con-
denser pressure.
(c) The glands system is activated. The steam ingestion in the
turbine cavity starts and lasts 1–5 hours, according to each
turbine specification.
(d) Once the steam ingestion ends, the condenser valve closes
and the ambient air enters the turbine cavity. The natural
cooling continues until the next event.
Figures 18 and 19 show the calculated temperature distribution
on the Alstom 460 MW HP turbine at 8 hours and 60 hours after
natural cooling start. Figure 20 shows the comparison between the
calculated and measured temperature at thermocouple Th22. For
this particular machine, the 15
C temperature difference between
measurement and calculation recorded during the first 3 hours (see
Fig. 20) is an indication that the steam mass flow ingested through
the hot gland was lower than the nominal value, but the similar
slope of the measured and calculated temperature confirms that
the over-conductivity function contributed correctly to the global
heat transfer process. Another good verification is presented in
Fig. 21.
The turbine valves are not axisymmetric parts, meanwhile the
outer casing was assumed axisymmetric. The conversion of the
3D nonaxisymmetric parts to 2D is presented in detail in Refs. [2]
and [5]. The good matching presented in Fig. 21 is a confirmation
that the 3D–2D conversion works correctly.
on the Alstom 1100 MW HP turbine at 8 hours and 60 hours after
natural cooling start. We retrieve the same behavior as KA26-1 IP
turbine—the rotor and casings cool down slightly faster than the
control valves during the first hours than the control valves.
Fig. 17 Alstom IP 1100 MW turbine. Temperature distribution
Fig. 18 Alstom 460 MW HP turbine. Temperature distribution
at 8 hr after natural cooling start.
Fig. 20 Alstom 460 MW HP turbine. Temperature variation at
Th22. Calculated versus measured data.
Fig. 16 Alstom HP 1100 MW turbine. Temperature distribution

Figure 24 shows a comparison between the measured and cal-
culated temperature at turbomax location. The deviation ranges
within 10–12
C. On Alstom machines, the turbomax sensor cav-
ity is filled with MgO, which has a lower conductivity than the
inlet spiral metal. That means the turbomax temperature is slightly
delayed versus the sharp temperature drop within the first hours
after natural cooling start. That explains the deviation marked in a
circle on Fig. 24.
on the Alstom 1100 MW IP turbine at 8 hours and 60 hours after
natural cooling start. Figure 27 shows a comparison between the
measured and calculated temperature at turbomax location. Being
a double-flow turbine, the outer face of the outer casing in the 2D
Fig. 21 Alstom KA26-1 HP turbine. Temperature variation at
Th32. Calculated versus measured data.
Fig. 24 Alstom 1100 MW HP turbine. Temperature variation at
Turbomax location. Calculated versus measured data.
Fig. 25 Alstom 1100 MW IP turbine. Temperature distribution
Fig. 26 Alstom 1100 MW IP turbine. Temperature distribution

model is almost fully covered by the exhaust columns and the
control valve. This feature required a special attention to the inter-
face between the axisymmetric and the plain domains. In this
order, the exhaust columns and the control valve were separated
from the outer casing and a condition of equal heat flux was
imposed on each interface. By this approach, the deviation
between the measured and calculated temperatures remained
within 5–12
C (see Fig. 27). The highest deviation occurs within
the first hours after natural cooling start due to the slow turbomax
time reaction, as noted above for the 1100 MW HP machine.
Conclusions
The over-conductivity function K(T) defined in Eq. (2) proved
to be robust and reliable when applied on steam turbines with dif-
ferent configurations. The over-conductivity function was verified
on the following three machines:
• Alstom 460 MW HP 50 Hz turbine
• Alstom 1100 MW HP 50 Hz turbine
• Alstom 1100 MW IP 50 Hz turbine
The verifications showed that the deviation of the calculated
temperatures ranges within 0–18
C versus measurements along
the whole 96 hr of natural cooling process. The deviation scatter is
the same both on the calibration machine and on the verification
machines, which means the over-conductivity function K(T) is
dependent on the local temperature gradient and not dependent on
the turbine configuration.
During natural cooling or startup process, when the control
valve is closed, the temperature gradient on the fluid domains is
the main driver of the flow within the turbine cavity. The follow-
ing equation captures this feature:
V ¼ fðT; pÞ Á rT
The proportionality function f(T, p) has an analytical equation
depending on the over-conductivity K(T),
fðT; pÞ ¼
k
qcp
Á 1 À KðTÞð Þ Á
DT
rT Á rT
These results allowed the estimation of the equivalent velocity V in
the turbine cavity during the natural cooling process—0m/s–0.05m/s.
Nomenclature
a1, a2, a3 ¼ calibration parameters
Cp ¼ specific heat at constant pressure
f ¼ proportionality function between V and rT
h* ¼ fluid total enthalpy
HP ¼ high pressure
HTC ¼ heat transfer coefficient
IP ¼ intermediate pressure
K(T) ¼ over-conductivity function
M ¼ fluid mass flow
t ¼ time
T ¼ fluid temperature
Tm ¼ metal temperature
V ¼ equivalent velocity
x, r ¼ axial and radial coordinates
D ¼ Laplacian operator
k ¼ fluid thermal conductivity
k* ¼ equivalent fluid thermal conductivity
q ¼ density
r ¼ gradient operator
References
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“Experimental Investigation Into Thermal Behavior of Steam Turbine
Components—Temperature Measurements With Optical Probes and Natural
Cooling Analysis,” ASME J. Eng. Gas Turbines Power, 136(2), p. 021602.
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Behavior of Steam Turbine Components: Part 2—Natural Cooling of Steam Tur-
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[3] Spelling, J., Joecker, M., and Martin, A., 2011, “Thermal Modeling of a Solar
Steam Turbine With a Focus on Start-Up Time Reduction,” ASME Paper No.
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Conjugate Heat Transfer Simulation Methodology for Prediction of Steam Tur-
bine Cool-Down Phenomena and Shell Deflection,” ASME Paper No. GT2014-
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Behaviour of Steam Turbine Components: Part 1—Temperature Measurements
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Startup and Impact on LCF Life,” ASME Paper No. GT2013-94356.
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Thermal Behavior of Steam Turbine Components: Part 4—Natural Cooling and
Robustness of the Over-Conductivity Function,” ASME Paper No. GT2014-
25247.
Fig. 27 Alstom 1100 MW IP turbine. Temperature variation at
turbomax location. Calculated versus measured data.

Alstom Power Steam Turbine Cooling Analysis

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