EVALUATION OF EROSION RISK FOR A COGENERATION [615846]

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EVALUATION OF EROSION RISK FOR A COGENERATION
STEAM TURBINE WHEN STEAM PARAMETERS CHANGE

Gabriel Negreanu 1, Ion Oprea 1, Radu B ăcanu 2, Dragos Baciu 2

1University Politehnica of Bucharest
2Elsaco Electronic Boto șani

ABSTRACT

The paper analyses the possibility of erosion risk increase for the last blade of a back-pressure
steam turbine when steam conditions before and after turbine are changing due to various operational
regimes. A complete verification “stage by stage” c alculus has been performed, in order to reveal the
geometrical dimensions (average diameters, lengths of nozzles and blades, characteristic angles) and
operational ones (adiabatic and internal enthalpy d rops, absolute and relative steam velocities, inter nal
efficiencies and powers). After that, a behavioral model for unrated charges was setup and boundaries
conditions (such as pressure and temperature of liv e steam or back-pressure) were modified, according
to real operational regimes. Some collected paramet ers (moisture, pressure, tip velocity) were
collected as inputs for several erosion criteria.

1. INTRODUCTION

Steam expansion in the turbine is a fast-moving the rmodynamic process. The
condensation process does not start on the saturati on curve (x=1), as in a quasi-static process,
but is delayed and starts on constant humidity curv es known as Wilson curve. The delay of
the condensation phenomenon are characterized by th e speed of expansion:

dx dp
pc
ddp
ppa− =τ− =1ɺ (1)

The Wilson curves corresponding to the different ex pansion rates (Figure 1) show that the
delay is even higher as the expansion speed increas es.

Figure 1. Wilson curves for initiation of Figure 2. Velocity diagrams for wet steam
condensation in the turbine (index w – wa ter droplets)

1email: [anonimizat]

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At a certain moment in the turbine stage the humidi ty is in two forms:
• droplets driven by the vapor stream; the trajectory of these drops depends on the mode
of formation, size and drive speed;
• film on the surface of the nozzles and blades, form ed by dropping, drifting in motion
at a low speed. The film breaks at the nozzle exit edge in the form of droplets of
relatively large diameter, in the order of magnitud e of the thickness of the edge.

The fine droplets are trained at speeds and traject ories close to vapor, the large droplets in
the macrodispersion fraction have very different ve locities and trajectories, their impact with
the pallet entrance edge causing its erosion (Figur e 2).
Assessing the risk of erosion is difficult to do by using theoretical elements. Basically,
relatively simple criteria are used that take into account the amount of moisture, impact
energy and steam parameters.
The condensing turbines, in order to increase perfo rmance, work with low condenser
pressures, the lower limit being imposed by the coo lant temperature or the risk of erosion. The
usual range of these pressures is pc = (0,07 ÷ 0,03) bar. The risk of erosion generally occurs at
the last step stage blades characterized by high hu midity ( y0> 0,05 respectively x0 <0,95) and
low p0 pressure <0,3 bar and the long blade length leads to high peripheral speeds in the range
u = (400 ÷ 550) m/s.
Under these conditions, the risk of erosion has to be assessed and measures taken to avoid
it, by protecting the edge of the blades, changing the parameters of the steam, intensifying the
internal collection of moisture. Changes in live st eam parameters, such as temperature drop
(Figure 3) or increase in pressure (Figure 4), whic h increase the humidity at the turbine outlet,
must be accompanied by an erosion hazard assessment using criteria set by various turbine
manufacturers (Table 1).

Figure 3. Live steam temperature drop on F igure 4. Live steam pressure increase on
the final vapor content of the s team the final vapor content of the steam

The influence of the exhaust condensing pressure dr op is very important too. Coolant
temperature is a natural limit to lowering condense r pressure in order to increase enthalpy
yield and fall. Another limit is given by the incre ase of steam humidity at the turbine
discharge, (decrease of the vapor fraction).
Operating with a higher exhaust pressure than the c ondensing rated value is so called
“worsened vacuum” regime and contributes to the dec rease of the moisture (a positive effect
for the erosion), but produces also an efficiency d rop for the last stage, due to the “breaking
effect”.

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Table 1 Erosion criteria for the last stage blades of the steam turbines
Criterion Reference Equation Erosion risk assesment
Escher Wyss (1) [1] 2
2 0
400 200 
ηρ=u c yEa E<1 no erosion risk
1≥E erosion risk;
blades should be
protected Escher-Wyss (2) [2,3] 4
2 0
100 200 
ηρ=u c yEa
KWU [1] 2
02
0
3000 =ndpyE E<0. 2 no erosion risk
0,2< E<0.8 erosion risk;
E>0.5 blades should be
protected
Hitachi [2,3] ( )8 , 0
1244 , 2 01 , 0 3 , 4 y u E ⋅−⋅⋅= E<2 no erosion risk
2< E<4 erosion risk
E>4 very high erosion
risk
where: 0y [-] – humidity at stage inlet;
1y [-] – humidity between nozzles and blades;
ρ [kg/m 3] – steam density, at the stage outlet;
η – coefficient of quality for the moisture reduct ion system: ( 1=η for modern
systems; 1 8 , 0<<η for old systems);
0p [bar] – pressure at stage inlet;
c1a [m/s] – axial velocity at nozzles outlet;
c2a [m/s] – axial velocity at blades outlet;
u [m/s] – peripheral velocity at blade’s tip.

2. METHODOLOGY

2.1. Turbine operating parameters
The analyzed steam turbine holds an impulse control stage and 16 reaction stages. The
main operating parameters are:
• Live steam nominal parameters: p0n =49,0 bar, t0n =447 °C;
• Minimal live steam pressure: p0min =44,0 bar; Minimal live steam temperature:
t0min =390 °C;
• Nominal steam mass flow rate: nm0ɺ=20,7 t/h; Maximal steam mass flow rate:
max
0mɺ=21,5 t/h: Minimal steam mass flow rate: min
0mɺ=8 t/h;
• Nominal parameters of the steam extraction for the dea erator: pD=5,75 bar; tD=217 °C;
Dmɺ=0,408 t/h;
• Condensing pressure: pCn =0,89 bar; pCmin =0,52 bar.
• Rotation speed: n= 9944 rot/min;

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2.2. Nominal regime design/verification calculus
By not having a precise step-by-step calculation of the no minal steam turbine regime (on
which modeling of non-nominal regimes is based), we pro ceeded to a design/verification
calculation using the geometric dimensions and the nominal parameters presented in
paragraph 2.1.
The impulse control stage has an isentropic drop of 140 kJ/kg, an average diameter
d1=0,47 m, an admission grade ε=0,32 and an internal efficiency ηi=0,715. The internal power
produced by the control stage is 578 kW, representing a bout 15 % of overall turbine internal
power.
Starting from the exit point in the control room chamber, the real process in the pressure
stages can be drawn, based on the deaerator paramet ers ( pD = 5.75 bar; tD = 217 ° C) and the
pressure at the condenser ( pCn = 0.89 bar). By the energy balance (imposing the rated
electrical power at the 3.6 MW e generator output) the real expansion process in the h-s
Mollier diagram. The parameters of this process are pres ented in Table 2.

Table 2 Parameters of the real expansion process in the pressure stage
High Pressure Section Low Pressure Section
p0TPCIP = 29.40322 bar p0TPCJP = 5.75 bar
h0TPCIP = 3210.805 kJ/kg h0TPCJP = 2888.703 kJ/kg
s0 TPCIP = 6.901083 kJ/kgK s0TPCJP = 7.066408 kJ/kgK
p2TPCIP = 5.75 bar p2TPCJP = 0.89 bar
t2TPCIP = 217 șC h2tTPCJP = 2547.295 kJ/kg
h2tTPCI P= 2810.668 kJ/kg HtTPCJP = 341.4084 kJ/kg
HtTPCIP = 400.1363 kJ/kg ηiTPCJP = 0.745221
h2TPCIP = 2888.703 kJ/kg HiTPCIP = 254.4246 kJ/kg
HiTPCIP = 322.1012 kJ/kg h2TPCJP = 2634.279 kJ/kg
ηiTPCIP = 0.804979 – v2TPCJP = 1.859481 m3/kg
mTPCIP = 5.749444 kg/s x2TPCJ P= 0.984313 –
s2TPCJP = 7.301797 kJ/kgK
mTPCJP = 5.636111 kg/s

2.3. Non nominal regimes modeling

For these regimes we used the hybrid method described in [7]. The method is based on
the relationship between pressure distribution and mass-flow rate at partial loads (Stodola):

11
2
22
12
22
1
TT
p pp p
mm n
n n n⋅
−−= (2)

and the dependence internal efficiency versus load, rep resented by the relative fictive
velocities ratio fic
v
fic nu
cr
u
c= 
      (3)

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for control stage: ( )



⋅⋅−⋅⋅=−
'
0'
0
04
/ 010 283 , 0vp
mkkc u RATEAU iɺη (4)

and pressure stages: ()v vsi
i r r−⋅= 2 η (5)

3. RESULTS AND CONCLUSIONS

We ran several tests, presented in table 3.

Table 3 Parameters of analyzed operating modes
Nr.crt [kg/s] p0[bar] t0[șC] pC[bar]
OM1 5.75 49 447 0.89
OM2 2.22 49 390 0.43
OM3 2.22 29 350 0.43
OM4 2.22 47 445 0.89

• Operating mode 1 is the nominal mode, as a nominal flow o f the district heating water
flows through the condenser; it is noted that the exit poin t in the turbine is above the
Wilson curve, which means that the water droplets have n ot yet formed and only the
last stage works partially under the saturation curve.
• Operating mode 2 is the mode in which the live steam flo w is kept at the technical
minimum and its pressure is brought to its nominal value, while the temperature drops
with 57 degrees Celsius; it is the most unfavorable in ter ms of humidity, five stages
working with humid saturated steam. It has also the lowe st evacuation vapor content
(0.948)
• Operating mode 3 is a start-up one, limited as duration; It is noted also that 5 stages
operate under the saturation curve
• Operating mode 4 is a partial mode with minimal steam flow a t which nominal
pressure is maintained at the condenser by regulating th e flow rate of district heating
water. It is noteworthy the operation of the last stage in b rake mode with power
consumption and negative internal efficiency.

Table 4 Erosion criteria
Nr.crt xC EW(1) <1 EW(2) <1 KWU <0.2 Hitachi <2
[-]
OM1 0.986 0 0 0 0.0110
OM2 0.948 0.022 0.2629 0.0089 0.0311
OM3 0.949 0.0022 0.2568 0.0085 0.0306
OM4 0.958 0.0024 0.2829 0.0063 0.0261

No risk for erosion, all the criteria from Table 1 returned values less than limits. The red
curve of constant vapor content x=0.88 has never be en touched by the expansion lines.

The expansion lines are presented in figure 5. The gree n curve represent the saturation line
(x=1), the brown one the Wilson curve.

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OM1 OM2

OM3 OM4
Figure 5: Expansion lines in Mollier diagram for the four ca ses

AKNOWLEDGMENTS

„This work was supported by the project UPB: T-ME 16 -17-01, financed by Elsaco Electronic
and by the grant of the Romanian Ministery of Resea rch and Innovation, CCCDI – UEFISCDI,
project number PN-III-P1-1.2-PCCDI-2017-0404 / 31PC CDI/2018”

References
[1] Grecu T., Cardu M., Nicolau, I., “Turbine cu abur”, Editura Tehnic ă, 1976
[2] Leyzerovich A. Sh., “Wet Steam Turbines for Nuc lear Power Plants”, Penwell Corporation, Ed. I, 200 5.
[3] Leyzerovich A. Sh., “Steam Turbines for Modern Fossil-Fuel Power Plants ” , The Fairmont Press-Inc.,
2007.
[4] Negreanu G., Oprea I ., Le calcul de verification pour le regim de projec t d'un etage de turbine qui utilise
de le vapeur humide, International Simposium on Nuc lear Energy, Bucure ști 1993.
[5] Oprea I , Contribu ții privind curgerea aburului umed în treptele turbi nelor, Sesiune de comunicãri
știin țifice, ICSITEE, Bucure ști 1989.
[6] Oprea I., Negreanu G., Aspects of the Saturat ed Steam Turbine Calculation for Partial Loading,
International Simposium on Nuclear Energy, Bucure ști 1993.
[7] Negreanu G, „Teoria și modelarea turboma șinilor” , Editura Printech 2007, ISBN 978-973-718-624-9.