Component 56: Steam Turbine (Extended)

In This Topic

Component 56: Steam Turbine (Extended)

Specifications

Line connections
1	Inlet
2	Outlet
3	Extraction 1
4	Extraction 2
5	Shaft entry
6	Shaft exit
7	Outlet for controlling purposes Information exit for outlet pressure (P2) or the sum of the escaping mass flow
8	Inlet for the measured pressure at line 1
9	Inlet for the measured enthalpy at line 1

General User Input Values Characteristic Lines Physics Used Displays Example

General

Component 56 models a turbine stage, a set of stages or a section: e.g. from entry to the first extraction, or from extraction i to extraction i+1, or from last extraction to exit. The extraction in this case is the connection provided irrespective of whether steam really bled out or not.

The turbine is defined by pressure at the inlet and the efficiency. In most cases, the pressure at the outlet is defined by the pressure at the inlet of the following turbine stage. In the case of the last turbine stage, the pressure at the outlet has to be defined by using a component 33.

When the exhaust steam at a last turbine stage is not led through connection 2 e.g. for condensation into the condenser, but instead through one of the two extraction connections, connection 2 has to be equipped with a blind line and the mass flow must be defined as zero using component 33 (start value).

The properties described so far do not differ from the properties of component 6 (steam turbine type 1).

The flow characteristic (inlet pressure as a function of mass flow) is determined by means of the conical law of Stodola.

P1- Calculation in part load

At partial load, component 56 calculates inlet pressure P1 as a function of mass flow, outlet pressure and its specific volume from the Stodola Law:

See also and for the formulation of the Stodola law: Turbines - OffDesign - Stodola

In the chapter "Part load calculation of the steam turbine", M1N, P1N, P2N and V1N designate the nominal values in the design case or M1, P1, P2 and V1 the corresponding quantities under the current conditions.
As in the design case, the outlet pressure P2 is always determined by external components.

Flag FSPECQ for Specifying Power or Mass Flow

As in the case of the simple steam turbine (Component 6), this component now features a flag FSPECQ as well. It serves to set whether the shaft power is to be calculated from the mass flow (FSPECQ=0, default) or the mass flow is to be calculated from the shaft power (FSPECQ=1).

With the mode FSPECQ=1, a feed water pump turbine can be modelled where the shaft power results from the required pump power.

The calculation of the mass flow, however, is extremely disadvantageous for the convergence behaviour and should therefore only be used if necessary. In particular, it cannot be used when connecting several turbine disks in series.

However, there are some additional, essential characteristics, which open up further application areas:

Outlet losses through definition of a characteristic line.
Piston losses through definition of a characteristic line.
Optional use of characteristic lines in relative or absolute display.
Correction of the efficiency, when moisture is present, with the help of the Baumann factor. Possibility of an additional manual correction by means of a weighting factor.
Consideration of the swallowing capacity for the last stage by default setting of a maximum volume mass flow at the outlet. When the limiting capacity is exceeded, the outlet pressure assigned to the swallowing capacity is made fixed. This pressure lies at a logical connection and hence can be used for control purposes.
Regulated steam extraction, if more steam is extracted than led into the turbine. The sum of all steam extractions is shown on a logic connection and so can also be used for control purposes.

User Input Values

FMODE	Calculation mode Like in Parent Profile (Sub profile option only) Expression =0: GLOBAL =1: Local off-design =-1: Local design
FP1N	Inlet pressure default type Like in Parent Profile (Sub profile option only) Expression =0: P1=P1NSET =1: P1 given from outside
P1NSET	Inlet pressure setting (nominal)
FDHLO	Determination of the outlet losses (only for FABB=1) Like in Parent Profile (Sub profile option only) Expression =0: Loss as user input value DHLON =1: Loss from the absolute DHLON-characteristic line
DHLON	Outlet losses (nominal) defined as speed losses [see example for the usage]
QLPN	Piston losses (nominal) See instructions further below
FQLMRN	Switch for specification of mechanical losses Like in Parent Profile (Sub profile option only) Expression =1: absolute mechanical loss QLMN=QLMRN =2: relative: mechanical loss QLMN=QLMRN * MULQ*Q5
QLMRN	Mechanical losses (nominal) owing to the setting of the FQLMRN
FSPECQ	Specification of power or mass flow Like in Parent Profile (Sub profile option only) Expression =0: Flow given externally , power calculated =1: Power given externally , flow calculated
ETAIN	isentropic efficiency (nominal) [See instructions further below]
MULQ	Factor, with which the calculated power is multiplied (performance factor)
FBAU	Efficiency correction for steam wetness Like in Parent Profile (Sub profile option only) Expression =0: Factor=1.0 =1: Baumann factor is calculated
BFAC	Baumann correction factor Factor for manually influencing the set or calculated Baumann-correction-factor At BFAC=0, neither the set nor the calculated Baumann factor has got any influence on the efficiency. [See below for usage of FBAU].
P1MIN	Minimum pressure for P1 which it is not allowed to fall below in the off-design mode.
FPX	Stop pressure calculation Like in Parent Profile (Sub profile option only) Expression =0: No calculation of the turbine stop pressure =1: Calculation of the turbine stop pressure If the volume mass flow at exit is larger than the maximum volume mass flow VMX, then a relaxation is done in the turbine till the pressure, from which the maximum volume flow results.
FSC1	Shaft connection Like in Parent Profile (Sub profile option only) Expression =0: On HP-side with shaft inlet =1: On HP-side with shaft outlet
FABB	Multi-function variable (see below for usage) Like in Parent Profile (Sub profile option only) Expression =0: Standardized characteristic line (eta and outlet losses) =1: Absolute characteristic line (eta and outlet losses)
FETA	Determination of the off-design efficiency (only for FABB=0) Like in Parent Profile (Sub profile option only) Expression =0: Eta for off-design f1(M1/M1N) =1: Eta for off-design f1(P1/P2)/(P1N/P2N) =2: Eta for off-design f1(VM1/VM1N) =-1: Power specification (Q6) =-2: Enthalpy specification (H2)
RVMX2	Like in Parent Profile (Sub profile option only) Expression Referred swallow volume flow (used only for FABB=0) [see below for usage]
FETAIN	Design eta (only for FABB=1) Like in Parent Profile (Sub profile option only) Expression =0: from ETAIN =1: from absolute characteristic line eta ETAIN = f1 (VM1)
FETAI	Determination of the off-design efficiency (only for FABB=1) Like in Parent Profile (Sub profile option only) Expression =0: owing to the definition of FETAIN =1: from absolute characteristic line 4, ETAI = f4 ((P1/P2)/(P1N/P2N)) =-1: Power specification (Q6) =-2: Enthalpy specification (H2)
FADAPT	Flag for adaptation polynomial ADAPT / adaptation function EADAPT Like in Parent Profile (Sub profile option only) Expression =0: Not used and not evaluated =1: Correction [ETAI = ETAIN * Char Line factor polynomial] =2: Replace [ETAI = ETAIN polynomial] =1000: Not used but ADAPT evaluated as RADAPT (Reduction of the computing time) = -1: Correction [ETAI = ETAIN * Char Line factor function] = -2: Replace [ETAI = ETAIN function] = -1000: Not used but EADAPT evaluated as RADAPT (Reduction of the computing time)
EADAPT	Adaptation function
P2N	Outlet pressure (nominal)
T1N	Inlet temperature (nominal)
M1N	Mass flow at the inlet (nominal)
VM1N	Volume flow at the inlet (nominal)
VM2N	Volume flow at the outlet (nominal)
VMX	Stop volume flow (FABB=1)

The parameters marked in blue are reference quantities for the off-design mode. The actual off-design values refer to these quantities in the equations used.

Generally, all inputs that are visible are required. But, often default values are provided.

For more information on colour of the input fields and their descriptions see Edit Component\Specification values

For more information on design vs. off-design and nominal values see General\Accept Nominal values

Below is a summary table of the meaning of some key variables, depending on the selection for FABB.

FABB=0

FABB=1

ETAIN

In design case the specification value ETAIN is valid as nominal value.

In the off-design case, characteristic line 1 gives relative values. These can be selected with three different options. The selection index is FETA.

FETA=0 : ETAI/ETAIN = f1 (M1/M1N)

FETA=1 : ETAI/ETAIN = f1 ((P1/P2)/(P1N/P2N))

FETA=2 : ETAI/ETAIN = f1 (VM1/VM1N)

ETAIN

In design case either the specification value ETAIN is valid as nominal value or the nominal value is determined from the characteristic line 1. Selection index is FETAIN

Characteristic line 1 absolute.

FETAIN=0 : ETAIN = ETAIN as specified

FETAIN=1 : ETAIN = f1 (VM1)

In the off-design case, either the value ETAIN, which is determined for the design case, is used for off-design ETAI, or it is determined from the characteristic line 4.Selection index is FETAI. Characteristic line 4 supplies absolute values.

FETAI=0 : ETAI = ETAIN

FETAI=1 : ETAI/ETAIN = f4 ((P1/P2)/(P1N/P2N))

DHLON

In the design case, the specification value DHLON is valid as nominal value.

In the off-design case, the characteristic line 2 returns relative values.

DHLO/DHLON = (VM2/VM2N)**2 * f2 (VM2/VM2N)

DHLON

In the design case, either the specified value DHLON is valid as nominal value, or else it is determined from characteristic line 2. The selection index is FDHLO. Characteristic line 2 is valid absolute.

FDHLO=0 : DHLON = DHLON as specified

FDHLO=1 : DHLON = f2 (VM2)

In the off-design case, either the value DHLON is valid, which is determined in the design mode, for off-design DHLO or else it is determined from characteristic line 2. The selection index is FDHLO. Characteristic line 2 returns absolute values.

FDHLO=0 : DHLO = DHLON

FDHLO=1 : DHLO = f2 (VM2)

QLPN

In the design case, the specification value QLPN is valid as nominal value.

In the off-design case, characteristic line 3 is valid relatively.

QLP/QLPN = f3 (P1/P1N)

QLPN

In the design case, the specification value QLPN is valid as nominal value.

In the off-design case, characteristic line 3 is valid relatively.

QLP/QLPN = f3 (P1/P1N)

QLMRN

if FQLMRN=absolute, then QLM=QLMN=QLMRN

if FQLMRN=relative, then QLM=QLMN=QN*QLMRN

QLMRN

if FQLMRN=absolute, then QLMN=QLMRN

if FQLMRN=relative, then QLMN=QN*QLMRN

VMX2

not used

VMX2

VM2MAX=VMX is used as swallow volume (not RVMX2).

RVMX2

VM2MAX=RVMX2*VM2N is used as swallow volume (not VMX)

RVMX2

not used

Characteristic lines

ETAI/ETAIN = f1 (M1/M1N) for FETA=0

ETAI/ETAIN = f1 ((P1/P2)/(P1N/P2N)) ) for FETA=1

ETAI/ETAIN = f1 (VM1/VM1N) ) for FETA=2

DHLO/DHLON = (VM2/VM2N)**2 * f2 (VM2/VM2N)

QLP/QLPN = f3 (P1/P1N)

ETAI/ETAIN = f4 ((P1/P2)/(P1N/P2N))

Physics used

Equations

All cases

P1 Calculation

{

For design mode (Globalized and FMODE=design), then {

P1 = P1N }

For off-design (GLOBAL=off-design or FMODE=off-design)

{ P1 is calculated from the steam cone equation of STODOLA

see: Part-load - Turbine

if P1 < P1MIN, then { P1 = P1MIN }

Calculation of the isentropic gradient DHS

Calculation of the saturation temperature T1S

Calculation of the saturation temperature T2S

{

see: TURB_DHS

T1 = f(P1,H1)

T1S = fsat(P1) saturation temperature

if T1 > T1S, then { S1 = f(P1,T1) }

else{ S1 = f(P1,H1) }

S2S = S1 isentropic expansion

TX2S= f(S2S,TX2O) (with TX2O as old value of TX2S)

TX2O= TX2S

T2S = fsat(P2)

ifTX2S > T2S ---> H2S = f(P2,TX2S)

else H2S = f(P2,S2S )

DHS = H1-H2S

}

Calculation of the steam content X1

Calculation of the specific volume V1

Calculation of the volume flow VM1

see volume flow

{

if T1 > T1S then { X1 = 1.0D0 }

else { X1 = f(P1,H1) }

if X1=0 or X1=1, then { V1 = f(P1,T1) }

else {V1 = X1*f"(P1)+(1-X1)*f'(P1) }

VM1 = M1*V1

}

Calculation of the isentropic efficiency from the characteristic lines

1 or 4 with SPEZ PRESET ETAIN

calculated value ETAI

see: DTUR_KENNL

{

if FABB=0, then {

for design case then { ETAI=ETAIN }

else {

for FETA=0 then ETAI/ETAIN=f1(M1/M1N)

for FETA=1 then ETAI/ETAIN=f1(P1/P2)/(P1N/P2N)

for FETA=2 then ETAI/ETAIN=f1(VM1/VM1N)

}

if FABB=1 then {

for design case then {

for FETAIN=0 then ETAI=ETAIN

for FETAIN=1 then ETAI=f1(VM1)

}

else {

for FETAI=0 then ETAI=ETAIN

at FETAI=1 then ETAI=f4((P1/P2)/(P1N/P2N))

}

Measurement value correction for the efficiency

ETAI : from the characteristic line calculation

ETAI_MCC : ETAI with measurement value correction

{

MC:= Measurements

-------------------------------------------------------------

MC= 0 : design interpretation (full load)

MC= 1 : design control calculation (part-load)

-------------------------------------------------------------

Comparison between interpretation conditions (full load)

MC = 2 : as built / design

MC = 4 : operation / new state

-------------------------------------------------------------

Comparison between test calculation conditions (off-design)

MC = 3 : as built / design

MC = 5 : operation / as built

for design{

if FCMP=0, then { ETAI_MCC = ETAI }

else {

ETAI_MCC = ETAI

if MC=2, then { ETAI_MCC = ETAI*C_AD }

if MC=4, then { ETAI_MCC = ETAI*C_AD*C_OA }

}

for off-design then{

if FCMP=0, then { ETAI_MCC = ETAI }

else {

ETAI_MCC = ETAI

if MC=3, then { ETAI_MCC = ETAI*C_AD }

if MC=5, then { ETAI_MCC = ETAI*C_AD*C_OA }

}

Wetness correction of the efficiency

ETAI_MCC : after measurement value correction

ETAI_WC : ETAI_MCC with wetness correction

BAU_COR : Correction for Baumann factor

X2O : X2 from the last iteration

{

Y_WET = (2-X1-X2O)*0.5*BAU_COR

ETAI_WC = ETAI_MCC - BFAC * Y_WET

}

Calculation of the outlet loss including the wetness correction

DH, H2A, T2A and VM2

2A = State before the outlet loss

DHL_VR Outlet loss before the last iteration step

{

if measurement value exists (MC=1 to 5), then {

H2A = H9 - DHL_VR

DH = H1 - H2A }

else {

DH = DHS * ETAI_WC

H2A = H1 - DH

}

T2A = f(P2,H2A)

T2O = T2A

H2 = H2A

}

Calculation of the steam content X2

Calculation of the specific volume V2

Calculation of the volume flow VM2

s.: Volume flow

{

if T2A > Tsat2, then { X2 = 1 }

else { X2 = f(P2,H2A) }

if X2=0 or X2=1, then { V2 = f(P2,T2A) }

else { V2 = X1*f"(P2)+(1-X2)*f'(P2) }

VM2 = M2*V2

X2O = X2

}

Calculation of the exhaust steam loss from characteristic line 2

SPEZ Input DHLON

calculated value DHL_VR

s.: DTUR_VERL_KENNL

{

if FABB=1, then {

if FDHLO=0 , then { DHL_VR = DHLON }

else {characteristic line 2

DHL_VR = f2(VM2) }

}

if FABB=0, then {

if design case then { DHL_VR = DHLON }

else {characteristic line 2

VV = VM2/VM2N

DHL_VR = (DHLON*VV**2) * f2(VV) }

}

Calculation of the piston loss from the characteristic line 3

SPEZ Input QLPN

calculated value QL_P

see: DTUR_KOLBEN_VERL_KENNL

{

if FABB=1, then {

for design case {QL_P = QLPN }

else { characteristic line 3

QL_P = QLPN*f3(P1/P1N) }

}

if FABB=0, then {

for design, then {QL_P = QLPN }

else { characteristic line 3

QL_P = QLPN*f3(P1/P1N) }

}

remaining losses

{

if QLMRN < 0.0 , then {ETAM = 1.0 + QLMRN

QL_M=0 }

else {ETAM = 1

QL_M = QLMRN }

}

H2-calculation, state after turbulence

{

Y_WET = (2.0-X1-X2)*0.5*BAU_COR

ETAI_WC = ETAI_MCC - BFAC * Y_WET

if a measurement is present (MC=1 to 5), then {

H2 = H9

H2A = H2 - DHL_VR

DH = H1 - H2A

ETAI_MES = DH/DHS

ETAI_MES = ETAI_MES + BFAC * Y_WET

DHSUM = H1 - H2 }

else {

DH = DHS * ETAI_WC

H2A = H1 - DH

H2 = H2A + DHL_VR

DHSUM = H1 - H2 }

}

Efficiency control during the series of measurements

Calculation of the correction factors as ratio of the

measurement value to the value calculated from the characteristic lines

{

if a measurement exists (MC=1 to 5), then {

if MC=2 or MC=3, then C_AD = ETAI_MES/ETAI

if MC=4 or MC=5, then C_OA = ETAI_MES/ETAI

}

else {

C_AD = 1

C_OA = 1 }

}

BAUMANN correction

see: BAUMANN_KORREKTUR

{

if FBAU=1, then {

if X1 >= 1 and X2 < 1, then {

S_S1 = f (P1,T1)

S_S2 = f (P2,H2)

P_S1 = f"(S_S1,T1)

P_S2 = f"(S_S2,T1)

H_S1 = f"(P_S1,T1)

H_S2 = f"(P_S2,T1)

ZW1 = H1 - H_S1

ZW2 = H_S2 - H2

ZW = ZW1 + ZW2

BAU_COR = ZW2/ZW }

else { BAU_COR = 1 }

if FBAU=0 , then { BAU_COR = 1 }

}

STOPPAGE

{

P2_LINIE=P2

in design mode and FPX = 1, then {

if VMX<= VM2, then { P2_EXPA = PX2*VM2/VMX }

if P2_LINIE >= P2_EXPA, then { P2_EXPA = P2_LINIE }

}

T2 = f(P2,H2)

M1 = M2 + M3 + M4

P3 = P2

T3 = T2

H3 = H2

Q3 = M3 * H3

P4 = P2

T4 = T2

H4 = H2

Q4 = M4 * H4

M2 = M1 - M3 - M4

Q2 = M2 * H2

if FSC1 = 0 FACT = 1

if FSC1 = 1 FACT = -1

H6 = (M1*(H1-H2) + M5*H5*FACT - QL_P - QL_M)/M6

Component Displays

	Display Option 1		Display Option 2
	Display Option 3		Display Option 4

Example

Click here >> Component 56 Demo << to load an example.

Settings

Turbines - OffDesign - Stodola

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