Gas Turbine Performance

1
Gas Turbine Performance University of Puerto Rico
at Mayaguez Class Slides, 8/31/2006 R.
McGurgan
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Quiz 1 Preliminary Feedback Graded papers to
be returned next Tuesday. Overall Impression
The quality of work is very good, often
excellent. Keep up the good work !! Why do I say
this ? Systematic solutions. Applicable laws
are stated and applied. Presentations are clear,
well organized, and legible. Do not underestimate
the importance of these features. Numerical or
algebraic errors are easier to detect when the
thought process ( application of basic laws ) is
explained. Communication skills ( verbal
written ) are critical in the world of industry.
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Items to Note How many could complete this quiz
without notes ? Pressure Loss DP/P ( Pi
Po ) / Pi 1 Po/Pi Compressor-Turbine
energy balance uses real work terms. ( next 2
slides ) Nozzle Expansion Process ( slides 3-5
following)
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GRAPHICAL REPRESENTATION OF BASIC PROCESSES
COMPRESSION
P CONSTANT
T3
T3
ACTUAL
T
IDEAL
EXPANSION
T2
T4
S
ACTUAL
mC cp DTC mT cp DTT
T
IDEAL
T5
T5
S
5
Efficiency ( Compressor or Turbine ) Relates
Ideal to Real Temperature Rise
Compressor efficiency defines relationship
between compressor pressure ratio and compressor
temperature ratio.
Turbine efficiency defines relationship between
turbine expansion ratio and turbine temperature
ratio.
6
Nozzle
Control Volume
h5 T5 P5
Pam
No heat or shaft work crosses control volume
surface. Therefore, _______ is constant.
The nozzle is assumed ideal, therefore what can
be calculated ?
7
Nozzle
Control Volume
h5 T5 P5
Pam Ps8
No heat or shaft work crosses control volume
surface. Therefore, total enthalpy is constant,
h5 h8 ( 1st Law, Open System ).
The nozzle is assumed ideal, therefore what can
be calculated ? Ts8 f( P5 , Ps8 , T5 , g ) (
Isentropic Relation ).
8
TOTAL AND STATIC QUANTITIES FOR
PRESSURES AND TEMPERATURES 1. Total
Energy is Fixed htotal
hstatic 1/2 V2 /Jgc h - BTU/lb V- ft/sec
gc 32.2 ft/sec/sec J 778 Ft-Lb/BTU
2. Process is adiabatic (diffusion and/or
expansion) Ptotal /
Pstatic (Ttotal/Tstatic)Cp/R
h8
hs8
V8
9
Temperature-Entropy (T-S) Diagram Illustrates the
Role of Components in the Thermodynamics of the
Cycle ( Cycle Shown Applies to Core Flow )
Heat Addition
Turbine Expansion
Compression
Nozzle Expansion
Inlet Diffusion
S
10
THERMODYNAMIC ANALYSIS
SOME DEFINITIONS A REVIEW TO GET US STARTED
(IDENTIFIABLE, UNIQUE CHARACTERISTIC. E.G.,
PRESSURE, TEMPERATURE, ENTROPY, ETC.)
PROPERTY
(FIXED SET OF PROPERTIES)
STATE
(SUBSTANCE CHANGES FROM ONE STATE TO ANOTHER)
PROCESS
(SERIES OF PROCESSES WHERE INITIAL STATE FINAL
STATE)
CYCLE
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THERMODYNAMIC ANALYSIS
WHAT IS A THERMODYNAMIC CYCLE? (A CYCLE IS WHAT
HAPPENS TO A WORKING SUBSTANCE I.E., HISTORY.
AN ENGINE IS A DEVICE THAT MAKES CYCLES HAPPEN.)

• WORK

T C
2
3
CARNOT (IDEAL)
T
(ENGINE)
S C
S C
4
1

• WORKING SUBSTANCE

T C
S
CLOSED/INTERMITTENT

• HEAT OUT (qREJ)

V C
3
S C
2
OTTO (IDEAL)
T

• HEAT IN (qA)

S C
4
1
V C
P C
3
S
BRAYTON (IDEAL)
S C
T
2
OPEN/CONTINUOUS
S C
4
1
P C
S
1
2
3
4
COMPRESSOR
TURBINE

• WORKING SUBSTANCE

(ENGINE)
BURNER
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THERMODYNAMIC ANALYSIS
FUNDAMENTAL GAS PROPERTY AND PROCESS
RELATIONSHIPS THAT YOU WILL NEED
ALL GASES
dh dT

• CP
• Cv

• R CP Cv
• Pv RT
• h u Pv

du dT
ISENTROPIC
Pdv Tds du Pdv 0 du Pdv ln P ln v lnR
lnT
(IDEAL WORK FOR GAS) (ANY IDEAL
PROCESS) (REVERSIBLE ADIABATIC ISENTROPIC) (GAS
LAW) (DIFFERENTIAL FORM OF GAS LAW)
(CP In (TFINAL/TINIT) R In (PFINAL/PINIT)
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THERMODYNAMIC ANALYSIS
THERMO CYCLE RELATIONSHIPS YOU WILL NEED
A. ALL CYCLES
NET WORK HEAT ADDED HEAT
REJECTED WNET qADD qREJ CYCLE
EFFICIENCY NET WORK / HEAT
ADDED ?CYCLE WNET/qADD
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THERMODYNAMIC ANALYSIS
THERMO CYCLE RELATIONSHIPS YOU WILL NEED
B. CARNOT CYCLE
(IDEAL)
TMAX
2
3
(TMAX TMIN) ?S
?CYCLE
T
TMAX ?S
S C
S C
1
4
1 1/(TMAX/TMIN)
TMIN
S
CARNOT PRINCIPLE FOR BEST EFFICIENCY, ADD HEAT
AT HIGHEST POSSIBLE TEMPERATURE AND REJECT HEAT
AT LOWEST POSSIBLE TEMPERATURE (USUALLY
SURROUNDING AMBIENT TEMPERATURE)
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THERMODYNAMIC ANALYSIS
THERMO CYCLE RELATIONSHIPS YOU WILL NEED
WNET qADD qREJ CP(T3 T2) CP (T4
T1) ?CYCLE WNET/qADD CP(T3 T2) CP (T4
T1)/CP(T3 T2)
C. IDEAL BRAYTON CYCLE
(T1)
(T4 T1)
(T4/T1 1)
1
3
1
x
P C
(T3 T2)
(T3/T2 1)
(T2)
S C
2
T
4
SINCE, (PMAX/PMIN) (P2/P1) (T2/T1)CP/R
(P3/P4) (T3/T4)CP/R THEN, T2/T1 T3/T4 AND
T4/T1 T3/T2 !
S C
P C
1
S
SO, ?BRAYTON 1 1/(T2/T1) 1 1/(P2/P1)R/CP
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THERMODYNAMIC ANALYSIS
T-S DIAGRAMS AND THE EQUIVALENT CARNOT CYCLE
ILLUSTRATE BRAYTON CYCLE TRENDS IDEAL CYCLE
EFFICIENCY
FOR AN EQUIVALENT CYCLE
TADD AVERAGE TEMPERATURE OF HEAT ADDITION TREJ
AVERAGE TEMPERATURE OF HEAT REJECTION
1
? 1
(TADD/TREJ)
LOW PRESSURE RATIO
MEDIUM PRESSURE RATIO
HIGH PRESSURE RATIO
BRAYTON CYCLE TRENDS
T
T
T
S
S
S
INCREASING PRESSURE RATIO
SO ? 1
AS PRESSURE RATIO INCREASES,
1
INCREASES
(AVE TEMP ADDED) ? (AVE TEMP REJECTED) INCREASES
(TADD/TREJ)
IDEAL BRAYTON
?CYCLE
PRESSURE RATIO
PRESSURE RATIO
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THERMODYNAMIC ANALYSIS
T-S DIAGRAMS AND THE EQUIVALENT CARNOT CYCLE
ILLUSTRATE BRAYTON CYCLE TRENDS IDEAL CYCLE
NETWORK
TMAX CONSTANT
T
T
T
TMIN CONSTANT
S
S
S
(NET WORK IS SHADED AREA)
INCREASING PRESSURE RATIO
(?T GOES UP) WHILE, (?S GOES DOWN)
?S
PRESSURE RATIO
PRESSURE RATIO
?hCYCLE/hAMB
WHICH GIVES AN OPTIMUM VALUE BUT INCREASES
WITH INCREASED TMAX
PMAX/PMIN