Gas Turbine Performance, Simplified

 It is generally known by observation that gases have particular characteristics.  Variables like pressure (P), temperature (T) and volume (V) have a special relationship in gases that is best understood when considering the model below.  In words, Pressure (P) multiplied by Volume (V) and then divided by Temperature (T) is always constant.  It is a different constant for each gas.  Air, which includes many gases, would have still a different constant than the particular gases in the mixture.  Finally, when fuel (natural gas, for instance) is mixed with air in a gas turbine combustion system, still another constant is realized.  However, when considering the various stages of the Brayton Cycle, the specific constant does not matter in the analysis.
In equation form, that would be:

(P) multiplied by (V)  then divided by (T) = constant

or simply (P x V) ÷ T = constant

This relationship holds through all stages of the gas turbine. It is important, however, that the units of each of the three variables be correct.  In English units, that would be:

• Pressure (P) in pounds per square inch absolute, (psia)
• Temperature (T) must be in degrees Rankin, (˚R). That is, to convert from Fahrenheit to  Rankin, it would be:  T (˚R) = T (˚F) + 460
•  Volume (V) must be in cubic inches, (in³)
  
  Or it can be said, simply:

P (psia)  x  V (cubic inches) ÷ T (degrees R) = constant

  For the four regions of the gas turbine on the pressure-volume (PV) diagram we have:

Region  1 – 2     Region 2 – 3   Region 3 – 4  Region 4 – 1
Compresion      Combustion     Expansion       Exhaust

Thus, we have:

P1  x V1   =    P2 x V2   =    P3 x V3   =    P4 x V4
     T1                  T2                   T3                  T4

 

Imagine a cubic foot of air.  Assume that the “box” of air has dimensions of 12 x 12 x 12 inches, as it enters the compressor.  Try to envision this air cube passing through the gas turbine.

• From the compressor inlet (point 1) the air cube passes through the axial-flow compressor diminishing in size through each stage.
• The air cube, now smaller in size, leaves the compressor discharge (point 2) and enters the combustors at essentially the same pressure.  That is, P2 = P3.
• Then the smaller air cube expands through the combustors to the first stage turbine nozzle, to a point just in front of the turbine buckets at essentially constant pressure (point 3).
• After expanding through the turbine stages, the air cube increases in size, continuing  out the exhaust reaching approximately the same pressure as the compressor inlet (point 4),  That is, P4 = P1.

Fig 1-1 - Brayton Cycle-Pressure Volume Diagram

  We know that pressure, volume and temperature are variables.  However, they only vary throughout the gas turbine cycle in the relationship described above.  Also, notice that the pressure from points P2 to P3 is considered constant, horizontal line on the P-V diagram.  Thus, in the combustion zone, they would then P2 and P3 cancel out on each side of in the following equation leaving:

V2 =  V3

T2     T3

The formula only works for temperatures in degrees Rankin.  Converting to Fahrenheit we have
___V2___ =       ___V3___
(T2 + 460)           (T3 +460)

Take a typical General Electric model series MS5001P, a very popular gas turbine in the world-wide market.  Assume that the turbine firing temperature is Tf = 1800 degrees Fahrenheit.  Assume that the air temperature at the discharge of the compressor is approximately 500 F.  Thus, we would have:
___V2___    =       ___V3___
(500 + 460)           (1800 + 460)

___V2___ =       ___V3___
(960)                   (2260)
Thus, in the gas turbine’s combustion system, the pressure remains essentially constant (P2 ≈ P3).  However, the volume more than doubles, or in this case V3 = 2.35 (V2)

Fig 1-2 - Compressor End View of a Typical Gas Turbine

View of the gas turbine in Fig. 1-2 above showing the compressor and turbine rotor installed inside the casings.  Notice how the compressor stage passageways diminish in size as the air flows through the turbine (getting smaller with every stage).  In Fig. 1-3 below, the compressor rotor blades diminish in size from the R-0 stage to the R-16 stage; again, the air passage ways for the air to flow diminish through this 17-stage compressor.

Fig 1-3 - Compressor Rotor View

Gas turbine performance can be affected by many variables.  One of the most important factors is the change of ambient temperature at the compressor inlet.  Figure 1-4 below shows how changes in ambient temperature impact such variables as Heat Rate, Exhaust Temperature, Exhaust Flow, Fuel Flow and Power Output.  Notice how the Heat Rate (thus the Thermal Efficiency) improves on colder days.  Fuel Flow does increase, as does Power Output.  However, notice that the slope of the Power line is steeper than that of the Fuel Flow, which flattens the Heat Rate line.  More power output for less fuel means higher efficiency.

Fig 1-4 - The Effects of Changes in Compressor Inlet Temperature

So what can I do to improve gas turbine performance without spending tons of money?

• Check compressor discharge pressure (CPD). If it is low, you should clean the compressor by on-line washing or other techniques.
• Boroscope the turbine on a regular basis. If the trailing edge of the first-stage turbine nozzle is distorted or missing metal, performance will suffer. The forces acting on the buckets that develop power output is diminished by a reduction in back pressure on the compressor reduces CPD.
• Be sure that the inlet guide vane (IGV) angles are set properly. This can be determined during a boroscope inspection.  Incorrect settings can reduce air flow and adversely affect power output.
• Record FSNL Data. Once the gas turbine reaches operating speed (called Full Speed, No Load or FSNL), record the following data: 

           1. Compressor Discharge Pressure (CPD)

           2. Fuel Flow (gpm, if liquid fuel or SCFM, if gas fuel)

           3. Average Turbine Exhaust Temperature (TTXM)

           4. Megawatts (MW) – Zero at the moment.

         

Then begin loading the generator and record power output (MW) and observe the other data points (CPD, FF and TTXM) until base load is reached.  These variables should increase in essentially equal proportions from the FSNL data.  Once base load is reached, you should determine if the correct turbine firing temperature, Tf is reached.  

Taken from Lucier Blog