Analysis of General Electric LM2500 G4+ DLE Aeroderivative Gas Turbine Thermal Fluid Systems - ME 343

Ben Uriell, Daniel Sullivan, and Jonathan Toth The University of Texas at Austin

5/7/17

Table of Contents

Executive Summary 2

Introduction 3

Background: Aero-Derivative Gas Turbines for Power Production 3

Formulation of Computer Model 4

Algorithms and Calculation Procedure 5 1.Property Calculator 5 2. Phase 1 Matlab Model 6 3. Phase 2 Matlab Model 12

Combustor Benchmarking Against Problem 13.xx 14

Calibration of the Model 15

Case Studies of GE LM2500 19

NOx Formation and Control 22

Conclusions and Recommendations 23 Summary of Observations 23

References 26

Appendices 27 Property Calculator Equations 27 Sample Calculations: Phase 1 Brayton Cycle Calculations 28 Sample Calculations: Combustion Analytical Model 30

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Executive Summary

A thermodynamic analysis of the LM2500+G4 turbine in a three phase project that consisted of

the Property Calculator, Phase 1 Model, and Phase 2 Model. Each section required us to build a Matlab

model that would be able to calculate and model the LM2500+G4 turbine that is used in the University of

Texas (UT) power plant. By the end of the Phase 2 Model all components of the Matlab code had been

integrated into a fully working and accurate model of the UT power plant. We used output data from the

power plant to fine tune the efficiencies used in the model to produce realistic results. The efficiencies

associated with the minimum error on net work for the Low and High pressure stages of the compressors

and turbines are as follows: LPC = 92.5%, HPC = 92.5%, HPT = 93.5%, and LPT = 78.5%. With these

tuned efficiencies the max power output rated efficiency of the phase 2 model is 39.5%, which

corresponds to the maximum efficiency of the LM2500+ G4. With the now tuned model, a sensitivity

study was conducted in order to determine the key parameters that most affect the net work and the cycle

efficacy. For the output work the ambient temperature had the greatest impact by changing the net work

by close to 20% with a change of 40 degrees Fahrenheit. Changing the compressor or turbine efficiency

by 8% caused roughly a 10% change in net work as well. For the cycle efficiency the key sensitivities

were, in order, changing the turbine efficiency, the compressor efficiency, and the ambient air

temperature and the resulting cycle efficiency changes were 10%, 7%, and 2% respectively. The project

also encompassed background research on the LM2500 series of turbines and the production of harmful

byproducts, such as NOx, in the real world. Between the research and our extensive computational

analysis of the turbine system we were able to gain a considerable understanding of the thermodynamic

process used to generate power.

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Introduction The following report discusses the standards in natural gas power generation and showcases a

Matlab analysis of a LM2500+G4 turbine. In the report there will be sections that discuss background

information of turbines, the formulation of a Matlab model, a case study to determine key sensitivities, a

discussion on real world formation of NOx byproducts and how to control the emissions, and finally the

end conclusion and recommendation from the project. Background information of the LM2500 series of

turbines is discussed at length in order to give a frame of reference before an in-depth analysis of the

thermodynamic process that occur within the turbine is explained in the next section of the report. A

comparison between the Matlab model, a base case and the University of Texas power plant in order to

calibrate the model for higher accuracy. The case study varies several key parameters of the turbine, by a

set amount, in order to determine the key sensitivities of the system. Under ideal conditions no NOx

byproducts are formed so we discuss the real world methods that limit these byproducts that the model

does not calculate. Key conclusions from the report and recommendations for future implementations of

the project comprise the final section of the paper. After conducting this analysis we should have gained a

greater understanding in how power is generated on a large scale and how models relate to real world

data.

Background: Aero-Derivative Gas Turbines for Power Production Modern natural-gas fueled power plants operate with the general system of gas turbines that

consist of the compressor, combustor, and turbine sections. The compressor takes the inlet air flow and

compresses it to small volumes and high pressures before entering the combustor. In the combustor the

compressed air is combined with fuel creating a mixture that is ignited at temperatures above 2000 °F.

The high temperature gas then expands as it passes through the turbine sections causing the turbine blades

to rotate and generate power for the compressor and electric generator. While all types of gas turbines

operate under these principles, there are two main types of gas turbines that are commonly used: heavy

frame engines and aero-derivative engines (“How Gas Turbine Power Plants Work”). In this project we

analyzed the performance of an aero-derivative engine that is used in the UT power plant. Key features of

the aero-derivative engines are the high compression ratios they operate under and how compact they are.

For UT’s power needs, the more compact engine design is the sensible choice.

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The UT power plant uses a LM2500+G4 turbine which is the newest model of the LM2500 line.

The figure below is an image of the LM2500+G4.

Figure 1: LM2500+ DLE gas turbine.

The LM2500 line has two model types which are a six stage low speed model that operates at a nominal

speed of 3600 rpm and a two stage high speed model that operates at 6100 rpm. All of these engine types

typically have a lifespan of roughly 51 million operating hours and display thermal efficiencies ranging

between 35.8% and 39.6%. The +G4 boasts the highest efficiency of the line mostly due to its

improvements of the LM2500+ in regards to flow capacity, compression ratio, and maximum firing

temperature. The combustor in the +G4 also has minor improvements over the LM2500+ model for DLE

applications, including the addition of bolt-on heat shields which reduce the amount of maintenance that

must be done. The gas turbine also effectively works in a cogeneration power plant as demonstrated by

UT’s power plant. Excess heat and power from the +G4 is used to power a steam powered turbine that

creates additional net power and effectively utilizes some heat that simply would have been lost to the

surroundings otherwise. In UT’s case the extra heat is also used in the heating system of the entire

campus. With a cogeneration model such as UT’s the total thermal efficiency rises into the mid-low 40’s

compared to just the +G4 39.6% efficiency. (Badeer)

Formulation of Computer Model The matlab program written to model the LM2500+ G4 at the UT powerplant was created in three

phases: The Property Calculator, Phase 1 Model, and Phase 2 Model. Code from each phase was

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incorporated into the subsequent phase of the project. The structure of the code and calculation

procedures are outlined in the following three sections.

Algorithms and Calculation Procedure

1.Property Calculator The working fluid of the Brayton cycle is an ideal gas mixture, so the first task was to create a

Matlab program that could easily calculate the thermodynamic properties of ideal gas mixtures. All ideal

gas mixture equations referenced in this section are indexed in the appendix.

The polynomial cp expressions for each gas provided in table Table 3s of Schmidt, et al were used

as the basis to complete the required property calculations. These functions are valid from 273-1800 K for

the gasses in the ideal gas mixtures encountered in the project. The inputs to the property calculator are

mole fractions of constituents (yi), Temperature (Tmix), and Pressure (Pmix). The property calculator

outputs the following mixture properties: constant pressure specific heat (cp), constant volume specific

heat (cv), enthalpy (h), internal energy (u), specific gas constant (R), molecular weight (M), entropy (s), p

naught (p°), and ratio of specific heats (k).

Separate Matlab functions were written to perform each of the calculations shown in the

appended equations. An object oriented approach was decided on, so a gas class and mixture class were

created. This allows properties and constants to be easily assigned to a specific gas or mixture of gases.

The object oriented approach was decided on early in the project, because it was recognized that the

properties of an ideal gas mixture would be needed at each state of a thermodynamic cycle. The

procedure followed to determine what functions needed to be written and what additional properties were

required is described below.

Equations 1, 2, and 3 show how calculations of Mmix, mass fraction of gases in mixture (xi), and

Rmix are completed respectively. These properties were calculated first because they could determined

directly from the inputs and constants, and a separate Matlab function was written for each property.

Next, the function to calculate cp of an individual gas at a specified temperature was written utilizing Eq.

5. With cp and xi known, a cp,mix function was written implementing equation 4. Because of the relationship

between cp, cv, and R that holds for an ideal gas, Eq. 7 is solved to determine cv,mix given cp,mix and Rmix.

Finally, k can be determined with Eq 12.

The values calculated up to this point have not required reference values, but the properties

remaining will require references pulled from the tables in Schmidt et al. Argon has a constant specific

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heat, so its reference h and u were set to 0 kj/(kg K) at 0 K. s0 for Argon was set at 298 K according to the

Property Calculator FAQ document. The other 4 gases have cp expressed as a polynomial that isn’t

accurate below 273 K, so 0 K cannot be taken as a reference temperature. We decided on 1000 ℃ as our

reference, and looked up h, u, and s0 at that temperature from the Schmidt ideal gas tables for Nitrogen,

Oxygen, Carbon Dioxide, and Water. Again, because we used values from the Schmidt tables at our

reference temperatures we are actually using the same reference values as the Schmidt tables. Therefore,

our calculated properties should agree with the tabulated values. We chose 1000 ℃ as our reference

temperature because it is at the middle of the temperature range of interest. This will minimize error

because the cp polynomial expression will only have to be integrated over half of the temperature range.

The numerical reference values are shown in the “Constants and Reference Values” section of the

appendix.

With our references set, Eqs. 8 and 10 can be combined to determine hmix. Eqs. 9 and 11 together

calculate umix. Next, s0mix and smix are calculated with Eqs. 13, 14, and 15. Finally, p0mix is addressed by

looking up a reference value for air at 1000 ℃ in table 5s (p0ref, air). With a known reference, p0mix is

obtainable with Eq. 16.

The figures below show the properties of air calculated with the property calculator plotted

against the tabulated values.

Figure 2: Property calculator outputs for air (blue line) vs. actual values (red *).

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2. Phase 1 Matlab Model With the property calculator outputting satisfactory results for the temperature ranges required for

modeling the LM2500+ G4, the next step was implementing an analytical solution into a Matlab program.

The first Matlab model was a simplified model, as the combustion process was approximated as heat

transfer.

In order to model the behavior of the LM2500+ G4 at the UT powerplant, the input design

parameters were considered first. These parameters were given as constants for phase 1:

● LPC Compression ratio = 6

● HPC Compression ratio = 4

● Bypass air mass flow percentage = 0%

● LPC Efficiency = 82%, HPC Efficiency = 84%

● HPT and LPT Efficiencies need to be determined through reverse engineering

● Generator Efficiency = 97.7%

● Firing Temperature, T4 = 2200 degrees F

To solve for the turbine isentropic efficiencies, the cycle was solved through with a set of nominal

input operating conditions. These values correspond to one of the tests conducted and are displayed in the

Full Load Performance LM2500+ G4 excel sheet provided. All of the equations used to solve through the

cycle are displayed in the sample calculations section of the appendices.

● Inlet air pressure = 14.417 psi

● Inlet air temperature = 65 degrees °F

● Relative humidity = 60%

● Dry air mass flow rate = 189.7 lb/s

● Inlet pressure drop = 4 in H20

● Exhaust pressure drop = 10 in H20

● LHV of fuel = 20,185 BTU/lb

● Output power = 30.6 MW

The major assumptions made when solving through the Brayton cycle for phase 1 are listed below

1. Dry Air is modeled as an ideal gas mixture with the following composition

a. Mole Fraction Nitrogen = 0.78084

b. Mole Fraction Oxygen = 0.20947

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c. Mole Fraction Argon = 0.00934

d. Mole Fraction Carbon Dioxide = 0.00035

2. Combustion is modeled as a heat transfer process

3. The cp polynomial expressions are accurate enough from -100 to 2000 ⁰C to calculate properties.

4. None of the water vapor in the inlet air condenses at any point during the cycle.

5. The HPT work is used to power the LPC and HPC

6. The LPT work is output to the generator

The Matlab program was written so that it was capable of solving the nominal case and could

solve the cycle at other base cases (various inlet temperatures and mass flow rates). This was done by

creating matlab classes for each device in the cycle, each junction between devices, and the working fluid

which is an ideal gas mixture of dry air and water vapor. The working fluid class builds on the property

calculator program, and provides an easy way to calculate fluid properties given the fluid composition,

temperature, and pressure. By using classes, the program is much more abstract, and the cycle can be

easily modified by adding more instances of devices as needed. If a new device, such as a recuperator,

were to be added to the cycle, then a new class could be written that solves for the states at the inlets and

outlets of the recuperator. A recuperator with specific design parameters would now be an easy addition

to make to any Brayton cycle in the program.

The constructors of the device classes accept the inlet fluid, the design parameters, and any

known output parameters as arguments. The remaining output parameters are solved for using the

equations shown in the sample calculations. For example, the compressor and turbine classes are shown

below and explained with comments. The remainder of the code is attached as a zip file.

______________________________________________________________________________ classdef Compressor < handle

%The inlet and design parameters of the compressor are arguments of the %constructor. The outlet parameters are then calculated in the %constructor. The compression ratio, efficiency, Inlet pressure, and %Inlet temperature must be known to solve for outlet conditions. Properties %properties associated with a compressor InletNode OutletNode = Node(0); Efficiency %Isentropic efficiency ho_s %Isentropic outlet enthalpy ho_a %actual outlet enthalpy To_s %isentropic outlet temp

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To_a %actual outlet temp Compression_Ratio Work end methods function c = Compressor(InletNode, InletFluid, Eff, Comp_ratio, outletstation) c.Efficiency = Eff; %setting compressor efficiency c.InletNode = InletNode; %associating the compressor with an inlet node c.Compression_Ratio = Comp_ratio; %setting compression ratio c.OutletNode.Station = outletstation; %setting outlet station number c.OutletNode.P = InletNode.P*Comp_ratio; %Solving for outlet pressure (inlet pressure * Compression ratio)

c.To_s = T_s_Solver(InletFluid, InletFluid.P*Comp_ratio); %solving for isentropic outlet temperature c.ho_s = mass_hmix(InletFluid.MIX,c.To_s); %solving for isentropic outlet enthalpy with property calc c.ho_a = (c.ho_s - InletFluid.H)/Eff + InletFluid.H; %solving for actual outlet enthalpy c.To_a = T_h_solver(InletFluid, c.ho_a); %solving for temperature given an enthalpy c.OutletNode.T = c.To_a; %setting outlet node temp to compressor outlet temp c.OutletNode.h = c.ho_a; %setting outlet node enthalpy to outlet enthalpy c.Work = c.OutletNode.h - c.InletNode.h; %calculating specific compressor work

end

end end

______________________________________________________________________________ The InletNode argument of the constructor is an instance of the Node class. A Node just stores

the temperature, pressure, and enthalpy at that thermodynamic station. The stations in order are 1, 2, 25,

3, 4, 48, 5, and 6 as given in the assignment handout. A node is created for each thermodynamic station,

and this allowed us to easily export the properties at each station for display in a chart. Two new functions

had to be written as part of solving the compressors, T_s_Solver and T_h_solver. The first step of solving

through the compressor requires solving for isentropic outlet temperature. Mixture entropy is shown in

Eq. 1.

n(y ) n(P /P ) (17)smix = s0mix − R * (ymix * l mix + l ref

For the isentropic process, inlet entropy equals outlet entropy, so these two equations are set equal. Inlet

and outlet pressure are known, y is known, so at the outlet can be solved for. is a function ofs0mix s0

mix

temperature, but the property calculator has no way to output a temperature given . T_s_Solvers0mix

implements the bisection method to solve for the isentropic outlet temperature, by varying temperature

until is within an acceptable range of the value solved for with Eq. 1. Isentropic outlet enthalpy iss0mix

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easily calculated given isentropic temperature. The same method is required when solving for actual

outlet temperature. The actual outlet enthalpy is solved for with equation 2.

(18)f f iciency E = h − hout,s inh − hout,a in

Then temperature is varied iteratively until the property calculator outputs an enthalpy within an

acceptable range of T_h_solver uses the bisection method to solve for the temperature of the ideal.hout,a

gas mixture given an enthalpy.

The eff argument is simply the efficiency, and Comp_ratio is the given compression ratio.

outletstation is the thermodynamic station number at the outlet of the compressor.

______________________________________________________________________________ classdef Turbine < handle

%This class solves for the outlet conditions of a turbine given certain %inputs. If any of the constructor inputs are not known, they need to %be set to 0. The turbine properties are solved for differently %depending on what other properties are given as knowns. * properties InletNode OutletNode = Node(0); Efficiency %turbine isentropic efficiency ho_s %outlet isentropic enthalpy ho_a %outlet actual enthalpy To_s %outlet isentropic temp To_a %outlet actual temp Work %turbine work P_out %outlet pressure end methods

function c = Turbine(InletNode, InletFluid, eff, outletpressure, work, outletstation) c.Efficiency = eff; %setting efficiency c.InletNode = InletNode; %associating turbine with an inlet node c.OutletNode.Station = outletstation; %associating turbine with an outlet station number if (outletpressure==0) %If outlet pressure is not known, then efficiency and work must be known to solve for outlet conditions. c.ho_a = InletFluid.H - work; %solving for actual outlet temperature c.To_a = T_h_solver(InletFluid, c.ho_a); %iteratively solving for outlet temperature once outlet enthalpy is known c.ho_s = InletFluid.H - work/eff; %solving for isentropic outlet enthalpy c.To_s = T_h_solver(InletFluid, c.ho_s);%iteratively solving for outlet temperature once isentropic outlet enthalpy is known c.P_out = exp((mass_s0mix(InletFluid.MIX,c.To_s)-mass_s0mix(InletFluid.MIX,InletFluid.T))/InletFluid.MIX.R)*InletFluid.P;

%solving for outlet pressure of the isentropic case. It is given to use the isentropic outlet pressure as the actual outlet pressure end if (work==0) %if work is unknown, then outlet pressure and efficiency must be known to solve for outlet conditions

c.P_out = outletpressure; %setting outlet pressure c.To_s = T_s_Solver(InletFluid, outletpressure); %iteratively solving for outlet isentropic temperature

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c.ho_s = mass_hmix(InletFluid.MIX, c.To_s); %calculating isentropic outlet enthalpy c.ho_a = InletFluid.H - eff * (InletFluid.H - c.ho_s); %solving for actual outlet enthalpy given efficiency and isentropic enthalpy c.To_a = T_h_solver(InletFluid, c.ho_a); %iteratively solving for actual outlet temperature c.Work = InletFluid.H - c.ho_a; %calculating work

end if(eff==0) %if efficiency is unkonw, outlet pressure and work must be known to solve for efficiency c.Work = work;

c.P_out = outletpressure; %setting outlet pressure c.ho_a = InletFluid.H - c.Work; %calculating outlet enthalpy c.To_a = T_h_solver(InletFluid, c.ho_a); %iteratively solving for actual outlet temperature given c.To_s = T_s_Solver(InletFluid, outletpressure); %iteratively solving for isentropic outlet temperature c.ho_s = mass_hmix(InletFluid.MIX, c.To_s); %calculating isentropic outlet enthalpy c.Efficiency = (c.ho_a - c.InletNode.h)/(c.ho_s - c.InletNode.h); %outlet pressure

end c.OutletNode.P = c.P_out; c.OutletNode.T = c.To_a; c.OutletNode.h = c.ho_a; end

end End _______________________________________________________________________________________________________________

The turbine class is very similar to the compressor class, except logic is needed in the constructor

to determine how to solve for the remaining properties. This is because different information is known for

the HPT compared to the LPT, and the knowns are different for the nominal case than for the other base

cases. For example, in the nominal case the HPT inlet temperature and pressure are known, the outlet

pressure is given, and the work is equal to the work of the LPC and HPC. The efficiency and outlet

temperature can be solved for given these parameters. When solving the HPT in the other cases, net work

and efficiency are known, but the outlet pressure is not known. The if statements make this one class

capable of solving turbines with different known parameters. Any unknown arguments in the constructor

must be set to 0.

The outputs from the phase 1 model were compared with the actual values given in the GE Full

Load Performance spreadsheet. Net work, fuel mass flow rate, and cycle efficiency are shown in the

following figures. The model correctly predicted the trends of each output parameter, but the errors were

not satisfactory because combustion was not being modeled correctly. The output parameters of phase 1

with the following efficiencies are shown in the figures below for quick review.

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Figure 2: Actual Net work and predicted Net Work with Phase 1 Model.

Figure 3: Cycle efficiency calculated with phase 1 model.

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Figure 4: Fuel mass flow rate calculated with phase 1 model and actual value.

3. Phase 2 Matlab Model Implementing the combustion process in MATLAB for phase 2 was simple as a combustor class

was already written for phase 1 of the project. However, the constructor of the combustor class needed to

be edited because previously the combustion process was modeled as a heat transfer process.

The available GE data from the Full Load Performance spreadsheet for fuel volume fractions

were hardcoded into an array for all the non-zero entries. This data was then used to calculate the

equivalent fuel that could be used for the combustion reaction. A second array was necessary to store all

the carbon, hydrogen, oxygen, and nitrogen coefficients for each constituent of the fuel. This second

array was two-dimensional, nine rows by four columns. Multiplying the mole fraction array, a one by

nine vector, by this matrix of coefficients resulted in the equivalent chemical formula for the fuel. Once

the equivalent fuel is known, the molar mass of the equivalent fuel is determined.

Next, the fuel lower heating value was calculated. Values of the molar lower heating value for

each fuel constituent were obtained and stored in a vector. Multiplying this vector by the fuel mole

fraction vector outputted the equivalent fuel’s lower heating value. The LHV can be converted between

mass based or molar based units since the molar mass is known.

The combustor class was used to handle the final calculations of the model. Inputs were added to

combustor constructor for the lower heating value and the equivalent fuel chemical formula. The

combustor class already had an input for an inlet fluid object, which contains the mole fractions of the

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inlet air constituents, temperature, and fluid properties. The air fuel ratio was then calculated using a

derived algebraic solution for a combustor with a known outlet temperature and fuel. The algebraic

solution was derived from an energy balance across the combustor and a mass balance from the chemical

equation. The resulting chemical reaction is shown below assuming complete combustion.

(19)H O N (O N CO Ar H O) CO H O z )N ( H O Ar)CL M Q T + z 2 + yO2

yN22 + yO2

yCO22 + yAr

yO2+ yO2

yH O22 → L 2 + 2

M2 + ( yO2

yN2 + 2T

2 + z yO2

yH O22 + yAr

yO2

L, M, Q, and T are determined from the equivalent fuel calculation and z is an unknown that

needs to be determined with the energy balance. The terms come from the mole fractions of the inletyO2

yN2

air and determine the number of moles of each gas in the air per mole of oxygen. The energy balance can

be simplified to equation 20 assuming the combustor to be adiabatic. This is the same equation used to

calculate the adiabatic flame temperature of a combustor. Every reactant and product is assumed to be in

the gaseous state and the ideal gas assumption is used making the pressure of the combustor have no

effect on the enthalpies.

(h (T ) (T ))q0comb = ∑

PAp p p − hp ref − (h (T ) (T ))∑

RAR R R − hR ref (20)

Tp is the temperature of the products and TR is the temperature of the reactants. The reference

temperature is taken as 25 degrees celsius. The AR/P terms are the coefficients of each molecule in the

reaction, and the unknown, z, appears in these terms of the equation. The enthalpy of combustion (LHV),

product temperature, and reactant temperature are known, s z can be solved for. The reaction was written

for one mole of fuel, so the molar air fuel ratio is calculated as follows.

) (21)olar AF R M = (1z + yO2

yN2 + yO2

yCO2 + yAryO2

+ yO2

yH O2

Once the air fuel ratio was calculated the mole fractions of the combustion products were

calculated and stored as a property of the Combustor class. When MATLAB returned from the

Combustor class to the main the mole fractions of the combustor products were used to create a new

instance of the working fluid class to be used for the remainder of the cycle. Cycle_solver_phase_2.m is

the script that executes the model in the attached code.

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Combustor Benchmarking Against Problem 13.xx After the combustion process was modeled in the combustor class, the accuracy needed to be

checked against a problem solved analytically with tabulated values. Homework problem 13.xx was used

to benchmark the combustor model. The parameters of interest are the calculated Lower Heating Value of

the fuel and the Air Fuel Ratio. Problem 13.xx is outlined in Figure 5. The fuel is assumed to be 50%

methane and 50% propane. The lower heating values of the fuels were used, since at 900 Celsius all of the

water is assumed to be vapor.

Figure 5: Problem 13.xx input and output conditions.

The input and output conditions of the problem were input to the combustor Matlab model, and the

specified parameters were compared to the analytical solutions in Table 1.

Table 1: Comparison of Matlab combustor model to analytical solution for 13.xx.

Property Analytical Solution Combustor Matlab Model

Error %

LHV (kJ/kmol) 1,424,388 1,423,270 0.08

LHV (kJ/kg) 47,480 47,335 0.31

Molar AFR 59.64 59.54 0.17

Mass AFR 57.59 57.13 0.80

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The errors are associated with the Property Calculator, and stem from the use of the specific heat

polynomial functions that are used to calculate all thermodynamic properties of the ideal gas mixture. The

outputs are close enough to the analytical solution to determine that the model is working correctly. The

full matlab code associated with this process is found in Combustor.m and CombustorTest.m.

Calibration of the Model After confirming that the combustor model was accurate, the Matlab model needed to be

calibrated against the test data provided in the GE Full Load Performance spreadsheet. To calibrate the

model, the efficiencies of the HPC, LPC, HPT, and LPT were varied independently from .75 to .95 to

minimize the squared error of the net work over the temperature range 30 - 110 degrees Fahrenheit. This

temperature range was chosen because the net work plateaus below 30 Fahrenheit in the GE data. This

cause of this plateau is not known, so temperature below 30 F could not be correctly modeled in Matlab.

One hypothesis for the change in the net work vs. inlet temperature trend is that the turbine is reaching

maximum allowable output power at 30 Fahrenheit.

For each set of efficiencies the sum of the squared error was stored in a 4x4 array, and the

minimum of that array was found once all iterations had been completed. The range of efficiencies were

iterated through with four for loops. This is not the most efficient method of optimization, however it was

effective enough for the computation time required for this model. The calibration process is completed in

the matlab file “cycle_solver_phase_2_calibration.m”.The efficiencies associated with the minimum error

on net work are as follows: LPC = .925, HPC = .925, HPT = .935, LPT = .785. The comparison of the

predicted and actual net work is shown in Figure 6.

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Figure 6: Calibrated Net Work plotted with actual Net Work.

The calibrated net work matches closely with the actual net work reported in the Full Load

Performance data for temperatures greater than 30 Fahrenheit. To confirm that the optimization had

converged on the correct minimum net work error, the other operating parameters were studied.

Calculated fuel flow and actual fuel flow are shown in Figure 7.

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Figure 7: Actual and model predicted fuel mass flow rate for all inlet temperatures.

The fuel mass flow rate predicted by the model had also converged closer to the actual value.

Although the trends do not match as well as the net work, the fuel mass flow is predicted much more

accurately than it was during Phase 1 of the project. Next the cycle efficiency was analyzed, and is shown

in Figure 8.

Figure 8: Cycle efficiency calculated with phase 2 model.

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The max power output rated efficiency of the LM2500+ G4 is 39.5%, which corresponds to the

maximum efficiency of the cycle predicted by the phase 2 model. With the model calibrated to minimize

error of net work output, both the the cycle efficiency and fuel mass flow rates predicted by the model

also converged to the actual values. It was concluded that the turbine and compressor efficiencies

mentioned earlier had correctly calibrated the Matlab model. With the model correctly calibrated, the

sensitivity studies were completed next. The details and findings of the sensitivity study are outlined in

the following section. All sensitivity studies were conducted with the efficiencies in Table 2.

Device Low Pressure Compressor

High Pressure Compressor

High Pressure Turbine

Low Pressure Turbine

Efficiency (%) 92.5 92.5 93.5 78.5

Table 2: Device efficiencies that minimize the error on Net Work.

Case Studies of GE LM2500 To determine how sensitive the cycle is to each individual operating parameter, a base case first

needs to be established. The base case operating parameters are outlined in Table 3 and the base case

outputs are shown in Table 4.

Table 3: Base case operating parameters

Parameter Combustor Firing Temp (F)

LPT Efficiency %

Compressor Efficiency (HPC,

LPC)

RH % Ambient Temp (F)

Base Value 2200 78.5 92.5 60 65

Table 4: Base case output parameters.

Output Net Work Cycle Efficiency Heat Rate (BTU/kWh)

Base Value 30.584 MW .3874 8,808.6

Each operating parameter is varied a specified amount, and the change in Net Work and Cycle Efficiency are observed. Figure 9 captures the change in Net Work caused by varying the input parameters.

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Figure 9: Sensitivity of Net Work to specified input parameters.

Based on the results of the net work sensitivity study, it is clear that the ambient humidity has a

relatively insignificant effect on the work output. Varying the relative humidity from 20% to 80% only

causes a 1% change in net work.

The output work is most sensitive to the ambient temperature. The net work varies 0.145 MW/F,

and that is why the UT powerplant cools the ambient air during the summer with a massive rooftop air

conditioning system. The power required to cool the inlet air is less than the power gains resulting from

the lower inlet temperature.

Varying the LPT and Compressor efficiencies by + and - 8% causes similar changes in net work.

This is as expected, because a more efficient work input device requires less work. Likewise, increasing

the efficiency of a work output device will cause the actual work to become closer to the maximum

possible isentropic work.

Finally, increasing the turbine inlet temperature by 100 degrees Fahrenheit increases the net work

by 8% and decreasing the firing temp by the same amount causes a 8% drop in work. The turbine inlet

temperature has an upper limit due to the material properties of the HPT blades. At such high

temperatures the blades cannot withstand the stresses, and as a result there is a significant effort focused

on cooling the turbine blades. Some common techniques include ceramic coatings, single crystal turbine

blades to improve thermal conduction coefficients, and cooling with compressor bleed air (Xu, Bo,

Hongde, Lei, 2015).

Figure 10 shows the sensitivity of cycle efficiency to the same set of parameters.

20

Figure 10: Sensitivity of Cycle efficiency to specified operating parameters.

The Matlab model predicts that the cycle efficiency is most sensitive to the LPT efficiency. The

LPT produces all of the output work, and the rest of the cycle remains unaffected when varying the LPT

efficiency. A higher LPT efficiency results in more work out and the same heat in, and decreasing the

LPT efficiency lowers work out while heat in remains the same.

The second most sensitive parameter is the compressor efficiency. By increasing the compressor

efficiency, the amount of work required to drive the compressors decreases and net work increases. Net

work is calculated with the following equation.

et W ork LP T W ork ompressor W ork N = − C (22)

The ambient temperature also has a significant effect on the cycle efficiency. Decreasing the

ambient temperature causes a 2% increase in efficiency. This is the other reason that the UT powerplant

chooses to cool the inlet air.

The relative humidity and turbine inlet temperature have a minimal effect on the cycle efficiency

in this model. A summary of the sensitivity analysis is provided in table 5.

Table 5: Summary of sensitivity study results.

Case Net Work

(MW)

% change Thermal

Efficiency

(%)

% change Heat Rate

(Btu/kWh)

% change

Base 30.584 0 .3874 0 8,808.6 0

21

Turbine

Inlet +100

33.278 8.81 .3881 0.18 8792.4 -0.18

Turbine

Inlet -100

27.915 -8.73 .3862 -0.31 8834.9 0.30

LPT +8% 33.701 10.19 .4268 10.17 7,994.0 -9.25

LPT -8% 27.467 -10.19 .3479 -10.20 9,808.2 11.35

Compressor

+8

33.67 10.09 .4061 4.83 8,402.4 -4.61

Compressor

-8%

26.588 -13.07 .3602 -7.02 9,471.8 7.53

Ambient

Temp +40

24.565 -19.68 .379 -2.17 9,002.4 2.20

Ambient

Temp -40

36.129 18.13 .3936 1.6 8,669.5 -1.58

Ambient

Humidity

+40%

30.754 0.56 .3869 -0.13 8,819.1 0.12

Ambient

Humidity

-40%

30.416 -0.55 .3878 0.1 8,798.1 -0.12

NOx Formation and Control

In the Matlab model the combustion process was assumed to be complete, meaning all of the fuel

was oxidized, and only water and carbon dioxide were formed as products during the combustion process.

Thermodynamically this is a good assumption, however other compounds can be formed at the high

temperatures of the combustor which are environmentally harmful.

22

NOx is a combustion product which is formed in power cycles at high pressures and temperatures.

The gas is known to adversely affect human health, and has been observed to cause breathing problems,

headaches, chronic reduced lung function, and eye irritation (“NOx Gases in Diesel Car Fumes”). Three

main methods have been developed to help regulate these emissions: wet low emission, selective

catalytic reduction, and dry low emission.

Wet low emission technology reduces the concentration of NOx produced by diluting the

combustion process with water or steam. The extra water or steam will lower the flame temperature of

the combustion process, therefore decreasing the amount of NOx in the products. By lowering the flame

temperature however, the cycle efficiency will decrease as well. The extra water that is being added into

the combustion process will absorb much of the energy that would have raised the temperature of the

original products. Another drawback to the system is a higher operating cost; adding water into the

combustion process increases the amount of maintenance that must be done on the combustor. This

technology is chosen for use at many combined cycle and cogeneration plants as high pressure steam and

water is readily available. Water may be taken from the HRSG or elsewhere in the system. Early

versions of this technology in the 1980’s were able to reduce the NOx emissions to 42 ppm. Later

development allowed the emissions from WLE to reach around 25 ppm (Klein).

Selective catalytic reduction is a chemical process. Ammonia is used alongside a catalyst

structure to convert NOx into nitrogen and water. Typical catalysts are made from ceramic materials.

Titanium oxide, vanadium oxide, molybdenum oxide, and some precious metals are commonly used.

This process will usually occur in the waste heat recovery unit. Ammonia offers its own set of challenges

however as it’s extremely hard to transport or handle. The UT power plant has a storage tank for this

process; however instead of ammonia urea is stored, which is then converted to ammonia as needed.

While NOx emissions may be reduced with this method, the risk of ammonia emissions will increase

(Klein). In total SCR is able to reduce NOx emissions to as low as 20 ppm.

The final method, dry low emission, is what the UT power plant uses on the LM2500+G4. The

dry low emission method is a modification of the combustion process, similar to the wet low emission.

By using lean pre-mixed fuel in conjunction with an advanced control system the turbine can minimize

local flame temperatures within the combustor to reduce NOx emissions (Klein). These systems are

heavily reliant on the advanced control of the combustion process. When the system is not running

optimally guide vanes may be closed or compressor discharge air may be bled (Kristin). The GE data

shows that the estimate of the NOx emissions from the LM2500+G4 DLE steadily held at 25 ppmvd,

which was referenced at 15% O2.

23

Conclusions and Recommendations

Summary of Observations The development of a MATLAB simulation for the GE LM2500+G4 required a large amount of

code to be written. By implementing a class-based structure for thermodynamic property calculations,

many later stages of the project were greatly simplified. Implementing gas and mixture classes led to

readable and short code which allowed for quick property calculations for very abstract mixtures.

While writing code with classes was more difficult and abstract, the ability to have very readable

and concise code was very desirable for later phases of the project which were much more analysis

driven; being able to quickly change many system parameters without searching through hundreds of

lines of improvised scripts would simplify later steps of the project. For phase 1 of the project classes for

the turbines, combustor, compressors, guide vanes, nodes, working fluid, and wet air were created to fully

implement the simulation of the GE LM2500+G4. Initial simulations with the given design and input

parameters outputted very accurate output parameters. By matching the inlet air mass flow rate to the

measured quantity of the GE Data, our simulation produced slightly more accurate output than when ran

with the 189.7 pounds per second of the nominal case. While the net power output matched well, the

cycle efficiency and fuel mass flow rate were not as accurate; this was attributed by the simplified

implementation of the combustion process in phase 1. A more complex implementation was needed for

the combustor.

As the combustor class had already been created, the full combustion process was implemented

within the class. The class-based system allowed the combustion process to be completely encapsulated

within the combustor class. The fuel composition was obtained from the GE spreadsheet and combined

with our implementation of the combustion class our simulation was now complete. Once calibrated the

model and simulation predicted values for the net power, fuel mass flow rate, and cycle efficiency that

were very accurate over the inlet temperature range.

Sensitivity studies performed on our final simulation demonstrated how the inlet conditions and

design parameters would vastly change the turbine performance. The net power output of the cycle was

found to be very dependent on the inlet air temperature. Humidity on the other hand had negligible

effects. The cycle efficiency was most sensitive to changes in the efficiencies of the turbines and

compressors, which was expected. The ambient temperature also had a significant effect on the overall

24

cycle efficiencies. Lower inlet air temperatures would lead to higher power output and higher cycle

efficiency.

The final result of the project was an in-depth understanding of the Brayton cycle and knowledge

of current technology present in aeroderivative gas-power turbines such as the GE LM2500+G4.

The sensitivity study after calibration gave insight into how our design parameters affect the

overall Brayton cycle. The cycle efficiency and net power both were dependent on the inlet air

temperature which explained very well why the UT power plant would cool the intake air before using the

turbine. Increasing the high pressure turbine firing temperature also raised net power output significantly,

and it became clear why current research focused on turbine blade cooling and material selection. These

realizations were expected, but the process of writing the simulation itself allowed for a deeper

understanding of the how and why behind the process.

The simulation highlighted the power of the analysis that was learned in class. While the GE

LM2500+G4 is a very complex system, the simulation, calibration, and reverse-engineering process took

a matter of months and yielded a fairly accurate model. This speaks to the power and applicability of the

analysis techniques which were taught in class. Being charged with writing a simulation for the GE

LM2500+G4 seemed daunting and difficult at first but now it is evident and intuitive how the laws of

thermodynamics drive the design of all the constitutive components.

Recommendations

The project itself could be more equitably distributed across the semester. All of the necessary

theory required to start the property calc was taught within the first few weeks. If the property calculator

due date were advanced slightly, more time would be available for the later project phases. The later

phases simply require much more code that implements more complex calculations, including solver

algorithms, and having more time allocated for those sections would allow for much cleaner code to be

produced for the final project. Phase 1 itself should have more time allocated to it. Phase 2 required low

amounts of code compared to phase 1 and could maybe also reduced in duration to add time to phase 1.

25

References

Badeer, G. H. (2005). GE’s LM2500 G4 Aeroderivative Gas Turbine for Marine and Industrial

Applications . General Electric Company, 1-12. Retrieved May 7, 2017, from

https://powergen.gepower.com/content/dam/gepower-pgdp/global/en_US/documents/techni

cal/ger/ger-4250-ge-lm2500-g4-aero-gas-turbine-marine-industrial-applications.pdf.

How Gas Turbine Power Plants Work. (n.d.). Retrieved May 07, 2017, from

https://energy.gov/fe/how-gas-turbine-power-plants-work

Li Xu, Sun Bo, You Hongde, Wang Lei, Evolution of Rolls-royce Air-cooled Turbine Blades and Feature

Analysis, Procedia Engineering, Volume 99, 2015, Pages 1482-1491, ISSN 1877-7058,

http://dx.doi.org/10.1016/j.proeng.2014.12.689.

(http://www.sciencedirect.com/science/article/pii/S1877705814038065)

Klein, Manfred. "Emissions Control for Gas Turbine Systems." Decentralized Energy. N.p., 3 Jan. 2012.

Web. 30 Apr. 2017.

Kristin Sundsbø Alne (June 2007). "Reduction of NOx Emissions from the Gas Turbines for Skarv Idun

(Master of Science in Energy and Environment)". NTNU. Retrieved 2017-04-30.

"NOx Gases in Diesel Car Fumes: Why Are They so Dangerous?" Phys.org - News and Articles on

Science and Technology. N.p., 23 Sept. 2015. Web. 07 May 2017.

26

Appendices

Property Calculator Equations

(Mi is the molecular weight of individual gas) (1)MM mix = ∑

iyi i

xi = yi *M i

Mmix(2)

(Ri is specific gas constant) (3)RRmix = ∑

ixi i

(4)ccp,mix = ∑

ixi p,i

(5)a T T T )/M (T in Kelvin) (a, , , constants f rom table 3s) cp = ( + b + c 2 + d 3 b c d (6) cp = cv + R

(7) cp, mix = cv, mix + Rmix

(8)h − href = ∫T

T refT

c dTp

(9)(T )u − uref = ∫T

T refT

c dTp − R − T ref

(10)hhmix = ∑

ixi i

(11)uumix = ∑

ixi i

(12)k = cv

cp

(13)(T ) (T )s 0 − s0

ref = ∫T

T refT

c dTp

(14)ss0mix = ∑

ixi i

0

(15)R ln(y ) ln( )smix = s0mix − ∑

iyi mix i − Rmix P ref

P mix

(16)p0mix = p0

ref ,mixexp(s (T )/R )0

mix mix

exp(s (T )/R )0mix ref mix

27

Sample Calculations: Phase 1 Brayton Cycle Calculations

28

29

Sample Calculations: Combustion Analytical Model

30

31