MATLAB AND SIMULINK TECHNIQUES IN PERFORMANCE …

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MATLAB AND SIMULINK TECHNIQUES IN PERFORMANCE MODELLING AND

CHARACTERISING OF CRITICAL VARIABLES THAT IMPACTS THE

PERFORMANCE OF A TURBOFAN ENGINE

P. B. SOB

Department of Mechanical Engineering, Faculty of Engineering and Technology, Vaal University of Technology,

Vanderbijlpark 1900, Private Bag X021, South Africa

ABSTRACT

Due to an increase in complexity and high cost in the design of gas turbines, modelling and simulation have shown to be

cost-effective since critical operating variables can be optimise for better performance. In addition, modelling reduces a

lot of design time and design errors that are critical in precision engineering. In this project, Matlab simulink and

Solidworks are used to simulate and characterise the critical operating variables that impacts the performance of a

turbofan two-spool turbofan engine at different altitudes especially cruising altitude. Solidworks is then utilised to

perform a fluid flow analysis for the system at high temperature operating conditions. The design will use an axial

compressor as well as a high pressure (HP) and low pressure (LP) turbine. The approach is to mathematically model

each component using known design parameters and thermodynamics equations. The bypass ratio and fuel mass flow

will be varied with the aim to observe an alteration in engine performance to indicate a directly proportional relationship

between the bypass ratio and the thrust. It was revealed that when the turbofan engine is running at high cruising

altitude, the engine achieves low thrust specific fuel consumption.

KEYWORDS: MATLAB Simulink, Solidworks, Performance, Turbofan, Design & High pressure and low pressure

Received: Feb 01, 2021; Accepted: Feb 21, 2021; Published: Mar 17, 2021; Paper Id.: IJMPERDAPR202124

NOMENCLATURE

T Temperature, K

P Pressure, kPa

𝑟𝑝 Pressure ratio

R Specific gas constant, J/kg K

𝐶𝑝 Specific heat capacity, kJ/kg

h Enthalpy, kJ/kg

𝜌 Density, kg/𝑚3

s Entropy, kJ/K

𝛾 Isentropic coefficient

�̇� Mass flow rate, kg/s

Orig

ina

l Article

International Journal of Mechanical and Production

Engineering Research and Development (IJMPERD)

ISSN (P): 2249–6890; ISSN (E): 2249–8001

Vol. 11, Issue 2, Apr 2021, 317-332

© TJPRC Pvt. Ltd.

318 P. B. SOB

Impact Factor (JCC): 9.6246 NAAS Rating: 3.11

v Velocity, m/s

g Gravitational acceleration, 𝑚/𝑠2

z Displacement, m

𝑊𝑖𝑛 Work input, kJ/kg

𝑊𝑜𝑢𝑡 Work output, kJ/kg

𝑄𝑖𝑛 Heat input, kJ/kg

TIT Turbine inlet temperature

HV Heating Value, J/kg

HPT High Pressure Turbine

LPT Low Pressure Turbine

TSFC Thrust Specific Fuel Consumption

CC Combustion Chamber

INTRODUCTION

A gas turbine is a rotary heat engine that converts heat energy from fuel to mechanical energy. There are different types of

gas turbines and turbofan is one of the gas turbines that has long been used in modern industry to drive aircraft and jets

alike [1-2]. According to [1] turbofan has been used more frequently in a commercial airplane, this comes after observing

high fuel efficiency and thrust. Furthermore, this kind of engine due to its high bypass flow it produces low noise,

therefore, can comply with airport noise regulations during taxiing or loading [1-3]. Electronics systems in a modern

airplane have been seen to increase for each new design and this leads to high power demand resulting in complex gas

engine design [4-8].

According to the Federal Aviation Administration (FAA) Aviation Safety Information Analysis and Sharing

(ASIAS) analysis, 1,740 out of 8,657 aviation accidents that happened between 2003 and 2007 were mainly due to weather

conditions [1-6]. Besides weather conditions, many plane crashes have been reported due to BASH (Bird Aircraft Strike

Hazard) or bird strike [5-8]. According to Richardson & West, the fowl strike has resulted in the loss of 283 jets and 141

deaths between 1959 and 1999 [5-8]. To avoid such accidents, there are many engine testing facilities built across the

globe which tests the endurance and reliability of jet engines under extreme weather conditions [5-8]. To make airborne

travel safer, several pre-flight tests have been designed for the jet engines, such as bird ingestion test, cold water test, and

freeze ball test for which a simulated environment is created at engine testing facilities [4-8].

In these facilities, the availability of engines for testing is not possible throughout the year [4-8]. Moreover, the

temperature that is required for the testing of the engines should be around -8°F [5-8]. More affairs happened in the past

years, whether you are trained or not, whether you good in maintenance or not several accidents happened and the loss of

personnel and the aircraft were numbered [6-8]. So to overcome these challenges and to refrain from the said unfortunate

incidents that happened over in past, extensive study is required that can propel effectual training to the operators’

harmless and profitable manner [8]. To design this complex design, a more economical method such as modelling will be

Matlab and Simulink Techniques in Performance Modelling and Characterising of 319

Critical Variables that Impacts the Performance of a Turbofan Engine


beneficial. Modelling is beneficial because it allows engineers to predict gas turbine behaviour/performance before the first

traditional model can be built therefore reducing cost and time. The purpose of this paper is to conceptualise, model, and

simulate the turbofan engine with all the necessary design parameters and thermodynamic considerations. The methods

employed were model and optimise for optimal design performance and the behaviour of all the components within the

system as well as the internal processes in the system was optimise for performance improvement and efficient operation at

cruising altitude.

METHODOLOGY

Theoretical Background and the working principle of a Turbofan Engine

The incoming air is captured by the engine inlet and some of the incoming air passes through the fan and

continues into the core compressor and then the combustion chamber, where it is mixed with fuel and combustion occurs.

The hot exhaust passes through the core and fan turbines and then out the nozzle, as in a basic turbojet. The rest of the

incoming air passes through the fan and bypasses, or goes around the engine, just like the air through a propeller. The air

that goes through the fan has a velocity that is slightly increased from the free stream. So, a turbofan gets some of its thrust

from the core and some of its thrust from the fan as shown in Figure 1.

Figure 1: Turbofan Engine Hot and Cold Sections with System Components

The ratio of the air that goes around the engine to the air that goes through the core is called the bypass ratio.

Because the fuel flow rate for the core is changed only a small amount by the addition of the fan, a turbofan generates more

thrust for nearly the same amount of fuel used by the core. This means that a turbofan is very fuel-efficient and it has a

High bypass ratio and is nearly as fuel-efficient as turboprops. Because the fan is enclosed by the inlet and is composed of

many blades, it can operate efficiently at higher speeds than a simple propeller. That is why turbofans are found on high-

speed transports and propellers are used on low-speed transports. Low bypass ratio turbofans are still more fuel-efficient

than basic turbojets. Many modern fighter planes use low bypass ratio turbofans equipped with afterburners. They can then

cruise efficiently but still have high thrust when dogfighting. Even though the fighter plane can fly much faster than the

speed of sound, the air going into the engine must travel less than the speed of sound for high efficiency. Therefore, the

airplane inlet slows the air down from supersonic speeds as given by the Brayton Cycle (SHAMBU.S, 2016) (Curtler,

2020).

320 P. B. SOB


(a) (b)

Figure 2 (a) Brayton Cycle T-s Diagram and (b) P-v and T-s Diagrams

Brayton cycle is a thermodynamic cycle that was developed in 1870 by George Brayton to be utilise in

reciprocating engines. It was later when the Brayton cycle started to be used to describe the thermodynamics of gas turbine

engines. An ideal Brayton cycle is comprised of four reversible processes which are: (a) Isentropic compression, (b)

Isobaric heat addition (c) Isentropic expansion and (d) Isobaric heat rejection. An ideal Brayton cycle has limitations since

most processes are irreversible hence an actual/ real Brayton cycle was developed. To account for this irreversibility,

isentropic efficiency is derived which is the ratio of isentropic work to actual work, its value is less than 1. Figure 2 above

shows a T-s diagram for the Brayton cycle, at inlet air is drawn toward the compressor (0-2). As air is drawn into the

compressor it is then compressed to pressure 3. The compressed air is mixed with fuel around open flames where

combustion takes place (3-4). The exhaust at high temperature and pressure from the combustor is allowed to expand

inside the turbine (4-5) before being exhausted through a nozzle to the atmosphere (5-8). The energy balancing for a steady

flow process can be expressed as,

(qin – qout) + (win – wout) = ∆ℎ [1]

The heat throughout the system during operation can be given as

Qin = h3 – h2 = cp (T3 – T2) [2]

Qout = h4 – h1 = cp (T4 – T1) [3]

Regeneration can be done using the hot air exhausting from the turbine to heat the exit flow of the compressor.

Part of the heat rejected is reused as the thermal efficiency of the Bryton cycle increases. The regeneration decreases the

heat input expectations for the same network output as shown in Figure 3.




Figure 3: T-s Diagram

The extent to which a regenerator approaches an ideal generator is called the effectiveness, 𝜀 and is written as

𝜀 = 𝑞regen, act / qregen, max = (h5 – h2) / (h4 – h2) [4]

The derived equation given by (4) is impacted by the fan performance during operation. The fan assumes a

significant function in creating most of the push produced by the turbofan engine. This fan is legitimately associated with

the low-pressure compressor and the low weight turbine. Air enters the engine by going through the fan; the greater part of

the air goes around the center of the engine when it’s going through the fan. The air that moves around the center of the

motor is called the bypass air. The bypass air is accelerated out of the rear of the engine by the fan, which makes the push.

Any excess air enters the center of the engine and after enters the low-pressure compressor.

The compressor is primarily used to set up the air for burning by adding energy as pressure and heat. The

compressor has two regions known as the low pressure and the high-pressure compressor. The low-pressure compressor is

associated with the fan and the low-pressure turbine. The low-pressure turbine drives the air further once more into the

motor by the lines of rotating blades. As the air is pushed in reverse it makes the air volume pressurized. The high-pressure

compressor is associated with the high-pressure turbine. Much the same as the low-pressure compressor also the high-

pressure compressor likewise has columns of turning sharp blades which power air further into the engine, however at a

higher pressure and higher temperature. The below formulas will be used in calculating the map together with different

parameters. This is the place where the ignition happens. A combustor is a still chamber inside the center of the motor. The

reason for the combustor is to add much more energy to the air. In the combustor, fuel is infused and blended in with the

air. The fuel-air combination is then touched off, making an expansion in temperature and empowering the flow. The high

expansion in energy moves the energy towards the high-pressure turbine.

This is where development happens, and it occurs inside the high-pressure turbine and the high-pressure turbine.

The turbine is like the compressor it also has turning blades. The motivation of the turbine is to remove energy from the

flow, which is then used to turn the compressor and the fan. The high-pressure turbine is driven by the high-pressure air

that goes through it. This is the last segment that the air goes through prior before leaving the engine. The reason for the

322 P. B. SOB


exhaust nozzle is to move the core flow out of the engine, which provides thrust. The fume nozzles likewise direct pressure

inside the engine, which helps components to function properly. The design shown in Figure 4 was proposed in this study

and the relevant model and simulation was done for optimal design performance

Engine Design Layout

Figure 4: Layout of the Engine

(a) (b)

(c)

Figure 5: Solidworks representation of the Turbofan Engine

Ambient Inlet Fan HPC CC

bypass air

HPT LPT Mixer Nozzle Ambient

HP shaft

LP shaft




Table 1: Design Parameters for Simulation

Design Parameters

�̇�𝑎𝑖𝑟 1300 kg/s

Air specific heat capacity 1.005 kJ /kg K

𝛾 1.4

R 0.287 kJ /kg K

Diffuser efficiency 0.98

Fan pressure ratio 1.65

Fan efficiency 0.93

Air bypass to inlet ratio 10

Compressor pressure ratio 60

Compressor efficiency 0.91

�̇�𝑓𝑢𝑒𝑙 1.2 kg/s

HV-kerosene 43.25kJ/kg

Gas specific heat capacity 1147 kJ /kg K

𝛾 gas 1.33

Combustion chamber pressure drop 2%

Combustion chamber efficiency 0.987

HP Turbine efficiency 0.93

HP Turbine maximum temperature 1500 K

LP Turbine efficiency 0.97

Hot Nozzle efficiency 0.95

Cold Nozzle efficiency 0.95

NUMERICAL MODELLING AND SIMULATION

To model the turbofan engine, a complete analysis of the system components is necessary. Mathematical processing of the

compressor, as well as the HPT and LPT as far as thermodynamic processes are concerned, gives the equations which was

used to develop the relevant MATLAB algorithm codes and used to determine the, energy balance in the system as per the

Law of Conservation of Energy for each step of the process is used as a premise.

�̇�𝑖𝑛 + �̇�𝑖𝑛 + ∑ �̇� (ℎ +1

2𝑖𝑛 𝑣2 + 𝑔𝑧) = �̇�𝑜𝑢𝑡 + �̇�𝑜𝑢𝑡 + ∑ �̇� (ℎ +1

2𝑜𝑢𝑡 𝑣2 + 𝑔𝑧) [5]

The work coming into the compressor from the shaft is denoted by �̇�𝑖𝑛 and the effective work done in the system

can be given as

�̇�𝑖𝑛 + �̇�ℎ1 = �̇�ℎ2 [6]

Alternatively, in terms of temperature and specific heat in the system it can be expressed as,

�̇�𝑖𝑛 = �̇�𝐶𝑝𝑔(𝑇2 − 𝑇1) [7]

Through isentropic compression, we can compute 𝑇2 from the pressure ratio 𝑟𝑝 and TIT given as

𝑇2

𝑇1= (𝑟𝑝)

𝛾−1

𝛾 [8]

From the energy balance, we obtain the following equation,

324 P. B. SOB


�̇�𝑖𝑛 + �̇�ℎ2 = �̇�ℎ3 [9]

Alternatively,

�̇�𝑖𝑛 = �̇�𝐶𝑝(𝑇3 − 𝑇2) [10]

And

�̇�𝑖𝑛 = �̇�𝑘𝑒𝑟𝑜𝑠𝑒𝑛𝑒 × 𝐻𝑉𝑘𝑒𝑟𝑜𝑠𝑒𝑛𝑒 [11]

Given that the work of the turbine drives the compressor,

�̇�𝑜𝑢𝑡 + �̇�ℎ4 = �̇�ℎ3 [12]

Also,

�̇�𝑜𝑢𝑡 = �̇�𝐶𝑝(𝑇3 − 𝑇4) [13]

To suggest that,

�̇�𝑜𝑢𝑡−𝑡𝑢𝑟𝑏𝑖𝑛𝑒 = �̇�𝑖𝑛−𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑜𝑟 [14]

Due to isentropic expansion, the turbine and nozzle are computed as such to find the temperature at exit:

𝑇5

𝑇3= (

𝑃5

𝑃3)

𝛾−1

𝛾 [15]

For the nozzle, the energy balance becomes

ℎ4 = ℎ5 +1

2𝑣5

2 [16]

To model the engine performance, a MATLAB algorithmic code comprising of the numerical analysis was

computes with engine thermodynamic processes of the engine, with input variables of the inlet conditions as well as

parameters being simulated as shown in the algorithm in Figure 6.

function [T2] = Tcompexit(T1,Pr,gamma)

%isentropic compression

%T2 - T at compressor exit

%Pr - pressure ratio for compressor

%gamma - 1,4

T2 = T1*(Pr)^((gamma-1)/gamma);

function [Win] = Wincomp(m1,Cp,T2,T1)

%work input to compressor from turbine




%compressor energy balance

%m1 is mass flow rate of air

%Cp is 1005kJ/kg

Win = m1*Cp*(T2-T1);

function [Qin] = Qcomb(m2,hvf)

%combustion energy balance

%m2 is mass flow rate of fuel

%hvf is heating value of fuel in MJ/kg

Qin = m2*hvf;

function [T3] = Tinturbine(Qin,m2,Cp,T2)

%T3 - turbine inlet temperature

T3 = T2+(Qin/(m2*Cp));

function [WTout] = Wturbine(Win)

%ideally, W into compressor = Wout Turbine

WTout = Win;

function [T4] = TT4HP(WTout,m1,Cp,T3)

%outlet temperature T4 of HP turbine

T4 = T3-(WTout/(m1*Cp));

function [T5] = TT5LP(T3,Pr,gamma)

%isentropic expansion of LP turbine relative to CC temperature exit

326 P. B. SOB


T5 = T3*(Pr)^((gamma-1)/gamma);

function [v6] = vel6(Cp,T4,T3)

%velocity at nozzle exit

v6 = 2*Cp*(T4-T5);

function [F] = Fthrust(v6,m1)

F = m1*v6;

Published with MATLAB® R2019a

Figure 6: MATLAB Code for Numerical Modelling

One of the approaches that are used to simulate a turbofan engine is MATLAB Simulink. Before commencing, the

following assumptions are made, first is that there is no mixing, this means that gases from the cold nozzle do not mix with

gases from the hot nozzle. Secondly, there is no air bleeding therefore the whole core mass flow is used within the core. To

model a turbofan in Simulink, several main subsystems are designed which represent atmosphere condition, diffuser, fan,

HP Compressor, combustion chamber, HP Turbine, LP Turbine, Core nozzle, Fan nozzle, and Thrust. The layout of all

these main subsystems can be seen in figure 7 below.

The operation of this model can be summarised in this manner, airflow from left to right in figure 7. Based on

altitude input, the atm subsystem provide air density, temperature, pressure, and sound speed at that altitude. The atm

outputs are then sent into the diffuser subsystem where fan mass flow, total temperature, and pressure are calculated. Air

from the diffuser is compressed by a fan and HP compressor before entering into the combustion chamber subsystem. At

this point, the air is a very high pressure, fuel is then added to this air and combustion take place increasing air

temperature. The air is then allowed to expand through HP and LP turbines and transferred to a nozzle that produces an air

jet. Thrust subsystem block calculates thrust from both cold and hot nozzle inputs.

https://www.mathworks.com/products/matlab/




Figure 7: Screenshot of Matlab Block Simulation

To simulate atmospheric conditions, COESA block from aerospace is utilized, from altitude input, it able to

extrapolate air temperature, pressure, and density. Since pressure is provided in Pa, a gain block is used to convert it to

KPa, this can be seen in figure 8 below.

Figure 8: Atm Subsystem Block.

Figure 9 below shows the inlet Mach number subsystem. Since plane takeoff at a certain speed then changes to

cruising speed, the model also has to accommodate this change in speed. A switch block is added with altitude as a trigger,

this allows inlet Mach number for takeoff and cruising to be calculated.

328 P. B. SOB


Figure 9: Inlet Mach Number Subsystem.

To check if a nozzle is chocked or not, the critical pressure check subsystem for the cold and hot nozzle in Figures

10 and 11 is designed.

Figure 10: Hot Nozzle Critical Pressure Check Subsystem.




Figure 11: Fan Nozzle Subsystem.

RESULTS AND DISCUSSIONS

This analysis aims to show how thrust, TSFC, power, and TIT change with respect to altitude therefore altitude is an

independent variable in figure 12. The analysis then proceeds to analyse how different values of bypass ratio affect engine

performance at 20m and 11 000m altitude, in this case, bypass ratio is an independent variable in figure 13 & 14. Figure 12

below shows results of altitude vs thrust, TSFC, power, CC exit Temperature while the bypass ratio is set to be constant at

10. For thrust, power, and CC exit temperature graphs, there is a decrease as altitude increase, these are due to a decrease

in inlet temperature and pressure. Furthermore, the thrust graph sudden decrease followed by an increase while TSFC,

power, and cc exit temperature graphs show a sudden spike followed by a decrease, this is a result of the change from

takeoff speed to cruising speed.

Figure 12: Simulation Results - Altitude vs Thrust, TSFC, Power, CC Exit Temperature

330 P. B. SOB


Figure 12 and figure 13 present Bypass ratio vs Thrust, TSFC, Power and CC Exit Temperature at 20m and 11

000m altitude respectively. In figure 12, it is seen that as the bypass ratio approaches 15, the turbine maximum temperature

limit is exceeded. This limit is because of turbine material temperature limitation, if exceeded turbine will experience

thermal fatigue and fail. Furthermore, a high bypass ratio means high bypass mass flow therefore fan size has to be

increased to achieve this bypass ratio increasing drag force, weight, and manufacturing cost. The upside of a high bypass

ratio can also be seen on TSFC and thrust plot, this graph shows a decrease in TSFC and an increase in thrust as the bypass

ratio increase. This might be because a high percentage of thrust is due to the cold nozzle, therefore a high fraction of

thrust is produced without fuel.

Figure 13: Simulation Results - Bypass ratio vs Thrust, TSFC, Power and CC Exit Temperature (20m)

Figure 14: Simulation Results - Bypass ratio vs Thrust, TSFC, Power and CC Exit Temperature (11 000m)




Figure 15: Solidworks Simulation for Air Flow

The simulation was done using SolidWorks professional 2016. The aim of this simulation was to obtain the

maximum and minimum velocities that the engine can withstand while maintaining the desired efficiency as air passes

throughout. The shell/ body housing the shafts and blades was set as fixed parameters and meshing points. The highest

pressure for the whole engine was set to be 10 184 Kpa, and speed of the shafts to be 12 0000 rpm rotating in the clockwise

direction. The simulation only takes air flowing in the Z-axis into account. Figure 15 shows the cross section surrounding

air being sucked into and out the engine. The green lines represent air flow, and as shown in the cross section, air is

compressed as it enters the engine and compressed again as it exists to increase thrust and efficiency. The maximum and

minimum velocities from the simulation are 77.576 and -55.839 m/s, respectively. The simulated results are just ok and not

far off from estimated results. For better results, calculates can be redone to validate the results, and newer versions of the

software can be utilized as they are more advanced and have added real life simulation parameters.

CONCLUSIONS AND RECOMMENDATIONS

In this paper, the turbofan performance was monitored through the use of mathematical modelling as well as adhering to

thermodynamic formulae that govern the processes. Through theoretical simulation with a Matlab and Solidworks, a

turbofan was built and a simulation run based on the parameters which were present to standard conditions of airplanes for

sonic speed. The simulation was done on a turbofan model at different altitudes including take-off and cruising altitude.

According to research done, a simulation approach can be economically beneficial as well as improving the reliability of

the engine. Three tests were done, which are at different altitudes, different bypass ratio values at take-off altitude, and

different bypass ratio values at cruising altitude. It can be seen from figure 14 that as altitude increase from take-off to

cruising, thrust increases while TSFC, power, and CC exit temperature decrease. Furthermore, figure 13 and figure 14

shows that as the bypass ratio increases, there is an increase in thrust to some point to indicate a directly proportional

relationship. Additionally, TSFC decreases to some point while the bypass ratio increases, power remains constant. Figure

14 shows a rapid increase in CC exit temperature as compared to the figure. Based on these results, it is recommended that

332 P. B. SOB


the engine operates at a high cruising altitude to achieve low TSFC while within material limits – which speaks to the fuel

efficiency. Secondly, selection for bypass ratio should be done at take-off altitude not cruising altitude, and CC exit

temperature must be monitored to ensure TIT is not exceeded.

REFERENCES

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https://www.grc.nasa.gov/WWW/K12/airplane/aturbf.html#:~:text=How%20does%20a%20turbofan%20engine,with%20fuel

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3. Shailesh Kumar, M. A. I. O. T., 2017. Shailesh Kumar, MAHARAJA AGARSAIN INSTITUTE OF TECHNOLOGY “Turbofan

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6. Winnipeg, 2015. Winnipeg Alternative Media, May 19, 2015. [Online] Available at:

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XeQkK5jFL1EYqmc1zjQR_bsCdg:1605553477586&source=lnms&tbm=isch&sa=X&ved=2ahUKEwiS4svl4IftAhUEsXEKHd

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7. Grc.nasa.gov. 2020. Turbofan Engine. [Online] Available at: <https://www.grc.nasa.gov/www/k-12/airplane/aturbf.html>

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8. Chawla, H. S., 2016. Jet Engine Testing Training. In: Design and Development of Jet Engine Testing Training. Winnipeg,

Manitoba, Canada: Harjot S. Chawla, p. 2.

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