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AERO 4402 Project Assignment

Optimization of a Turbofan engine for a Business Jet

Department of Mechanical and Aerospace Engineering

Carleton University, Ottawa ON

To:

Professor. H.I.H. Saravanamuttoo

From:

Student Name: Min Youn

Student Number: 100823571

Email:minyoun@cmail.carleton.ca

Date: Thursday, October 16, 2014

mailto:minyoun@cmail.carleton.camailto:minyoun@cmail.carleton.camailto:minyoun@cmail.carleton.camailto:minyoun@cmail.carleton.ca

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Abstract

This report studies engine properties of a long range business jet. It is designed to have a long

range and cruise at Mach 0.88 aircraft with a maximum cruise speed of Mach 0.92, both at

15,000 metre. One of the biggest issues of designing a commercial aircraft engine is selecting its

optimum bypass ratio (BPR) and overall pressure ratio (OPR) since both are directly related to

engine efficiency and performance. The optimum BPR and OPR are decided by selecting the

corresponding lowest specific fuel consumption (SFC) and highest thrust values to allow the

engine to operate at maximum cruise speed.

This documents starts off with a detailed introduction to the selecting process and assumptions

that are made for further analysis. This is followed by underlying theory and the basic concept of

designing a turbofan engine. The specific thrust, SFC and cruise thrust are calculated using a

Matlab program with the BPR and OPR. The optimum BPR and OPR are selected with given

condition.

The discussion section follows next which explains problems requested in the assignment. The

report finally ends with a conclusion to the document with the effect of BPR and OPR on a

turbofan engine.

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Table of ContentsAbstract........................................................................................................................................... 2

1.0 Introduction.......................................................................................................................... 5

2.0 Theory.................................................................................................................................. 52.1 Bypass Ratio and Overall Pressure Ratio............................................................................ 6

2.2 Specific Fuel Consumption.................................................................................................. 7

2.3 Rotor Cooling Bleed............................................................................................................ 7

2.4 Choke Flow.......................................................................................................................... 7

3.0 Procedure............................................................................................................................. 8

3.1 Determining suitable values of BPR and OPR.................................................................... 8

3.2 Estimate fuel burn for range of 12,000km........................................................................... 9

3.3 Stating all assumptions made, estimate the range obtainable at Mach 0.92 ........................ 9

3.4 If the LPT polytropic efficiency was 88%, calculate the effect on thrust and SFC........ 10

4.0 Results................................................................................................................................ 11

5.0 Discussion.......................................................................................................................... 13

5.1 Determining suitable values of BPR and OPR.................................................................. 13

5.2 Comparing range of aircraft at Mach 0.88 and Mach 0.92................................................ 13

5.2.2 Effect of engine speed on its efficiency......................................................................... 13

5.3 Comparing selected design with existing designs............................................................. 14

5.4 How LPT polytropic efficiency affects on thrust and SFC................................................ 14

6 Conclusion............................................................................................................................. 15

Reference...................................................................................................................................... 15

Appendix....................................................................................................................................... 16

List of FiguresFigure 1. ..................................................................................................................................................... 6

Figure 2. ........................................................................................................................................ 6

Figure 3. ...................................................................................................................................... 12

Figure 4. ...................................................................................................................................... 14

Figure 5. ........................................................................................................................... Appendix

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List of TablesTable 1. ...................................................................................................................................................... 3

Table 2. ......................................................................................................................................... 9

Table 3. ....................................................................................................................................... 11

Table 4. ....................................................................................................................................... 12

Table 5. ....................................................................................................................................... 12

Table 6. ....................................................................................................................................... 13

Nomenclature

Air mass flow rate bypasses the engine

Air mass flow rate through core of the enginePo Stagnation pressure

Pc Critical pressure at the nozzle

To Stagnation temperature

Air density

Specific heat ratio

C Velocity

Efficiency

A Area

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1.0 IntroductionThe objective of this report is to determine optimized BPR and OPR of a business jet engine with

given condition. [Table 1.] The optimum BPR and OPR can be determined by calculating the

lowest SFC and enough thrust. Since the lowest SFC means that the engine requires the lowestfuel consumption to make a specific amount of thrust, it is directly related with engine efficiency.

There are some underlying assumptions of this report; for example, all the drag forces acting

against the aircraft are neglected, so that there are no losses from aircraft drag forces and the

required thrust of the aircraft is assumed to be at least 1663.58lbf (7400N) in dynamic condition.

BPR and OPR cannot be increased to their maximum value because there is a size limitation on a

business jet aircraft. This report has been studied with BPR and OPR in range of 4 to 6 and 16 to

25 respectively.

Table 1. Initial conditions

ConditionsAmbient temperature 216.7K

Ambient pressure 0.1211bar

Speed of sound at 15,000m 295.1m/s

Fan pressure ratio 1.68

Turbine inlet temperature 1450K

Rotor cooling bleed 5%

Combustion pressure loss 6%

Fan diameter 1.25m

Polytropic efficiency, all components 90%

Combustion efficiency 99%

Mechanical efficiency 99%

Intake efficiency 91%

Nozzle efficiency 100%

2.0 TheoryTo move an aircraft through the air, thrust must be generated by a propulsion system. Nowadays,

turbofan engine is one of the most common propulsion systems because of its high thrust and

fuel efficiency. Components of the turbofan engine are mainly a fan, compressors, combustor,

turbine and nozzle. First of all, high velocity of air passes through the fan. Then, the air is

divided by two section; one into a core of the engine and another into bypasses the core. The

ratio of the air that goes around the engine, bypass flow, to the air that goes through the core is

called the bypass ratio (BPR). Temperature and pressure of the air that goes through the core of

engine is highly increased by the compressor section. This air is mixed with fuel and combusts to

produce thrust through the hot nozzle. Therefore, air that goes through the core of engine

produces significantly higher thrust than the thrust produced by bypass.

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2.1

Bypass Ratio and Overall Pressure Ratio

According to Aircraft Design, A Conceptual Approach, Daniel P. Raymer [1], the bypass ratio is

the mass flow ratio of the bypassed air, to the air that goes into the core of the engine.

Eq (1)Where

In theory, selecting higher BPR increases overall system efficiency of an engine. Engines create

thrust by increasing the momentum of the air coming into the front to the end. Large amount of

bypass air with lower speed carries away less energy for the same momentum; while jet engine

without bypass ratio has to carries higher energy with higher speed for the same momentum.

However, as the BPR increases, the size of engine also increases. In this report, due to the

ground clearance and easy installation, mid-range of BPR is concerned such as 4 to 6.

The overall pressure ratio indicates the ratio of the stagnation pressure, which is measured at the

inlet of an engine, and rear of the compressor.

Eq (2)Where Po3is pressure at the rear of compressor and Po1is pressure at the inlet of engine. [figure 1]

Since high pressurized air carries higher temperature and that produces higher energy during

combustion. Similar to the BPR, increasing OPR value also increases size of the engine. In this

report, OPR is concerned in range of 16 to 25.

Figure 1. Schematic of bypass turbofan engine [3]

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2.2

Specific Fuel Consumption

The specific fuel consumption (SFC) is a main criterion of selecting the BPR and OPR value for

the engine. Since higher SFC engine needs more fuel than lower SFC engine to produce same

amount of thrust, the lower SFC engine would be ideal. By increasing the BPR and OPR, the

lower value of SFC can be determined. Since in this report, the required thrust of the aircraft is

assumed to be 1663.58lbf (7400N), a lower SFC should be selected which can also produce high

enough thrust to 1663.58lbf (7400N).

2.3

Rotor Cooling Bleed

The rotor cooling bleed, is applied to improve the

performance of an aircraft engine by permitting the use

of higher turbine-inlet temperatures.[Figure 2.] It is

important to extract turbine inlet temperature (TIT)

because the direct consequence of cooling the turbine

inlet air is power output augmentation. Research, done

by NASA, shows that when the coolant was bled, the

produced thrust was increased by 3 percent and it also

slightly increased amount of SFC. This increases the

overall efficiency of the aircraft engine performance.[2]

2.4

Choke Flow

One of the important processes of designing an aircraft engine is to determine its choke flow

condition. With a given pressure and temperature, when a flowing fluid passes through a

restriction such as aircraft nozzle into a lower pressure which can be ambient pressure, the fluid

velocity increases. This can be proven by Bernoullis equation.

Eq (3)At the same time, conservation of mass principle is applied to this situation, so fluid velocity

through the restriction increases. Within these conditions, if mass flow rate of the fluid does not

increase, then choked flow occurs. In aircraft nozzle condition, the choked condition at the

nozzle of engine can be determined using the following equation.

Eq (4)

Where and , then for the cold nozzle

Figure 2. Schematic of cooling air [3]

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Eq (5)

Where and , then for the hot nozzle

The results of the equations are 1.893 and 1.853, both called critical pressure ratio, rc. The engine

nozzle is choked if

Eq (6)

And engine nozzle is not choked if

Eq (7)

Normally, aircraft engine thrust can be calculated with

Eq (8)Where and .However, if the flow is choked at the nozzle, then the engine produces thrust with ram drag.

Eq (9)Where

and

.

3.0 Procedure

3.1

Determining suitable values of BPR and OPR

Using Matlab program, the BPR with increase of 0.2 from 4.0 to 6.0 has been made as inputs

with one fixed OPR to get SFC and specific thrust at each data points. After the first iteration,

another test has been done with same BPR increase, but different value of OPR with increase of

1. The BPR ranged from 4 to 6 and the OPR ranged from 16 to 25. However, as the required

thrust assumed to be 1663.58lbf (7400N), any data points that produce less than this required

thrust have been discarded. [Table 3.] The sample calculations of the result are shown in the

appendix.

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The optimized values of BPR and OPR are selected based on the Figure 3 in result section 4.0.

The selected BPR and OPR values are 4.4 and 23 respectively. The detail reasons why BPR and

OPR are selected to be 4.4 and 23 will be discussed in discussion section 5.1.

3.2

Estimate fuel burn for range of 12,000km

Amount of fuel burn for range of 12,000 km can be calculated using SFC and thrust value.

Eq (10)To get the time,

Eq (11)

Where the velocity is given as Mach 0.88 at 15,000m height and range is given to be 12000km.

Therefore time can be determined. Using this time, fuel weight can be calculated.

Fuel weight=ThrustEq (12)A detail calculation for estimating fuel burn is shown at appendix.

3.3 Stating all assumptions made, estimate the range obtainable at

Mach 0.92At the previous section 3.2, the amount of fuel burn is determined for assumptions tabulated in

Table 2.

Table 2. Assumptions for section 3.3

Using the same conditions with section 3.2, range of the aircraft can be obtained at Mach 0.92.

Eq (13)Where the velocity can be calculated with Mach 0.92 and speed of sound at 15,000m altitude and

time can be obtained using SFC.

Assumptions

Speed Mach 0.92 Range 12,000km

BPR 4.4 Altitude 15,000m

OPR 23 Fuel weight 8190.05kg

Thrust 7540N SFC 24.046(g/s)/N

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Eq (14)Where the fuel weight, thrust and SFC is given. Thus, time can be determined.

3.4 If the LPT polytropic efficiency was 88%, calculate the effect on

thrust and SFC

If the low pressure turbine polytropic efficiency decreased to 88%, from 0.9, then work of low

pressure turbine would be decreased. This can be calculated from the following equation.

Eq (15)

Where for fuel and air mixture, then polytropic expansion can be obtained. Using thispolytropic expansion, the SFC and thrust of the engine can be obtained and compared with the

original SFC and thrust.

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4.0 ResultsThe design point is highlighted in the table 3.

Table 3. key values of an engine by Matlab iteration

OPR BPR Thrust[N] SFC[g/s/KN] SpThrust[N/(kg/s)]16 4 8087.108 25.926 200.603

16 4.2 7878.816 25.588 195.436

16 4.4 7683.754 25.266 190.597

16 4.6 7500.402 24.959 186.049

17 4 8067.3 25.63 200.111

17 4.2 7859.8 25.295 194.964

17 4.4 7665.454 24.975 190.143

17 4.6 7482.747 24.671 185.611

18 4 8045.202 25.353 199.563

18 4.2 7838.491 25.021 194.43618 4.4 7644.854 24.705 189.632

18 4.6 7462.783 24.404 185.116

19 4 8021.217 25.094 198.968

19 4.2 7815.288 24.765 193.86

19 4.4 7622.35 24.451 189.074

19 4.6 7440.903 24.153 184.573

20 4 7995.662 24.851 198.334

20 4.2 7790.505 24.524 193.245

20 4.4 7598.255 24.213 188.477

20 4.6 7417.418 23.918 183.991

21 4 7968.791 24.62 197.668

21 4.2 7764.394 24.296 192.598

21 4.4 7572.819 23.988 187.846

22 4 7940.807 24.402 196.974

22 4.2 7737.157 24.081 191.922

22 4.4 7546.241 23.775 187.186

23 4 7911.874 24.194 196.256

23 4.2 7708.956 23.876 191.223

23 4.4 7518.684 23.573 186.503

24 4 7882.127 23.996 195.518

24 4.2 7679.925 23.68 190.50224 4.4 7490.28 23.381 185.798

25 4 7851.675 23.806 194.763

25 4.2 7650.173 23.494 189.764

25 4.4 7461.138 23.197 185.075

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Figure 3. Specific thrust v.s. SFC at TIT = 1450 K

Table 4. Final design point data

Design pointBPR 4.4

OPR 23

SFC [(g/s)/N)] 23.573

Specific Thrust[N/(kg/s)] 186.503

Cruise Thrust at Mach 0.88 [N] 7518.684

Required Thrust [N] 7400

Static Thrust [N] 33888.396

Table 5. Fuel Estimation

Fuel EstimationSFC [g/s/N] 23.6512

Thrust [N] 7493.9

Time [sec] 46209.3

Velocity Mach 0.88

Range [m] 120000

Fuel weight [kg] 8190.05

22.5

23

23.5

24

24.5

25

25.5

26

26.5

180 185 190 195 200 205

SFC[g/s/KN]

SpThrust [N/(Kg/s)]

SpThrust v.s. SFC at TIT=1450K

OPR: 16

OPR: 17

OPR: 18

OPR: 19

OPR: 20

OPR: 21

OPR: 22

OPR: 23

OPR: 24

OPR: 25

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Table 6. Range Estimation

Range Estimation

SFC [g/s/N] 23.046Thrust [N] 7540.8

Velocity Mach 0.92

Time [sec] 45167.55

Fuel weight [kg] 8190.05

Range [m] 12262

5.0

Discussion

5.1 Determining suitable values of BPR and OPR

First of all, as discussed in theory, higher values of BPR and OPR increase efficiency of engine.

Moreover, data analysis by Matlab program shows that the engine tends to have higher

efficiency at higher BPR and OPR.[Table 3.] For example, At OPR = 16 and BPR = 4, the SFC

value is 25.926 (g/s)/N, while at OPR = 25 and BPR 4.4, the SFC value is 23.573. As the SFC

has been discussed in section 2.2, higher SFC engine produces more thrust, but also consume

more fuel. However, the OPR and BPR cannot be chosen as highest as they can be because

higher OPR and BPR engines are heavy and large. In this report, as required thrust is assumed to

be 7400N, the engine needs to have higher than the required thrust but lowest SFC.

5.2 Comparing range of aircraft at Mach 0.88 and Mach 0.92

With underlying assumptions made in section 3.2 (Teble 2.), range of the selected engine can be

obtained at speed of Mach 0.92. The result shows that the aircraft can fly more distance in Mach

0.92 than Mach 0.88 with same amount of fuel. This represent that turbofan, itself is more

efficient at high speed of engine RPM. (Assuming that there is no aerodynamic drag force during

the test.)

5.2.2 Effect of engine speed on its efficiencyBy comparing both conditions which is the aircraft speed at Mach 0.88 and 0.92, the percentage

of increase in velocity is 4.5%, but SFC is 2.3% with the same amount of fuel consumption. This

is because the power of the engine produces is P = F*V. Even though the SFC is also increased

at high speed, the percentage of increase in velocity is twice much higher, so that the engine

power output is more efficient at higher engine rotational speed, RPM. However, this assumption

is only applied to the engine because when the aircraft drag effect are accounted for, the engine

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will not be efficient at supersonic speed. At the supersonic speed, the aircraft will have large drag

forces. Therefore, in real case, just higher speed of aircraft will not make it as efficient. Figure 4

shows that the engine efficiency versus free stream velocity to the engine inlet.

5.3 Comparing selected design with existing designs

Compare to the selected design which has BPR 4.4 and OPR 23, most of business jet aircraft

have higher BPR and OPR. For example, E-190 (Embraer) has GE CF34-10E engine has BPR =

5.2 and OPR 29 and ACJ318 (Airbus) has CFM56-5B9 engine also has BPR = 5.9 and OPR =

32.6. This is mainly because they need more efficient engines, but do not need high speed. Since

this report is requested to design a high speed business jet, BPR = 4.4 is suitable. The OPR is

directly related with engine efficiency but also its size. As you increase OPR, the engine gets

heavier, so not suitable for a long range jet aircraft. Therefore, OPR = 23 is selected.

5.4

How LPT polytropic efficiency affects on thrust and SFC

If the low pressure turbine has a lower efficiency, it would decrease thrust and increase SFC.

With 90% LPT polytropic efficiency, To6 and Po6 are calculated to be 784.272 K and 0.4515

Bar respectively. If the LPT polytropic efficiency is decreased by 2%, then To6 remains at the

same value, but the Po6 decreased to 0.4288 Bar. The corresponding SFCs with 90% and 88% of

efficiencies are calculated to be 23.573 (g/s)/N and 23.818 (g/s)/N. Thrust is decreased from

7518.684 N to 7441.3 N. It is expected because if the turbine is decreased, then it would have

worse SFC and output.

Figure 4. Propulsive efficiency v.s.Free stream velocity [4]

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6 ConclusionIn conclusion, this report studied the design of a turbofan engine for a business jet. The engine is

requested to have suitable bypass ratio and overall pressure ratio. Result of calculations show

that it is suitable to have BPR with 4.4 and OPR with 23 because the engine has the highestefficiency at lower BPR and higher OPR. However, the engine needs to produce high enough

thrust to meet the aircrafts required thrust.

Reference1. Aircraft Design: A Conceptual Approach, 5thedition, Daniel P. Raymer, AIAA Education series,

2012

2. NACA RESEARCH MEMORANDUM, CALCULATED EFFECTS OF TURBINE ROTOR-

BLADE COOLING-AIR FLOW, L. Arne and Alfred J. Nachtigall, Lewis Flight Propulsion

Laborator, Cleveland, Ohio, August 13, 1951 [Online]

http://naca.central.cranfield.ac.uk/reports/1951/naca-rm-e51e24.pdf

3. Gas Turbine Theory, 4ed, H Cohen, GFC Rogers, HIH Saravanamuttoo, Longman, 1996

4. Performance Flight Testing Phase, Volume I, Chapter 7 Aero Propulsion, USAF TEST PILOT

SCHOOL, EDWARDS AFB, CA, February 1991

http://naca.central.cranfield.ac.uk/reports/1951/naca-rm-e51e24.pdfhttp://naca.central.cranfield.ac.uk/reports/1951/naca-rm-e51e24.pdfhttp://naca.central.cranfield.ac.uk/reports/1951/naca-rm-e51e24.pdf

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Appendix