Analysis of Pratt & Whitney's PurePower Geared Turbofan PW1100G … · 2020. 12. 30. · PurePower...

Analysis of Pratt & Whitney's PurePower Geared Turbofan PW1100G-JM Engine

John Connolly, Robert Lew, Michael Marcolini, Scot Surprenant Mechanical Engineering (BS) Candidates, Wentworth Institute of Technology, Boston, MA

Technical Advisor: Haifa El-Sadi, Ph. D Associate Professor, Wentworth Institute of Technology, Boston, MA

This report is an elementary analysis of the Pratt & Whitney PW1100G-JM turbofan engine, an important new step in P&W’s geared-turbofan family. Dimensions are pulled from reference diagrams. Analysis is performed on each major stage of the engine: inlet diffuser, high pressure compressors, combustion chamber, high pressure turbines, and the exit nozzle. For the purpose of simplicity, engine cooling and bypass air are omitted.

1 American Institute of Aeronautics and Astronautics

I. Introduction

Turbofans are a type of jet engine used on a variety of aircraft seen in both the commercial and military industries today. The defining characteristic of a turbofan is that only a small portion of the air that enters the engine passes through the combustion chamber. The mechanical energy created is used to spin the fan near the inlet of the engine which is used to push large volumes of air, or bypass stream, out of the engine, generating a majority of the thrust. This design is highly efficient when compared to previous jet engine designs.

The turbofan engine chosen to reconstruct through CFD analysis and FEA simulations is the Pratt and Whitney geared turbofan PW1100-JM. The PW1100-JM engine is used on the Airbus 320neo, and has several other variants in the PW1000G family. This engine can produce 24-33 thousand pounds of thrust. The engine has a reduction gearbox between the fan and the LPT to change RPMS between sectors for different torque. The HPT enables lower fan pressure ratios, as well as higher bypass ratios. The main purpose of the geared turbofan is to reduce fuel consumption, which in turn reduces carbon dioxide emissions, and it also cuts noise generation. The engine consists of 3 LPC stages, 8 HPC stages, 2 HPT stages, and 3 LPT stages that will be simulated and analyzed in this report.


II. Diffuser

In order to understand the performance of the diffuser, a model must be created. Fluid flow in the model will be simulated with ANSYS Fluent.

The focus of this study is to understand the performance of the PW1100G-JM. The high pressure stages of the turbojet are the primary source of power. The low pressure system’s purpose is to power the engine’s cooling system. For this reason, the low pressure system of the engine will be ignored. The diffuser will be modeled as a single large system: it will not only encompass the large diffuser and two smaller ones, but also the bypass fan and channels, as well as the low pressure compressors (see below).

Model:

To develop dimension for our model, a scale factor was used to determine the diameter of the inlet from a diagram. The length used was the length of the modeled section: from the leading edge of the nacelle to the first stage of the high pressure compressor. For the model, all internal components will be ignored and modeled as fluid.


This is the diagram used for creating preliminary dimensions. The first dimension indicates the diagram length (inppt) and the second value is the proportional actual value (inact).

Dimension Value Source

Diffuser Inlet Radius (R1) 32.2 in Scale factor determined from fan diameter on diagram.

Diffuser Outlet Radius (R2) 53.1 in Given scale factor (R2 = 1.65 * R1).

Diffuser Length 88 in Scale factor determined from fan diameter on diagram.

The diffuser model created in SolidWorks:

Meshing:

The model was exported as a general 3D model

(.STEP) and imported as geometry in ANSYS Workbench. The next step is to create the mesh for the diffuser. The diffuser will be modeled as internal flow.

Mesh Details Value

Cell Quantity 19800

Node Quantity 21375

Element Size 0.1 m


The next step in the CFD model is to set boundary conditions in Fluent. Data about the

performance of the PW1000G-JM and A320neo can be used to calculate the boundary conditions. First, the cruise altitude of the A320neo is 38,000 feet. At this altitude, the properties of air are posted values:

Property Value

Material Air

Altitude 11600 m

Temperature 219 K

Ambient Pressure 23800 Pa

Diffuser Inlet Boundary Conditions:


Velocity 233 m/s Cruise velocity of A320neo.

Supersonic/Gage Pressure 35922 Pa Given equation: (1 ) a ]P o = P * [ + 2

k−1 * M 2 kk−1

where a /M = v √kRT

Fluent fixes the properties of air with the velocity, gage and absolute pressures. It also calculates

a mass flow rate at the inlet. This value is used as the boundary condition for the outlet (mass is conserved). Diffuser Outlet Boundary Conditions:


Mass Flow Rate 598.2 kg/s (Fluent calculate mass flow rate from the inlet).m′in = m′out


Diffuser Simulation Results:

Fluent solves the system by applying the Navier-Stokes equations at each node and solving the matrices. The solver found a converged solution in 35 iterations.

Velocity Contour Pressure Contour Temperature Contour

Property Inlet Outlet

Mass Flow Rate 598.2 kg/s -598.2 kg/s

Velocity (Mass-average) 233 m/s 86.8 m/s

Pressure (Mass-average) -1269 Pa 22649 Pa

Temperature (Mass-average) 219 K 219 K

Enthalpy (Mass-average) - 76 kJ/kg

The properties calculated for the outlet of the diffuser will be used as the inlet for the first high

pressure compressor stage.


III. Compressor

Properties at the outlet of the diffuser will be used for the air properties at the inlet of the first compressor stage.

Property Inlet

Velocity 285 ft/s

Pressure 970 lbf/ft2

Enthalpy 157.9 BTU/lbm

To calculate mass-flow rate, the bypass ratio and mass-flow rate of the diffuser were used.

Mass-Flow Rate 110 lbm/s

EES Code:

"Known Info" T_in = 394.2 [R]; V_1 = 284.78 [ft/s]; h_1 = 157.88 [Btu/lbm]; P_1 = 970.0992 [lbf/ft^2]; k = 1.4; C_p = 0.24 [Btu/lbm*R]; mdot=110 [lbm/s]; w = 316.7 [s^-1]; D=2.5 [ft]; "Pressure Ratio" T_0 = T_in + (V_1^2 / (2*C_p))*convert(ft^2/s^2*R,Btu/(lbm*R)) "Calculating relative speed of rotor blade" U = ((D/2)*((2*3.1415))*w), W_x = -U "Calculating blade relative velocity" W_1 = sqrt(W_x^2+(V_1^2)), B_1 = arctan(W_x / V_1), "B_2 is turning angle" B_2 = B_1 + 15[deg] U_w2 = V_1 * tan(B_2) "Calculate the portion of the relative blade speed associated with the actual air velocity" "Calculate the actual air"


W_2 = V_1/cos(B_2) U_v2 = W_x - U_w2 V_2 = sqrt(V_1^2 + U_v2^2) T_shaft = mdot*(D/2)*(- U_v2)*convert(lbm*ft^2/s^2, lbf*ft) "Calculating Power Output" t_ Power = T_shaft * 2*3.1415*w W_stage = Power/mdot*convert(lbf*ft/lbm, BTU/lbm) T_02 = T_0 + W_stage / C_p r_p = (T_02/T_0)^(k/(k-1))/35 P_8=(r_p)^7*P_1 (P_8/P_1)=(T_8/T_0)^(k/(k-1))

EES Output:


After eight stages of compression, the properties of the air are tabulated below.

Property Outlet

Velocity 1788 ft/s

Temperature 467 °R

Pressure 11.5 psi

Enthalpy 110 BTU/lbm°R

IV. Combustion Chamber

The energy source of the engine comes from the combustion of fuel. The combustion stage is

after compression. In the combustion chamber, fuel is mixed into the airflow and ignited. After the fuel is ignited, more air is mixed into the stream to further cool the airstream to prevent damage to the turbines. There are several different types of combustion chambers, the combustion chamber in the PW1100G-JM is can-annular. In the diagram above, a cross section of the combustion chamber phase is shown. The


central area of the engine is excluded as this volume is occupied by the primary engine shaft, not air / fuel mix.

After the air is compressed through the eight high pressure compressor stages, it is expanded using a small diffuser. This increases the pressure and slows the air to a subsonic speed before entering the combustion chamber.

In this enlarged diagram, points of the combustion chamber are marked A, B, and C. The properties of the air are calculated at each point. At A, the exit properties of the high pressure compressor are applied. Then, the air undergoes isentropic expansion in the diffuser. Using isentropic relationships, the properties of air are calculated at B. Heat is added in the combustion chamber with fuel injection. To calculate the combustion product properties at C, isobaric heat addition relationships are applied.

Initially, these properties were to be solved using Engineering Equation Solver (EES). The solver code is shown below.


Due to the SARS-CoV-2 pandemic, remote licensing could not be obtained for EES. Therefore, the properties for each combustion chamber phase were recalculated using Microsoft Excel.

First, some constant properties of air were established:

Properties of Air Variable Value (D) Unit

3 Specific Heat Ratio k 1.4 -

4 Gas Constant R 53.35 (ft*lbf)/(lbm*R)

5 Specific Heat (isobaric) c_p 194.8 (ft*lbf)/(lbm*R)

Outputs of the high pressure compressor were used as inputs for the diffuser as shown below.

Compressor Outputs Variable Value (D)

Unit Notes

8 Temperature (static) T_A 467 R From compressor

9 Temperature (stagnation) T_oA R

10 Pressure P_A 11.5 psi From compressor

11 Density Rho_A lbm/ft^3

12 Mach # Ma_A -

13 Velocity V_A 1788 ft/s From compressor

14 Enthalpy h_A 110 BTU/(lbm*R) From compressor

15 Area A_A 0.878 sq ft From measurement ppt

16 Speed of Sound a_A ft/s

17 Air Mass Flow Rate m_dota 110 lbm/s From inlet diffuser


Outputs of the high pressure compressor were used as inputs for the diffuser as shown below.

CC Diffuser Inputs Variable Value (D)

Unit Notes Equation

20 Temperature (static) T_A 467 R From compressor

21 Temperature (stagnation)

T_oA R

22 Pressure P_A 11.5 psi From compressor

23 Density Rho_A lbm/ft^3

24 Mach # Ma_A 1.69 - Calculation 1 =D25/D26

25 Velocity V_A 1788 ft/s From compressor

26 Speed of Sound a_A 1060 ft/s Calculation 1 =SQRT(D3*D4*32.2*D20)

27 Area Ratio (A_A/A*)

1.326 - Calculation 2 =(1/D24)*((2/($D$3+1))*(1+((D24^2)*($D$3-1)/2)))^(($D$3+1)/(2*($D$3-1)))

28 Area A_A 0.878 sq ft From measurement ppt

29 Pressure Ratio (P_A/P_oA)

0.207 - Calculation 3 =((1+((D24^2)*($D$3-1)/2))^($D$3/($D$3-1)))^(-1)

30 Temperature Ratio (T_A/T_o)

0.637 - Calculation 3 =(1+(D24^2)*($D$3-1)/2)^(-1)


Using isentropic relations, the properties of air were calculated at the exit of the diffuser (A to B).

CC Diffuser Outputs Variable Value (K)

Unit Notes Equation

20 Temperature (static) T_B 1000 R Assumed from H

21 Temperature (stagnation) T_oB 1005.2 R Calculation 5 =K20/K30

22 Pressure P_B 54.67 psi Calculation 4 =K29/D29*D22

23 Density Rho_B lbm/ft^3

24 Mach # Ma_B 0.161 - Calculation 1 =K25/K26

25 Velocity V_B 250 ft/s

26 Speed of Sound a_B 1551 ft/s Calculation 1 =SQRT(D3*D4*32.2*K20)

27 Area Ratio (A_B/A*) 3.646 - Calculation 2 =(1/K24)*((2/($D$3+1))*(1+((K24^2)*($D$3-1)/2)))^(($D$3+1)/(2*($D$3-1)))

28 Area A_B 2.415 sq ft Calculation 2b

=D28*K27/D27

29 Pressure Ratio (P_B/P_oB)

0.982 - Calculation 3 =((1+((K24^2)*($D$3-1)/2))^($D$3/($D$3-1)))^(-1)

30 Temperature Ratio (T_B/T_o) 0.995 - Calculation 3 =((1+((K24^2)*($D$3-1)/2))^($D$3/($D$3-1)))^(-1)

31 Critical Stagnation Temperature Ratio

(T_oB/T_oB*)

0.117 - Calculation 6, heat addition

=((1+$D$3)*(K24^2)*(2+($D$3-1)*(K24^2)))/((1+$D$3*(K24^2))^2)

32 Critical Stagnation Temperature

T_oB* 8611 R Calculation 7 =K21/K31


These values were used for the heat addition calculations in the combustion chamber.

Combustion Chamber Inputs

Variable Value (D)

Unit Notes Equation

35 Critical Temperature (Stagnation)

T_oB 1005 R From diffuser, T_oB =K21

36 Critical Temperature (Stagnation)

T_oC 8611 R From diffuser, T_oB*

=K32

The operating conditions of the combustion chamber are tabulated below.

Combustion Chamber Results

Variable Value (D) Unit Notes Equation

35 Specific Heat Addition q 1481546 (ft*lbf)/lbm Calculation 8 =D5*(D36-D35)

36 Specific Heat Addition q 1904 (BTU)/lbm Calculation 8 =K35/778

37 Air Fuel Ratio AF 30.2 - Calculation 9, based on 100% Excess air

=7.58/0.251

38 Fuel Mass Flow Rate m_dotf 3.64 lbm/s Calculation 10 =D17/K37

Combustion is not performed completely stoichiometrically. There is an excess of air because there is an excess of heat created during combustion. If this reaction was performed stoichiometrically, the heat in the engine would cause the materials of the engine to fail. This excess heat is used to energize the excess air, where the energy is consumed by the turbine stage.

This analysis shows that fuel is added at a rate of 3.64 lb/s. Real turbofans operate more efficiently, consuming about 1.2 lb/s. The error in this analysis likely occurs from an inaccurate mass flowrate of air in the combustion chamber in tandem with a slightly inaccurate air/fuel ratio, which is calculated based on an assumption of excess air.


VI. Turbine

A turbine is a rotary mechanical device that extracts energy from the fluid flowing through it, and

turning it into useful work for the engine. A turbine consists of a rotary assembly, which is a shaft with blades attached. The blades are able to catch the rotational energy from the fluid and convert it to the rotors. During the turbine stage, secondary cooling comes in to try and cool the fluid as much as possible to mitigate the damage caused on the remainder of the engine. Thermal issues in the turbine are a common issue for engine failure as it will lead to thermal fatigue and eventually structurally unsound mechanical parts (thermal-mechanical fatigue). The following image shows the specifics on the PW1100G-JM.

The PW1100G-JM turbine consists of a flow running axial down the shaft, hitting two high pressure stages, and 3 low pressure stages.

Turbine Inputs Variable Value Unit Equation

M_2 M_2 1.1 -

M_3R M_3R 0.9 -

Polytropic Efficiency 0.9 -

Specific heat g? gc_p 7378 ft^2/s^2*R -


Angle α 68 degrees -

Aft Combustion Temp Tt_1 3200 R -

Tt_2 3200 R -

Omega Ω 0.25 - -

Turbine Exit Variable Value Unit Equation

velocity Prime V' 4858.971 ft/s SQRT(E13*E15)

Total Velocty at Station 2

V_2 3882.687 ft/s E27*SQRT(E21/(1-E21/2))

Stage Axial Velocity

u 1454.48 ft/s E28*COS(RADIANS(E14))

Tangential Velocity at Station 2

vt_2 3599.965 ft/s E28*SIN(RADIANS(E14))

Rotor Relative vt_2

v_2r 1170.479 ft/s E30-0.5*E27

Tan beta 2 tan(β_2) 0.804741 (ft*lbf)/(lbm*R) E31/E29

Rotor Relative Total Temp

T_2r/Tt_1 0.846027 - 1+(E17)^2*(0.5-(E30/E27/E17))

T_2r 2707.288 R E33*E15

Flow Angle at Station 3

tan(β_3) 1.27776 Degrees SQRT((E33/E23*E22/(1+E22/2)-1))

Tangential Velocity at Station 3

v_3 1858.226 ft/s E29*E35-E17

Stage Exit Flow Angle

Tan(α_3) 1.277588 Degrees E36/E29

Static Temperature at Station 3

T_3/Tt_1 0.728079 - E33/(1+E22/2)

T_3 2329.852 R E38*E15


Temp Ratio Tt_3/Tt_1 0.846008 - E38+E23*(1+E37^2)/2

Pressure Ratio rp 0.676924 - (E40)^(E4/SQRT((E4-1)*E12))

Tau = Tt_3/Tt_1 τ 0.728079 - E38

Turbine Efficiency

ηt 2.577581 - (1-E42)/(1-(E41)^(0.4/1.4))

VII. Nozzle

A nozzle in an engine is a relatively simple device, it is just a specially shaped tube through which hot gases flow. Nozzles however have a relatively important task, they produce thrust, conduct exhaust gases back to the free stream, and set the mass flow rate through the engine. In most turbofan engines, they use a specific type of nozzle called a co-annular nozzle. This is a nozzle that combines both streams of fluid into a single flow which helps with efficiency of the engine and that they also tend to make a quieter engine. An example of a co-annular nozzle is shown below.


Nozzle Inputs Variable Value Unit Equations

Primary Nozzle Mass Flow Rate (M-Dot) m_8 200 lbm/s 200

Flow Coefficient C_D 0.965 - 0.965

Pt_9/Pt_8 0.98 - 0.98

Pressure at Exit of Turbine Pt_8 30 psi 30

Pt_9 29.4 psi E10*E11

Temperature at Exit of Turbine Tt_8 2329.852 R 2329.852

Primary Nozzle Half Angle (theta) 20 degrees 20

Primary Nozzle Throat Area A_8 706.8583 in^2 PI()*E19^2

Secondary Nozzle Throat Area A_9 1385.442 in^2 PI()*E20^2

Area Ratio A_9/A_8 1.96 - E16/E15

R g_c R_g_c 1716 ft^2/s^2*R 1716

radius r_8 15 in 15

radius r_9 21 in 21

Atmospheric pressure at cruising altitude P_o 2.71 psi 2.71

Nozzle Exit Variable Value Unit Equation

Effective Nozzle Area A_8e 732.4957 in^2 E15/E9

Ideal Mass Flow Rate Primary m_8i 207.2539 lbm/s E8/E9

Area Ratio A/A_star 2.03109 - E17/E9

Ideal Mach number Secondary m_9i 2.2145 - 1/C28*((2/(C2+1))*(1+(C2-1)/2*C29^2))^(2.4/0.8)

Pressure Ratio P_9i/Pt_9i 0.277123 - (1+(E2-1)/2*E29)^(-E2/(E2-1))

Pressure At Secondary P_9i 8.313702 psi E11*E30

Velocity At Secondary V_9i 5050.544 ft/s SQRT(E18*E13)*SQRT(2*E2/(E2-1)*(1-E30)^((E2-1)/E2))


Area Ratio A/A_star9 1.990466 - E10*E17/E9

Mach number exit m_9 2.192 - 1/C33*((2/(C2+1))*(1+(C2-1)/2*C34^2))^(2.4/0.8)

Pressure Ratio P_9/pt_9i 0.28017 - (1+(E2-1)/2*E34)^(-E2/(E2-1))

Exit Pressure P_9 8.236989 psi E35*E10*E11

Exit Velocity V_9 5047.498 ft/s SQRT(E18*E13)*SQRT(2*E2/(E2-1)*(1-E35)^((E2-1)/E2))

Velocity coefficient C_v 0.999397 - E37/E32

Angularity Coefficient C_A 1 - 1

Gross Thrust Coefficient C_fg 0.9246 - C9*C38((1-(C31/C11)^L26)/(1-(C21/C11)^L26))^0.5*(1+L27(1-C21/C36)/((C12/C36)^K26-1))

Gross Thrust F_actual 8245.611 lbf E8*E37/E18+(E36-E21)*E16

Velocity S V_s 5219.127 ft/s SQRT(E18*E13)*SQRT(2*E2/(E2-1)*(1-(E21/E11))^((E2-1)/E2))

Ideal Thrust F_ideal 630.3522 lbf E27*E42/E18

Nozzle Adiabatic Efficiency η_n 0.998794 - E37^2/E32^2

Pressure Ratio r_P_n 0.98 - E12/E11


IX. Conclusion

The PW1100G-JM is an important engine for the future of commercial aircraft. This engine will be used on two commercial airliners that will be extremely popular in the coming decades: both the Mitsubishi Transport Jet (MTJ) and the A320neo. The A320neo is the newest jet in the Airbus 300 series, the common domestic passenger aircraft- therefore this engine’s efficiency will have a profound impact on the aerospace industry.

This engine is a turbofan and 92% of its airflow is bypassed (meaning only 1/12 of the air is compressed and combusted). Pratt & Whitney has achieved a great amount of efficiency with this engine by continuing to apply a gearbox between the main engine shaft and the turbofan. This allows the compressor and turbine to spin at higher speeds and allows for extreme optimization of the turbofan blades.

The model and analysis of this report is extremely elementary and seeks to explain the function and basic operating conditions of each of the stages in the engine. The thrust study in the nozzle section only accounts for the thrust created by the processed air. The PW1100G-JM is a turbofan engine so most thrust comes from the turbofan itself. The processed air accounts for 8k lb of thrust, or approximately 30% of the total thrust. The other 70% of the thrust comes from the turbofan and the bypassed air, amounting to a total of 25k lb of thrust.

Error in this analysis likely arose from the omission of the low pressure stages in the compressor and turbine. These stages alter the air properties and ultimately affect the engine’s performance. More importantly, dimensions and properties and only reference values- the true values are not available to the public because of intellectual property reasons.

This analysis was an excellent experience to understand the operating conditions of a typical turbofan engine. It showcases how a compressible fluid can be scientifically analyzed, applied and optimized for a distinct purpose. It is truly an amazing piece of engineering and shows the seemingly endless optimization opportunities for a machine of this complexity.


X. References

Ehrich, Fredric F., and Alexander D. Baxter. “Medium-Bypass Turbofans, High-Bypass Turbofans, and

Ultrahigh-Bypass Engines.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 27 Sept. 2015, www.britannica.com/technology/jet-engine/Medium-bypass-turbofans-high-bypass-turbofans-and-ultrahigh-bypass-engines#ref135183.

“GTF Family.” Pratt & Whitney, pwgtf.com/wp-content/uploads/2019/06/PW-GTF-Family-Product-Card-June-2019.pdf.

“Pratt & Whitney GTF Family Engines.” MTU Aero Engines, pwgtf.com/wp-content/uploads/2019/06/PW-GTF-Family-Product-Card-June-2019.pdf.

“PurePower Engine Family Specs Chart.” Pratt & Whitney, large.stanford.edu/courses/2014/ph240/suresh1/docs/pwspecs.pdf.

“PW1100G-JM.” PW1100G-JM - MTU Aero Engines, www.mtu.de/maintenance/commercial-aircraft-engine-services/engine-portfolio-mro/narrowbody-and-regional-jets/pw1100g-jm/.


Date post:	20-Feb-2021
Category:	Documents
Upload:	others
View:	11 times
Download:	2 times

Analysis of Pratt & Whitney's PurePower Geared Turbofan PW1100G … · 2020. 12. 30. · PurePower...

Documents