Class 9: Turbomachine Design Turbomachine comprised of rows of stators and rotors –can be as little as single rotor row (fan) Compressor Modeling –0D:

Class 9: Turbomachine Design

• Turbomachine comprised of rows of stators and rotors– can be as little as single rotor row (fan)

• Compressor Modeling– 0D: Thermodynamic or cycle analysis

• Provides inlet / exit thermodynamic and efficiency for each component

– 1D: Actuator disc or meanline aerodynamic analysis• First thermodynamics, then velocity triangles• specify area or Cx• model spanwise effects• no specified efficiency, but calculate losses of

specified blades (CML)

Compressor Design• 0-dimensional analysis: cycle code [NPSS, SOAPP, DIGITEM]

– treat compressor as a module, element or single unit that performs performance calculations

• specify inlet, outlet bleed flows

• call compressor map based on experimental data

– calculates unscaled performance based on user supplied maps

Compressor Turbine

W

2 2

2 3 2 3

4 5 4 5

5

2 2

: 740 , 1230 , , 185 / sec

: 2170 , ?, , 185 / sec

30,700 1680

c

out in

c t

V VW h h

Compressor T R T R V V m lb

Turbine T R T V V m lb

W Hp W T R

Numerical Propulsion System Simulation (NPSS)NASA Glenn RC Code

• NPSS is a full propulsion system simulation tool used to predict and analyze the aerothermodynamic behavior of gas turbine engines.

• NPSS is a numerical "test cell" that enables engineers to create complete engine simulations.

• NPSS allows engine designers to analyze different parts of the engine simultaneously, perform different types of analysis simultaneously (e.g., aerodynamic and structural).

JT8D-200 Series Engine

Ex.:Twin Spool Unmixed Flow Turbofan

0D Model Set-up and Execution

• Double Click on bam.bat file in bam directory • Open File “class_shaft.bam” using File Open menu.

– Model is a Single Spool Turboshaft– Inlet -> High Compressor-> Burner-> High Turbine-> Nozzle– See Figure 1 for Block diagram. This graphic will appear in

the lower half of the Graphical User Interface (GUI) when the model is loaded.

– Design Point• Click on “Design Point” tab in GUI to vieiw design inputs.

– Change viewer.switchSolverOutput value to “ON”– Change viewer.switchBasicOutput value to “ON”– Change viewer.switchCsvOutput value to “ON”– Select “Apply”.


• Variable Output List– Click on “Viewer Var List” in GUI to view output parameters.– At bottom of GUI window – input desired output file name (e.g.

“test”)– Select “Reset” then “Apply”.

• Parameters Definitions– Click on small arrow on upper left corner of GUI to view

parameter definitions and units.– Execute – Click on the “Design Point” box at the bottom of the GUI.

• Click on “Execute”.• Output

– test.bamout – text output.– test.csv – comma separated variable output readable in excel.


Run off-design parametrics

[1] over operating line, [2] over constant speed, [3] for different efficiencies to plot PR versus mass flow.

Twin Spool Unmixed Flow Turbofan–Configuration• Turbofan Model at the Design Point and Offdesign

FN = 5000 lbf, OPR = 25, Wc Inlet = 1000 lbm/sec • Baseline Component Polytropic Efficiencies at 90% • Fan Pressure Ratio = 1.6, LPC PR = 2.5, HPC PR = 10.0

– What are T3, T4, Wfuel, N2C25, HPC WcIn, HPC ad, Fg, and Fram ?

Set up an Off-design sweep of N2HPC from 10,000 to 11,400 RPM

• Plot the HPC Operating Line and HPC ad vs. HPC WcIn

OPROPR

T4T4Primary NozzlePrimary Nozzle

WcWc Secondary NozzleSecondary Nozzle

T3T3

Design Point

Off-Design sweep of N2HPC

Include this code for generating the sweep of N2HPC from 10,000 to 11,400 rpm

Remember to click “ApplyApply” before executing the run.

*** UTC PROPRIETARY *** PRATT & WHITNEY Build-A-Model Parametric Environment Version v2.0.1Data Set = Initial Design Point

Amb.alt Amb.MN Amb.dTs Amb.Ts Amb.Ps Amb.Tt Amb.Pt Amb.humSp Perf.Fg Perf.Fram Perf.Fd Perf.Fn Perf.Fnc 35000 0.8 0 393.854 3.45782 444.433 5.27195 0 14210 9210.02 0 5000 21250.3

Perf.pwrSD Perf.Wfuel Perf.SFC PerfInst.Fg PerfInst.Fram PerfInst.Fd PerfInst.Fn PerfInst.Fnc PerfInst.pwrSD PerfInst.Wfuel PerfInst.SFC CpwrH.pwr CpwrL.pwr 0 2958.44 0.591688 14210 9210.02 0 5000 21250.3 0 2958.44 0.591688 0 0

FusEng.Wfuel FuhxPri.dhFuel FuhxPri.Wfuel InEng.PqP InEng.PqP2 InEng.Fram NozPri.CdTh NozPri.Cv NozPri.AeTh NozPri.Ath NozPri.PR NozPri.Fg NozSec.CdTh 0.82179 0 0.82179 0.99 0.988595 9210.02 0.99 0.99 533.997 539.391 1.72932 2154.67 0.99

NozSec.Cv NozSec.AeTh NozSec.Ath NozSec.PR NozSec.Fg FsEng.Wc SpltFan.BPR CmpFSec.WcIn CmpFSec.PR CmpFSec.Nc CmpFSec.eff CmpFSec.effPoly CmpFSec.pwr 0.99 1709.18 1726.45 2.41161 12055.4 982.011 7.11606 870.948 1.6 3240.88 0.893113 0.9 8101.64

CmpH.WcIn CmpH.PR CmpH.Nc CmpH.eff CmpH.effPoly CmpH.pwr CmpL.WcIn CmpL.PR CmpL.Nc CmpL.eff CmpL.effPoly CmpL.pwr TrbH.Wp 55.9833 10 11207.2 0.86543 0.9 10135.4 120.996 2.5 3240.88 0.886391 0.9 2389.42 14.0706

*** UTC PROPRIETARY *** PRATT & WHITNEY Build-A-Model Parametric Environment Version v2.0.1Data Set = New Design Point

Amb.alt Amb.MN Amb.dTs Amb.Ts Amb.Ps Amb.Tt Amb.Pt Amb.humSp Perf.Fg Perf.Fram Perf.Fd Perf.Fn Perf.Fnc 35000 0.8 0 393.854 3.45782 444.433 5.27195 0 10743.1 8021.7 0 2721.36 11565.9

Perf.pwrSD Perf.Wfuel Perf.SFC PerfInst.Fg PerfInst.Fram PerfInst.Fd PerfInst.Fn PerfInst.Fnc PerfInst.pwrSD PerfInst.Wfuel PerfInst.SFC CpwrH.pwr CpwrL.pwr 0 1691.41 0.621531 10743.1 8021.7 0 2721.36 11565.9 0 1691.41 0.621531 0 0

FusEng.Wfuel FuhxPri.dhFuel FuhxPri.Wfuel InEng.PqP InEng.PqP2 InEng.Fram NozPri.CdTh NozPri.Cv NozPri.AeTh NozPri.Ath NozPri.PR NozPri.Fg NozSec.CdTh 0.469836 0 0.469836 0.99 0.988785 8021.7 0.99 0.99 533.808 539.199 1.34411 1126.33 0.99

Design point and Offdesign sweep, relative to peak ad

High Pressure Compressor Operating Line

Design PointWc = 55.98PR = 10.0

1.0

3.0

5.0

7.0

9.0

11.0

13.0

20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0

Wc (lbm/sec)

Pre

ss

ure

Ra

tio

• HPC Off-design Results– Maximum adiabatic efficiency occurs lower on the operating line

• Peak Efficiency = 88% adiabatic88% adiabatic• Peak Efficiency occurs near 10,900 RPM10,900 RPM (corrected speed)• Set HPC Design Pressure Ratio to 8.318.31• Resize Engine to achieve HPC WcIn = 50 lbm/secHPC WcIn = 50 lbm/sec

Efficiency Lapse with with Corrected Speed

Design Efficiency = 0.865

0.82

0.83

0.84

0.85

0.86

0.87

0.88

0.89

20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0

Wc (lbm/sec)

Ad

iab

ati

c E

ffic

ien

cy

Peak ad

Idle

Updating the HPC design data

On the “Design PointDesign Point” page update the HPC design information based on the off-design run at 10,900 RPM

Remember to click “ApplyApply”

Updating the HPC design speed

STD

HPC

TT

NCN

5.2

mechanical2252

RPM900,1067.51865.5942mechanical N

RPM671,112mechanical N

PointDesign at65.5945.2 RT

Remember to click “ApplyApply”

Additional Balances

Under “Additional BalancesAdditional Balances” – deactivate the balances previously set-up for

• Core Size

• Velocity Jet Ratio

Add a new balance for HPC Inlet flow CmpH.WcIn

Remember to click “ApplyApply” before executing the run.

The new balance allows the engine bypass ratio to be changed to meet the HPC inlet flow required at maximum ad.

balance names are user defined

Results

Interesting Results

• Fuel consumption decreases .06%.

• Over 14,366 lbm/year fuel saved for a twin engine aircraft flying approx 18 hr/day, including 12 hours of cruise flight per day.

• $68,000/yr saved (Jet A $4.73/gal)

• Turbine Cooling Air Temperature decreases 6%

• OPR decreases 16.8% while BPR increases 16.3%

Interesting Results

• Fuel consumption decreases .06%.

• Over 14,366 lbm/year fuel saved for a twin engine aircraft flying approx 18 hr/day, including 12 hours of cruise flight per day.

• $68,000/yr saved (Jet A $4.73/gal)

• Turbine Cooling Air Temperature decreases 6%

• OPR decreases 16.8% while BPR increases 16.3%

Parameter Original Design Re-Design % ChangeCmpH.WcIn (lbm/sec) 55.98 49.85 -10.96%

CmpH.PR 10 8.31 -16.90%

N2C25 (rpm) 11207.2 10900.0 -2.74%

T2.5 (Rankine) 594.65 594.65 0.00%

T3 (Rankine) 1214.3 1141.5 -5.99%

T4 (Rankine) 2655 2750 3.57%

Wfuel (lbm/hr) 2958.44 2956.80 -0.06%ad 0.865 0.880 1.68%poly 0.900 0.909 1.01%

OPR 25 20.78 -16.88%

Fram (lbf) 9210 9379 1.83%

Fgross (lbf) 14210 14379 1.19%

Fnet (lbf) 5000 5000 0.00%

Core Size 8 8.31 3.88%

Bypass Ratio 7.12 8.28 16.29%

Jet Velocity Ratio 0.80 0.82 2.50%

Single Spool Turboshaft – Overview

• Primary Cycle Parameters– Optimized to Minimize Fuel Consumption and Maximize Power

• Overall Pressure Ratio (OPR or P3QP2)

• Cycle Temperature (RIT or T4)

– Engine “Sized” to Meet Power Demands (Design Point)

• Inlet Flow (Wc) Set to Match Power Requirement

– Note – Sizing is Direct Driver on Weight

• Generally Speaking– Increasing T4 Reduces Engine Size for a Given Power Requirement

– Increasing OPR Reduces Fuel Consumption

• To a Point, then the Trend Reverses

• Component Efficiencies Strongly Influence These Trades

– Same Holds for Cooling Air, Parasitic Losses, etc.

Twin Spool unmixed flow Turbofan – Overview Engine Rematch Example

• Primary Cycle Parameters– Optimize to Minimize Fuel Consumption and Cruise Thrust

• Overall Pressure Ratio (OPR or P3QP2) was set at 25.0

• Spool mechanical speeds set

– 3000 RPM for Fan, Low PC, and Low PT

– 12000 RPM for High PC and High PT

• Bypass Ratio set 7.0

• Core Size set at 8.0 lbm/sec

• Jet Velocity Ratio set at 0.80 (NozSec.Vactual/NozPri.Vactual)

• Component polytropic efficiencies set

– Fan p = 0.90

– LPC, HPC, HPT, LPT p = 0.90

• Engine “Sized” to Meet Power Demands (Design Point)

– 5000 lbf Net Thrust at 35,000 ft., Mach 0.80

• Design Inlet Flow (Wc) Set to meet Thrust Requirement

• 1000 lbm/sec (NPSS will use this value at the start of solver iterations)

• Generally Speaking

– Increasing T4 Increase Cycle Efficiency and Reduces Engine Size

However, the turbines are subjected to higher temperatures

– Increasing OPR Reduces Fuel Consumption

• However, the temperature of the engine cooling air increases

– More air required to achieve required cooling

– Reduced part life at elevated operating temperatures• In this example we will examine the effects of resetting the HPC

operating parameters at the design point (to highest ad)

Engine Rematch example

Turbofan Cruise to Midflight Idle




Single Spool Turboshaft Configuration• Construct and Execute a Cycle for the Following

– T4 = 2000° R, OPR = 12, 100#/s Wc• Baseline Component Efficiencies =85% (HPC and HPT)• Burner Pr Loss = 5%, Nozzle PR = 1.05

– What Flow is Required to Produce 10000 SHP– What is the Impact of Changing T4 +500°– What About Increasing Component Efficiency 5%

OPR BurnerPr Loss

T4 NozzlePR

Wc

Thermodynamic View of the Gas Turbine Cycle

• Ideal Brayton Cycle • Realistic Brayton Cycle With Nonisentropic Compression and Expansion Paths

Constraints on Gas Turbine Cycle Parameters

• Minimum (ambient) and maximum (turbine metalography limits) temperature levels set design cycle

• Low compressor Pr [cycle 1-K1-K2-K3-K4] – absorbs little work and turbine produces

little work.

• High compressor Pr [cycle 1-B2-B3-B4]– results in high compressor exit

temperature little heat can be added (by combustor) without exceeding turbine limits

Design Constraints Coupling Compressor & Turbine

Typical HPC (N2) Compressor Map Over Range of Operation

Meanline Calculations

• Meanline is the midpoint between hub and tip

• Meanline represents the first solution for velocity triangles of machine

• Calculations performed at one radial location for each axial station

• Many Uses for Meanline Calculations– Predict efficiency potential– Optimize configurations– Predict off-design trends

– Convert P0 & T0 data to Loss & Velocity diagrams, stage characteristics

– Basis for stability analysis

Meanline Calculations

• Meanline Calculation Types

Design - Given Po & To, calculate velocity diagrams & select airfoils

Off-design - Given airfoils, calculate velocity diagrams,

P0 & T0

Cascade data correlations available in meanline

programs

Design Meanline Calculations

• Known for Rotor Leading Edge:

P01 T01 m (flow)

Aan1 Aan2 (Annulus area)

1 U1 = U2 = U

R p

Sufficient airfoil parameters

• Calculate– Pr, if loss coefficients and rotor exit angle are known– Rotor exit angle 2 and loss coefficients of rotor exit Po2 and To2

known


• All problems use same technique at Rotor Leading edge.

• Determines M1

• M1 P/P01, T/T01 from isentropic relations• P01, T01, P/P01, T/T01 P1, T1

• M1, T1 C1

• C1, U, 1 Cu1, Cx1, Wu1, W1, 1

• W1, T1 M1R

• M1R, P1, T1 T01R, P01R

• This completely determines flow at rotor leading edge.

0

0 1 1

,cosan

RTmf M

P A g


• Design Problem:

Know P02 & T02 (Note that an efficiency is

used here)

Find Exit Velocity, Angle &

• By Euler's Equation: U

TTgJCCC puu

010212


• Guess Cx2

• Cu2 [from Euler equation], Cx2 C2, 2

• C2, To2 T2

• C2, T2 M2, FP02

02 02 2 202

( 1)

2( 1)2

02 2 2

cos

11

2

an

gm FP P A

RT

FP M M


• Vary Cx2 until continuity matches.

• M2, P02, T02 P2, T2

• U, Cu2 Wu2

• Cx2, Wu2 W2, 2

• T2, W2 M2R

• T2, P2, M2R T02R, P02R


• Now have complete exit velocity diagram

• Method applies to turbine & compressor

• Determine loss coefficients:

101

0201

PP

PP

R

RR

2/21

0201

W

PPZ RR


• Can analyze Loss vs Incidence, Dfactor, Mach number, etc.

• Can use given P0 & Loss correlations to determine efficiency, mean camber, loading, solidity, etc.

202

0201

PP

PPY

R

RR

/1

012

/10222

/1

/1

R

R

PP

PP

Off-Design Meanline Calculations

• Off-Design Problem for Compressor:

• Know 2 & for given airfoil shape, Determine Pr &

• Solve Continuity in the Rotating Reference Frame:

1010102 PPPP RRR

0202

02 2 2cosR

RR an

RTmFP

P A g


• FPt2R M2R

• M2R, To2R, Po2R T2, P2, W2

• W2, 2, U Wu2, Cx2, Cu2, C2, 2

• C2, T2 M2

• M2, T2, P2 Po2, To2

• Po1, Po2, To1, To2 Pr,


• For the turbine, knowing 2 & (or Y)

• Guess M2R:

• and:

• Vary guessed M2R to convergence.Same solution as compressor except different loss coefficient definition!

2

12

22

2

0102 2

111

RRR MPP

1

2 1202 2 2

11

2R R RFP M M

02 02 2 202

cosR R anR

gm FP P A

RT

Compressor Design Meanline Example

Given: rotor stator

mass flow = 100 lb/sec = 1.4

Wheel speed = 1350 ft/sec, constant

Find: rotor and stator loss coefficient []rotor and stator solidity []

Station 1 2 3 Area – Sq In 44.0 39.6 37.5 To - R 1094 1213 1213 Po – psia 200 282 279 Dfactor 0.475 0.5


• Continuity can be solved at stations 1 & 3:

• Iteration at station 1:

Guess 1 M1 from FP0

From M1, T01 T1, C

From C, 1 Cx1, Cu1

From Cx1, Aan1 m (flow)

• Same iteration can be done at station 3. This gives:

0

0 320 cos 1 .2

RTm MFP

AP g M

03

01

41.17

0.20

4219.0

4991.0

3

1

M

M


0498.11

1 21

1

01

MT

T

sec/45.1582

08.10421

ftgRTa

RT

sec/13.270sin

sec/80.789

111

111

ftCC

ftaMC

U


• Euler's Equation needed at station 2

• Iteration:

Guess

mP lbBtuTCh /56.2800

sec/78.799012 ft

U

hgJCC UU

2

1/ 22 22 2 2

02

711.0 / sec

1070.12 / sec

48.36

X

x U

C ft

C C C ft


22

2 02

2 2

22

2

0 32

0 00

1117.72

1638.81 / sec

.653

.51081 .2

cos 100 / sec

P

m

CT T R

gJC

a gRT ft

CM

a

MFP

M

gm FP AP lb

RT


Mach numbers that satisfy continuity have been found at all stations. The velocity diagram is solved as usual:


• Relative frame total pressure is needed for rotor

• Loss Coefficients [Compressible]:

049.101

0201

PP

PP

rel

relrelrotor

043.202

0302

PP

PPstator


• Solidity using

• So

1 22

1 1

12

/

U Ufactor

W WWD

W W

where c s

254.1rotor

700.1stator

Documents

Class 9: Turbomachine Design Turbomachine comprised of rows of stators and rotors –can be as little as single rotor row (fan) Compressor Modeling –0D: