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Meanline Analysis of Turbines with Choked Flowin the Object-Oriented Turbomachinery Analysis
Code
Eric S. Hendricks
NASA Glenn Research Center
AIAA SciTech 2016San Diego, CA
Turbomachinery Analysis In Conceptual Design
Conceptual Engine Design ProcessGlassman, NASA-CR-198433
Conceptual design process focuses on a rapid analysis ofdesign alternatives and relies on lower-fidelity analysis tools
Turbomachinery analysis commonly uses meanline andstreamline simulation tools 2
The Object-Oriented Turbomachinery Analysis Code(OTAC)
Developed by NASA GRC using the Numerical PropulsionSystem Simulation (NPSS) codeAnalysis capabilities:
Compressor and turbine componentsAxial and centrifugal designsMeanline and streamline modelsUser defined loss models
Results for several compressor and turbine models validatedagainst results from similar analysis codes (Jones,ISABE2015-20015)
Limitation of the code was identified when analyzing turbineswith flow near or at the limiting choked mass flow rate
Study Objective
Enhance the analysis capabilities of OTAC by enabling analysis ofchoked flow in turbine meanline models
3
Presentation Outline
1 Overview of OTAC Models
2 Relevant Choked Flow Characteristics
3 Improvements to OTAC
4 Results
5 Conclusions
4
Presentation Outline
1 Overview of OTAC Models
2 Relevant Choked Flow Characteristics
3 Improvements to OTAC
4 Results
5 Conclusions
5
OTAC Components and Models
Six new objects created in NPSS for OTAC:
OTAC Start
Blade Row
Blade Segment
Transition Section
Expander
Reducer
Objects are combined to form turbomachinery models
OTACstartTransition
DuctTransition
DuctFlow End
Blade Row(Stator)
Blade Segment
Blade Row(Rotor)
BladeSegment
Shaft
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OTAC Blade Segment Equations
Stator
Rotor
0
1
2
V
U
VU
Vθ
α
β
VzV
α
αβ
Vz=Vz,rel
Vz=Vz,relVrel
Vrel
Vθ,rel
Vθ,rel
Vθ
Vθ
1 min = mout
2 ht,out − ht,in =ω (routVθ,out − rinVθ,in)
3 Pt,out = Pt,out,ideal − floss (args)
4 βout = βm,out + δ
5 rout = rm,out
6 Aout = Am,out
7 φout = φm,out
7
Typical OTAC Model Inputs and Solver Setup
Top-Level Solver
Vane Blade Row Solver
IndependentsExitIMach
ExitIFlowIAnglePressureIRatio
ExitITotalIEnthalpyExitIMeanIRadius
DependentsMachineIExitIArea
TargetIExitIFlowIAngleExitIPressureIfromILosses
EulerIEquationMachineIExitIMeanIRadius
IndependentsNone
DependentsNone
Case InputsInletITotalIPressure
InletITotalITemperatureInletIMassIFlowIRate
InletIFlowIAngleShaftISpeed
Rotor Blade Row Solver
IndependentsExitIMach
ExitIFlowIAnglePressureIRatio
ExitITotalIEnthalpyExitIMeanIRadius
DependentsMachineIExitIArea
TargetIExitIFlowIAngleExitIPressureIfromILosses
EulerIEquationMachineIExitIMeanIRadius
8
Presentation Outline
1 Overview of OTAC Models
2 Relevant Choked Flow Characteristics
3 Improvements to OTAC
4 Results
5 Conclusions
9
Supersonic Flow Characteristics
Throat
UnchokedCFlowFlow angle matchesblade metal angle
plus deviation
RegionCofPrandtl-MeyerCExpansionCandCShockCWaves
ChokedCFlowFlow angle deviates from blade to match exit static pressure
10
Mach-Area Relationship as a Function of Flow Angle
0.0 0.5 1.0 1.5 2.0
Mach Number
0
1
2
3
4A/A
∗
α = 0◦α = 15◦α = 30◦
α = 45◦
α = 60◦
11
Presentation Outline
1 Overview of OTAC Models
2 Relevant Choked Flow Characteristics
3 Improvements to OTAC
4 Results
5 Conclusions
12
Three Improvements Required for Turbine Meanline Models
1 Add calculations for throat area and choked flow constraint toeach blade row
2 Revise case inputs to define a unique solution
3 Revise the model solver setup to enable application of the flowconstraint, determine the proper exit flow angle and changethe case inputs
13
Calculations for Throat Area and Choked Flow Constraintin Each Blade Row
1 Calculate the critical pressure ratio and actual pressure ratio
PRcr =Pt,rel,in
Ps,th,M=1.0PR =
Pt,rel,in
Ps,out
2 Determine throat properties
Choked flow (PR >= PRcr ): throat properties and areadetermined from a sonic Mach numberUnchoked flow (PR < PRcr ): throat properties and areadetermined based on the exit static pressure
3 If model is in design mode, throat area is saved for off-designanalysis
4 Blade row throat flow constraint equation compares actualflow per throat area to the flow per area required for chokedconditions
mAcr
≤ mAth
14
Revisions to Case Inputs
Default OTAC model setup had mass flow as a case inputproducing three possible results:
Mass flow rate is below choked value producing a uniquesolutionMass flow rate matches choked value producing an infinitenumber of solutionsMass flow rate is above choked value producing no feasiblesolutions
Specifying the turbine exit static pressure as a case inputprovides a unique solution for all flow regimes
Unchoked case: exit static pressure sets mass flow rateChoked case: exit static pressure sets exit flow angle fromchoked blade row
15
Revisions to Model Solver Setup
Attach flow constraints computed for each blade row to theflow angle dependent (Eq. 4) using feature of NPSS Newtonsolver
Move independents and dependents from each blade rowsolver to the top-level solver
Mach number independentExit flow angle independentExit area dependentTarget flow angle dependent (including flow constraint)
Add mass flow rate as an independent and exit static pressureas a dependent to the top-level solver
16
Revised OTAC Model Inputs and Solver Setup
Top-Level Solver
Vane Blade Row Solver
IndependentsPressurebRatio
ExitbTotalbEnthalpyExitbMeanbRadius
DependentsExitbPressurebfrombLosses
EulerbEquationMachinebExitbMeanbRadius
IndependentsInletbMassbFlowbRate
VanebExitbMachbNumberVanebExitbFlowbAngle
RotorbExitbMachbNumberRotorbExitbFlowbAngle
Case InputsInletbTotalbPressure
InletbTotalbTemperatureExitbStaticbPressureInletbFlowbAngle
ShaftbSpeed
Rotor Blade Row Solver
IndependentsPressurebRatio
ExitbTotalbEnthalpyExitbMeanbRadius
DependentsExitbPressurebfrombLosses
EulerbEquationMachinebExitbMeanbRadius
DependentsExitbStaticbPressure
VanebTargetbExitbFlowbAngle*VanebMachinebExitbArea
RotorbTargetbExitbFlowbAngle+RotorbMachinebExitbArea
ConstraintsVanebAllowablebMassbFlowbRate*RotorbAllowablebMassbFlowbRate+
17
Presentation Outline
1 Overview of OTAC Models
2 Relevant Choked Flow Characteristics
3 Improvements to OTAC
4 Results
5 Conclusions
18
Results Overview
Several single-stage and multi-stage turbines were modeledusing the new method for all cases (subsonic and supersonic)
Results shown in the form of turbine performance maps withcorrected flow and efficiency as functions of pressure ratio andpercent corrected speed
All models use the Kacker-Okapuu loss correlations withincidence losses from Moustapha, Kacker and Tremblay
19
Single-Stage Turbine with Choking in Vane
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Pressure Ratio
4
5
6
7
8
9
10
CorrectedFlow,lbm/sec
50%
60%
70%
80%
90%
100%
110%
120%
130%
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
Pressure Ratio
40%
50%
60%
70%
80%
90%
100%
E�ciency
20
Experimental Results for a Single-Stage Turbine withChoking in Vane
Szanca and Schum, NASA-SP-290
21
Single-Stage Turbine with Choking in Rotor
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Pressure Ratio
4
6
8
10
12
14
CorrectedFlow,lbm/sec
50%
60%
70%
80%
90%
100%
110%
120%
130%
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Pressure Ratio
40%
50%
60%
70%
80%
90%
100%
E�ciency
22
Experimental Results for a Single-Stage Turbine withChoking in Rotor
Szanca and Schum, NASA-SP-290
23
Single-Stage Turbine with Choking Transition
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Pressure Ratio
4
5
6
7
8
9
10
CorrectedFlow,lbm/sec
50%
60%
70%
80%
90%
100%
110%
120%
130%
1.0 1.2 1.4 1.6 1.8 2.0 2.2
Pressure Ratio
40%
50%
60%
70%
80%
90%
100%
E�ciency
24
Four-Stage Turbine
1 2 3 4 5 6 7 8
Pressure Ratio
4
6
8
10
12
14
CorrectedFlow,lbm/sec
50%
60%
70%
80%
90%
100%
110%
120%
130%
1 2 3 4 5 6 7 8
Pressure Ratio
40%
50%
60%
70%
80%
90%
100%
E�ciency
25
Presentation Outline
1 Overview of OTAC Models
2 Relevant Choked Flow Characteristics
3 Improvements to OTAC
4 Results
5 Conclusions
26
Summary and Future Work
Improvements were made to the Object-OrientedTurbomachinery Analysis Code (OTAC) to enable analysis ofmeanline turbine models with choked flow
Adds calculations for throat area and choked flow constraintModifies analysis case inputs to include exit static pressureRevises the internal solver setup
Maps produced with new method exhibit characteristicsmatching those found in experimental results
Areas for future work:
Extending this method for application to streamline turbinemodelsDeveloping a similar method for capturing choked flow incompressors
27
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