Performance Limits of Turbomachines

Performance Limits of Turbomachines

David K. Hall

Gas Turbine LaboratoryDepartment of Aeronautics and Astronautics

Massachusetts Institute of TechnologyCambridge, MA 02139

January 26, 2010

Objective and Challenges

Objective

Examine, in a rigorous manner, the limits (and possible future advances)of turbomachine efficiency

Determine the best we can do

Challenges

What are unavoidable contributors to loss (inefficiency)?

◮ Skin friction will always be present

◮ What can be eliminated?

What assumptions frame the question?

◮ Examples: boundary layer transition criteria, compressibility

David K. Hall (MIT Gas Turbine Lab) Performance Limits of Turbomachines Research Exam 1/26/10 2 / 19

Framing the Issues to Address

What does “the best we can do” mean?

The challenge is not how to calculate, but deciding what to calculate.


Framing the Issues to Address

What does “the best we can do” mean?

The challenge is not how to calculate, but deciding what to calculate.

Losses approach: count only those which cannot be eliminated

◮ Viscous dissipation associated with boundary layers

◮ Rotor-casing gap flow loss (zero gap leads to large loss, 3D effect)

Flow regimes approach: consider features with largest impact

◮ Incompressible flow calculations

◮ Boundary layer transition: consider range from natural transition tofully turbulent


Previous Work

Denton, 1993. Loss Mechanisms in Turbomachines

◮ Entropy generation, various loss sources

Storer & Cumpsty, 1994. An Approximate Analysis and Prediction Method

for Tip Clearance Loss in Axial Compressors

◮ Entropy generated by tip clearance flow

Dickens & Day, 2008. The Design of Highly Loaded Axial Compressors

◮ Simplified profile model for predicting profile losses, trends

Drela, 2009. Power Balance in Aerodynamic Flows

◮ Power- rather than drag-based approach for aerodynamic flows


Stage Performance Estimation

Estimate attainable turbomachinery efficiency by assessing dissipationassociated with unavoidable contributors to loss

◮ Based on local flow irreversibilities (not loss correlations)◮ Allows for calculation of advanced-core engine performance


Stage Performance Estimation

Estimate attainable turbomachinery efficiency by assessing dissipationassociated with unavoidable contributors to loss

◮ Based on local flow irreversibilities (not loss correlations)◮ Allows for calculation of advanced-core engine performance


Main Messages

Small increases in gas turbine component efficiency (∼ 2%) can have alarge effect on cycle efficiency (∼ 10%).

Model developed to estimate performance limits based on defining localirreversibilities

Theoretical limit an appreciable amount (2%) above current performance

Procedure developed for special case to address long-standing issue:

◮ Lower limit of two-dimensional profile loss


NASA N+3 Project Background

Metric NASA Goal

Fuel Burn 70% reduction

Noise 71 EPNdB below Stage 4

LTO NOx 75% reduction below CAEP 6

Field Length Explore metro-plex concepts

Identify technology and configuration concepts to meet N+3 goals for2030-2035 time frame.

◮ Estimates of component efficiency used in performance calculations

◮ Establishing upper limits on component performance provides context◮ Maximum benefit expected from engine advances◮ Difficulty of reaching given level of performance


Component Performance and Engine Efficiency

10 20 30 40 50 6011

12

13

14

15

16

Pressure ratio

Thr

ust−

Spe

cific

Fue

l Con

sum

ptio

n (T

SF

C)

η = 0.89η = 0.94

14% 17%

Cycle results calculated using semi-perfectgas engine cycle model (not discussed here)

◮ Representative turbofan cycle

◮ Mission and cycle held fixed

◮ Component efficiencies η varied

◮ Bypass ratio optimized for minimumTSFC

◮ Component efficiency alone has significant effect on cycle efficiency

◮ Greatest benefit if pressure ratio is optimized


Stage Characterization: Meanline DesignMeanline Flow Geometry

Flow coefficient φStage loading coefficient ψDegree of reaction ΛChord/pitch ratio σReynolds number Re

Blade Velocity Distribution

Linear blade velocity distribution◮ Function of above parameters

◮ Linear variation across pitch on huband casing


Stage Charactarization: 3D Annulus Geometry

Blade aspect ratio ARRadius ratio rhub/rtipTip clearance height ratio τ/h


Performance: sum inefficiencies due to various losses

Losses included (cannot be eliminated)Blade surface dissipation Turbulent boundary layer calculation (so far)Wake mixing 2D control volumeEndwall losses constant dissipation coefficientTip clearance losses 2D mixing model (rotor only)

Losses not included (may be mitigated in the future)

◮ Parasitic losses, leakage flows

◮ Losses due to three-dimensional effects

◮ Shock losses


Stage Efficiency and Non-Dimensional Parameters

Stage efficiency calculated by adding all loss sources

ηstage = 1 −

(

Φblade + Φwake + Φwall + Φgap

P

)

stage

Parametric dependence

Efficiency η = F

8

>

>

>

>

>

>

>

>

>

>

<

>

>

>

>

>

>

>

>

>

>

:

Flow coefficient φStage loading coefficient ψ

ff

Independent

Reynolds number ReRadius ratio rhub/rtip

Aspect ratio ARTip gap height ratio τ/h

9

>

>

=

>

>

;

Stage location/size

Degree of reaction Λ

Chord/pitch ratio σ

ff

Design variables

Plot results as countours of efficiency on a flow coefficient-stage loadingcoefficient plane


Compressor Efficiency Limits

00

0

0

00

0

0.50.50.5

0.50.5

0.50.

5

0.5

0.750.750.75

0.750.75

0.75

0.750.

75

0.75

0.80.80.8

0.8

0.8

0.8

0.8

0.8

0.80.

8

0.8

0.850.850.85

0.85

0.85

0.85

0.85

0.85

0.85

0.85

0.850.

85

0.85

0.9

0.90.9

0.90.

9

0.9

0.9

0.9

0.9

0.9

0.90.

9

0.9

0.92

0.92

0.92

0.92

0.920.92

0.92

0.92

0.92

0.920.

92

0.92

0.93

0.93

0.93

0.93

0.93

0.93

0.93

0.93

0.93

0.930.

93

0.93

0.94

0.94

0.94

0.94

0.940.

94

0.94

0.94

0.94

0.94

0.95

0.95

0.95

0.95

0.950.

95

0.95

0.96

0.96

0.96

0.96

0.960.

96

0.96

0.97

0.97

0.97

0.97

0.970.

97

0.97

0.97

5

0.97

5

0.975

0.975

0.9750.

975

0.98

0.98

0.98

0.98

0.980.

98

0.98

0.98

5

0.98

5

0.985

0.985

0.9850.

985

0.99

0.99

0.99

0.99

0.990.

99

0.99

0.99

5

0.99

5

0.995

0.995

0.9950.

995

1

1

11

1

1

1

Flow coefficient φ = Vx/U

Sta

ge lo

adin

g co

effic

ient

ψ =

∆ h

t/U2

Stage efficiency η

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Independent Variables


Stage loading coefficient ψ = ∆ht/U2

Fixed parameters: representative of LPC stage

Inlet axial Reynolds number 500,000Hub-to-tip ratio 0.8Blade aspect ratio 1.0Rotor tip clearance gap 1% blade height

Chosen design variables

Reaction 50%Chord/pitch ratio ⇐ Diffusion factor = 0.47

◮ Maximum efficiency (under the assumptions): 94%

◮ Optimum blade loading◮ Tradeoff, high overspeeds vs many blades

◮ Flow separates above critical blade loading (blank region)


Model agrees with existing information (Dickens, 2008)


Sta

ge lo

adin

g co

effic

ient

ψ =

∆ h

t/U2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.8

0.85

0.9

Loss build-up model 1D correlation

◮ General trends: location of peak, rate of drop away from peak

◮ Efficiency greater in magnitude (expected)


Loss Breakdown, 50% Reaction

Rotor blade23%

Rotor wake5%

Rotor endwall20%

Rotor tip clearance8%

Stator endwall16%

Stator wake5%

Stator blade23%


Lower Limit of Profile Loss

Goal: minimize loss (objective), find optimum velocity distribution (designvariables), given meanline flow parameters (design parameters)

Objective Calculation

◮ Cascade vortex lattice method (assume thin airfoil, finite camber)

(vupper, φ, ψ,Λ) ⇒ (vlower, σ)

◮ Boundary layer calculation (Drela)

(Re, vupper, vlower) ⇒ η

Optimization

◮ Automatic Differentiation (AD) software

η(vupper,Λ;φ,ψ,Re) ⇒ ∇η

◮ Broyden-Fletcher-Goldfarb-Shanno (BFGS) gradient-based optimizer

⇒ (ηmax, v∗

upper,Λ∗) = F(φ,ψ,Re)


Path to the Thesis

Complete Compressor Analysis

◮ Stage performance estimation and demonstration

◮ Profile loss assesment◮ Laminar flow and transition◮ Optimization process

Turbine Analysis

◮ Finite airfoil thickness

◮ Cooling flow and entropy generation


“Intellectual Nuggets”

Rational discrimination of procedure for defining a best case

◮ Logic behind choices of where to be optimistic vs conservative

Bottom-up loss model

◮ First of its kind, based on local irreversibilities

Profile Performance Limit

◮ Special case; answers “what is the best we can do?” fortwo-dimensional turbomachinery profile loss


Summary

Cycle studies show increases in gas turbine component efficiency canprovide a large benefit in overall fuel efficiency

A framework for estimating the upper bound on turbomachine efficiency isdeveloped

◮ Based on local flow irreversibilities

◮ Shows significant advances in component efficiency possible

Optimization of inputs (including velocity distribution) will allow forcalculation of minimum profile loss


Performance Limits of Turbomachines

Documents

research exam 1 26 10

core engine performance

local ow irreversibilities

lower limit

loss correlations

component performance

performance limits

entropy generation