Document
Optimization of Turbine Engine Cycle Analysis with
Analytic Derivatives
Tristan Hearn, Eric Hendricks, Jeffrey Chin, Justin Gray,
Kenneth T. Moore
NASA Glenn Research Center, Cleveland, OH
th
June 16 , 2016
Faster engine cycle optimization
Optimization of a separate flow turbofan design was performed with
analytic derivatives using the cycle analysis code Pycycle
Computation cost on average was 1/3 that of an optimization
performed on an NPSS implementation, with finite-difference
derivatives
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Pycycle Overview
Pycycle is a 1D cycle modeling tool similar to NPSS, but with an extra
level of decomposition
This allows for the implementation of analytic derivatives
Justin S. Gray et al. “Thermodynamics For Gas Turbine Cycles With Analytic Derivatives in OpenMDAO”. . In: 2016 AIAA SciTech Conference . American Institute of Aeronautics and Astronautics, Jan. 2016.
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Analytic derivatives within OpenMDAO
OpenMDAO computes coupled derivatives for complex multidisciplinary
models automatically
y x, y F ( x, y ) x C C C 1 2 3 y Forward:
( )
− 1
d F ∂ F ∂ F ∂ R ∂ R
= − (1)
d x ∂ x ∂ y ∂ y ∂ x
i i i
︸︷︷︸ ︸︷︷︸ ︸︷︷︸
︸ ︷︷ ︸
m × 1 m × 1 m × n n × 1 Adjoint:
( ) T
− 1 T T
d F ∂ F ∂ R ∂ F ∂ R
i i i
= − , (2)
d x ∂ x ∂ y ∂ y ∂ x
︸︷︷︸ ︸︷︷︸ ︸︷︷︸
︸ ︷︷ ︸
1 × k 1 × k n × k 1 × n Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Analytic derivative benefits
Analytic derivatives provide significant computational savings for gradient
based optimization
Computational Cost vs # of Design Variables ALPSO SNOPT - Fwd. Analytic Time (sec) SNOPT - FD SNOPT - Adjoint Analytic 1 2 3 4 5 10 10 10 10 10 Number of Design Variables Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Turbofan model structure
A separate flow turbofan model was built in both Pycycle and NPSS and
optimized in OpenMDAO
F ram Perf f 13 f F Duct N ozzle g byp byp F g f f f f f f f f f 0 2 2 . 3 2 . 5 3 4 4 . 5 5 7 Split Comp Duct N ozzle FC Inlet Fan Burner TurbineH TurbineL core core N N mech mech trq trq 2 1 ShaftH N mech N mech trq trq 2 1 ShaftL Minimize: TSFC With respect to: 1 ≤ FPR ≤ 2 1 ≤ CPR ≤ 30 1 ≤ BPR ≤ 12 lbm 1 ≤ W ≤ 2000 s Such That: OPR = 30 F = 25 , 000 lbf n ◦ T ≤ 3000 R
Flight condition: 35,000 ft, 0.8 MN
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Resulting designs
Pycycle and NPSS based optimizations drove towards the same answer
Baseline Optimized (Pycycle) Optimized (NPSS)
FPR 1 . 5 2 . 0 2 . 0
CPR 10 . 3 15 . 0 15 . 0
BPR 5 . 0 12 . 0 12 . 0
W 500 . 0 1069 . 2 1032 . 40
TSFC 0 . 612 0 . 331 0 . 320
Mass flow and TSFC vary between codes due to a thermodynamic
discrepancy
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Tolerances obtained
− 5
Both internal solver tolerances were set to 10
Pycycle converged to much tighter tolerances overall
Pycycle NPSS
− 15 − 3
Max. constraint violation 3 . 5 · 10 1 . 2 · 10
− 6
ShaftL 1 . 64 · 10 − 0 . 022
net pwr.
− 8 − 6
ShaftH 6 . 11 · 10 2 . 826 · 10
net pwr.
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Optimization performance metrics
Analytic Derivatives give fewer iterations and lower wall time on average
Pycycle NPSS − 5 − 4 − 3 − 3 − 3 FD step size - 10 10 0 . 99 · 10 10 1 . 01 · 10 SNOPT iterations 44 120 58 721 11 98 Run time (s) 3753 30912 12796 131581 1071 18788
NPSS optimizations were highly sensitive to step size
Difference in compute cost is primarily due to the difference in the
cost of computing derivatives
Tight tolerance requires more iterations for each FD step
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives
Conclusions
Results suggest analytic derivatives are suitable for optimization of
engine cycle analysis
Optimizations performed using engine cycle analysis outperform
analyses performed using finite-difference derivatives
Access to analytic adjoint derivatives will enable more ambitious
MDO problems (propulsion-airframe, propulsion-mission, etc.)
Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives