Shape Optimization of an ORC Radial Turbine Nozzle

Transcription

SHAPE OPTIMIZATION OF AN
ORC RADIAL TURBINE NOZZLE
D. Pasquale, A. Ghidoni & S. Rebay
Università degli Studi di Brescia,
Dipartimento di Ingegneria Meccanica e Industriale,
Via Branze 38, 25123 Brescia, Italy
Delft - September 22th − 23th , 2010
Outline
1
Introduction
ORC Turbine
Objectives
Tri-O-Gen Design
2
Methodology
Optimization Algorithm
3
Results
Optimization Strategies Comparison
Optimized Results
Outline
1
Introduction
ORC Turbine
Objectives
Tri-O-Gen Design
2
Methodology
3
Results
Optimized Results
Outline
1
Introduction
ORC Turbine
Objectives
Tri-O-Gen Design
2
Methodology
3
Results
Optimized Results
Introduction Methodology Results
ORC Turbine Objectives Tri-O-Gen Design
Small Power Output ORC Turbine (< 500kWe )
High molecular-weight fluids (e.g. Toluene)
Expansion:
I
real gas effects
I
high pressure ratio
I
high volume ratio
I
low specific enthalpy drop
Challenging Design:
I
small-size turbomachinery
I
moderate/high rotational
speed
I
few stages
Intensive use of CFD to design high-efficiency and optimized turbines
Objectives
General Geometry Parameterization
I
development of a generic blade shape parameterization
suitable for radial and axial supersonic geometries
General Optimization Procedure
I
development of an efficient, effective and fully automated
optimization procedure
I
comparison of different optimization strategies in terms of
convergence rate
Test Case
I
improve the performance of the original Tri-O-Gen stator
in terms of flow uniformity and shock losses
Tri-O-Gen Original Stator Design
Turbine Features
I
I
I
one stage radial inflow turbine (' 150kWe )
high expansion ratio β ' 62
low degree of reaction
Mach number
I
I
highly tangential flow
high Mach number
Total Pressure
I
I
strong shock wave
flow dis-uniformity
Genetic Algorithm
Off-line trained Metamodel
Objective Function Definition
Minimization of one objective function
sum of three non-concurrent contributions:
ϕ = ϕM + ϕα + ϕP0loss
Mach number deviation
v q
2
u1P
M −M
u q cj Mj j Mtollmix
u j=1
ϕM = t
q
P
1
q
j=1
cj M j
Flow angle deviation
v q
2
u1P
α −α
u q cj Mj jαtolltrg
u j=1
ϕα = t
q
P
1
q
j=1
Total pressure losses
cj Mj
ϕP0loss =
1−P0
mix
P0
toll
where:
αtrg = 106[◦ ]
αtoll = 1[◦ ]
and q is the number of grid nodes at the outlet bound
Mtoll = 0.025
P0toll = 0.05
Original TriOgen Design Performance
ϕdes = 2.035 + 1.761 + 3.533 = 7.329
Geometry Generation
B-Spline Curves
B(u) =
n
X
Ni (u)Pi
y
i=1
I
cubic curves
I
C 2 continuous at the junctions
I
chordal parametrization
x
δ
α
prmx
y
Thr
Thθ
β
x D. Pasquale, A. Ghidoni & S. Rebay
Design Variables
I
throat angle and position (δ, Thr , Thθ )
I
trailing edge aperture angle (α)
I
trailing edge discharge angle (β)
I
1 d.o.f. for each free control point
(prmx ) of 2 curves (diverging part)
Grid generation and CFD solver
adMesh
I
fully automated 2D unstructured
mesh generator
I
hybrid anysotropic elements
I
based on the
advancing-Delaunnay algorithm
zFlow
I
hybrid Finite Element (FE)/Finite Volume (FV)
RANS solver
I
linked to FluidProp, a fluid library for
thermodynamic and transport properties
calculation using state of the art physical models
CFD Solution
an Example
Grids
I
2D unstructured grid with local
refinements
I
three different spacing:
very coarse (' 2000 cells)
coarse (' 5000 cells)
fine (' 35000 cells)
Flow Solver
I
inviscid flow (2D Euler equations)
I
accurate toluene thermodynamic
properties (Lemmon - Span EOS)
Bounday Conditions:
I total inlet pressure and
temperature
I
static backpressure (β ' 58)
Optimization Strategy
Off-Line Trained Metamodel
Design Of Experiment
Nexus
I
Latin HyperCube allocation
I
correlation based on entropy
formulation
Kriging
I
I
commercial multi-disciplinary and
multi-objective optimisation
framework
several gradient-based and
evolutionary algorithms available
I
constant, linear and quadratic
base functions
I
Gaussian and exponential
interpolating functions
Artificial Neural Network
I
several metamodels available
I
one and two layers
I
GUI and batch-mode
I
five to twenty neurons
I
early-stopping technique
Optimization Strategies Comparison Optimized Results
GA vs MetaModels
8
Test Case
GA
1 ANN 2L10N
3 ANN 2L10N
1 KRG qd exp
1 KRG qd exp
I
coarse grid
I
10 design variables
(throat with 2 d.o.f)
ϕ
1 Metamodel (ϕ) or
3 Metamodels ( ϕM , ϕα , ϕP0loss )
6
5
4
0
200
400
600
800
1000 1200 1400 1600 1800 2000
CFD Calls
KRIGING
ANN
8
8
1 ANN 1L10N
1 ANN 2L5N
1 ANN 2L10N
3 ANN 1L10N
3 ANN 2L5N
3 ANN 2L10N
6
5
4
1 KRG cn exp
1 KRG ln exp
1 KRG qd exp
1 KRG qd gau
3 KRG qd exp
3 KRG qd gau
7
ϕ
7
ϕ
I
7
6
5
0
40
80
120
160
200
CFD Calls
4
0
40
80
120
160
CFD Calls
200
Optimized Results: Fixed Throat
8 design variables
found after 102 CFD
simulations
ϕ = 0.912 + 1.476 + 3.143
= 5.531
2.85
1.00
Original
Optimized
Original
Optimized
Original
Optimized
-102
2.80
0.95
-104
α
P0/Pref
0.90
M
2.75
-106
2.70
0.85
-108
2.65
2.60
1.0
0.5
0.0
-0.5
-1.0
-110
1.0
0.80
0.5
θ/θpitch
0.0
-0.5
θ/θpitch
-1.0
0.75
1.0
0.5
0.0
θ/θpitch
-0.5
-1.0
Optimized Results: Throat with 1 d.o.f. (r )
9 design variables
found after 125 CFD
simulations
ϕ = 0.947 + 1.196 + 1.266
= 3.409
2.85
1.00
Original
Optimized
Original
Optimized
-102
2.80
0.95
-104
α
P0/Pref
0.90
M
2.75
-106
2.70
0.85
-108
2.65
0.80
Original
Optimized
2.60
1.0
0.5
0.0
-0.5
-1.0
-110
1.0
0.5
θ/θpitch
0.0
-0.5
θ/θpitch
-1.0
0.75
1.0
0.5
0.0
θ/θpitch
-0.5
-1.0
Optimized Results: Throat with 2 d.o.f. (r , θ)
10 design variables
found after 278 CFD
simulations
ϕ = 0.944 + 1.043 + 1.271
= 3.258
2.85
1.00
Original
Optimized
Original
Optimized
-102
2.80
0.95
-104
α
P0/Pref
0.90
M
2.75
-106
2.70
0.85
-108
2.65
0.80
Original
Optimized
2.60
1.0
0.5
0.0
-0.5
-1.0
-110
1.0
0.5
θ/θpitch
0.0
-0.5
θ/θpitch
-1.0
0.75
1.0
0.5
0.0
θ/θpitch
-0.5
-1.0
Preliminary Results: Half Number of Blades
10 design variables
found after 205 CFD
simulations
ϕ = 0.961 + 1.217 + 0.934
= 3.112
2.85
1.00
Original
Optimized
Original
Optimized
-102
2.80
0.95
-104
α
P0/Pref
0.90
M
2.75
-106
2.70
0.85
-108
2.65
0.80
Original
Optimized
2.60
1.0
0.5
0.0
-0.5
-1.0
-110
1.0
0.5
θ/θpitch
0.0
-0.5
θ/θpitch
-1.0
0.75
1.0
0.5
0.0
θ/θpitch
-0.5
-1.0
Optimized Results: Summary
Objective Function
Design
Original
Thfix
Th1dof
Th2dof
Th2dof, Z
2
ϕM
2.035
0.912
0.947
0.944
0.961
%
−55.2
−53.5
−53.6
−52.8
%
ϕα
1.761
1.476
1.196
1.043
1.217
%
ϕP0
ϕ
−16.2
−32.1
−40.8
−30.9
3.533
3.143
1.266
1.271
0.934
−11.0
−64.2
−64.0
−73.6
7.329
5.531
3.409
3.258
3.112
Downstream Mixed Flow Parameters
Design
M
Original
Thfix
Th1dof
Th2dof
Th2dof, Z
2.726
2.747
2.781
2.781
2.788
2
%
+0.77
+2.02
+2.02
+2.27
%
loss
α [◦ ]
−106.15
−106.50
−106.50
−106.46
−106.47
%
−0.33
−0.33
−0.29
−0.30
P0
%
0.8234
0.8429 +2.37
0.9369 +13.78
0.9365 +13.74
0.9532 +15.76
−24.5
−53.5
−55.5
−57.5
Conclusions
Achieved so far
I
general blade parameterization based on B-Spline curves
I
comparison of a standard Genetic Algorithm optimization with respect
to off-line trained Metamodels
I
real turbine nozzle shape optimization based on Euler equations
and real gas equation of state
I
comparison of selected geometries with respect to the original design
Future development
I
extension to turbulent flows
I
extension to Multi-Objective Optimization
I
extension to three-dimensional geometries
I
further investigation for more efficient optimization algorithm
(e.g. Hierarchical, Metamodel-Assisted Evolutionary Algorithms)
THANK YOU ALL!

Shape Optimization of an ORC Radial Turbine Nozzle

Transcription

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