Software-Engineering und Optimierungsanwendungen in der Thermodynamik

Software-Engineering und Optimierungsanwendungen in der Thermodynamik Optimierung 3 Optimization Frameworks Prof. Dr. Rolf Dornberger Optimization: 3 Optimization Frameworks 30.04.2006

3 Optimization Frameworks 3 Optimization Frameworks 3. Example: Multidisciplinary Turbomachinery Design Optimization 3.2 Optimization Framework 3.3 Example: 30.04.2006 2

3. Example: Multidisciplinary Turbomachinery Design Optimization aerodynamics: efficiency, losses,... structural dynamics: stresses, frequencies,... manufacturing aspects: mechanical integrity,... economic factors: manufacturing cost, life cycle cost,... thermodynamics: combustion, heat transfer,... governmental regulations: emission, noise,... Various competitive disciplines are involved in turbomachinery design. The challenge is to design the best turbomachinery (compromise) in all disciplines, but not necessarily the best in each single discipline. Many different optimization algorithms and programs are available. Good algorithms for multidisciplinary design optimization (MDO) very limited. 30.04.2006 3

3. Example: Multidisciplinary Turbomachinery Design Optimization Optimizer Evaluator Blade Generator Grid Generator Controller Data Collection Postprocessing CFD-Solvers Computational expensive solvers (CFD: several hours) Very complex automation process Fine-tuning of an existing design Mostly one objective (efficiency) Many design constraints 30.04.2006 4

3.2 Optimization Framework Optimizer Parameterization Evaluator Controller Preevaluation Solvers Multi-Disciplinary and Multi-Objective Optimization requires: Reasonable optimization strategies Special optimization and evaluation methods Sophisticated optimization environment and parallelization 30.04.2006 5

3.2 Optimization Framework o O: Optimizer e E: Evaluater r P:Parameterization y x z R: Preevaluation p s S: Solver Optimizer O: o = ( x, x2, K, x o j = O( o j, o j Parameterization P: p j = P ( o j, y ) Solver S: s j = S( p j ) Preevaluation R: rj = R ( s j, z ) Evaluator E: e j = E( r j ) n x ) 2, K, o j =, e j, e initialparameter set,and j 2, K, e ) j 2 30.04.2006 6

3.2 Optimization Framework: Various Optimizer and Evaluator ) ) Assessment Assessment Schemes: Schemes: weighted weighted sum sum Pareto Pareto assessment assessment...... 2) 2) Constraint Constraint Treatment: Treatment: penalty penalty functions functions dual dual Lagrange Lagrange problem problem...... o O: Optimizer e x E: Evaluater r ) ) Search Search Methods: Methods: Incremental Incremental Search Search Monte Monte Carlo Carlo...... 2) 2) Analytic Analytic Methods: Methods: Quasi-Newton Quasi-Newton (BFGS, (BFGS, DFP, DFP, SD) SD) Least-Square Least-Square Minimization Minimization (LM, (LM, GN) GN) Sequential Sequential Quadratic Quadratic Programming Programming Simplex Simplex...... 3) 3) Stochastic Stochastic Methods: Methods: Evolution Evolution Strategy Strategy Genetic Genetic Algorithm Algorithm Simulated Simulated Annealing Annealing...... 30.04.2006 7

3.2 Optimization Framework: Various Solvers Mathematical models Turbomachinery analysis (e.g. mean stage model) p Flow path design S: Solver CFD analysis (e.g. Stage3D) s FE structural analysis 30.04.2006 8

3.2 Optimization Framework: Parameterization for 3D-CFD Optimization Design Variables: engineering parameters o P:Parameterization p CFD input y profile generation profile stacking blade generation meshing 30.04.2006 9

3.2 Optimization Framework: Preevaluation for 3D Optimization z r R: Preevaluation s postprocessing CFD and thermo MDO postprocessing structure and manufacturing F a $$$ postprocessing costs and regulations F y F x 30.04.2006 0

3.2 Optimization Framework: Response Surfaces and Neural Networks p Train Response Surface p Neural Network S: Solver Response Surface s s Response Surface Use Response Surface as Solver S: Solver p Response Surface Polynomial Approximations s 30.04.2006

3.2 Optimization Framework User: engineering work, supervises process,... Design Parameters clever MOO algorithms implementation for automated use Solver Solver 2 simulation: software or experiments Solver 3 MOO software tool Response 30.04.2006 2

3.3 Multi-Objective Optimization in Preliminary Turbomachinery Design Thermodynamic Turbine Model: shape => efficiency efficiency Mechanical Integrity: => stress, frequency (=> life time) feasible design space Cost Analysis: => first costs (=> runtime costs) cost Pareto-Optimization: efficiency/cost/stress Pareto-front with Pareto-optimal solutions 30.04.2006 3

3.3 Multi-Objective Optimization in Preliminary Turbomachinery Design mean stage inlet p a outlet p e turbine axis Goal: maximize efficiency, minimize cost, minimize material stress Design Variables: Diameters, stage loading, chord lengths,... 30.04.2006 4

3.3 Multi-Objective Optimization in Preliminary Turbomachinery Design ) ) Assessment Assessment Schemes: Schemes: weighted weighted sum sum Pareto Pareto assessment assessment...... 2) 2) Constraint Constraint Treatment: Treatment: penalty penalty functions functions dual dual Lagrange Lagrange problem problem...... penalty P i 000 hard lower soft upper soft hard constraint i 30.04.2006 5

3.3 Multi-Objective Optimization in Preliminary Turbomachinery Design p in thermodynamic steam turbine model p out Compute all Pareto-optimal solutions Choose the appropriate designs Increase efficiency by 2-5% and/or save manufacturing costs by 40% efficient, but very expensive turbines efficiency Pareto-optimal solutions efficiency less efficient, but cheaper turbines structural loading /cost /cost 30.04.2006 6

3.4 Response Surfaces in Preliminary Turbomachinery Design y( x, x, L, x ) = c 0 + i i p ii i i p c c x i + + L+ i... i i i. L i p j= 2 2 2 2 n x x i i 2 c p n i n x j x 2 w3 w4 x 4 x w2 w u b synapse summation y g(u) bias Polynomial Approximations Neural Networks 30.04.2006 7

3.4 Response Surfaces in Preliminary Turbomachinery Design mean stage inlet p a outlet p e turbine axis 30.04.2006 8

3.5 Example: Optimization in 3D Turbomachinery Design Goal: Minimize entropy production (=> maximize efficiency) Design Variables: Bend blades in axial and circumferential direction (lean and sweep) R otor S tator Axial direction 30.04.2006 9

3.5 Example: Minimization of Entropy Rise over Stator and Rotor optimization parameters best fitness fitness 30.04.2006 20

3.5 Example: Minimization of Entropy Rise over Stator and Rotor sweep flow lean Benefits of automated optimization software: lean sweep Stator Rotor Automation runs optimization process 24h a day Even computational expensive optimizations (e.g. 3D CFD) become very attractive entropy production Stator Rotor Axial direction entropy production over optimization steps (20 steps in 6h) 30.04.2006 2 optimization step

3.6 Example: Brick Tower Develop new better optimization methods for new (exotic) applications σ 6 ( ) σ max i i 4 σ 5 σ 4 σ 3 2 3 Cross-sections of the bricks for 4 special solutions: 2 3 4 Fundamental frequency σ 2 σ highest stress lowest stress highest frequency lowest frequency 30.04.2006 22

3.7 Example: Automated MOO for Burner Optimization m air pulsation emission (NOx) m fuel m fuel = m = i i const NOx Fuel flow distribution in burner optimized for minimizing simultaneously pulsation and emissions (NOx) atmospheric burner test rig Dättwil (2000) Convergence towards Pareto-optimal designs pulsation 30.04.2006 23

3.7 Example: Automated MOO for Burner Optimization NOx minimal pulsation increased lifetime: 70% pulsation reduction initial fuel flow distribution reduced emissions: 25% NOx reduction multi-objective: simultaneously NOx & pulsation minimized minimized NOx & pulsation minimal NOx Pareto-optimal solutions Pareto-optimal solutions cover all possible design alternatives pulsation 30.04.2006 24