1. MULTI-DISCIPLINARY ANALYSIS, INVERSE DESIGN AND OPTIMIZATION George S. Dulikravich Professor and Director, MAIDO Institute Department of Mechanical and Aerospace Engineering The University of Texas at Arlington dulikra@mae.uta.edu ( Thanks to my students, postdocs and visiting scientists)

2. Professor Dulikravich has authored and co-authored over 300 technical publications in diverse fields involving computational and analytical fluid mechanics, subsonic, transonic and hypersonic aerodynamics, theoretical and computational electro-magneto-hydrodynamics, conjugate heat transfer including solidification, computational cryobiology, acceleration of iterative algorithms, computational grid generation, multi-disciplinary aero-thermo-structural inverse problems, design and constrained optimization in turbomachinery, and multi- objective optimization of chemical compositions of alloys. He is the founder and Editor-in-Chief of the international journal on Inverse Problems in Engineering and an Associate Editor of three additional journals. He is also the founder, chairman and editor of the sequence of International Conferences on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES). Professor Dulikravich is a Fellow of the American Society of Mechanical Engineers, an Associate Fellow of the American Institute of Aeronautics and Astronautics, and a member of the American Academy of Mechanics. Professor Dulikravich is also the founder and Director of Multidisciplinary Analysis, Inverse Design and Optimization (MAIDO) Institute and Aerospace Program Graduate Student Advisor at UTA.

4. A sketch of my current research interests Geometry Parameterization Computational Grid Generation Flow-Field Analysis Thermal Field Analysis Stress-Deformation Field Analysis Electric Field Analysis Magnetic Field Analysis Conjugate (Concurrent) Analysis Multi-Disciplinary Inverse Problems Multi-Disciplinary Optimization & Design

5. Multi-Disciplinary Analysis, Inverse Design and Optimization (MAIDO) Aerodynamics Heat Conduction Structures Conjugate Heat Transfer Aero- Elasticity Thermo- Elasticity Aero-Thermo-Elasticity T Q T T Q U U? P P

6. Parallel Computer of a “Beowulf” type Based on commodity hardware and public domain software 16 dual Pentium II 400 MHz and 11 dual Pentium 500 MHz based PC’s Total of 54 processors and 10.75 GB of main memory 100 Megabits/second switched Ethernet using MPI and Linux Compressible NSE solved at 1.55 Gflop/sec with a LU SSOR solver on a 100x100x100 structured grid on 32 processors (like a Cray- C90) GA optimization of a MHD diffuser completed in 30 hours. Same problem would take 14 days on a single CPU

7. Conjugate Simulation of Internally Cooled Gas Turbine Blade Static temperature contours and grid in the leading edge region

8. Head Cooling Simulation Animated view of outer surface mesh

9. Electro-Magneto-Fluid-Dynamics (EMFD): active control of large-scale single crystal growth, enhanced performance of compact heat exchangers, control of spray atomization in combustion processes, reduction of drag of marine vehicles, flow control in hypersonics, fast response shock absorbers, hydraulic transmission in automotive industry, free-flow electrophoretic separation in pharmaceutics, large scale liquid based food processing, biological transport under the influence of EM fields, fuel cells and batteries, electro-polymers and other smart materials, etc.

10. EMHD Conservation of Linear Momentum

11. EMHD Conservation of Energy Conservation of Mass

12. EMHD Maxwell’s Equations

14. Multi-Disciplinary Analysis (Well-defined or Direct Problems) Multi-disciplinary engineering field problems are fully defined and can be solved when the following set of information is given: 1.governing partial differential or integral equation(s), 2.shape(s) and size(s) of the domain(s), 3.boundary and initial conditions, 4.material properties of the media contained in the field, and 5.internal sources and external forces or inputs.

15. Multi-Disciplinary Inverse Problems (Ill-posed or ill-defined) If any of this information is unknown or unavailable, the field problem becomes an indirect (or inverse) problem and is generally considered to be ill posed and unsolvable. Specifically, inverse problems can be classified as: 1. Shape determination inverse problems, 2. Boundary/initial value determination inverse problems, 3. Sources and forces determination inverse problems, 4. Material properties determination inverse problems, and 5. Governing equation(s) determination inverse problems. The inverse problems are solvable if additional information is provided and if appropriate numerical algorithms are used.

16. Inverse prediction of temperature-dependent thermal conductivity of an arbitrarily shaped object

17. Inverse determination of boundary conditions

18. Inverse Determination of Convective Boundary Condition on a Rectangular Plate

24. Hybrid Constrained Optimization Minimize one or more objective functions of a set of design variables subject to a set of equality and inequality constraint functions. ALGORITHMS Gradient Search (DFP, SQP, P&D) Genetic Algorithm(s) Differential Evolution Simulated Annealing Simplex (Nelder-Mead) Stochastic Self-adaptive Response Surface (IOSO)

26. DETERMINATION OF UNSTEADY CONTAINER TEMPERATURES DURING FREEZING OF THREE- DIMENSIONAL ORGANS WITH CONSTRAINED THERMAL STRESSES Use finite element method (FEM) model of transient heat conduction and thermal stress analysis together with a Genetic Algorithm (GA) to determine the time varying temperature distribution that will cool the organ at the maximum cooling rate allowed without exceeding allowed stresses

27. Diffuser flow separation with no applied magnetic field Significantly reduced diffuser flow separation with optimized distribution of magnets located in the geometric expansion only

32. Two-stage axial gas turbine entropy fields and total efficiencies before and after optimization of hub and shroud shapes using a hybrid constrained optimizer

33. Results Comparison of 3 optimized airfoil cascades against the original VKI airfoil cascade.

34. Multi-objective Constrained Design Optimization Comparison of total pressure loss versus total lift for optimized airfoil cascades and the inversely designed original VKI airfoil cascade.

35. Internally cooled blade example and its triangular surface mesh

36. Passage shape in x-z plane for initial design and for IOSO optimized design

37. Principal stress contours for initial design and for IOSO optimized design of cooling passage

38. Temperature contours on pressure side for initial design and for IOSO optimized design

39. Temperature contours on suction side for initial design and for IOSO optimized design

40. Objective function convergence history and Temperature constraint function convergence history

41. Extremum search dynamic

51. Optimization of chemical composition of an alloy Purpose: To determine optimal properties of an alloy having different chemical compositions by using an existing database Problem features: variable parameters: chemical composition of an alloy C, S, P, Cr, Ni, Mn, Si, Cu, Mo, Pb, Co, Cb, W, Sn, Al, Zn, Ti ( 8…17 variables). criterion: Stress (PSI – maximize); Operating temperature (T – maximize); Time to "survive" until rupture (Hours – maximize). mathematical model: have none; use an existing database

52. Optimization of chemical composition of an alloy (8…17 chemical components in a steel alloy ) C, S, P, Cr, Ni, Mn, Si, Cu, Mo, Pb, Co, Cb, W, Sn, Al, Zn, Ti

53. Optimization of chemical composition of an alloy Problem No. 1.

54. Optimization of chemical composition of an alloy Problem No. 1. If a researcher knows exactly in what temperature span the alloy being designed will work, it is more efficient that the problem of two-criteria optimization be solved with additional constraint for the third efficiency parameter. This figure presents interdependence of the optimization criteria built on the obtained set of Pareto optimal solutions. Analysis of this picture shows that the increase of temperature, for instance, leads to the decrease of compromise possibilities between PSI and HOURS.

55. Optimization of chemical composition of an alloy Problem No. 2-6. This slide presents results of solution of five additional two-criteria problems in which PSI and HOURS were regarded as criteria, and different constraints were placed on temperature: Problem 2. -, number of Pareto optimal solutions is 20. Problem 3. -, number of Pareto optimal solutions is 20. Problem 4. -, number of Pareto optimal solutions is 20. Problem 5. -, number of Pareto optimal solutions is 15. Problem 6. -, number of Pareto optimal solutions is 10. Maximum achievable values of PSI and HOURS, and possibilities of compromise between these parameters largely depends on temperature. For instance, the increase of minimum temperature from 1600 to 1900 degrees leads to the decrease of attainable PSI by more than twice. At the same time, limiting value of HOURS will not alter with the change of temperature. Further increase of temperature leads to further decrease of other parameters, by both limiting value and compromise possibility. The decrease of the number of optimization criteria (transition from three- to two-criteria problem with constraints) leads to the decrease of the number of additional experiments, at the expense of both decreasing the number of Pareto optimal points and decreasing the variation range of chemical composition of alloys.

56. Optimization of chemical composition of an alloy Problem No. 1. Larsen-Mueller diagram for 3-criteria optimization results. Larsen-Mueller diagrams for five 2-criteria optimization problems results

57. Inverse problem of finding chemical composition of an alloy with specified properties (Problem # 8 ) Purpose: To define chemical composition of an alloy for required properties of material by using an existing database Problem features: variable parameters: chemical composition of the alloy C, S, P, Cr, Ni, Mn, Si, Mo, Co, Cb, W, Sn, Zn, Ti ( 14 variables). criterion: (multi- objective statement – 10 simultaneous objectives) Stress (PSI) (PSI-PSI req.)**2 –> minimize Operating temperature (T) (T-T req.)**2 –> minimize Time to "survive" until rupture (Hours) (Hours-Hours req.)**2 –> minimize Cr -> minimize; Ni->minimize; Mo->minimize; Co->minimize; Cb >minimize; W >minimize; Sn >minimize; Zn >minimize; Ti >minimize; constraints: none mathematical model: have none; use an existing experimental database

58. Comparative Analysis of Inverse Problem Formulations for Determining Chemical Composition of an Alloy Eps str Eps t Eps h Eps sum N Const N Obj N Point (Poreto) N Calls Score Prob.1.408E-19.356E-06.536E-06.297E-0603504170.590 Prob.2.269E-08.267E-07.172E-08.104E-073117030.246 Prob.3.897E-10.143E-09.134E-12.777E-1033504450.817 Prob.4.434E-13.289E-12.244E-18.111E-1231110200.246 Prob.5.413E-13.139E-05.549E-06.646E-062116010.239 Prob.6.954E-06.576E-15.980E-04.646E-062117740.180 Prob.7.408E-10.515E-10.299E-12.309E-102117760.256 Prob.8.714E-09.928E-09.127E-10.552E-09310468341.000

59. My current management views