Cfd-based Surrogate Modeling Of Liquid Rocket Engine Components Via .

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CFD-BASED SURROGATE MODELING OF LIQUID ROCKET ENGINE COMPONENTSVIA DESIGN SPACE REFINEMENT AND SENSITIVITY ASSESSMENTByYOLANDA MACKA DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYUNIVERSITY OF FLORIDA20071

2007 Yolanda Mack2

To my son, Trevor.3

ACKNOWLEDGMENTSI would like to thank the people in my life who have supported me during my graduatestudies. In particular, I would like to thank my advisor, Dr. Wei Shyy, for his support and forpushing me to strive for excellence. I also thank Dr. Raphael Haftka for his guidance throughthe years on my research. I thank the members of my supervisory committee members, Dr.Corin Segal, Dr. William Lear, Dr. Andreas Haselbacher, and Dr. Don Slinn, for reviewing mywork and offering suggestions during my studies. I thank Dr. Nestor Queipo for inviting me toexplore new methods and new ideas that have been invaluable in my work. I thank Dr.Siddharth Thakur and Dr. Jeffrey Wright for their troubleshooting assistance over the years. Ithank Mr. Kevin Tucker and the others that I have collaborated with at NASA Marshall SpaceFlight Center along with the Institute for Future Space Transport under the ConstellationUniversity Institute Project for providing the motivations for my work as well as financialassistance. I would also like to thank Zonta International and the South East Alliance forGraduate Education and the Professoriate for their financial support and recognition.I thank Antoin Baker for his love and support through any difficulty as we pursued ourgraduate degrees. I would like to thank my father, Calvin Mack, for his gentle guidance, and mymother, Jacqueline Mack, to whom I express my deepest gratitude for her unconditional love andassistance over the years. I thank my sisters, Brandee and Cailah Mack, and other members ofmy family for their undying support and for forever believing in me.4

TABLE OF CONTENTSpageACKNOWLEDGMENTS .4LIST OF TABLES.8LIST OF FIGURES .10ABSTRACT.15CHAPTER1INTRODUCTION .171.1 Thrust Chamber Characteristics .181.1.1 Rocket Engine Cycles.191.1.2 Engine Reliability Issues .201.2 Current and Past Design Practices.211.2.1 Rocket Engine Injector Design.221.2.2 Rocket Engine Turbine Design .241.3 CFD-Based Optimization .251.3.1 Optimization Techniques for Computationally Expensive Simulations .251.3.2 Design Space Refinement in CFD-Based Optimization Using SurrogateModels.291.4 Summary.301.5 Goal and Scope .312OPTIMIZATION FRAMEWORK.352.1 Optimization Using Surrogate Models .362.1.1 Design of Experiments .362.1.2 Surrogate Model Identification and Fitting .382.1.2.1 Polynomial response surface approximation.392.1.2.2 Kriging .412.1.2.3 Radial basis neural networks.442.1.3 Surrogate Model Accuracy Measures .472.1.3.1 Root mean square error .472.1.3.2 Coefficient of multiple determination .482.1.3.3 Prediction error sum of squares.492.2 Dimensionality Reduction Using Global Sensitivity Analysis.492.3 Multi-Objective Optimization Using the Pareto Optimal Front .522.4 Design Space Refinement Techniques .542.4.1 Design Space Reduction for Surrogate Improvement .562.4.2 Smart Point Selection for Second Phase in Design Space Refinement.592.4.3 Merit Functions for Data Selection and Reduction .612.4.4 Method of Alternative Loss Functions .655

3RADIAL TURBINE OPTIMIZATION .753.1 Introduction.763.2 Problem Description .793.2.1 Verification Study .793.2.2 Optimization Procedure.813.3 Results and Discussion .813.3.1 Phase 1: Initial Design of Experiments and Construction of ConstraintSurrogates .813.3.2 Phase 2: Design Space Refinement .843.3.3 Phase 3: Construction of the Pareto Front and Validation of ResponseSurfaces.863.3.4 Phase 4: Global Sensitivity Analysis and Dimensionality Reduction Check.873.4 Merit Function Analysis .883.4.1 Data Point Selection and Analysis .883.4.2 Merit Function Comparison Results.893.5 Conclusion .914MODELING OF INJECTOR FLOWS .1054.1 Literature Review .1064.1.1 Single-Element Injectors .1064.1.2 Multi-Element Injectors.1074.1.3 Combustion Chamber Effects and Considerations.1084.1.4 Review of Select CFD Modeling and Validation Studies .1124.2 Turbulent Combustion Model.1174.2.1 Reacting Flow Equations.1174.2.2 Turbulent Flow Modeling.1204.2.3 Chemical Kinetics .1244.2.4 Generation and Decay of Swirl .1254.3 Simplified Analysis of GO2/GH2 Combusting Flow .1275SURROGATE MODELING OF MIXING DYNAMICS.1375.1 Introduction.1375.2 Bluff Body Flow Analysis .1385.2.1 Geometric Description and Computational Domain .1395.2.2 Objective Functions and Design of Experiments .1405.3 Results and Discussion .1425.3.1 CFD Solution Analysis.1425.3.2 Surrogate Model Results .1435.3.3 Analysis of Extreme Designs .1455.3.4 Design Space Exploration .1475.4 Conclusions.1486INJECTOR FLOW MODELING.1576

6.1 Introduction.1576.2 Experimental Setup.1586.3 Upstream Injector Flow Analysis .1596.3.1 Problem Description.1596.3.2 Results and Discussion .1606.3.3 Conclusion.1626.4 Experimental Results and Analysis .1636.5 Injector Flow Modeling Investigation .1666.5.1 CFD Model Setup.1676.5.2 CFD Results and Experimental Comparison of Heat Flux .1686.5.3 Heat Transfer Characterization.1696.5.4 Species Concentrations.1706.6 Grid Sensitivity Study.1716.7 Conclusion .1737MULTI-ELEMENT INJECTOR FLOW MODELING AND ELEMENT SPACINGEFFECTS.1917.1 Introduction.1917.2 Problem Set-Up .1937.3 Feasible Design Space Study.1957.4 Design Space Refinement.1997.5 Conclusion .2038CONCLUSIONS .2198.1 Radial Turbine Efficiency and Weight Optimization.2208.2 Bluff Body Mixing Dynamics .2218.3 Single-Element Injector Flow Modeling .2228.4 Multi-Element Injector Flow Modeling.2228.5 Future Work.224REFERENCE LIST .225BIOGRAPHICAL SKETCH .2387

LIST OF TABLESTablepage1-1Summary of CFD-based design optimization applications with highlighted surrogatebased optimization techniques. .322-1Summary of DOE and surrogate modeling references. .672-2Design space refinement (DSR) techniques with their applications and key results.683-1Variable names and descriptions. .923-2Response surface fit statistics before (feasible DS) and after (reasonable DS) designspace reduction.933-3Original and final design variable ranges after constraint application and designspace reduction.933-4Baseline and optimum design comparison. .934-1Selected injector experimental studies.1284-2Selected CFD and numerical studies for shear coaxial injectors.1294-3Reduced reaction mechanisms for hydrogen-oxygen combustion. .1295-1Number of grid points used in various grid resolutions.1495-2Data statistics in the grid comparison of the CFD data. .1495-3Comparison of cubic response surface coefficients and response surface statistics.1505-4Comparison of radial-basis neural network parameters and statistics. .1505-5RMS error comparison for response surface and radial basis neural network. .1505-6Total pressure loss coefficient and mixing index for extreme and two regular designsfor multiple grids.1515-7Total pressure loss coefficient and mixing index for designs in the immediatevicinity of Case 1 using Grid 3. .1516-1Flow regime description. .1746-2Effect of grid resolution on wall heat flux and combustion length.1756-3Flow conditions.1758

7-1Flow conditions and baseline combustor geometry for parametric evaluation. .2047-2Kriging PRESSrms error statistics for each design space iteration. .2059

LIST OF FIGURESFigurepage1-1Rocket engine cycles.331-2SSME thrust chamber component diagram .331-3SSME component reliability data .341-4Surrogate-based optimization using multi-fidelity data.342-1Optimization framework flowchart.692-2DOEs for noise-reducing surrogate models.702-3Latin Hypercube Sampling. .702-4Design space windowing .712-5Smart point selection.712-6Depiction of the merit function rank assignment for a given cluster.722-7The effect of varying values of p on the loss function shape.722-8Variation in SSE with p for two different responses .732-9Pareto fronts for RSAs constructed with varying values of p.732-10Absolute percent difference in the area under the Pareto front curves .743-1Mid-height static pressure (psi) contours at 122,000 rpm. .943-2Predicted Meanline and CFD total-to-static efficiencies. .943-3Predicted Meanline and CFD turbine work. .953-4Feasible region and location of three constraints.953-5Constraint surface for Cx2/Utip 0.2.963-6Constraint surfaces for β1 0 and β1 40. .963-7Region of interest in function space.973-8Error between RSA and actual data point.973-9Pareto fronts for p 1 through 5 for second data set.9810

3-10Pareto fronts for p 1 through 5 for third data set .993-11Pareto Front with validation data.993-12Variation in design variables along Pareto Front.1003-13Global sensitivity analysis .1003-14Data points predicted by validated Pareto front compared with the predicted valuesusing six Kriging models based on 20 selected data points.1013-15Absolute error distribution for points along Pareto front.1013-16Average mean error distribution over 100 clusters.1023-17Median mean error over 100 clusters.1033-18Average maximum error distribution over 100 clusters .1033-19Median maximum error over 100 clusters .1044-1Coaxial injector and combustion chamber flow zones. .1304-2Flame from gaseous hydrogen – gaseous oxygen single element shear coaxialinjector. .1304-3Multi-element injectors.1314-4Wall burnout in an uncooled combustion chamber. .1324-5Test case RCM-1 injector. .1324-6Temperature contours for a single element injector. .1334-7CFD heat flux results as compared to RCM-1 experimental test case. .1344-8Multi-element injector simulations .1354-9Fuel rich hydrogen and oxygen reaction with heat release.1365-1Modified FCCD. .1515-2Bluff body geometry .1515-3Computational domain for trapezoidal bluff body.1525-4Computational grid for trapezoidal bluff body. .1525-5Bluff body streamlines and vorticity contours.15211

5-7Comparison of response surface (top row) and radial basis neural network (bottomrow) prediction contours for total pressure loss coefficient.1545-8Comparison of response surface (top row) and radial basis neural network (bottomrow) prediction contours for mixing index (including extreme cases) .1545-9Comparison of response surface (top row) and radial basis neural network (bottomrow) prediction contours for mixing index (excluding extreme cases) .1555-10Variation in objective variables with grid refinement .1555-11Difference in predicted mixing index values from response surface (top row) andradial basis neural network (bottom row) prediction contours constructed with andwithout extreme cases .1565-12Comparison of response surface and radial basis neural network prediction contoursfor mixing index at B* 0 and h* 0 .1566-1Blanching and cracking of combustion chamber wall due to local heating nearinjector elements. .1756-2Hydrogen flow geometry. .1766-3Hydrogen inlet mesh. .1766-4Z-vorticity contours.1776-5Swirl number at each x location.1776-6Average axial velocity u and average tangential velocity vθ with increasing x .1786-7Reynolds number profiles .1786-8Non-dimensional pressure as a function of x.1786-9Hydrogen inlet flow profiles.1796-10Combustion chamber cross-sectional geometry and thermocouple locations. .1796-11Estimated wall heat flux using linear steady-state and unsteady approximations. .1806-121-D axisymmetric assumption for heat conduction through combustion chamber wall .1806-13Estimated wall temperatures using linear and axisymmetric approximations.1816-14Temperature (K) contours for 2-D unsteady heat conduction calculations .1816-15Experimental heat flux values using unsteady assumptions .18212

6-16Computational model for single-element injector flow simulation .1826-17Velocity contours vx(m/s) and streamlines.1836-18Temperature (K) contours.1836-19CFD heat flux values as compared to experimental heat flux approximations. .1836-20Wall heat transfer and eddy conductivity contour plots. .1846-21Streamlines and temperature contours at plane z 0.1846-22Heat flux and y profiles along combustion chamber wall.1856-23Temperature and eddy conductivity profiles at various y locations on plane z 0 .1856-24Mass fraction contours for select species.1866-25Mole fractions for all species along combustion chamber centerline (y 0, z 0) .1876-26Select species mole fraction profiles.1886-27Sample grid and boundary conditions.1896-28Computational grid along symmetric boundary. .1896-29Wall heat flux and y values for select grids .1896-30Comparison of temperature (K) contours for grids with 23,907, 31,184, 72,239, and103,628 points, top to bottom, respectively.1907-1Injector element subsection.2057-2Design points selected for design space sensitivity study .2067-3Effect of hydrogen mass flow rate on objectives.2067-4Oxygen iso-surfaces and hydrogen contours. .2077-5Hydrogen contours and streamlines.2077-6Maximum heat flux for a changing radial distance r*.2087-7Heat flux distribution. .2087-8Maximum heat flux as a function of aspect ratio.2097-9Design points in function and design space.2097-10Merit function (MF2) contours for .21013

7-11Kriging surrogates based on initial 16 design points. .2107-12Kriging surrogates and merit function contours for 12 design points in Pattern 1 .2117-13Kriging surrogates and merit function contours for 12 design points in Pattern 2. .2127-14Kriging fits for all 15 design points from Pattern 1 .2137-15Kriging fits for all 12 design points from Pattern 2. .2137-16Pareto front based on original 16 data points (dotted line) and with newly addedpoints (solid line). .2147-17Approximate division in the design space between the two patterns based on A) peakheat flux .2157-18Variation in flow streamlines and hydrogen contours in design space.2157-19Location of best trad

1 cfd-based surrogate modeling of liquid rocket engine components via design space refinement and sensitivity assessment by yolanda mack a dissertation presented to the graduate school

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