Surrogate-based Analysis and Optimization

https://eprints.soton.ac.uk/65935/01/Forr_09.pdf

Recent advances in surrogate-based optimization

Recent progress in flapping wing aerodynamics and aeroelasticity

The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

http://www2.mae.ufl.edu/haftka/eoed/protected/ASME04.kriging.pdf

Use of Kriging Models to Approximate Deterministic Computer Models

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs...

https://epubs.siam.org/doi/pdf/10.1137/16M1082469

Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization

Computational fluid dynamics (CFD) has the potential to improve the historical rocket injector design process by evaluating the sensitivity of performance and injector-driven thermal environments to the details of the injector geometry and key operational parameters. Methodical verification and validation efforts on a range of coaxial injector elements have shown the current production CFD capability must be improved in order to quantitatively impact the injector design process. This paper documents the status of a focused effort to compare and understand the predictive capabilities and computational requirements of a range of CFD methodologies on a set of single element injector model problems. The steady Reynolds-Average Navier-Stokes (RANS), unsteady Reynolds-Average Navier-Stokes (URANS) and three different approaches using the Large Eddy Simulation (LES) technique were used to simulate the initial model problem, a single element coaxial injector using gaseous oxygen and gaseous hydrogen propellants. While one high-fidelity LES result matches the experimental combustion chamber wall heat flux very well, there is no monotonic convergence to the data with increasing computational tool fidelity. Systematic evaluation of key flow field regions such as the flame zone, the head end recirculation zone and the downstream near wall zone has shed significant, though as of yet incomplete, light on the complex, underlying causes for the performance level of each technique. 1 Aerospace Engineer and Combustion CFD Team Leader, MS ER42, NASA MSFC, AL 35812, Senior Member, AIAA. 2 Professor and Director, Computational Combustion Laboratory, School of Aerospace Engineering, 270 Ferst Dr., Atlanta, GA 30332, Associate Fellow, AIAA. 3 Reilly Professor of Engineering, School of Mechanical Engineering, 585 Purdue Mall, West Lafayette, IN 47907, Fellow, AIAA. 4 Principal Member of Technical Staff, Combustion Research Facility, 7011 East Avenue, MS9051, Livermore, CA 94550, Associate Fellow, AIAA. 5 J. L. and G. H. McCain Endowed Chair, Mechanical Engineering, 104 Research Building East, University Park, PA 16802, Fellow, AIAA. American Institute of Aeronautics and Astronautics 1

/pdf/validation-of-high-fidelity-cfd-simulations-for-rocket-24gmou97m3.pdf

Validation of High-Fidelity CFD Simulations for Rocket Injector Design

Theresponsesurfacemethodologyforrocketengineinjectordesignoptimizationforwhichonlymodestamounts of data may exist is examined. Two main aspects are emphasized: relative performance of quadratic and cubic polynomial response surfaces and enhancement of the e delity of the response surface via neural networks. A data set of 45 design points from a semi-empirical model for a shear coaxial injector element using gaseous oxygen and gaseous hydrogen propellants is used to formulate response surfaces using quadratic and cubic polynomials. This original data set is also employed to train a two-layered radial basis neural network (RBNN). The trained network is then used to generate additional data to augment the original information available to characterize the design space. Quadratic and cubic polynomials are again used to generate response surfaces for this RBNN-enhanced data set. The response surfaces resulting from both the original and RBNN-enhanced data sets are compared for accuracy. Whereas the cubic e t is superior to the quadratic e t for each data set, the RBNN-enhanced data set is capable of improving the accuracy of the response surface if noticeable errors from polynomial curve e ts are encountered. Furthermore, the RBNN-enhanced data set yields more consistent selections of optimal designs between cubic and quadratic polynomials. The techniques developed can be directly applied to injectordesign and optimization for rocket propulsion.

Response Surface and Neural Network Techniques for Rocket Engine Injector Optimization

A computational-fluid-dynamics-based design optimization approach, utilizing the response surface method, has been proposed for a single-element rocket injector. The overall goal of the effort is to demonstrate the integration of a set of computational and optimization tools to enable the injector designer to objectively determine the trades between performance and life during the design cycle. Using design of experiment techniques, 54 cases are selected, and computational solutions based on the Navier‐Stokes equations, finite rate chemistry, and the k‐e turbulence closure are obtained. The response surface methodology is employed as the optimization tool. Four independent design variables are selected, namely, H2 flow angle, H2 and O2 flow areas with fixed flow rates, and O2 posttip thickness. Design optimization is guided by four design objectives. The maximum temperature on the injector element oxidizer posttip, the maximum temperature on the injector face, and a combustion chamber wall temperature are chosen as life indicators. The length of the combustion zone is selected as an indicator of mixing and performance. In the context of this effort, the design optimization tools performed efficiently and reliably. In addition to establishing optimum designs by varying emphasis on the individual objectives, better insight into the interplay between design variables and their impact on the design objectives is gained. The need to include environmental design objectives early in the design phase is clearly established.

Computational-fluid-dynamics-based design optimization for single-element rocket injector

This paper puts forth the case for the need for improved injector design tools to meet NASA s Vision for Space Exploration goals. Requirements for this improved tool are outlined and discussed. The potential for Computational Fluid Dynamics (CFD) to meet these requirements is noted along with its current shortcomings, especially relative to demonstrated solution accuracy. The concept of verification and validation is introduced as the primary process for building and quantifying the confidence necessary for CFD to be useful as an injector design tool. The verification and validation process is considered in the context of the Marshall Space Flight Center (MSFC) Combustion Devices CFD Simulation Capability Roadmap via the Simulation Readiness Level (SRL) concept. The portion of the validation process which demonstrates the ability of a CFD code to simulate heat fluxes to a rocket engine combustor wall is the focus of the current effort. The FDNS and Loci-CHEM codes are used to simulate a shear coaxial single element G02/GH2 injector experiment. The experiment was conducted a t a chamber pressure of 750 psia using hot propellants from preburners. A measured wall temperature profile is used as a boundary condition to facilitate the calculations. Converged solutions, obtained from both codes by using wall functions with the K-E turbulence model and integrating to the wall using Mentor s baseline turbulence model, are compared to the experimental data. The initial solutions from both codes revealed significant issues with the wall function implementation associated with the recirculation zone between the shear coaxial jet and the chamber wall. The FDNS solution with a corrected implementation shows marked improvement in overall character and level of comparison to the data. With the FDNS code, integrating to the wall with Mentor s baseline turbulence model actually produce a degraded solution when compared to the wall function solution with the K--E model. The Loci-CHEM solution, produced by integrating to the wall with Mentor s baseline turbulence model, matches both the heat flux rise rate in the near injector region and the peak heat flux level very well. However, it moderately over predicts the heat fluxes downstream of the reattachment point. The Loci-CHEM solution achieved by integrating to the wall with Mentor s baseline turbulence model was clearly superior to the other solutions produced in this effort.

P. Kevin Tucker

Papers

Surrogate-based Analysis and Optimization

Validation of High-Fidelity CFD Simulations for Rocket Injector Design

Response Surface and Neural Network Techniques for Rocket Engine Injector Optimization

Computational-fluid-dynamics-based design optimization for single-element rocket injector

CFD Code Validation of Wall Heat Fluxes for a G02/GH2 Single Element Combustor