Surrogate-based Analysis and Optimization

A new correlation-based transition model has been developed, which is built strictly on local variables. As a result, the transition model is compatible with modern computational fluid dynamics techniques such as unstructured grids and massively parallel execution. The model is based on two transport equations, one for intermittency and one for a transition onset criterion in terms of momentum-thickness Reynolds number. A number of validation papers have been published on the basic formulation of the model. However, until now the full model correlations have not been published. The main goal of the present paper is to publish the full model and release it to the research community so that it can continue to be further validated and possibly extended or improved. Included in this paper are a number of test cases that can be used to validate the implementation of the model in a given computational fluid dynamics code. The authors believe that the current formulation is a significant step forward in engineering transition modeling, as it allows the combination of transition correlations with general-purpose computational fluid dynamics codes. There is a strong potential that the model will allow the first-order effects of transition to be included in everyday industrial computational fluid dynamics simulations.

Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes

The custom in surrogate-based modeling of complex engineering problems is to fit one or more surrogate models and select the one surrogate model that performs best. In this paper, we extend the utility of an ensemble of surrogates to (1) identify regions of possible high errors at locations where predictions of surrogates widely differ, and (2) provide a more robust approximation approach. We explore the possibility of using the best surrogate or a weighted average surrogate model instead of individual surrogate models. The weights associated with each surrogate model are determined based on the errors in surrogates. We demonstrate the advantages of an ensemble of surrogates using analytical problems and one engineering problem. We show that for a single problem the choice of test surrogate can depend on the design of experiments.

Ensemble of surrogates

A model for the prediction of laminar-turbulent transition processes was formulated. It is based on the LCTM (‘Local Correlation-based Transition Modelling’) concept, where experimental correlations are being integrated into standard convection-diffusion transport equations using local variables. The starting point for the model was the γ-Re
 θ
 model already widely used in aerodynamics and turbomachinery CFD applications. Some of the deficiencies of the γ-Re
 θ
 model, like the lack of Galilean invariance were removed. Furthermore, the Re
 θ
 equation was avoided and the correlations for transition onset prediction have been significantly simplified. The model has been calibrated against a wide range of Falkner-Skan flows and has been applied to a variety of test cases.

A One-Equation Local Correlation-Based Transition Model

This document is the User''s Manual for the CFL3D computer code, a thin-layer Reynolds-averaged Navier-Stokes flow solver for structured multiple-zone grids. Descriptions of the code''s input parameters, non-dimensionalizations, file formats, boundary conditions, and equations are included. Sample 2-D and 3-D test cases are also described, and many helpful hints for using the code are provided.

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CFL3D User''s Manual (Version 5.0)

There is growing interest to adopt supersonic turbines for rocket propulsion. However, this technology has not been actively investigated in the United States for the last three decades. To aid design improvement, a global optimization framework combining the radial-basis neural network (NN) and the polynomial response surface (RS) method is constructed for shape optimization of a two-stage supersonic turbine, involving O(10) design variables. The design of the experiment approach is adopted to reduce the data size needed by the optimization task. The combined NN and RS techniques are employed. A major merit of the RS approach is that it enables one to revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a predefined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials consideration.

Shape optimization of supersonic turbines using global approximation methods

A three-dimensional Navier-Stokes analysis of heat transfer and aerodynamic performance is presented for a low-speed linear turbine cascade. The numerical approach used in this analysis consists of an alternate-direction, implicit, approximate-factorization, time-marching technique. An objective of this investigation has been to establish the computational grid density requirements necessary to predict blade surface and endwall heat transfer accurately, as well as the exit plane aerodynamic total pressure loss and flow angle distributions

Navier–Stokes Analysis of Turbine Blade Heat Transfer and Performance

Turbine performance directly affects engine specific impulse, thrust-to-weight ratio, and cost in a rocket propulsion system. A global optimization framework combining the radial basis neural network (RBNN) and the polynomial-based response surface method (RSM) is constructed for shape optimization of a supersonic turbine. Based on the optimized preliminary design, shape optimization is performed for the first vane and blade of a 2-stage supersonic turbine, involving O(10) design variables. The design of experiment approach is adopted to reduce the data size needed by the optimization task. It is demonstrated that a major merit of the global optimization approach is that it enables one to adaptively revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a pre-defined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials considerations.

/pdf/shape-optimization-of-supersonic-turbines-using-response-8p9z7tpk9j.pdf

Shape Optimization of Supersonic Turbines Using Response Surface and Neural Network Methods

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/77366/AIAA-2007-5551-433.pdf?sequence=1

Daniel J. Dorney

Papers

Shape optimization of supersonic turbines using global approximation methods

Navier–Stokes Analysis of Turbine Blade Heat Transfer and Performance

Shape Optimization of Supersonic Turbines Using Response Surface and Neural Network Methods

Improving the hydrodynamic performance of diffuser vanes via shape optimization

A study of turbine performance increases through airfoil clocking