# Optimizing Gas Turbine Performance Using the Surrogate Management Framework and High-Fidelity Flow Modeling

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## Abstract

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## 1. Introduction

## 2. High-Fidelity Modeling of Compressible Flow in a Gas Turbine Stage

#### 2.1. Moving-Domain Finite Element Formulation of Compressible Flows

#### 2.2. Model of the Turbine Stage

## 3. Design Optimization Methodology

#### 3.1. Surrogate Management Framework

#### 3.2. SMF Modifications for VSGTE Optimization

#### 3.3. Design and Analysis Spaces

#### 3.4. Evaluation of Analysis-Space Parameters

#### 3.5. Objective Function and Constraints

## 4. Optimization Results

#### 4.1. Convergence of the SMF Algorithm

#### 4.2. Flow Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Stator and rotor airfoil profiles at different blade heights and their baseline (0${}^{\xb0}$) and articulated positions. Baseline positions are colored in black and articulated positions are colored in gray. The articulation angle is shown by the red arc and highlighted using the red arrow. A positive angle corresponds to a counterclockwise articulation.

**Figure 4.**Scatter plot of the 50 cases selected by the LHS approach that make up the initial data set. Unfeasible designs are colored in red.

**Figure 5.**Scatter plot of the cases ranked by the objective function value. Cases in the initial data set are denoted by circles while the remaining cases are denoted by squares. The color fill of the circles and squares corresponds to the value of the objective function.

**Figure 6.**Scatter plot of the cases ranked by the shaft torque value with rank 1 being the highest. Cases in the initial data set are denoted by circles while the remaining cases are denoted by squares. The color fill of the circles and squares corresponds to the value of the torque. The baseline design is denoted using a triangle with the torque value of ${\tau}_{ref}=151.2$ N·m.

**Figure 7.**Scatter plot of the cases ranked by the adiabatic efficiency value with rank 1 being the highest. Cases in the initial data set are denoted by circles while the remaining cases are denoted by squares. The color fill of the circles and squares corresponds to the value of the adiabatic efficiency. The baseline design is denoted using a triangle with the efficiency value of ${\eta}_{ref}=84.9$%.

**Figure 8.**Scatter plot of efficiency vs. torque for all the cases showing the Pareto optimal frontier.

**Figure 9.**Flow field comparison using streamline and Q-criterion plots between the optimal and baseline cases. The stator plots use absolute velocity while the rotor plots use relative velocity.

**Figure 10.**Flow field comparison using streamline and Q-criterion plots between five different cases taken from the design space. The stator plots use absolute velocity while the rotor plots use relative velocity.

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**MDPI and ACS Style**

Kozak, N.; Rajanna, M.R.; Wu, M.C.H.; Murugan, M.; Bravo, L.; Ghoshal, A.; Hsu, M.-C.; Bazilevs, Y. Optimizing Gas Turbine Performance Using the Surrogate Management Framework and High-Fidelity Flow Modeling. *Energies* **2020**, *13*, 4283.
https://doi.org/10.3390/en13174283

**AMA Style**

Kozak N, Rajanna MR, Wu MCH, Murugan M, Bravo L, Ghoshal A, Hsu M-C, Bazilevs Y. Optimizing Gas Turbine Performance Using the Surrogate Management Framework and High-Fidelity Flow Modeling. *Energies*. 2020; 13(17):4283.
https://doi.org/10.3390/en13174283

**Chicago/Turabian Style**

Kozak, Nikita, Manoj R. Rajanna, Michael C. H. Wu, Muthuvel Murugan, Luis Bravo, Anindya Ghoshal, Ming-Chen Hsu, and Yuri Bazilevs. 2020. "Optimizing Gas Turbine Performance Using the Surrogate Management Framework and High-Fidelity Flow Modeling" *Energies* 13, no. 17: 4283.
https://doi.org/10.3390/en13174283