In this project, we present the optimization process for improving the performance of a combustion chamber using the Design of Experiment (DOE) in ANSYS software.

We intend to optimize the design of a combustion chamber. Therefore, we defined 8 input parameters, including the cone angular velocity, outer diameter, cone height, cone length, air inlet diameter, fuel inlet diameter, air inlet offset, and fuel inlet offset. Then, we defined the outlet temperature, CO2 mass fraction, CO mass fraction, average temperature, total heat generation, and chamber heat flux as the target output parameters.

We used the Design Exploration tool to perform the optimization process.

First, we start with the Design of Experiment (DOE). We generated the design points using the Central Composite Design (CCD). According to the maximum and minimum ranges for all three input parameters, design points are generated.

Then, we continue with the Response Surface Methodology (RSM). We estimated the output parameter values ​​based on the Genetic Aggregation type.

Combustion Chamber Performance Optimization using Design of Experiments (DOE)

What is Design of Experiments (DOE)?

Design of Experiments (DOE), also known as Designed Experiments or Experimental Design, is a systematic methodology conducted under controlled conditions to discover unknown effects, test hypotheses, or demonstrate known phenomena. It establishes relationships between input factors affecting a process and the resulting output, enabling optimization of process inputs to achieve desired outcomes.

Sir Ronald A. Fisher pioneered this method in the 1920s and 1930s. DOE is a robust data collection and analysis tool applicable across various experimental scenarios. It enables simultaneous manipulation of multiple input factors to determine their effects on desired outputs (responses). By varying multiple inputs concurrently, DOE identifies critical interactions that traditional “one factor at a time” (OFAT) approaches might overlook. Experiments can examine all possible combinations (full factorial) or selected subsets (fractional factorial).

Well-designed experiments yield substantial information about response variables influenced by single or multiple factors. While many experiments hold certain factors constant while varying others, this OFAT approach is significantly less efficient than simultaneous multi-factor variation.

Multiple DOE approaches exist, including OFAT, Full Factorial, Fractional Factorial, Taguchi, and Response Surface Methodology (RSM). Among these, RSM demonstrates superior performance for experimental design applications.

What is Response Surface Methodology (RSM)?

Response Surface Methodology (RSM) comprises mathematical techniques that establish relationships between response variables and multiple independent (studied) variables. Introduced by Box and Wilson in 1951, RSM remains a fundamental experimental design tool. It combines statistical techniques with applied mathematics to construct experimental models aimed at optimizing responses (output variables) affected by several independent variables (input variables).

An experiment consists of a series of tests called runs. During each run, input variables are systematically modified to identify causes of response variable changes. RSM design construction is an iterative process that develops approximate models, tests them using goodness-of-fit methods, and repeats the process if results are unsatisfactory.

The objective is to identify and analyze variables affecting outputs using minimal experiments. RSM achieves optimal response surfaces by determining optimal response levels for each design variable through systematic exploration.

What is Optimization in ANSYS Fluent?

Optimization is the process of obtaining the best solution for selected parameters. ANSYS enables two optimization types:

1. Direct Optimization: Predicts system behavior without intermediary steps
2. Indirect Optimization: Utilizes RSM-generated data to develop mathematical functions for predicting system behavior

Both methods yield identical results through different procedural pathways.

Tutorial Learning Outcomes

Step 1: Theoretical Foundation

This tutorial, prepared by experienced MR-CFD engineers, begins with comprehensive coverage of DOE methods, including RSM and its historical development. You’ll learn the advantages, disadvantages, and theoretical aspects of various methods. The introductory section provides complete theoretical foundations, making it accessible even without prior DOE or optimization experience.

Step 2: RSM Optimization Process

The second section demonstrates RSM optimization using ANSYS software for combustion chamber parameter optimization. The step-by-step process includes:

• Geometry Design: Starting from scratch, designing and parametrizing the combustion chamber geometry
• Meshing: Generating computational grids over the designed geometry
• Fluent Setup: Configuring solver settings and defining necessary parameters
• Parameter Correlation: Identifying input parameters with significant effects on outputs to reduce computational time by eliminating less influential parameters
• Design Point Generation: Using Central Composite Design (CCD), an RSM subset, to create design point charts containing all required experiments by defining investigation ranges for each parameter

Indirect optimization in ANSYS uses RSM-generated data to extract mathematical functions predicting system behavior.

Step 3: Direct Optimization Process

This section explains direct optimization in detail. Unlike RSM, design points are created based on software requirements and predefined algorithms. As optimization progresses, the software may request additional sampling points for accurate mathematical function prediction. Upon completion, ANSYS provides three candidate points representing optimal solutions based on user-defined objectives.

Project Description

This project simulates combustion processes within a combustion chamber, monitoring parameters such as heat generation rate and pollutant formation. The objective is to optimize geometrical parameters to maximize heat generation while minimizing pollution formation.

Two optimization approaches are examined:

1. Indirect Optimization: Using RSM with CCD method to generate design points and perform parameter correlation analysis
2. Direct Optimization: Generating design points and defining objectives for software-driven optimization

Turbulence and Combustion Modeling:

• RNG k-epsilon model for turbulent flow equations
• Energy equation for temperature distribution and heat transfer
• Species transport model with volumetric reactions for combustion simulation

Input and Output Parameters

Geometry and Mesh

The geometry, designed in ANSYS Design Modeler, features:

• Four fuel inlets on the bottom face
• Four offset air inlets generating swirl flow
• A rotating cone enhancing swirl effects on combustion efficiency

Meshing, performed in ANSYS Meshing, applies specific body sizing to geometry generated from input parameters.

CFD Simulation Settings

General Settings:

• Pressure-based solver
• Steady-state simulation
• Gravity effects neglected

Models:

• Viscous: RNG k-epsilon with standard wall functions
• Species Transport: Volumetric reactions with eddy-dissipation turbulence-chemistry interaction
• Energy: Enabled

Boundary Conditions:

Solution Methods:

• Pressure-velocity coupling: Coupled
• Spatial discretization: Second-order for all variables

Results and Discussion

Goodness-of-fit graphs demonstrate excellent agreement between predicted values and simulated points, validating the reliability of optimal values. Various 3D response surfaces visualize results and illustrate mutual effects between input and output parameters.

Local sensitivity charts identify parameters with significant impacts on outputs. For this project, cone angular velocity and outer diameter substantially influence most output parameters.

Spider charts display parameter responses, revealing logical relationships. For example, when parameters 1, 2, 4, 5, and 6 reach maximum values, parameter 3 (CO mass fraction) reaches its minimum, consistent with complete stoichiometric reactions that maximize heat generation while minimizing CO formation.